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Primary Table of Contents [USER can navigate screens using: (1) RHS screen slider, (2) keyboard up/down arrows & PGUP/PGDN keys, (3) click on active links.]

Click here to jump to a description of our Capabilities (who we are and what we can do and have previously done).

Click here to see who we are NOT.

Click here to jump to our Mission Statement.

Click here to see our criticism of non-Kalman Filter approaches and specifically Particle Filters for usually NOT being real-time (because of underlying PDE's present).

Click here to view our development/derivation of Two Confidence Region (CR2) approach to failure detection from 1st principles.

Click here to view our refinement of Decentralized Kalman Filter approaches.

Click here to View how we combined both of the approaches immediately above to yield a satisfactory approach for handling NAV redundancy management.

Click here to view our 3 book chapters published on different aspects of Kalman Filtering.

Click here to view our publications on underlying numerical aspects of Kalman Filters.

Click here to view our publications on research relating to Exposure to enemy surveilance while maintaining sufficient NAV accuracy.

Click here to view our publications, which serve as evidence of our sufficient Breadth and Depth to handle a wide variety of applications.

Click here for details on our TK-MIP PC software product for design, Monte-Carlo simulation, and implementation of state-of-the-art estimation and/or Kalman Filters and related processing and tests of requisite regularity conditions being satisfied.

Click here for a discussion of Specialized Technology Topics in which we provide Expert Consulting.

Click here to see a list of our Recent Clients.

Click here to jump to an Overview Summary of our available Resources for Software Development.

Click here to jump to our Professional Affiliations.

Click here for an overview of our Honors and Awards.

Click here for a summary of our Critical Personnel.

Click here to view Previous Employers.

Click here to see some representatives of our ample Supporting Research, as reported in open literature peer-reviewed publications.

Click here to see a list of where Our Research and Results are cited by Other Independent Authors and Researchers.

Click here for Contact Information.

Go to TeK Associates CEO Thomas H. Kerr III’s qualifications to be nominated to be an IEEE Fellow.

Click here to view various IEEE positions held.

Click here to view non-IEEE positions, honors, and awards.

Click here to download a 1MByte pdf file that serves as an example of our expertise in strategic radar target tracking and in recent developments in Estimation Theory and in Kalman Filter-related technologies. In 2018. currently revising, reorganizing, and updating it (to also include more recent stability Proofs of non-divergence for certain special case EKF's via use of stochastic Lyapunov functions) before we insert graphics into this revision of the above paper.

Also see or click on https://archive.org/details/DTIC_ADP011192/page/n7/mode/2up/ 

Click here to download a 252KByte 2003 pdf file that discusses the PROs and CONs of Genetically Modified Organisms (GMO) [according to the Centers for Disease Control and Prevention there are an estimated 76 million cases of food-borne illnesses annually (in 2009), 5,000 of which prove fatal (according to page 8 of Massachusetts High Technology, Vol. 37, No. 32, 7-13 August 2009)]. As an endorsement of sorts, the above paper has been included in a specialized collection of papers on GMO by experts in the GMO area. I merely felt compelled to provide my own "two cents worth" since the stakes are so high for mankind. (It is #10 down on this list. My paper was written in 2003. Subsequently, Congress gave FDA the power to fine violators where before FDA could only raise a “red” flag.)

Click here to download a 213KByte pdf file with a detailed account of the current status of GLR and IMM.

Click here to download a 1.72MByte pdf file discussing and analyzing existing pitfalls associated with improper use of “shaping filters”.

Click here to download a 654KByte pdf file discussing and analyzing various existing results in random variables and statistics that affect parameter Identification and other aspects of estimation theory for random processes.

Click here to download a 1.56MByte pdf file that demonstrates our Navigation familiarity by our pioneering new developments in using Inertial Navigation Systems and GPS in support of airborne platforms performing terrain mapping, which is a slide presentation corresponding to: Kerr, T. H., Use of GPS\INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),Institute of Navigation Proceedings of GPS-94, pp. 1173-1188, 20-23 Sept. 1994.  Click here to download a 4.40MByte pdf file that conveys the entire report. (Thomas H. Kerr III became a senior member of AIAA via the required endorsements by running this specific report by Richard Battin [Draper Laboratory and MIT Aero. & Astro. Department] and by Prof. Wally Vander Velde [MIT Aero. & Astro. Department].)

Click here to download a 500KByte pdf file with a detailed account of the historical and current status of the rigorous handling of nonlinear control systems with stochastic inputs (a.k.a. random noise inputs) circa 1969 (a topic that we still follow). (Arthur Gelb, previously president of TASC, also offered an approximate solution using CADET®, as a software embodiment and implementation of the multi-input time-varying describing function techniques espoused in Gelb, A. and Vander Velde, W. E., Multiple-Input Describing Functions and Nonlinear System Design, McGraw-Hill Book Company, NY, 1968.)

Click here to download a 2MByte pdf file with excerpts of an important application example which exhibits our detailed knowledge of multi-channel Spectral Estimation approaches, techniques (and its underlying theory in the appendices) circa 1989 (a topic that we still follow).

Click here to download a 654KByte pdf file consisting of a TeK Associates' proposal solicited by Boeing (specifically by Sohail Y. Uppal, who probably took credit for our work in both of two consecutive summers) for which we were "stiffed" and not paid (yet TeK Associates still published 2 papers from it so it was not a total bust)! Fool us once, shame on you. Fool us twice, shame on us!

Click here to view our abstract for GNC Challenges for Miniature Autonomous Systems Workshop, 26-28 October 2009 to occur at Fort Walton Beach, FL

Click here to view our recent short comment submitted to the Institute of Navigation for publication in their Journal.

My Speculation on the cause of Boeing 737 MAX 8 Failure Also click here: to see the numerous recent cases of GPS and GNSS interference. 

Click here to see a 160 KByte quantitative analyses of the relative pointing accuracy associated with each of several alternative candidate INS platforms of varying gyro drift-rate quality (and cost) by using high quality GPS external position and velocity fix alternatives: (1) P(Y)-code, (2) differential mode, or (3) kinematic mode at  higher rates to enhance the INS with frequent updates to compensate for gyro drift degradations that otherwise adversely increase in magnitude and severity to the system as time continues to elapse. Click here to obtain the corresponding 1.40 MByte PowerPoint presentation.

Click here to obtain a detailed 296 Kilobyte resume for Thomas H. Kerr III. [Other shorter versions of his resume, specifically emphasizing only radar target tracking experience for strategic Upgraded Early Warning Radar (UEWR), are available in the pertinent sections under our Consulting Services” topic.]  Click here to obtain a less detailed 176Kilobyte resume for Thomas H. Kerr III emphasizing only software.  Click here to obtain a detailed 128Kilobyte resume for Thomas H. Kerr III emphasizing only his Navigation experience.

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Click here for TeK Associates physical brick and mortar location and how to get there.

Get free TK-MIP® tutorial software that demonstrates TeK Associates software development style.


Microsoft Word™ is to WordPerfect™ as TK-MIP™ is to ... everything else that claims to perform comparable processing! 

TeK Associates primary software product  for the PC is TK-MIPTM, which encapsulates both historical and recent statistical estimation and Kalman filtering developments and performs the requisite signal processing intuitively, understandably, efficiently, and for easily accessible I/O results that are being sought.

Harness the strength and power of a polymath to benefit you! It's all encapsulated within TK-MIPTM!

TeK Associates® continues to perform conceptual engineering design, analysis, and performance evaluations via physics, mathematical analysis, and computer-based simulations (Monte-Carlo), and our own in-house software implementations of mathematics-based algorithms (in either classical or modern computer languages) for further refined analysis of engineering applications. We also provide Independent Verification and Validation (IV&V) of software implementations provided by others and which also entails assessing the completeness and appropriateness of the associated software documentation and its supporting theoretical rationale. Our main specialty relates to Kalman filtering (as a slight aside, on 19 February 2008, Rudolf F. Kalman received the prestigious $500,000 Charles Stark Draper Prize for his original development consisting of 3 papers, one published in 1959 and the other two in the early 1960’s) and all its aspects including comparisons to other similar statistical estimation algorithms - especially those that involve further signal processing (beyond using Kalman filters merely to obtain precise real-time situational navigation or for tracking single targets) such as:

Failure\Fault detection and reconfiguration for navigation systems for a variety of platforms and hardware configurations, as driven by Failure Modes and Effects Analysis (FMEA) in the quest to attain 0.9999 to 0.99999 as Reliability\Availability goals for GPS use (such related reliability/availability impact analysis was performed by us at TASC for the C-4 and D-1 SSBN “Boomer” submarine inertial navigation system [e.g., SINS/ESGM] with pre-existing manual failure detection procedures that we subsequently augmented with our own automated failure or fault detection procedure for a special situation then being encountered, as our novel trail-blazing development for early modern Event Detection);
Receiver Autonomous Integrity Monitoring (RAIM) for GPS (a specific subset of the above);
Navigation Analysis (with accompanying realistic computer simulations) of Inertial Navigation Systems with updates from various alternative navaids (as performed over 6 years for C-4 Poseidon and D-1 Trident SSBN Submarine SINS/ESGM Navigation at TASC (for SP-2413) with Transit Navigation Satellite, Loran-C, and Bathymetric map-matching as the augmenting alternative external navaid fixes used to compensate for INS gyro drift over a mission; performed for 3 years at Intermetrics, Inc. for SSN-701 LaJolla attack submarine’s early use of GPS for NADC/NOSC customers; and for early Navy Airborne JTIDS; performed for other GPS and INS applications at Intermetrics, Inc. [e.g., MFBARS & ICNIA that fed into the Northrop/McDonnell  Douglas YF-23 Advanced Tactical Fighter]; performed design analysis on airborne GPS/INS operations from 1989-92 at the Lincoln Laboratory of MIT for DARPA; more recently performed [for ~ 2 months] on an airborne INS/DGPS Littoral Surveillance application: Navy Airborne Remote Optical Spotlight System (AROSS) for Arête Associates in 2003);  
Radar and Optics-based Target Tracker Design (as performed by us at Lincoln Laboratory for 3 years for strategic reentry vehicle target tracking [under the SDI umbrella] and later by us from 1997-2000 within National Missile Defense [NMD/UEWR] for MITRE, XonTech, and Raytheon) and associated Maneuver detection (which, as the mathematical dual of failure detection, utilizes the same identical solution techniques);
Decentralized\Distributed Kalman-like filters for parallel implementation (with R&D precedents performed by us at Intermetrics, Inc. for the Relative Navigation [RelNav] function of the Navy Joint Tactical Information Distribution System [JTIDS] in 1979-’81). ICNIA design for airborne navigation (and its failure detection and subsequent  reconfiguration) also utilized multiple decentralized Kalman filters. The C-4 back-fit and D-1 Submarine SINS/ESGM Navigation (by Sperry Systems Management) also successfully utilized three simultaneous Kalman filters: one 7-state STAR filter, modeling SINS alone; one 18-state filter, modeling ESGM alone; and one 15-state SINS/ESGM filter modeling the principal components of the joint operation of both SINS/ESGM working together. There was also a detailed 34-state truth model of the SINS with 3 conventional spinning rotor single input G-7B gyros, as present back in those days. The detailed truth model for the EGGM consisted of 100+ states and was modified and personally tailored by Dr. Thor Paulson [MIT] (before he retuned to Iceland) from the detailed error model inherited from the earlier airborne MICRON navigation system, when Rockwell Autonetics (CA) entered at the last minute yet won the ESGM competition against Honeywell (FL);
Cramer-Rao Lower Bound (CRLB) evaluation for the radar target tracking applications of others or of our own (as was performed by us for MITRE, XonTech, and Raytheon on the upgraded early warning radar [UEWR] for National Missile Defense from 1997-2000);
Maximum Likelihood Batch processing for statistical estimation applications (as was performed by us for MITRE, XonTech, and Raytheon on the upgraded early warning radar [UEWR] for National Missile Defense (NMD) from 1997-2000);
Generalized Likelihood Ratio (GLR) and Conventional Likelihood Ratio Evaluation for various applications (notably, for strategic radar target maneuver detection and for failure detection in navigation applications (as originally performed by us in the early and middle 1970’s for SINS/ESGM submarine navigation application);
Analysis of Multi-Target Tracking (MTT), as appended to tracking of individual targets, or as part of a super structure within which individual targets are tracked (such as in using Munkres’ algorithm, or Generalized Likelihood Ratio (GLR) with track-before-detect, or Hungarian algorithm, or Jonker-Volgenent-Castanon’s (J-V-C) algorithm, or Murty’s algorithm, or Blackman's Multi-Hypotheses Testing [MHT]);
Evaluating explicit analytical Measures of Effectiveness (MOE) for assessing performance trade-offs in each of the above areas (such as those that we analytically quantified and computationally evaluated in trading-off use of alternative navaids to maintain the requisite navigation accuracy [needed to compensate for time dependent growth in SSBN gyro drift-rate within the INS] versus sweeprate exposure to enemy surveillance during navaid “fix taking”) by computationally elucidating the “Pareto-optimal set” of alternative navaid fix strategies and mixes thereof;
Standards-based Input/Output (I/O) of sensor measurement data and subsequent output of computed results;
Independent Verification and Validation (IV&V) of Kalman filter-related software code (as had been performed by us at Intermetrics, Inc. for several different Navy Sonar and sonobuoy target tracking systems [Lofar, Difar, Passive Tracking Algorithm] and for other Navy applications over 6 years).

We have performed exploratory ground breaking investigations (such as those mentioned above) under DoD contracts in Exact and Approximate Nonlinear Filtering and in many of its variations and on their refinements in particular applications, as indicated above. We have prior background and experience in each of the above bullet topics, which are all mathematics-based (and we also know to include the physics-based constraints, possible military operational constraints and tactics, and we are aware of the hardware induced constraints, some of which frequently cause actual system behavior to degrade away from the ideal that is sought). We have followed this evolving algorithm technology (that is the cornerstone of modern navigation and target tracking) since its inception in the 1960s and we continue to do so. Because of our past experience, we are able to distinguish between important real evolutionary progress from the hype so prevalent with recent claims of “new results” in this technical area. While we are always open to new ideas and encourage novel imaginative approaches to solving problems, we also cross-check for consistency with the abutting existing supporting theory and precedents and previously established and substantiated analytical accoutrements as well as to test it within the crucible of practicability (in also considering application constraints and tactics-both our own and those of an enemy).

Click here to view more on the topics mentioned above for which we offer expert consulting services.   Click here to view more on our commercial software product: TK-MIP.

In more than 40+ years of professional practice, we have never been involved in any legal disputes whatsoever, nor in disputes or involvements relating to any of our professional activities, nor relating to our product outputs. Our outputs have consisted exclusively of written reports for our clients and the associated technical journal papers and conference articles that are in directly related areas. Any subsequent implementation of our ideas into actual weapons systems or in military platforms (i.e., vehicles) is independently performed by others. We are held harmless as a standard stipulation in all of our contracts for engineering analysis services. To be immediately useful and clearly understood by our clients and other readers, our written products are admittedly explicit (i.e., we cut to the chase and avoid innuendo) and are sometimes somewhat provocative but are always safely backed up with copious independent concrete reference citations and explicit confirming precedents as well as independently repeatable simulations by us and others “up the wazoo”. As a rule, TeK Associates avoids going out on a limb!

We also have considerable experience in the following areas:

·Statistical Analysis ·Multi-Channel Spectral Estimation ·Modern Time-Optimal (bang-bang) Control 
·LQG/LTR  Control ·Matrix Spectral Factorization (MSF) ·Automatic Target Recognition (ATR)  
·System Modeling ·Neural Networks/Fuzzy Control   ·Classical Control/Proportional-Integral-Derivative (PID)

·Analysis and simulation as well as Model-based software implementation of INS/GPS or INS/DGPS Navigation algorithms (based on fundamental psi-angle descriptions of misalignment angles due to gyro drift rates and accelerometer bias errors and underlying Gaussian White Noise (GWN) characterizations as well as on frequency and type of external navaid usage as fundamental drivers as well as gravity compensation model utilized, vehicle maneuvers experienced, and earth’s rotation for terrestrial applications)

·Sensor or Actuator Failure Detection in Navigation Systems such as with GPS RAIM (Receiver Autonomous Integrity Monitoring)

·Sensor Fusion for Kalman filter Applications (for Navigation, for Tracking, and for Image Enhancement)  

·Angle-Only Tracking (AOT) or Bearings-Only Tracking (BOT) for Passive sonar, jammed radar, optics

·Wavelets/Multi-rate Filters analysis and simulation for control and/or estimation applications

·Performance Analysis of other technologies that use the same tools as Kalman filter or Nonlinear filter derivation such as Bayesian Network applications

·Algorithm Specification/Design/Implementation or Independent Verification & Validation/Software Documentation

·Parameter Identification of Model for any Linear Time-Invariant (LTI) System , as computationally deduced

·System Simulation and Kalman Filter performance Evaluation (and for other Statistical Estimation Algorithms)

·Ferreting out Software flaws and Software Bugs (prior experience with our counter-examples can be provided upon request)  

·Electrical Network Synthesis using exclusively passive circuit elements (a'la Van Valkenberg: Brune, Reza, Bott-Duffin techniques)

·Providing a mechanism for our shrink-wrap TK-MIP® software product (currently in development for later release) to perform ordinary single Kalman Filtering (KF) with a possibly time-varying model, single Extended Kalman Filtering (EKF), single Iterated KF, or single Maximum Likelihood Minimum Variance Kalman smoothing (now denoted as retrodiction), or banks of simultaneous KF’s (i.e., IMM, with each individual KF or EKF assigned its own distinctly different system model) and yet be compatible with other PC-based software (accomplished through successful cross-program or inter-program communications and hand-shaking and facilitated by TeK Associates recognizing and complying with existing Microsoft Windows Standards for software program interaction such as abiding by that of ActiveX or COM). Therefore, TK-MIP® can be used either in a stand-alone fashion or in conjunction with other software for performing the estimation and tracking function, as indicated below:

TK-MIP® can interact with other software (by having adhered to the Microsoft COM standard)

Get free TK-MIP® tutorial software

TeK Associates TK-MIP®

Intercommunication to and fro via COM API’s

Other software abiding by COM like AGIs STK®§, NIs LabView®, MathWorks MatLAb®/Simulink® or even with MathSofts MathCad®

Interface capability

§AGI also provides their HTTP/IP-based CONNECT® API methodology to enable cross-communication with other external software programs (as well as providing the more recent COM/ActiveX option) and AGI promises to continue to support CONNECT® in order to have complete backwards compatibility with what older versions of STK could do.

Linux Operating Systems can also be accommodated using Mono®, a program that allows Linux Operating Systems to run .NET® applications (i.e., Microsoft products developed in Studio.NET normally require at least WindowsXP or Windows2000 or Vista or Windows 7 to Windows 11 to be the host Operating Systems for .NET applications). Version 1 Mono® was released by 29 October 2005. (By July 2007, two other software products, Mainsoft® and Wine®, have also emerged for providing compatibility of Window’s-based software to a Linux Operating System.)

While we vigorously vouch for the veracity of our TK-MIP software, for routine legal reasons, we must invoke the standard “shrink-wrap” software disclaimers and other prudent limitations on any possible liability exposure of TeK Associates.

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We also have experience investigating numerical analysis aspects such as: What intermediate algorithms should be used?, What will be the effect of round-off, register size, possible numerical sensitivities, convergence, and convergence rates? We have performed tallies of operations counts incurred, assessed how amenable algorithms are to decentralization or to parallelization (as, say, separate threads in embedded processors, as cordic algorithms, as systolic arrays, as neural networks, or, alternatively, as analog-based Monolithic Microwave Integrated Chips [MMIC]). We routinely apply the principles and techniques of modern mathematical analysis and appreciate the insights availed through its use. We also routinely track and use new developments in statistics and random process theory. To be cognizant of aspects related to countermeasures, we have worked in Search and Screening exercises in the past (and also published our results in the open, peer-reviewed professional literature) and so we are aware of sweep-rate characterizations of platform or antenna exposure to enemy surveillance as well as the adverse impact of increasing the duration of such exposure (as this also relates to Moving Target Indicators [MTI] and to “stop-move-stop strategies of radar or optical detection avoidance). We are aware that C3I system principles of operation must be well understood before one can figure out countermeasures (i.e., how to break it: C4I) or how to prevent having it broken (i.e., counter-countermeasures or C5I). We are cognizant of Old Crows Countermeasures Handbook and The Wild Geese (LORAN Association). While birds of a feather flock together, sometimes birds of different interest areas cross-breed and, as a consequence, have offspring where both interests/talents are combined within one individual!  Go to Top                   

  Go to Primary Table of Contents

TeK Associates Mission:

Our strong track record of participating in both evolutionary and revolutionary developments by historically trailblazing significant new results in estimation theory and in its practical applications stands on its own merits. We continue along this same course that we find so stimulating, lucrative, gratifying, and rewarding. We have innovative ideas (in our fields of specialization) and we first prove their utility theoretically and then confirm it in simulation and finally in implementation. Our commercial product TK-MIP for the PC is but one instantiation of our particular philosophical approach to software development, based on our novel insights (and extensive background in mathematical analysis, familiarity with other developments in the field, and our overwhelming desire to satisfy our users needs by making steps associated with its use crystal clear).  Recapitulating, in the estimation arena for a variety of platforms involving navigation or target tracking:

Can provide detailed rigorous technical analyses and supporting rationale based on principles in mathematics, probability & statistics (and stochastic or random processes), physics, and practical engineering concerns
Can provide system performance evaluations (via adequately detailed Monte-Carlo computer simulations);
Can provide critical insights into current status of the field (without hype);
Can provide new theoretical and technical developments in our specialties (where we have already done so many times before in proving that we have the necessary background and insight);
Can provide development and implementation of our own tested software (conventional or embedded) in several alternative computer languages (please click here for insights into our capabilities for embedded) , or...
Can provide Independent Verification and Validation (IV&V) of software developed by others (using our existing exhaustive repertoire of simple test problems with analytically known and theoretically justified closed-form solutions that should be the computed outcome of any new software under test) and cross-check the clarity of the associated documentation supplied by the developers and veracity of the developers’ supporting theoretical claims and associated supporting rationale.

All of the above are in line with our prior experience (since 1971) in a variety of defense areas including Submarine Inertial Navigation (and an understanding and facility with the underlying navigation error models constituting a psi-angle analysis of an Inertial Navigation System [INS], consisting of accelerometers and gyroscopes in an integrated whole); Air Force Aircraft Navigation and Radio Multi-lateration Relative Navigation (JTIDS RelNav) and communication (JTIDS/MUFBARS/ICNIA); Sonobuoy DIFAR/LOFAR target tracking; Search and Screening; (dielectric AN/BRA-34) Antenna Radar Cross-Section Detectability (and vulnerability to enemy jamming, spoofing, and other interference); NavSat (now defunct), LORAN-C (now defunct but due to return as eLORAN to strengthen against enemy spoofing of GPS/GNSS), Bathymetry (i.e., bottom sounding sonar map-matching using acoustic sensors in the Janus configuration [i.e., 2 pointing forwards and 2 pointing backwards]) and GPS analysis and usage on Submarines; and GPS analysis and usage in test aircraft (along with test plans and procedures for most of the above); and Early Warning Radar Target tracking considerations relating to the target tracking filters and estimation concerns (and the underlying mathematical models of all of the above and more). We are cognizant and capable in many other analytic areas (e.g., Reliability/Availability) as a consequence of our existing proficiency in Failure detection and in mathematics, physics, systems engineering, and software development involving challenging mathematics-based algorithms; especially regarding distributed or decentralized parallelization of such algorithms and in data fusion using either a  single Kalman filter or decentralized Kalman filters, while being wary and observant of existing application constraints.     Go to Top   Go to Primary Table of Contents

TeK Associates (registered by that name in Lexington, Massachusetts, USA back in 1992) has absolutely NO affiliation with other companies with similar names that have  subsequently sprouted up, such as:

· A-Tek Associates

· M-TeK Associates

· T E K Associates in Oxford, UK

· V-TEK  Associates

· B-Tek Associates

· S-TEK Associates

· Tek Search Associates

· Q-Tek Associates

· C-TEK Associates

· H-TeK Associates

· STAR TEK Associates

· W-TeK Associates

· Hybrid-Tek Associates

· TeK Associates, Ltd.

· L-Tek Associates

· TEK Associates, L.L.C.

· Arpan Tek Associates

· KRAF Tek Associates

· Hi-Tek Associates

· TEK Associates, Inc.

· TEK Associates

We suppose that  imitation (as has evidently occurred above) is the sincerest form of flattery.  However, it is our company that has performed the milestone research, has the results, and accompanying peer-reviewed open literature publications reporting (some of) our results.      Go to Top    Go to Primary Table of Contents

Profile of Critical Company Personnel:

Thomas H. Kerr III, the founder and CEO of TeK Associates since 1992 (until June, 2022), was born in Washington, DC. He received the B.S.E.E. in electronics (magna cum laude) from Howard University in 1967 and the M.S. and Ph.D. degrees (via a National Science Foundation traineeship) in the electrical engineering specialty of control and estimation from the University of Iowa, Iowa City, IA in 1969 and 1971, respectively. Click here to view his Entrepreneurial Elevator Speech.Click here too! [Thomas H. Kerr III is NO LONGER open or available to outside requests and assignments (except for those officially and explicitly sanctioned by his current employer, Zivaro, Inc.).]

Greek: αρετή  Icelandic: “Fyrsta flokks. Af alefli.” Hann er sinn eigin herra.”  German: Ich mache viele Uberstunden.” Please click on the above picture for more.

Dr. Thomas H. Kerr III’s practical industrial experience since 1971, as a mathematically-oriented R&D Algorithm Specialist, Systems Engineer, and Software Developer, has encompassed various Kalman filter theoretical evolutionary developments for DoD applications in submarine and aircraft Inertial Navigation Systems (INS), in Global Position Satellite System (GPS) receiver characterization and validation and in the incorporation of GPS receiver data (in weak, medium, and strong configurations) within an Inertial Navigation System (INS), in Lamps Difar Sonar/Sonobuoy target tracking, in Joint Tactical Information Distribution System (JTIDS) Relative Navigation (RelNav), in Integrated Communication, Navigation, and Identification for Avionics (ICNIA) [a combination of almost the exact same radio systems, as a precedent twenty five years earlier for the Advanced Tactical Fighter (ATF) F-22 Raptor, as was subsequently pursued by JTRS], and in radar target tracking for strategic reentry vehicles versus decoys [e.g., Strategic Defense Initiative (SDI), National Missile Defense/Upgraded Early Warning Radar (NMD/UEWR)], and support software issues for implementing promising algorithms-with particular emphasis by TeK Associates on novel state variable model-based Kalman filter (KF) applications. He also worked on critiquing the Honeywell Electro-Optical Missile Warning System (MWS) for helicopters and on critiquing an early (Magnavox) version of PINS navigation for Minesweepers while serving on a team representing U.S. Government interests. He has an awareness of current target observables, countermeasures, counter-countermeasures (e.g., Old Crow-related), sweeprate exposure to enemy surveillance, pattern recognition classification procedures, Neural Network (NN) limitations [some that he has not yet sufficiently publicized, other than here NOW,  regarding warnings about improper use of feed-forward control since some people actually argue that feed-forward control laws (nowadays, frequently availed through use of a NN) were the same as or equivalent to use of feedback control laws! Historically, the class of feed-forward controls is a much smaller subset of controls than those adaptive ones offered or availed via a more conventional feedback implementation (involving negative feedback and/or positive feedback https://www.electronics-tutorials.ws/systems/feedback-systems.html), as recognized by others more than 45 years ago [as discussed by W. M. Wonham, "Random Differential Equations in Control Theory," a chapter within Vol. 2 of the three volume set: Probabilistic Methods in Applied Mathematics, Vol. I (1968), Vol. 2 (1970), Vol. 3 (1973) by A. T. Bharucha-Reid (ed.). https://ntrs.nasa.gov/search.jsp?R=19700065159] before there was any financially motivated “axe to grid” and before the subsequent and consequential application “stakes were so high” regarding possible use of NN's in control applications. Feedback laws arose much earlier and properly accommodate “aging” of components and the associated “changes in parameter values” that subsequently occurred without needing to make any other accommodations other than, perhaps, ocassionally slightly changing the scalar gain constant “K”]. 

He was involved in Security aspects of World Wide Military Command and Control System (WWMCCS) during its epoch as a WWMCCS Improvement System (WIS). [WWMCCS was decommissioned in 1996 and replaced by Global Command and Control System.] For WIS, he was involved only in the multi-level Computer Security aspects and some vulnerability precedents of a networked distributed system, some hardware triaxial cable issues, some fiber-optic vulnerability issues, and use of encryption versus check-sum issues. He possesses expertise in the following Research and Development (R&D) areas:

Decentralized or Distributed (or as sometimes referred to as parallel) Kalman filters.
Various novel approximate approaches for handling nonlinear filtering by being alert to possible improvements to supplant, replace, or augment Extended Kalman Filters or Iterated Extended Kalman Filters, such as (please excuse the somewhat critical view point that I initially convey below as I get my licks in” [after waiting for ~20 years by intentionally delaying my critical responses until early 2019 so that I could not be accused of interfering with or attempting to block any potentially competitive algorithm developments or its subsequent evolution after encountering normal, likely temporary roadblocks to later be circumvented]). My criticisms being conveyed here now for the specialists are both from my own past experience and that of others, as identified. My tone will be more mellow further below (beyond this color) at the end of this critique of the 3 different current and prevalent alternative estimation approaches, as I later also discuss Fred Daum’s very nice and clear tutorial and summary of these same 3 competitive alternative estimation algorithms within his own overview status-of-the-field discussion that is generally accessible to all, including the non-specialists. While I have the highest regard for Fredrick E. Daum and his accomplishments, I don't always agree entirely with everything. My own criticisms precede Daum’s discussion below (but Daum’s comments are not criticisms) while mine are definitely criticisms and follow next:

-Particle Filtering (PF)-(only if they live up to their hype [which has not completely happened yet]) with careful assessment of their associated respective computational burdens. (PF provides very good tracking accuracy but can seldom be computed in real-time! Moreover, PF is not needed in situations where good mathematical models already exist for the system dynamics [such as objects acted upon solely by central forces, as with gravitational forces] and the process or plant noise is merely a minor consideration [especially when it is absent entirely, as is the case with radar tracking of RV’s in the midcourse phase (where the RV’s are to be kinetically intercepted) and for tracking all satellites, in general]. The strong suggestion that “particle filters should only be used for difficult nonlinear/non-Gaussian problems, when conventional methods fail” is made within the Epilogue on page 287, next to the last sentence of the 1st paragraph of the book: Ristic, Branko, Arulampalam, Sanjeev, Gordon, Neil, Beyond the Kalman Filter: particle filters for tracking applications, Artech House, Boston, 2004. (Moreover, pp. 271-283 in Section 12.5.2 discuss Rao-Blackwellized Particle Filters (for additional speeding up of the computations) as well and also discusses this topic further on page 287. Much benefit had already accrued by 2016 in use of Rao-Blackwellized Particle Filters.) Many researchers, like me, are somewhat suspicious when claims are made by other researchers that they used a Particle Filter for a particular application, when adequate linear Kalman Filters had been successfully used for that same particular INS/GPS airborne application for decades (prior to now being applied to an airborne drone, as recently claimed for a PF used by MIT/Draper Laboratory). I liked the older approach using conventional Kalman Filters for airborne INS/GPS and even jointly with JTIDS, as discussed in GPS/JTIDS/INS Integration Study-Final Report, Vol. II of IV, Details, Technical Report R-1151, C.S. Draper Laboratory, Inc., Cambridge, MA, Oct. 1977 to June 1978.

Since most recent so-called ground-breaking results for PF’s claim “orders-of-magnitude” improvements over prior original PF implementation/ formulation, which itself increase exponentially in complexity with dimension; so a several “orders-of-magnitude” improvement/reduction still leaves a net exponentially increasing computational burden overall. Richard Bellman identified a “Curse-of-Dimensionally” relating to the computational burden of his Dynamic Programming (DP) algorithm (a.k.a., a Viterbi algorithm equivalent), but Bellman’s Dynamic Programming came first in 1953 Rand Report: http://www.dtic.mil/dtic/tr/fulltext/u2/074903.pdf ) and “Curse-of-Dimensionally” was not claimed back then for Particle Filtering per se since Particle Filtering did not yet exist. Robert E. Larson (when he was a VP at Systems Control Inc. in Palo Alto, CA) published his approximate simplifications, in IFAC Automatica circa 1976, that Larson invoked for taming the Dynamic Programming CPU burden in order that its implementation would be tractable for practical applications. [R. E. Larson, A. J. Korsak, "A dynamic programming successive approximations technique with convergence proofs," Automatica (Journal of IFAC), Vol. 6, No. 2, pp 245-252, Mar. 1970 (https://doi.org/10.1016/0005-1098(70)90095-6). Principles of Dynamic Programming (Part 1 Basic Analytic and Computational Methods), by Robert E. Larson and John L. Casti, Marcel Dekker Inc., 1978; A Review of: “Principles of Dynamic Programming, Part II, Advanced Theory and Applications,” by Robert E. Larson and John L. Casti, Marcel Dekker Inc., 1982]. Since it was an algorithm that differed considerably from that of Particle Filters in structure, the same simplifications do not directly apply nor carry over and other simplifications for PF were needed, as sought by others within the last 20 years. That distinction was not originally clarified by those who were pursuing use of Particle Filters and sought to reduce the “Curse-of-Dimensionally” but needed to do so in different ways since the precedents used in reducing the computational burden for DP don’t strictly apply for PF’s.

When process noise is present (as well as the usual sensor measurement noise), because of the “Central Limit Theorem” and especially the “Central Limit Theorem (with weakened hypothesis but similar strong conclusion)”, the corrupting noises are usually Gaussian in general, and consequently don't require anything special beyond an EKF for successful tracking. The methodology for determining what measurements are needed, as availed from the full rank condition being satisfied from an associated “Observability” analyses or the weaker “Detectability” analysis routinely associated with KF (J. J. Deyst Jr., and C. F. Price, "Conditions for Asymptotic Stability of the Discrete(-time), Minimum Variance, Linear Estimator," IEEE Trans. on Automatic Control, Vol. 13, No. 6, pp. 702-705, Dec. 1968 and J. J. Deyst , “Correction to 'conditions for the asymptotic stability of the discrete minimum-variance linear estimator',” IEEE Trans. on Automatic Control , Vol. 18, No. 5, pp.  562-563, Oct. 1973.) and (somewhat by virtue of approximations but, recently, now exactly for some special case EKF's using stochastic Lyapunov functions) for EKF, apparently don’t exist for PF since there is no system model specified beforehand for a PF for which these conditions could be tested for compliance. Similarly, full rank conditions for “Controllability” or the weaker “Stabilizibility” also cannot be tested for compliance since there is no system model specified beforehand for a PF to be used in such a test.) Without such conditions being satisfied, how can analyzers and implementers be assured of the “stability” of a PF filter estimator to be assured that it is not “diverging” from the “true state”. I have appealed here to the very familiar ample framework that has existed for 4+ decades pertaining to use of available “Lyapunov functions” to demonstrate stability of KF’s (even if the underlying system is unstable, the KF estimator will still appropriately track it well) and approximately, through linearization, for EKF’s (and now exactly for some particular special case EKF’s using “stochastic Lyapunov functions”), where such a useful framework apparently does not yet exist for PF’s.

Unlike the benign situation for a purely linear Kalman filter (KF) that allows use of a so-designated separate “Covariance Analysis” (without any system sensor measurements needing to be specified or collected nor any explicit KF estimates needing to be specified or calculated) to set system “Error Budgets” beforehand that serve as “specifications” on the actual hardware to be implemented later along with the software algorithms under consideration now so that system accuracy goals may be met [as discussed on pp. 260-266, Sec. 7.4 of Gelb, Arthur (ed.), Applied Optimal Estimation, MIT Press, Cambridge, MA, 1974 and a view also confirmed in Maybeck, P. S., Stochastic Models, Estimation and Control, Vol. 1, Academic Press, NY, 1979], the PF has no such capability since PF Covariances are not available in that same way without PF estimates being simultaneously calculated. However, for EKF’s, the situation is similar to that for a PF since a linearization about an EKF estimate is usually needed at each time step in order to calculate the approximate covariances to be used in a “Covariance Analysis” for an EKF in order that an approximate “Error Budget” can be obtained.

When having “real-time” estimates is not an issue or constraint on the utility of estimator usefulness, such as in some Data Analytics situations where underlying “financial models” may be completely unknown and have a significant psychological component (sometimes related to seasons) and yet to be deciphered, a PF may be the best approach to use since there is plenty of data and, perhaps, less of a pressing need to obtain the estimation results in real-time (at lest not initially when attempting to reveal "cause and effect" for the first time in order to gain a better understanding of underlying relationships that exist and actually explain underlying relationships that dictate what is going on). Recall that Kalman smoothers (nowadays referred to as a Kalman “retrodiction”) are of three different forms: (1) “fixed interval” smoothing, (2) “single point (in time)” smoothing, or (3) “fixed-lag” smoothing are also NOT “real-time” algorithms but useful nonetheless such as in closely evaluating missile behavior at the particular event time when a later stage ignites and separates for a multistage rocket. Sometimes a KF smoother is implemented using two Kalman filters, one running “forwards” in time and the other running “backwards” in time (where initial conditions for the first and final conditions for the second are made to corroborate correctly (see “Backwards Markov Models” by Prof. George Verghese [MIT], who obtained  his Ph.D. at Stanford University on this topic under Prof. Thomas Kailath, but the aggregate of these two KF's being a smoothing solution that is still NOT real-time). As with PF's, the Kalman filter has also been historically derived by James S. Meditch (Boeing) [Meditch, J. S., Stochastic Optimal Linear Estimation and Control, McGraw-Hill, New York, 1969] and A. V. Balakrishnan, Kalman Filtering Theory, Optimization Software, Inc., Publications Division, NY, 1987 using Bayesian arguments similar to those used throughout for PF’s, as well as yielding the exact same KF form as independently derived and shown to simultaneously satisfy other important optimality criteria, as discussed immediately below:

Paralleling #6 above: My original Derivation of the Discrete-time Kalman filter using the Matrix Maximum Principle (I followed what Prof. Michael Athans [MIT] and Edison Tse did for the continuous-time case in 1967). 

(The image inserted above [and its references cited therein] is a screen shot from TeK Associates’ TK-MIP software product. Another missing detail is Ref. 29 Mendel, J. M., Lessons in Estimation Theory for Signal Processing, Communication, and Control, Prentice-Hall PTR, Englewood Cliffs, NJ, 1996.)

IMPORTANT: Use of Baysian statistical analysis is not a new tool for estimation applications developed specifically for handling derivations and implementation of Particle Filters (PF). Bayesian statistics have been used for such estimation applications for over 50+ years. 

The other new estimation candidates discussed herein evidently do NOT satisfy any of the first 4 optimality properties (depicted in the above image) except if/when they degenerate into a Kalman filter as an extreme case when system dynamics' description and measurement sensor observation description is exclusively linear and plant and measurement noises are only additive and Gaussian and the initial conditions are properly from a Gaussian distribution, independent of both the Gaussian plant and measurement noises.

-with hopes for benefits to PF in parallelization (multi-threaded parallel processing and/or embedded); I continue to follow recent developments in use of Particle Filters but also continue to have concerns about their failing to be real-time (except when they degenerate & essentially collapse into being merely EKF’s or KF’s [even if they are not explicitly acknowledged as being so]); I also noticed an incompatibility in current hopes for future parallel implementation of a Particle Filter as a further inherent barrier to PF ever being real-time: approaches currently being pursued to accomplish parallel implementation of pseudo-random number generators & maximizing the cycle before they repeat are based on use of Linear Congruential Generator (LCG) algorithmic structures & Mersenne primes to generate variates from a uniform distribution before converting to Gaussian, as needed for PF’s to utilize within numerous “mini-simulation” trials (that invoke use of a RNG within them) before each “measurement incorporation” step, being a huge CPU burden, somewhat ameliorated by performing sophisticated variants of the “Metropolis-Hastings-Gibbs” sampling/re-sampling. Donald Knuth only showed what tests LCG passes in The Art of Computer Programming, Vol. 2, Addison-Wesley, 1969. The late George Marsaglia (of Boeing) (https://en.wikipedia.org/wiki/George_Marsaglia) has warned for 30+ years that LCG yields variates that “lie in planes”, a weakness that has been verified by Profs. Persi Diaconis (Stanford Univ.), P. L’Ecuyer (Univ. of Montreal, Quebec, Canada), and many other current researchers in this area. Even if LCG were perfectly random (which it is not), by attempting a parallel implementation of it risks inadvertent early repetition by a 2nd , 3rd, or 4th LCG, etc. of being somewhere within the same sequence already initiated by an earlier LCG invocation, thus preventing the maximum cycle length from being attained for the following three integer parameters of the computer register: (a, b, and T) involved in the hardware implementation of an LCG [rigor regarding the proper selection of the above mentioned parameters, (a, b, and T), is provided near the bottom of the NEXT screen that pops up after the USER clicks the navigation button at the TOP of this screen labeled “TK-MIP for the PC”], before premature repetition of the series that is sought to be generated. This is the same reason why, as observed in the rigorous simulations of the 1970’s and 1980’s, only one LCG should be invoked (but repeatedly) in the implementation of LCG for a standard serial von Neumann machine. My long standing real-time PF concerns (stated above) are now somewhat mitigated in 2018: https://www.linkedin.com/pulse/new-quantum-method-generates-really-random-numbers-alvin-lieberman-/  (This link is accessible only from LinkedIn by registered LinkedIn users.) However, even this last hypothesized potential path offered from the link immediately above apparently does not yet exist as hardware (even though IBM [which claims to have achieved a working quantum computer in early January 2019], Google, some universities, and several smaller companies are working on it, as identified on the link just offered).

Prof. P. L’Ecuyer (Univ. of Montreal, Quebec, Canada) has proprietary improvements to eventual generation of Gaussian variates as his approach to a pseudo random number (prn) generator. (According to him, he has ostensibly provided these to The MathWorks and to other software developers for a hefty fee.) The conclusion to date is that the older approaches to generating Gaussian variates are not as good as the more recent approaches mentioned here. Apparently missing so far in PF considerations is any attention to the effect of less-than-ideal prn generation of uniformly distributed variates leading to less-than-ideal Gaussian generation. Since the Bayesian-based derivation of the PF strongly utilizes the properties of conditional probability density functions at several critical places, and, all the more, those of Gaussians; it is highly likely that the departure from ideal Gaussianess in what is actually used in implementing a PF will have a significant adverse affect in that PF’s performance. One could postulate a type of sensitivity analysis that should be performed for this situation in order to quantitatively gauge the effect on the expected consequential PF performance associated with one or the other of the two less-than-ideal approximate approaches to be used in PF implementation. A more recent alternative approach to PRN generation, that apparently offers a considerably longer cycle before repeating, is availed in Pei-Chi Wu, "Multiplicative, Congruential Random-Number Generators with Multiplier ± 2K1 ± 2K2 and Modulus [2p-1]," ACM Trans. on Mathematical Software, Vol. 23, No. 23, pp. 255-265, Jun. 1997.

--See M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Processing, vol. 50, pp. 174–188, Feb. 2002. https://www.irisa.fr/aspi/legland/ensta/ref/arulampalam02a.pdf 

--See R. van der Merwe and E. Wan, “Gaussian mixture sigma-point particle filters for sequential probabilistic inference in dynamic state-space models,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Hong Kong, 2003, pp. 701–704. https://www.gatsby.ucl.ac.uk/~byron/nlds/merwe2003a.pdf 

--See S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman Hall/CRC press, Boca Raton, 2003. [Use of a homotopy in conjunction with Particle Flow is an existing method for solving PDE's that predates Particle Filters (and people who utilize it in a PF context should have said so unless they are attempting to take credit for this too). Since a homotopy used here is a scalar function of the independent variable and must be a continuous monotonely increasing function, taking the logarithm of a homotopy is again a continuous monotonely increasing function and so is again a homotopy. The actual choice of the homotopy to be used is "up for grabs" for greatest convenience. Daum always emphasizes that he is using a log-homotopy function. It seems that there is no real difference between what Daum uses and what was standard in historically handling solutions of PDE's using a homotopy. Different investigators can use different scalar functions that exhibit the characteristics of a homotopy for gaining insights into the nature of the solutions of PDE's.

--Also see http://ieeecss.org/CSM/library/2010/june10/11-HistoricalPerspectives.pdf  

--Please see the excellent discussion of how a PF was implemented for their application: Yozevitch, R., Ben Moshe, B., “A Robust Shadow Matching Algorithm for GNSS Positioning,” Navigation: Journal of the Institute of Navigation (ION), Vol. 66, No. 2, pp. 95-109, Summer 2015 [Notice that they did not say that their PF was real-time] and some of their pertinent references: (1) Crow, F. C., Shadow Algorithms for Computer Graphics, ACM SIGGRAPH Computer Graphics, Vol. 11, No. 2, pp. 242-248, 1977; (2) Bourdeau, A., Sahmoudi, M., and Tourneret, J. Y., “Constructive Use of GNSS NLOS-MUltipath: Augmenting the Navigation Kalman Filter with a 3D Model of the Environment,” 15th International Conference on Information Fusion (FUSION), pp. 2271-2276, IEEE, 2012; (3) Thrun, S., Burgard, W., and Fox, D., Probabilistic Robotics, MIT Press, 2005; (4) Muralidharan, K. Khan, A. J., Misra, A., Balan, R. K., and Agarwal, S., “Barametric Phone Sensors: More Hype than Hope!,” Proceedings of the 15th Workshop on Mobile Computing Systems and Applications, ACM, 2014, 12; (5) DeBerg, M., Van Kreveld, M., Overmars, M., and Schwarzkopf, O. C., Computational Geometry, Springer, NY, 2000.

--Please consider that “Observability” and Controllability” yea/nay tests for linear systems with time-varying “System matrix”, “Obsevation matrix”, and “System Noise Gain matrix” are presented in Bucy, R. S., Joseph, P. D., Filtering for Stochastic Processes with Applications in Guidance, 2nd Edition, Chealsa, NY, 1984 (1st Edition Interscience, NY, 1968).

--A long view reveals that: tractable techniques for handling “fractional derivatives” for applications have been around for over 40+ years based on Cauchys integral theorem as a representation for derivatives in a Complex Variables context (where the order of the derivative is generalized using Cauchys theorem to no longer be restricted to being merely an integer) or by being based on a Fourier integral. Much of the theory and practical applications of “fractional derivatives” were worked out back then (40+ years ago), as pioneered and published in SIAM by Prof. Tom Osler: https://csm.rowan.edu/departments/math/facultystaff/math_full_part/osler.html.  Another useful more recent source on this topic is: Kenneth S. Miller and Bertram Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley Interscience Publication, John Wiley & Sons, Inc., NY, 1993.

--Other more mundane practical considerations: What will the practical challenges be for documenting Particle Filters for DoD applications in Principles of Operation (POPs) rationales and later in B1s, B2s,amd B3s or in C1s, C2s and C3s without a clear delineation of what the system dynamics matrices and sensor observation matrices and Noise Covariance Matrices are beforehand, as had been established as historical precedents in documentation for Kalman filter or for EKF tracking applications? [By the early 1980s, the aforementioned documentation for DoD tracking, Kalman filtering, and  EKF applications had already standardized on conventions for state variable notation that TASC (as also utilized/adherred to by Peter Maybeck [AFIT] in his 3 Volume textbooks, respectively, in 1979, 1980, and 1981, on this subject) had adopted and popularized as system: d[x(t)]/dt = F x(t) + B u(t) + w(t) and sensor measurements: z(t) = H x(t) + v(t), and independent zero mean white noise covariance matrices corresponding to w(t) and v(t) above, respectively, being: Q(t), R(t), and Kalman gain: K(t); the familiar TASC discrete-time notational conventions were also adopted.] Appropriate DoD documentation was indeed a challenge for Neural Network (NN) applications that still had to be trained to obtain the necessary weights for “Perceptrons” and multi-layer NNs. DoD documentation was also challenging for “Fuzzy Neural Networks”. Who or what organization is going to perform the necessary associated “IV&V” of PF documentation? I wish them good luck!

--The excellent and extremely readable book: Gelb, Arthur (ed.), Applied Optimal Estimation, MIT Press, Cambridge, MA, 1974 had a few errors (beyond mere typos); however, corrections are provided in Kerr, T. H., “Streamlining Measurement Iteration for EKF Target Tracking,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 2, Mar.1991 and in Kerr, T. H., “Computational Techniques for the Matrix Pseudoinverse in Minimum Variance Reduced-Order Filtering and Control,” in Control and Dynamic Systems-Advances in Theory and Applications, Vol. XXVIII: Advances in Algorithms and computational Techniques for Dynamic Control Systems, Part 1 of 3, C. T. Leondes (Ed.), Academic Press, NY, 1988 (as my expose and illustrative and constructive use of counterexamples).

--See Section 12 of: Kerr, T. H., Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic Results,” Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 142-168, San Diego, 29 July-3 Aug. 2001 for some warnings and concerns regarding the direct applicability of Yaakov Bar-Shalom and William Dale Blair (Editors), Multitarget-Multisensor Tracking: Applications and Advances, Vol. III, Artech House Inc., Boston, 2000 for the challenging case of a system with nonlinear dynamics. While Section 12 of the above just cited Kerr paper above was true in 2001, my 7 item comparison then between what was possible for KFs for explicitly linear systems and what was possible for EKFs and IMMs for nonlinear systems now needs modification in 2018, since now a few special case EKF’s can be shown to be stable using a stochastic Lyapunov function, as in: Jensen, Kenneth J., Generalized Nonlinear Complementary Attitude Filter, AIAA Journal of Guidance, Control, and Dynamics, Vol. 34, No. 5, pp. 1588-1593 , Sept.-Oct. 2011. [Jensen achieves the big stability breakthrough by providing a proof of this particular EKF’s global stability but now states that it possesses “almost” global asymptotic stability; however, the term “almost” is required terminology to keep probability theorists and purists happy with the wording of his new claim. Author Jensen attains his new results by utilizing appropriate stochastic Lyapunov functions (proper handling of such is due to Prof. Emeritus Harold J. Kushner, Brown Univ.). I don’t know whether Jensen was the first to achieve this new result? I am aware of at least two others who also did it.] Please forgive me as I use the following two images to explain and clarify the technical term “almost” that Jensen was obligated to invoke:

(The two images inserted above [and its references cited therein] are screen shots from TeK Associates’ TK-MIP software product.)

--I am aware that Fred Daum, Jim Huang, and Mike Hough (Raytheon) have jointly published a recent paper on the use of a PF for Strategic Early Warning Radar tracking of Reentry Vehicle targets but I have not yet seen it!  I look forward to viewing it soon. Maybe it will “calm my qualms” (but, perhaps, maybe not).

-The solving of Partial Differential Equations (PDEs) has been described by practitioners and others as an infinite-dimensional problem because of its numerical and computational complexity. It is reasonably well known that PDEs describe the time evolution that is needed to specify the associated probability density function underlying continuous-time optimal estimation for both linear and nonlinear systems. The important fundamental PDE describing this is known as the Kolmogorov equation (where there is, in general, a forwards (in time) and a backwards (in time) Kolmogorov equation that describe the statistical estimation situation in continuous-time) and the former is also known as the Fokker-Planck equation arising in optimal statistical estimation for both the case of the system being linear and the noises being Gaussian (which is very tractable since it degenerates and simplifies nicely to the standard Kalman Filter) and the general nonlinear case (usually very intractable and computationally tedious for all except the simplest of problems that, frequently, are neither realistic nor practical for most applications). Both of these PDE’s (of Parabolic type) deal with the time evolution of probability density functions (pdf’s) or, equivalently, the associated information flow. These are Non-Polynomial (NP) algorithms in general. Also see Pavel B. Bochev, Max G. Gunzburger, Least-Squares Finite Element Methods, Applied Mathematical Sciences, Vol. 166, Springer Science + Business Media, LLC, NY, 2009. There is a PDE textbook that was published within the last 15 years that routinely invokes use of scalar “homotopy” (but NOT log-homotopy since use of mere homotopy is sufficient, and use of log-homotopy in ultimately obtaining "particle flow" to characterize solution of the PDE appears to be a minor wrinkle similar to working with log-likelihood ratios in favor of likelihood ratios), and, further, has beautiful color images of associated “particle flows”, as are reminded there to be standard tools and methodologies for handling solutions of PDE’s. However, in general, PDE’s can not be solved in real-time! Sometimes speeded-up videos are shown to convey the trend of the solution process to an audience. However, within the following paper: Daum, F. E., Exact finite-dimensional nonlinear filters, IEEE Transactions on Automatic Control, Vol. 31, No. 7, pp. 616-622, Jul. 1986, a novel, insightful, and creative method was developed for decomposing the solution of the important PDE, described above, into two parts: the 1st  part was a large computational burden to be solved off-line beforehand and stored until needed; the 2nd part is to be solved on-line in real-time. The two parts, when put together, constituted a solution to the PDE described in the preceding paragraph and yields the exact optimal estimator or optimal filter for the nonlinear case. However, a constraint on the 2nd part that, thankfully, is absent from the 1st part is a need for the times at which the measurements arrive beforehand too! That is usually only the case for navigation applications with periodic updates such as by Omega (now defunct), Loran-C (now defunct but maybe coming back as eLORAN to help GPS recognize and compensate for GPS spoofing), or GPS and/or GNSS satellites in an unjammed benign environment; otherwise, the aforementioned navigation aid (i.e., are not deterministic in the time at which they occur and the exact time of an external position fix is not known beforehand because of complicating factors such as atmospheric interference (e.g., atmospheric scintillation for EWR) ; thus computational calculation of the 1st part beforehand is somewhat stymied! Radar applications seldom involve radar sensor measurements arriving at a strictly periodic rate that is known beforehand since targets are in motion and sometimes the radar platform is too, consequently, the round trip time of the radar pulse varies from transmitter to receiver even if the transmitter rate is periodic at a constant Pulse Repetition Frequency (PRF). Moreover, there is an historical precedent in the 1960s and early 1970s to avoid pre-calculated KF gains, as performed by Dr. Hy Strell and Norm Zabb (Sperry Systems Management as SSBN navigation work for SP-2413) which found pre-calculated KF gains satisfactory for simulations and test of concept for the Ships Inertial Navigation System (SINS) utilizing a 7-state STAtistical Reset (STAR) Kalman filter on a surface ship used strictly for testing but not satisfactory for the real world application for SSBN’s at sea because the external position fixes were seldom available exactly as pre-planned in attempting to synchronize to the pre-computed filter gains. Admittedly, this example is from a different application area entirely but it is more benign in general than that for radar applications. When there are problems within the more benign linear situation of navigation, the same problems will likely plague the slightly more challenging nonlinear situation of radar for the same reasons! However, more recent Boeing results: Schmidt, G. C., "Designing nonlinear filters based on Daum's theory," AIAA Journal of Guidance, Control, and Dynamics, Vol. 16, No. 2, pp. 371-376, Mar.-Apr. 1993, apparently offer a way around the limitation that I mentioned (see Schmidt's admission in his conclusion section of having obtained "mixed results", both good and bad). [It is, perhaps, worth mentioning in passing that there are two special cases of nonlinear filters that have an optimal estimator that is finite dimensional and the mean and variance are sufficient statistics, as in the purely linear system and Gaussian noises case: that of Benes and this other result of Daum (and subsequently by many others but there were some earlier investigations that served as analytic stepping stones that aided in this quest:
--Brockett, R., Finite Dimensional Linear Systems, Wiley, NY, 1970.

--M. Fujisaki, G. Kallianpur, H. Kunita, "Stochastic Differential Equations of Non-linéar filtering," Osaka J. of Mathematics, Vol. 9, pp. 19-40, 1972. 

--Y. Sunahara, A. Ohsumi, K. Terashima, H. Akashi, and Y. Takeuchi, "On Lie Algebraic Solution of a Class of Vector Stochastic Differential Equations and its Application to Stability Analysis," 10th JAACE Symposium on Stochastic Systems, Koyoto, pp. 17-20, 28-30 Nov. 1978.

--R. W. Brockett, "Remarks on Finite Dimensionai Non-linear Estimation," Asterisque, 1980 (Bordeaux 1978).

--Stephen I. Marcus and Alan S. Willsky, Algebraic Structure and Finite Dimensional Nonlinear Estimation, SIAM J. MATH. ANAL., Vol. 9, No.2, pp. 312-327, April 1978. http://ssg.mit.edu/group/willsky/publ_pdfs/20_pub_SIAM.pdf 

--Y. Sunahara, A. Ohsumi, K. Terashima, H. Akashi, "Representation of Solutions and Stability of Linear Differential Equations with Random Coefficients via Lie Algebraic Theory," 11th JAACE Symposium on Stochastic Systems, Koyoto, pp. 45-48, 27-29 Nov. 1979.

--Chikte, S. D., "Bilinear Systems with Nilpotent Lie Algebras: Least Squares Filtering," IEEE Trans. On Automatic Control, Vol. 25, No. 6, pp. 948-953, 1979.

--R. W. Brockett and J. M. C. Clark, "On the Geometry of the Conditional Density Equation," in Analysis and Optimization of Stochastic Systems (eds. O.  L. R. Jacobs et al.), Acad. Press, 1980. 

--Daum, F. E., "New Exact Nonlinear Filters," Bayesian Analysis of Time Series and Dynamic Models (edited by J. C. Spall), Chapt. 8, Marcel Dekker, New York, 1988. 

--D. Ocone, Topics in Nonlinear Filtering Theory, M.I.T. Ph.D. thesis, June 1980. 

--S. Marcus, S. K. Mitter and D. Ocone, "Finite Dimensionai Non-linear Estimation in Continuous and Discrete Time," in Analysis and Optimization of Stochastic Systems (eds. O.L.R. Jacobs et al.), Acad. Press, 1980. 

--V. E. Benes, "Exact Finite Dimensionai Filters for Certain Diffusions with Non-linear Drift," Stochastics, Vol. 5, pp. 65-92, 1981.

--Sanjoy K. Mitter, "Existence and Non-existence of Finite Dimensional Filters," publication date: indecipherable, but, perhaps, 1982; for reason for this ambiguity, please see last page, where the author doesn't explicitly state what the publication date is:

--S. K. Mitter, "On the Analogy between Mathematical Problems of Nonlinear Filtering and Quantum Physics," Ricerche di Automatica, Vol. 10, pp. 163-216, 1980.

--M. Hazewinkel and S. I. Marcus, "On Lie Algebras and Finite Dimensional Filtering," Stochastics, Vol. 7, pp. 29-62, 1982. 

--Daum, F. E., "Comments on 'Finite Dimensional Filters with Nonlinear Drift'," IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 2, pp. 689-691, Apr. 1998.

--Yau, S.S.-T., and Yau, S. T., "Addendum to 'Finite Dimensional Filters with Nonlinear Drift': A Response to F. E. Daum's Comments," IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 2, pp. 691-692, Apr. 1998.), 
but there are no realistic applications yet to which these results apply, as structurally revealed by MIT's Sanjoy K. Mitter within: http://web.mit.edu/~mitter/www/publications/33_exist_nonexist_FSI.pdf 
[Please notice that neither navigation applications nor target tracking applications exhibit this structure. Prof. Roger Brocket (Harvard Univ.) had utilized Lie algebras and associated Lie Bracket when he handled bilinear systems in the late 1960's and early 1970's, as did Willsky and Ho, discussed further down here]. However, they are all still useful for the valuable insights that they provide, possibly as test problems for performing IV&V of new software by cross-checking outputs against known closed-form output solutions beforehand for confirmation prior to inserting the final models of the actual ultimate intended application.

-Unscented Kalman Filter [also known as (a.k.a.), the Oxford Filter, a.k.a. the  Sigma-Point Filter]: Our historical apprehension regarding the Unscented Kalman Filter (UKF) is because of the presence of an unexplained factor (or unconstrained free real scalar parameter [not necessarily an integer], possibly positive, negative, or time-varying, at the whim of the analyst/implementer) that can serve as an expanding or contracting “twiddle factor” in the denominator of the gain expression that is consequentially inherited by the covariance equations; which, for linear systems, still appropriately computes the exact covariance associated with any approximate Gain that is used in an accompanying estimation filter (even if it is not the optimal “Kalman Gain”), as clearly explained on page 234 in Eq. 5.4.18 and further emphasized in the last sentence following Eq. 5.4.22 in: Brown, Robert Grover, Hwang, Patrick Y. C., Introduction to Random Signals and Applied Kalman Filtering, 2nd Edition, John Wiley & Sons, Inc., New York, 1983. The numerical comparison in Julier, S. J., Uhlmann, J. K., and Durrant-Whyte, H. F., “A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators,” IEEE Trans. on Automatic Control, Vol. 45, No. 8, pp. 477-482, May 2000 of UKF vs. EKF performance appears to be somewhat contrived since actual EKF practitioners would either take more frequent measurement fixes to supplement tracking the object’s trend and/or better pose the target model in the first place to take into account its known anticipated planar motion about a circular track of constant radius about the origin by merely posing the problem in (rho,theta) polar coordinates [with known constant angular velocity] as the two states of interest, or if the constant angular velocity is unknown beforehand, then including this unknown parameter as an additional state to be estimated using parameter identification techniques or by using an approach that came later: Souris, G. M., Chen, G., Wang, J., “Tracking an Incoming Ballistic Missile Using an Extended Interval Kalman Filter,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1, pp. 232-240, Jan. 1997, but Julier, S. J., Uhlmann, J. K., and Durrant-Whyte, H. F. do invoke conditions that are impossible to check beforehand e.g., [Julier, S. J. et al, op. cit., Eq. 2] since probability measure for x(k) is unknown); unconventional use of calculated covariance to account for nonlinear measurement equation and associated unconventional assumption of mean being zero and an unconventional proposed handling if mean is not zero (by their saying “it can be shifted”, but mean is in fact unknown so one can not know beforehand how much it should be shifted by, so USER is thus stymied in trying to proceed as they recommend [Julier, S. J. et al, op. cit., Sec. 4]; UKF also utilizes “mini-simulation” trials before each measurement incorporation step (but not as many as a PF would require). From Unscented Kalman Filter discussion in Wikapedia: "The Unscented Kalman Filter (UKF) uses a deterministic sampling technique known as the unscented transformation (UT) to pick a minimal set of sample points (called sigma points) around the mean. ... For certain systems, the resulting UKF more accurately estimates the true mean and covariance." To me, this is reminiscent of what Emeritus Prof. Ronald L. Klein (UWV) had published http://www.tekassociates.biz/serv04.htm#almosttop in many articles on Estimation Theory using Gaussian Quadrature (i.e., integration) and other quadrature formulas [in order to improve the accuracy of the "Propagate Step" integration (over the candidate time interval) of the system dynamics within an EKF]. Recall that Gaussian quadrature does not use equispaced time steps for evaluating constituent pieces but requires that thae constituent pieces be evaluated at specially designated points (and weights) as provided in Sec. 25 of Abramowitz and Stegun’s 1964 book, Handbook of Mathematical Functions, National Bureau of Standards [now National Institute of Standards and Technology (NIST)], Washington, D.C.

The above mentioned “Global Lipschitz condition” is much stronger in contrast to the mere “continuity condition” of the system dynamics being a sufficient condition on the nonlinear system dynamics for a deterministic nonlinear differential equation to have a solution. For uniqueness of the solution of the latter, only a “local Lipschitz condition” need be satisfied. The need for a global Lipschitz condition is discussed in Bucy, R. S., Joseph, P. D., Filtering for Stochastic Processes with Applications in Guidance, 2nd Edition, Chealsa, NY, 1984 (1st Edition Interscience, NY, 1968) (and is also discussed in: Kerr, T. H., “Applying Stochastic Integral Equations to Solve a Particular Stochastic Modeling Problem,” Ph.D. Thesis in the Department of Electrical Engineering, University of Iowa, Iowa City, Iowa, January 1971, where a detailed proof is provided on pp. 188-213 utilizing Ito integrals for stochastic integrands). 

--R. F. Curtain and, A. J.  Pritchard, Infinite Dimensional Linear Systems Theory, Springer, NY, 1978. (i.e., Systems described by Partial Differential Equations [ODE's] are infinite dimensional systems.)

So the numerical comparison between Julier, S. J., Uhlmann, J. K., and Durrant-Whyte, H. F., “A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators,” IEEE Trans. on Automatic Control, Vol. 45, No. 8, pp. 477-482, May 2000 is less of how well the UKF filter performed (as they claimed) but more about how bad an EKF can perform if it uses an inappropriate or bad model for the system. This should be NO surprise! A more appropriate posing of the estimation problem on a circle [SO(2)] is: Li, J. T.-H. Lo and A. S. Willsky, “Estimation for Rotational Processes with One Degree of Freedom-Part 1,” IEEE Trans. on  Automatic Control, Vol. 20, No. 1, pp. 10-21, Feb. 1975. 5_pub_IEEE.pdf 

Some space is allotted here now for some views of others that are pro-use of Unscented Filter or Sigma-Point Filters and even Particle Filters in specific applications:

-Sigma-Point Filtering for Integrated GPS and Inertial Navigation:

-Sigma-Point Filters in Robotic Applications:

-Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor-Fusion - Applications to Integrated Navigation:

-Robot Mapping Unscented Kalman Filter:

We are aware of the following Lockheed Martin Space Systems Company results and its references: Nima Moshtagh and Moses W. Chan, "Multisensor Fusion Using Homotopy Particle Filter," Proceedings of 18th International Conference on Information Fusion, Washington, DC, pp. 1641-1648, 6-9 July, 2015. As informative as this was (with a nice derivation of how to use log-homotopy), it still ignored saying anything about the size of the computer burden incurred with respect to being able to calculate anything along these lines in real-time. What else is new? They also use the trick of target motion in a circular track without expressing it in offset polar coordinates, as was also absent with an early Unscented Filter versus Kalman Filter example, as already discussed above.

Also see references in Maciej Janowicz, Joanna Kaleta, Filip Krzy˙zewski, Marian Rusek, and Arkadiusz Orlowski, "Homotopy Analysis Method for Stochastic Differential Equations with Maxima," International Workshop on Computer Algebra in Scientific Computing, pp. 233-244, CASC 2015.

-Also see: plethora of references in Hariharan, G., "A homotopy analysis method for the nonlinear partial differential equations arising in engineering," International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 18, No. 2, 2017.

-Please see: Daum, F. E., “Nonlinear filters: beyond the Kalman filter,” IEEE AandE Magazine, Vol. 20, No. 8, pp. 57-69, Sept. 2005 for an excellent, clear discussion of the three estimation algorithms that I have just critiqued above. My only complaint here is that Daum seems to have overlooked or missed the earlier Lie Algebra results of : Li, J. T.-H. Lo and A. S. Willsky, “Estimation for Rotational Processes with One Degree of Freedom-Part 1,” IEEE Trans. on  Automatic Control, Vol. 20, No. 1, pp. 10-21, Feb. 1975 as a precedent. [Willsky and Lo explicitly handle estimation on a circle, SO(2), rather than estimation on a sphere, SO(3), as NASA’s F. Landis Markley, et al deal with in their extensive NASA survey and comparison between approaches and techniques. However, Willsky and Lo are particularly lucid in their development and exposition and, moreover, within the last sentence of their conclusion, provide specifics of their suggested generalization to estimation results on arbitrary Abelian Lie groups, such as SO(3).] 5_pub_IEEE.pdf  Also see: Lo, J. T.-H. and Willsky, A. S., “Stochastic Control of Rotational Processes with One Degree of Freedom,” SIAM Journal on Control, Vol. 13, No. 4, 886ff, July 1975. Another aspect that Daum may have, perhaps, overlooked is the strong applicability of Lie Algebras well beyond mere separation-of-variables for PDE’s or ODE’s, as in: Wu, Y., Hu, X., Hu, D., Li, T., and Liam, J., “Strapdown Inertial Navigation System Algorithms Based on Dual Quaternions,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 41, No. 1, pp. 110-132, Jan. 2005 and Savage, P. G., “A Unified Mathematical Framework for Strapdown Algorithm Design,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 2, pp. 237-249, March-April 2006 and Bernard Friedland, “Analysis of Strapdown Navigation Using Quaternions,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 14 , No. 5, pp. 764-768, Sept. 1978 and Bell, D. J., “Manifolds and Lie Algebras,” in Mathematics of Linear and Nonlinear Systems: for Engineers and Applied Scientists, Clarendon Press, Oxford, UK, 1990.

Warning again: Precedents in use of “speeded up videos” to depict computational solution of PDE's have occurred frequently in the past so that the solutions “appear” to be proceeding in real-time (even though that is NOT the case)!

About 35+ years ago, there were claims from others that one was now able to computationally solve the Navier–Stokes equations (PDE's) in real-time for flow around an aircraft wing! What happened to this braggadocious claim? Seems as though it was not true either!

My immediately posted retort (in the middle of the night) to a Vice President of a Fortune 500 Defense firm [who had just claimed, in a public post on Linkedin, that their firm provided excellent tracking, as computed in “almost real-time”!] was that his admitting that such information was being computed by them in “almost real-time” is tantamount to “almost” avoiding a collision (for FAA/ARINC navigation applications) and “almost” intercepting the designated threatening enemy target (for DoD applications)! My point being that navigation information and target tracking results are needed in “real-time” and, to date, are only available for exact Kalman filter constructs (for the linear case with Gaussian noises or, at worse, noises from an Exponential family of distributions, where marginal and/or conditional distributions are still Gaussians) and also available for Extended Kalman Filter (EKF) constructs as well (as an approximate estimator for the nonlinear case).  The VP immediately retracted it before it could be viewed by a larger audience and was thus able to save face. (I actually did him a favor by my responding in this manner "for his trial run in the middle of the night" before anybody else saw it.)

For both navigation applications and target tracking applications, there are always specifications indicating the frequency of computed output estimates to be provided by the estimation algorithm. For navigation, for the short time between when estimates are available, the platform is proceeding using “Dead Reckoning”, https://www.google.com/search?source=hp&ei=U8B5XqyLD7OrytMPgveyEA&q=dead+reckoning&oq=Drad+Recon&gs_l=psy-ab.1.0.0i13l10.6322.14766..26055...0.0..0.199.851.8j2......0....1..gws-wiz.......0i131j0j0i10j0i13i10j0i13i5i30.9ANUljaMMYU 
https://en.wikipedia.org/wiki/Dead_reckoning, which is usually adequate. However, if there is a density of other maneuvering platforms in the same vicinity, there may be a problem relying only on Dead Reckoning (even for a short time epoch) and other further compensating techniques may be needed (such as use of VOR/DME, ILS, Tacan, altimeter, compass, etc.) For target tracking, there can also be additional processing needed by other augmenting algorithms to associate estimates with particular tracks in a multi-target tracking environment and, perhaps, also classification of the nature or identity of the targets using pattern recognition or discrimination/classification techniques-maybe as part of IFFN (Identification: Friend, Foe, or Neutral). So timeliness of computed estimates is of the essence before the further computations (just indicated here as being beyond mere Kalman Filter-like estimation) can proceed!

The overall performance of sigma-point  filters, Oxford filters (a.k.a., Unscented Kalman Filters) is not terrible. They are merely not quite as good as a Kalman-based filter in the application role. This aspect was analytically proved in Andrew Jazwinski's textbook beyond a shadow of a doubt. That these two filtering schemes work reasonably well is expected, as established in even earlier research results associated with so-designated "model following" in using the output of one linear system as input to another linear system even when the internal states of both don't correspond exactly yet still behave similarly.

An interesting article that also invokes a Genetic Algorithm approach: Xiyuan Chen, Chong Shen, and Yuefang Zhao, “Study on GPS/INS System Using Novel Filtering Methods for Vessel Attitude Determination,” in Special Issue of Marine Engineering and Applications, Research Article | Open Access, Volume 2013 |Article ID 678943 | 8 pages | https://doi.org/10.1155/2013/678943. Especially see the extensive references listing interesting alternative hybrid approaches to estimation.


Investigating new Markov Chain Monte-Carlo techniques (Metropolis-Hastings and Metropolis-Gibbs sampling and re-sampling) and associated supporting pseudo-random number and quasi-random number generation techniques so germane to PF (and quasi-random number generation techniques also relevant to encryption).
Angle-only tracking (AOT) or Bearings-0nly filtering (for passive sonar or range-denied jammed radar tracking)-all being highly nonlinear and also relevant to interceptor guidance laws (and fire control).
Kalman filter tracking accoutrements like the handling of multiple target tracks (e.g., through use of the Hungarian algorithm, or Munkres algorithm, or J-V-C algorithm, or Murtys algorithm, or Multiple Hypotheses Testing, or distributed Auction algorithm, or new wrinkle using Generalized Likelihood Ratios [GLR] for recent modern update to use of Track-before-Detect algorithms, or any other approaches to solving the Assignment Problem of Operations Research); Matrix Spectral Factorization; and Cramer-Rao Lower Bound (CRLB) analysis & evaluation.
Event detection (e.g., through use of Generalized Likelihood Ratio [GLR] or other comparable algorithms), which utilizes the outputs associated with Kalman filters or statistical estimation, to identify faulty navigation components (i.e., INS components, GPS receivers, Receiver Autonomous Integrity Monitoring [RAIM]) or target maneuvers within radar target tracking applications.
Self-assembling or self-organizing networked sensors (perhaps exploiting different sections of the electromagnetic spectrum for multi-spectral or hyper-spectral assessments or determinations), perhaps based on Kalman filter constructs or other comparable technologies.
Employing tactics for improving target observables such as engaging in certain sensor-host platform maneuvers to improve passive sonar observability, using aircraft maneuvers to eliminate ambiguity associated with several different candidate INS component sources of owncraft INS failure or to reveal the presence of such failures during early stages of a mission before they have deleterious impacts. (E.g., enemy use of decoy wooden gun barrels were eventually distinguished from actual metal ones using Infrared (IR) at sun down during first Iraq war, where Bud-Light of flashing InfraRed (IR) lights, only visible to those with IR goggles, were heroically developed by others over an extremely short schedule for aiding in Identification Friend or Foe [IFF] task).
Investigations into probability one convergence arguments for assessing estimator convergence to true targets instead of relying on mere mean-square-convergence arguments inappropriately extrapolated from multitudinous Monte-Carlo trials (especially since successful National Missile Defense (NMD) interception is a single sample event). Such developments would enable a more realistic design of experiments for NMD/GMD.
Partial Differential Equations (PDE-based) Kalman filter constructs for chemical or thermal conduction (not convection nor radiation) for thermal diffusion (expertise in parabolic PDE’s also extends to understanding methodology in proper use of Kolmogorov equation (a.k.a. the Fokker-Planck equation) arising for the underlying conditional probability density function underlying nonlinear filtering [and in similar PDE’s arising in Electromagnetic theory for the hyperbolic wave equation for transmission lines, wave guides, and antennas]).
2-D Kalman filters for image processing resolution enhancements (with these Kalman filter constructs, along with Decentralized Kalman filters & image registration being likely basis for multi-sensor fusion).
Multi-channel (approximate) generalizations to scalar Maximum Entropy spectral estimation (similarly model-based).
Use of a Kalman filter in sensor fusion applications.
He is enthusiastic about novel ideas from the above list (and elsewhere) that further network centric warfare (i.e., use of decentralized Kalman filters to obtain different complementary perspectives of the same targets by viewing from different aspect angles simultaneously from GPS-derived known locations of the sensors; perhaps also likely synchronized by GPS time; however, he is well aware that other more robust time standards and navigation standards are currently being pursued in 2018 and beyond for PNT, where DOT has taken over the reins from DoD in spearheading solutions for civilian applications while DoD is still pursuing solutions for military applications). He encourages using Kalman Filter-related technology to replace Matrix Spectral Factorization (MSF) in Space-Time Adaptive Processing (STAP) to achieve more robustness in STAP by perhaps accommodating some nonstationarity (in the statistical sense). He seeks to be aware of the emergence of disruptive technologies that may revolutionize certain critical areas related to national defense (but at the same time maintains a healthy skepticism until they actually prove themselves) and he tends to warn others if any perceived fraud is being perpetrated in any form (even if it takes the form of over zealous researchers perhaps overstating the capabilities of a new technique or ignoring its apparent limitations). He discourages invoking unwarranted hype in R&D endeavors.

He is an algorithm specialist who is heavy on the analysis, having taken Advanced Calculus, Complex Variables, Operational Mathematics (from Churchill s textbook), Point Set Topology, Modern Algebra, Real Analysis I, II and Measure and Integration Theory I, II from the mathematics department in graduate school well before it was in vogue to do so within an engineering curriculum (as it is now). He took the Graduate Record Exam and its mathematics specialty test in October 1967 and scored in the 98th percentile upon entering graduate school. However, he does not overly dwell on this aspect of his past. However, being mathematically oriented does help him to keep up with changes in technology since mathematics, although pervasive throughout technology, generally, has a longer time constant than the other areas of technology but, of course, it evolves too as new discoveries are made and interconnections revealed. He also follows through with “down to earth practical considerations. One of his goals is to help prevent engineers from going astray with the mathematics and getting hurt (or hurting anybody else and therefore to possibly avoid the usual finger pointing and “blaming the programmer when things go wrong because someone’s theoretically supporting mathematics was in error). Tom also took extra courses in physics too, like Modern Physics/Quantum Mechanics, Physical/Celestial Mechanics. 

As a Research & Development Engineer, Systems Engineer, and Software Developer, specializing in digital algorithms, he has worked in the estimation, simulation, and digital implementation area continuously since 1971. This includes 6 years on U.S. DoD (Poseidon\Trident) C-3 and C-4 back-fit submarines [which, in those days, used multiple Univac CP-890/YUK computers in the Navigation Room] and 6 years on Navy and Air Force aircraft Navigation (failure detection and reconfiguration in Navigation systems within own-craft position and attitude determination). He has some experience with sonar target tracking software algorithm evaluation Independent Verification and Validation (IV&V) and has performed Global Positioning Satellite (GPS) System integration Development Test and Evaluation [DT&E(OR)] Operational Readiness in attack submarines (specifically, on the SSN-701 LaJolla as a typical representative) and cross-checked their Department of Defense (DoD) spec compliance in monitoring performance in the GPS Phase II receiver competition between Magnavox and Rockwell Collins in the early 1980s and has investigated use of INS/GPS in other novel applications of airborne mapping in the 1990’s and in 2003 for the Navy AROSS airborne Littoral surveillance program (under subcontract for Arête) by performing a quantitative analysis of the relative pointing accuracy provided by each of several alternative candidate INS platforms of varying quality (and cost) by using high quality GPS [P(Y)-code, differential, or kinematic] fixes at a high rate to enhance the INS with frequent updates to compensate for degradations incurred with time due to inherent gyro drift rate characteristics of each less expensive INS candidate. He has also worked in strategic Radar target-tracking; and in some aspects of tactical and strategic Electronic Warfare (EW) pattern recognition applications for Honeywell Electro-Opticals helicopter Missile Warning System (MWS) in the early 1980’s and on Updated Early Warning Radar (UEWR) in 2000 (please click on Consulting Services button at top of this screen for specifics). The common thread is that almost all of the above projects involve Kalman filter signal processing or related estimation theory considerations. An exception was the work he did on security for the WIS program, which stands for WWMCCS Improvement System, and WWMCCS itself stands for World Wide Military Command and Control System (WWMCCS was decommissioned in 1996 and replaced by Global Command and Control System). He draws heavily from his prior experience  at General Electric Corporate R&D Center (71-73), The Analytical Science Corporation: TASC (73-79), Intermetrics, Inc. (79-86), and the Lincoln Laboratory of the Massachusetts Institute of Technology  (86-92), and at TeK Associates (92-present) and from work he performed on his clients projects. At Intermetrics, Inc., he also served as Interim Technical Editor of Navigation, The journal of the Institute of Navigation (standing in for his previous supervisor, Stephen Gilbert, for a year: 1985-86) during the transition period between Paul M. Janiczek (after Paul Janiczek got married and relinquished the position of editor) and years before the next full time editor was installed. Click here to see the numerous Continuing Education Courses Tom has taken to keep up with evolving technology.

As an algorithm and signal processing specialist, he generally focuses on system aspects related to optimal and sub-optimal estimation and Kalman filtering and in the underlying models and, in particular, to requisite further statistical processing of state estimates and covariances related to incident detection and tracking. He also has interests in GIS and enjoys developing Windows-based PC software and GUIs to prompt and constructively aid the user. He recognizes that GUIs can be implemented in interpretive software languages and still be faster than a humans response while numerical calculations are always to be implemented in truly compiled software languages to reap the benefit of speed, timeliness, and possibly parallelization. At General Electric Corporate Research & Development Center in the early 1970s, Tom was a protégée of his fellow coworkers in corporate software development of Automated Dynamic Analyzer (ADA) [but not the WPAFB-funded 1980s computer language known as Air Force Ada (discussed much further below), where both software approaches were named to honor the first computer programmer, Ada Lovelace]: being Joe Watson, Hal Moore, and Dr. Glen Roe (the degree to which this early exposure benefited Tom has only recently been fully realized, as that early experience continues to unexpectedly influence him over the 4+ decades that ensued).

Tom’s work and research experience has encompassed: estimation applications with standard Gaussian white noises or with non-standard Poisson or other point-process noises present (primarily in NAVIGATION and in RADAR and IR target tracking); spectral estimation in analyzing and emulating RADAR primary polarization (PP) and orthogonal polarization (OP) target signatures; decentralized and multi-rate filters; mathematical modeling and parameter identification for stochastic systems; team theory and zero-sum and nonzero-sum differential games (Stackelberg strategies and Nash equilibrium, signaling, coalitions); optimal search and screening; angle-only (a.k.a. bearings-only) tracking; fault\ failure detection in dynamical systems (and the mathematically identical areas of maneuver detection, change detection and\or incident detection); optimal-sensor-usage-alternation with a Kalman filter; determining Pareto-optimal strategies using the method-of-linear-combinations (for multi-criteria optimization); optimal control; algorithm convergence; engineering analyses; trade-off analyses\trade studies; computational techniques; control theory (modern state-space  based and classical frequency-domain based approaches including Matrix Spectral Factorization, Proportional-Integral-Derivative (PID) control compensation, calculus-of-variations, Pontryagin’s Maximum Principle); and the supporting underlying systems theory. His publications are frequently cited by other independent authors and researchers; explicit examples (a partial list obtained from Citation Index associated with the on-line “Web of Science” at any good research library [Ostensibly, my current Web of Science Researcher ID: K-4879-2019] (or from the PC-based relatively new “Publons”) by searching under “Kerr, T. H.”) being:

-Skog, I., Handel, P., In-Car Positioning and Navigation Technologies-A Survey, IEEE Transactions on Intelligent Transportation Systems, Vol. 10, No. 1, pp. 4-21, Mar. 2009. 

-Smith, M. A., On Doppler Measurements for Tracking, International Conference on Radar, Adelaide, Australia, Vol. 1 and 2, pp. 309-314, 2-5 Sep. 2008. 

-Shi, Y., Han, C.  Z., Lian, F., The Iterated divided difference filter, IEEE International Conference on Automation and Logistics, 1-3 Sep. 2008, Qingdao, Peoples Republic of China, Vols. 1-6, pp. 1799-1802, 2008. 

-Banani, S. A., Masnadi-Shirazi, M. A., A New Version of Unscented Kalman Filter, Proceedings of Conference of the World Academy of Science, Engineering, and Technology, Barcelona, Spain, Vol. 20, pp. 192-197, 25-27 Apr. 2007.

-Petsios, M. N., Alivizatos, E. G., Uzunoglu, N. K., Solving the association problem for a multistatic range-only radar target tracker, Signal Processing, Vol. 88, No. 9, pp. 2254-2277, Sep. 2008. 

-Xu, B. L., Chen, Q. L., Wu, Z. Y., et al, Analysis and approximation of performance bound for two-observer bearings-only tracking, Information Sciences, Vol. 178, No. 8, pp. 2059-2078, 15 Apr. 2008. 

-Hovareshti, P., Gupta, V., Baras, J. S., Sensor scheduling using smart sensors, Proceedings of 46th IEEE Conference on Decision and Control, New Orleans, LA, Vols. 1-14, pp. 6083-6088, 12-14 Dec. 2007.

-Gadzhiev, C. M., Determining the operating conditions of floating marine platforms based on the predicted motion control under conditions of wind and wave disturbances, Measurement Techniques, Vol. 51, No. 1, pp. 28-33, Jan. 2008.

-Choudhury, D. R., Shifted power method for positive semi-definite matrices using Gerschgorin, Proceedings of 10th World Multi-Conference on Systemics, Cybernetics and Informatics/12th International Conference on Information Systems Analysis and Synthesis, Orlando, FL, WMSCI 2006, Vol. IV, pp. 251-253, 16-19 Jul. 2006. 

-Fong, K. F., Loh, A. P., Tan, W. W., A frequency domain approach for fault detection, International Journal of Control, Vol. 81, No. 2, pp. 264-276, 2008. 

-Xu, B. L., Wu, Z. Y., Wang, Z. Q., Theoretic performance bound for bearings-only tracking, Proceedings of 6th International Conference on Machine Learning and Cybernetics, Hong Kong, Peoples Republic of China, Vols. 1-7, pp. 2300-2305, 19-22 Aug. 2007.

-Duan, F. Y., Wang, H., Zhang, L. J., et al, Study on fault-tolerant filter algorithm for integrated navigation system, Proceedings of IEEE International Conference on Mechatronics and Automation, 5-8 Aug. 2007, Harbin, Peoples Republic of China, 2007, Vols. I-V, pp. 2419-2423, 2007. 

-Tong, Z. M., Tang, W. Y., The application of data fusion in optical theodolite coordinate measurement system, art. no. 659510, Proceedings of Conference on Fundamental Problems of Optoelectronics and Microelectronics III, 12-14 Sep. 2006, Harbin, Peoples Republic of China, Pts. 1 and 2, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), Vol. 6595, pp. 5951-5951, Parts 1-2, 2007. 

-Kramer, K. A., Stubberud, S. C., Geremiam, J. A., Sensor calibration using the neural extended Kalman filter in a control loop, Proceedings of IEEE International Conference on Computational Intelligence for Measurement Systems and Applications, 27-29 Jun. 2007, Ostuni, Italy, pp. 19-24, 2007 

-Xu, B. L., Wu, Z. Y., Wang, Z. Q., On the Cramér-Rao lower bound for biased bearings-only maneuvering target tracking, Signal Processing, Vol. 87, No. 12, pp. 3175-3189, Dec. 2007. 

-Mironovskii, L. A., The use of analytical redundancy in navigational measuring systems,,” Proceedings of 4th International Seminar on Mathematical, Statistical, and Computer Support of Measurement Quality, 28-30 Jun. 2006, St. Petersburg, Russia, Measurement Techniques, Vol. 50, No. 2, pp. 142-148, Feb. 2007.

-Li, X. R., Jilkov, V. P., Survey of maneuvering target tracking. Part V: Multiple-model methods,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 41, No. 4, pp. 1255-1321, Oct. 2005. 

-Li, X. R., Jilkov, V. P., A survey of maneuvering target tracking: Approximation techniques for nonlinear filtering,” 16th Conference on Signal and Data Processing of Small Targets, 13-15 Apr. 2004 Orlando, FL, Signal and Data Processing of Small Targets 2004, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), Vol. 5428, pp. 537-550, 2004.

-Koutsoukos, X. D., Estimation of hybrid systems using discrete sensors,” Proceedings of 42nd IEEE Conference on Decision and Control, Maui, HI, Vols. 1-6, Dec. 09-12, 2003.

-Rapoport, I., Oshman, Y., A Cramér-Rao type lower bound for the estimation error of systems with measurement faults,” Proceedings of 42nd IEEE Conference on Decision and Control, 9-12 Dec. 2003, Maui, HI, Vols. 1-6, pp. 4853-4858, 2003.

-Bessell, A., Ristic, B., Farina, A., et al., Error performance bounds for tracking a maneuvering target,” Proceedings of 6th International Conference on Information Fusion, 8-11 Jul. 2003, Cairns, Australia, FUSION 2003, Vols. 1-2, pp. 903-910, 2003. 

-Xiong, W., He, Y., Zhang, J. W., Centralized multisensor nonlinear filter method,” Proceedings of 3rd International Symposium on Instrumentation Science and Technology, 18-22 Aug. 2004, Xian, People's Republic China, Vol. 2, pp. 526-530, 2004.

-Ristic, B., Farina, A., Hernandez, M., Cramér-Rao lower bound for tracking multiple targets,” IEE Proceedings-Radar, Sonar, and Navigation, Vol. 151, No. 3, pp. 129-134, Jun. 2004. 

-Behazin, F., Nabavi, B., Fesharaki, M. N., The reformulation and modification on iterated EKF for applications with large-dimension measurement,” Proceedings of 6th International Conference on Signal Processing, 26-30 Aug. 2002, Beijing, People's Republic of China, Vols. I and II, pp. 756-759, 2002.

-Simandl, M., Straka, O., Seting sample size in particle filters using Cramér-Rao bound,” Proceedings of 5th IFAC Symposium on Nonlinear Control Systems, 4-6 Jul. 2001, St. Petersburg, Russia, Nonlinear Control Systems 2001, Vols. 1-3, IFAC Symposia Series, pp. 681-686, 2002.

-Ning, X. L., Fang, J. C., A new method of autonomous navigation for deep space explorer based on information fusion,” Proceedings of 6th International Conference on Electronic Measurement and Instruments, 18-21 Aug. 2003, Taiyuan, People's Republic of China, Vols. 1-3, pp. 220-224, 2003. 

-Li, X. R., Jilkov, V. P., A survey of maneuvering target tracking - Part II: Ballistic target models,” Proceedings of 13th Conference on Signal and Data Processing of Small Targets, 30 Jul.-2 Aug. 2001, San Diego, CA, Proceedings of The Society of Photo-Optical Instrumentation Engineers (SPIE), Vol. 4473, pp. 559-581, 2001.

-Li, X. R., Jilkov, V. P., A survey of maneuvering target tracking - Part III: Measurement models,” Proceedings of 13th Conference on Signal and Data Processing of Small Targets, 30 Jul.-2 Aug. 2001, San Diego, CA, Proceedings of The Society of Photo-Optical Instrumentation Engineers (SPIE), Vol. 4473, pp. 423-446, 2001. 

-Li, X. R., Jilkov, V. P., A survey of maneuvering target tracking - Part IV: Decision-based methods,” Proceedings of 14th Conference on Signal and Data Processing of Small Targets, 2-4 Apr. 2002, Orlando, FL, Proceedings of The Society of Photo-Optical Instrumentation Engineers (SPIE), Vol. 4728, pp. 511-534, 2002. 

-El-Mahy, M. K., Efficient satellite orbit determination algorithm,” Proceedings of 18th National Radio Science Conference (NRSC 2001), 27-29 Mar. 2001, Mansoura, Egypt, Vols. 1 and 2, pp. 225-232, 2001.

-Parra-Michel, R., Kontorovitch, V.Y., Orozco-Lugo, A. G., Simulation of wide band channels with nonseparable scattering functions,” Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 13-17 MAY 2002 ORLANDO, FL, Vols. I-IV, pp. 2829-2832, 2002 

-Hanebeck, U. W. D., Recursive nonlinear set-theoretic estimation based on pseudo ellipsoids,” Proceedings of International Conference on Multisensor Fusion and Integration for Intelligent Systems, 20-22 Aug. 2001, Baden Baden, Germany, pp. 159-164, 2001. 

-Mosavi, M. R., Mohammadi, K., Improve the position accuracy on low cost GPS receiver with adaptive neural networks,” Proceedings of Student Conference on Research and Development-Globalizing Research and Development in Electrical and Electronics Engineering, 16-17 Jul. 2002, Shah Alam, Malaysia,, pp. 322-325, 2002.

-Campa, G., Fravolini, M. L., Napolitano, M, et al., Neural networks-based sensor validation for the flight control system of a B777 research model,” Proceedings of 20th Annual American Control Conference (ACC), 8-10 May 2002, Anchorage, AK, Vols. 1-6, pp. 412-417, 2002.

-Vershinin, Y. A., A data fusion algorithm for multisensor systems,” Proceedings of 5th International Conference on Information Fusion (FUSION 2002), 8-11 Jul. 2002 Annapolis, MD, Vol. I, pp. 341-345, 2002. 

-Chetouani, Y., Mouhab, N., Cosmao, J. M., et al., Application of extended Kalman filtering to chemical reactor fault detection,” Chemical Engineering Communications, Vol. 189, No. 9, pp. 1222-1241, Sep. 2002. 

-Stentz, A., Dima, C., Wellington, C., et al., A system for semi-autonomous tractor operations,” Autonomous Robots, Vol. 13, No. 1, pp. 87-104, Jul. 2002. 

-Carpenter, J. R., Decentralized control of satellite formations,” International Journal of Robust and Nonlinear Control, Vol. 12, No. 2-3, pp. 141-161, Feb.-Mar. 2002. 

-Mirabadi, A., Mort, N., Schmidt, F., A fault tolerant train navigation system using multi-sensor, multi-filter integration techniques,” Proceedings of International Conference on Multisource-Multisensor Information Fusion (FUSION '98), 6-9 Jul. 1998 Las Vegas, NV, Vols. 1 AND 2, pp. 340-347, 1998. 

-Degen, U., Operations research of tracking algorithms for air surveillance system,” Proceedings of International Conference on Multisource-Multisensor Information Fusion (FUSION '98), 6-9 Jul. 1998 Las Vegas, NV, Vols. 1 and 2, pp. 850-855, 1998.

-Fravolini, M. L., Campa, G., Napolitano, M., et al., Minimal resource allocating networks for aircraft SFDIA,” Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM '01), 8-12 Jul. 2001, Como, Italy, Vols. I and II, pp. 1251-1256, 2001. 

-Hasan, K., Hossain, J., Multichannel autoregressive spectral estimation from noisy observations,” Proceedings of 10th International IEEE Tencon Conference, 24-27 Sep. 2000, Kuala Lumpur, Malaysia, Vols. I-III, Intelligent Systems and Technologies for the New Millennium, pp. 327-332, 2000. 

-Simandl, M., Kralovec, J., Tichavsky, P., Filtering, predictive, and smoothing Cramér-Rao bounds for discrete-time nonlinear dynamic systems,” Proceedings of 14th IFAC World Congress, 5-9 Jul. 1999, Beijing, Peoples Republic of China, Automatica, Vol. 37, No. 11, pp. 1703-1716, Nov. 2001. 

-Leung, H., Zhu, Z. W., Performance evaluation of EKF-based chaotic synchronization,” IEEE Transactions on Circuits and System I-Fundamental Theory and Applications, Vol. 48, No 9, pp. 1118-1125, Sep. 2001. 

-Sivananthan, S., Kirubarajan, T., Bar-Shalom, Y., Radar power multiplier for acquisition of low observables using an ESA radar,” IEEE Transactions on Aerospace and Electronic Systems Systems, Vol. 37, No. 2, pp. 401-418, Apr. 2001. 

-Li, Y., Sundararajan, N., Saratchandran, P., Stable neuro-flight-controller using fully tuned radial basis function neural networks,” Journal of Guidance, Control, and Dynamics, Vol. 24, No. 4, pp. 665-674, Jul.-Aug. 2001. 

-Niu, R. X., Willett, P., Bar-Shalom, Y., Matrix CRLB scaling due to measurements of uncertain origin,” IEEE Transactions on Signal Processing, Vol. 49, No. 7, pp. 1325-1335, Jul. 2001. 

-Bergman, N., Doucet, A., Gordon, N., Optimal estimation and Cramér-Rao bounds for partial non-gaussian state space models,” Proceedings of International Symposium on the Frontiers of Time Series Modeling, 14-16 Feb. 2000, Annals of the Institute of Statistical Mathematics, Tokyo, Japan, Vol. 53, No. 1, Special Issue, pp. 97-112, Mar. 2001. 

-Mahapatra, P. R., Mehrotra, K., Mixed coordinate tracking of generalized maneuvering targets using acceleration and jerk models,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 36, No. 3, pp. 992-1000, Jul. 2000. 

-Mirabadi, A., Schmid, F., Mort, N., Fault detection and isolation in a multisensor train navigation system,” Proceedings 6th International Conference on Computer Aided Design, Manufacture, and Operation in the Railway and Other Advanced Mass Transit Systems, 2-4 Sep. 1998, Lisbon, Portugal, Computers in Railways VI, Advances in Transportation, Vol. 2, pp. 1025-1035, 1998. 

-Jayakumar, M., Banavar, R. N., Risk-sensitive filters for recursive estimation of motion from images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No. 6, pp. 659-666, Jun. 1998. 

-Tichavsky, P., Muravchik, C. H., Nehorai, A., Posterior Cramér-Rao bounds for discrete-time nonlinear filtering,” Proceedings of 1st European Conference on Signal Analysis and Prediction (ECSAP-97), 24-27 Jun. 1997 Prague, Czech Republic, IEEE Transactions on Signal Processing, Vol. 46, No. 5, pp. 1386-1396, May 1998. 

-Koshaev, D. A., A comparison of lower bounds of accuracy in problems of nonlinear estimation,” Journal of Computer and Systems Sciences International, Vol. 37, No. 2, pp. 222-225, Mar.-Apr. 1998. 

-Mazor, E., Averbuch, A., Bar-Shalom, Y., et al., Interacting multiple model methods in target tracking: A survey,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 34, No. 1, pp. 103-123, Jan. 1998. 

-Koshaev, D. A., Stepanov, O. A., Application of the Rao-Cramér inequality in problems of nonlinear estimation,” Journal of Computer and System Sciences International, Vol. 36, No. 2, pp. 220-227, Mar.-Apr. 1997. 

-on page 208 in Bevly, D. M., Parkinson, B., “Cascaded Kalman Filters for Accurate Estimation of Multiple Biases, Dead-Reckoning Navigation, and Full State Feedback Control of Ground Vehicles,” IEEE Trans. on Control Systems Technology, Vol. 15, No. 2, pp. 199-208, Mar. 2007.

-Lee, H. K., Lee, J. G., “Fault-Tolerant Compression Filters by Time-Propagated Measurement Fusion,” Automatica, Vol. 43, No. 2, pp. 355-361, Feb. 2007.

-Xu, B. L., Wu, Z. Y., Wu, Wang, Z. Q., “On the Cramér-Rao Lower Bound for Biased Bearings-Only Maneuvering Target Tracking,” IEEE Trans. on Signal Processing, Vol. 87, No. 12, pp. 3175-3189, Dec. 2007.

-Mironovskii, L. A., “The Use of Analytical Redundancy,” Measurement Techniques, Vol. 50, No. 6, pp. 142-148, Feb. 2007.

-Aloi, D. N., Alsliety, M., Akos, D. M., “A Methodology for the Evaluation of a GPS Receiver in Telematics Applications,” IEEE Trans. on Instrumentation and Measurement, Vol. 56, No. 1, pp. 11-24, Feb. 2007.

-Petsios, M. N., Alivizatos, E. G., Uzunoglu, N. K., “Manuvering Target Tracking Using Multiple Bistatic Range and Range-Rate Measurements,” IEEE Trans. on Signal Processing, Vol. 87, No. 4, pp. 665-686, Apr. 2007.                                                                                                                  

-on page 48 of Hue, C., Le Cadre, J.-P., Perez, P., Posterior Cramér-Rao Bounds for Multi-Target Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 37-49, Jan. 2006.

-Chetouani, Y., “Fault Detection in a Chemical Reactor by Using the Standardized Innovation,” Process Safety and Environmental Protection, Vol. 84, No. B1, pp. 27-32, Jan. 2006.

-Gupta, V., Chung, T. H., Hassibi, B., Murray, R. M., “On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage,” Automatica, Vol. 42, No. 2, pp. 251-260, Feb. 2006.

-Hwang, D. H., Oh, S. H., Lee, S. J., Park, C., Rizos, C., “Design of a Low-Cost Attitude Determination GPS/INS Integrated Navigation System,” GPS Solutions, Vol. 9, No. 4, pp. 294-311, Nov. 2006.

-Pulford, G. W., “Taxonomy of Multiple Target Tracking Systems,” IEE Proceedings-Radar, Sonar, and Communications, Vol. 151, No. 5, pp. 291-304, Oct. 2005.

-Ristic, B., “Cramér Rao Bounds for Target Tracking,International Conference on Sensor Networks and Information Processing, 6 Dec. 2005.

-Lee, T. H., Ra, W. S., Yoon, T. S., Park, J. B., “Robust Extended Kalman Filtering via Krein Space Estimation,” IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, Vol. E87A, No. 1, pp. 243-250, Jan. 2004.

-Hagan, M. T., Demuth, H. B., De Jesus, O., “An Introduction to the Use of Neural Networks in Control Systems,” International Journal of Robust and Nonlinear Control, Vol. E87A, No. 1, pp. 243-250, Jan. 2004.

-on page 2369 of Hernandez, M., Ristic, B., Farina, A., Timmoneri, L., A Comparison of Two Cramér-Rao Bounds for Nonlinear Filtering with Pd < 1,” IEEE Trans. on Signal Processing, Vol. 52, No. 9, pp. 2361-2370, Sept. 2004.

-on page 81 of Ristic, B., Arulampalam, S., Gordon, N., Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House, Boston, MA, 2004.

-in references of Mutel, L. H., Speyer, J. L., Fault-Tolerant GPS/INS Navigation System with Application to Unmanned Aerial Vehicles, Navigation: Journal of the Institute of Navigation, Vol. 49, No. 1, Spring 2002.

-in references of Tichavsky, P., Muravchik, C. H., Nehorai, A., Posterior Cramér-Rao Bounds for Discrete-Time Nonlinear Filtering, IEEE Trans. on Signal Processing, Vol. 46, No. 5, pp. 1386-1396, May 1998.

-in Siouris, G. M., Chen, G.-R., Wang, J.-R., Tracking an Incoming Ballistic Missile using an Extended Interval Kalman Filter, IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1, pp. 232-240, Jan. 1997.

-in Napolitano, M. R., Chen, C. L., Naylor, S., Aircraft Failure Detection and Identification using Neural Networks, AIAA Journal of Guidance, Control, and Dynamics, Vol. 16, No. 6, pp. 999-1009, 1998.

-in Napolitano, M. R., Neppach, C., Casdorph, V., Naylor, S., Innocenti, M., Silventri, G., Neural-Network-based Scheme for Sensor Failure Detection, AIAA Journal of Guidance, Control, and Dynamics, Vol. 18, No. 6, pp. 1280-1286, Nov.-Dec. 1995.

-in Grejner-Brzezinska, D. A., Da, R., Toth, C., “GPS error modeling and OTF ambiguity resolution for high-accuracy GPS/INS integrated system,” Journal of Geodesy, Vol. 72, pp. 626-638, 1998.

-in Farina, A., “Target Tracking with Bearings-Only Measurements,” IEEE Trans. on Signal Processing, Vol. 78, No. 1, pp. 61-78, Oct. 1999.

-in Ristic, B., Farina, A., Hernandez, M., “Cramér-Rao lower bound for Tracking Multiple Targets,” IEE Proceedings-Radar, Sonar, and Navigation, Vol. 151, No. 3, pp. 129-134, Jun. 2004.

-in Simandl, M., Kralovec, J., Tichavsky, P., “Filtering, Prediction, and Smoothing Cramér-Rao Bounds for Discrete Time Nonlinear Dynamic Systems,” Automatica, Vol. 37, No. 11, pp. 1703-1716, Nov. 2001.

-in Spall, J. C., Garner, J. P., “Parameter-Identification for State-Space Models with Nuisance Parameters,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 26, No. 6, pp. 992-998, Nov. 1990.

-in Da, R., Lin, C. F., “A New Failure-Detection Approach and its Application to GPS Autonomous Integrity Monitoring,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 31, No. 1, pp. 499-506, Jan. 1995.

-in Da, R., “Failure-Detection of Dynamical Systems with the State Chi-Square Test,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 17, No. 2, pp. 271-277, Mar.-Apr. 1994.

-in Leung, H., Zhu, Z. W., “Performance Evaluation of EKF-based Chaotic Synchronization,” IEEE Trans. on Circuits and Systems, Vol. 48, No. 9, pp. 1118- 1125, Sep. 2001.

-in Bergman, N, Doucet, A., Gordon, N., “Optimal estimation and Cramér-Rao Bounds for Partial Non-Gaussian State Space Models,” Annals of the Institute of Statistical Mathematics, Vol. 53, No. 1, pp. 97-112, Iss S I Mar. 2001.

-in Mahapatra, P. R., Mehrotra, K., “Mixed coordinate tracking of generalized maneuvering targets using acceleration and jerk models,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 36, No. 3, pp. 992-1000, Jul. 2000.

-in Park, S. T., Lee, J. G., “Improved Kalman Filter design for three-dimensional radar tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 2, pp. 727-739, Apr. 2001.

-in Reece, S., “Nonlinear Kalman filtering with semi-parametric Biscay distributions,” IEEE Trans. on Signal Processing, Vol. 49, No. 11, pp. 2445-2453, Nov. 2001.

-in Sivananthan, S., Kirubarajan, T., and Bar-Shalom, Y., “Radar Power Multiplier for Acquisition of Low Observables using an ESA Radar,” IEEE Trans. on Aero- space and Electronic Systems, Vol. 37, No. 2, pp. 401-418, Jan. 2001.

-in Lee, T. H., Ra, W. S., Jin, S. H., et al, “Robust extended Kalman filtering via Krein space estimation,” IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, No. 1, pp. 243-250, Jan. 2004.

-in Niu, R. X., Willett, P., Bar-Shalom, Y., “Matrix CRLB Scaling due to measurements of uncertain origin,” IEEE Trans. on Signal Processing, Vol. 49, No. 7, pp. 1325-1335, Jun. 2001.

-in Nabaa, N., Bishop, R. H., “Solution to a Multisensor Tracking Problem with Sensor Registration Errors,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 35, No. 1, pp. 354-365, Jan. 1999.

-in Rizos, Chris, “Quality Issues in Real-Time GPS Positioning,” International Association of Geodesy SSG 1.154, IUGG Congress, Birmingham, U.K., 18-29 July 1999.

-in Jayakumar, M., Banavar, R. N., “Risk-sensitive filters for recursive estimation of motion from images,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 20, No. 6, pp. 659-666, Jun. 1998.

-in Mazor, E., Averbuch, A., Bar-Shalom, Y., et al,  “Interacting multiple model methods in target tracking: A Survey,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 1, pp. 103-123, Jan. 1998.

-in Benhaim, Y., “Optimizing Multi-hypothesis Diagnosis of Control-Actuator Failures in Linear Systems,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 4, pp. 744-750, Jul.-Aug. 1990.

-in Li, X. -R.,  Bar-Shalom, Y., “Performance Prediction of the Interacting Multiple Model Algorithm,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 29, No. 3, pp. 755-771, Jul. 1993.

-in Campa, G., Fravdini, M. L., Seanor, B., et al, “On-line learning neural networks for sensor validation for flight control system of a B777 research scale model,” International Journal of Robust and Nonlinear Control, Vol. 12, No. 11, pp. 987-1007, Sep. 2002.

-in Korbicz, J., Fathi, Z., Ramirez, W. F., “State Estimation Schemes for Fault-Detection and Diagnosis in Dynamic-Systems,” International Journal of System Science, Vol. 24, No. 5, pp. 985-1000, May 1993.

-in Ghil, M., Malanotterizzoli, P., “Data Assimilation in Meteorology and Oceanography,” Advances in Geophysics, Vol. 33,  pp. 141-266, 1991.

-in Hanan, K., Yahagi, T., “An iterative method for the identification of multi-channel autoregressive processes with additive observation noise,” IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, No. 5, pp. 674-680, May 1996. 

-in Liggins, M. E., Chong, C. Y., Kadar, I., et al, “Distributed fusion architectures and algorithms for target tracking,” Proceedings of the IEEE, Vol. 85, No. 1, pp. 95-107, Jan. 1997.

-in Doerschuk, P. C., “Cramér-Rao Lower Bounds for Discrete-Time Nonlinear Filters,” IEEE Trans. on Automatic Control, Vol. 40, No. 8, pp. 1465-1469, Aug. 1995.

-in Lu S., Doerschuk, P. C., “Performance Bounds for Nonlinear Filters,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1, pp. 316-319, Jan. 1995.

-in Zolghadri, A., Bergeon, B., Monison, M., “A Two Ellipsoid Overlap Test for On-line Failure Detection,” Automatica, Vol. 29, No. 6, pp. 1517-1522, 1993.

-in Zolghadri, A.,  “An Algorithm for Real-Time Failure Detection in Kalman Filters,” IEEE Trans. on Automatic Control, Vol. 41, No. 1, pp. 232-240, Oct. 1996.

-in Wahnon, E., “A Min-Max Testing Approach to Failure-Detection and Identification,” Lecture Notes in Control and Information Sciences, Vol. 144, pp. 487-496, 1990.

-in Golovan, A. A., Mironovskii, L. A., “An Algorithmic Control of Kalman Filters,” Automation and Remote Control, Vol. 54, No. 7, pp. 1183-1194, Jul. 1993.

-in Gadzhiev, C. M., “Prediction of failures in linear-systems with the use of tolerance ranges,” Measurement Techniques, Vol. 35, No. 8, pp. 851-896, Aug. 1992.

-in Gadzhiev, C. M., “Prediction the Technical State of Dynamic Systems by a Kalman Filter Updating Sequence,” Automation and Remote Control-Part 2, Vol. 54, No. 5, pp. 851-854, May 1993.

-in Mertikas, S. P., Rizos, C., “On-line Detection of Abrupt Changes in the Carrier-Phase measurement of GPS,” Journal of Geodesy, Vol. 71, pp. 469-482, 1997.

-in Hagan, M. T., Demuth, H. B., De Jesus, O., “An introduction to the use of neural networks in control systems,” International Journal of Robust and Nonlinear Control, Vol. 12, No. 11, pp. 959-985, Sep. 2002.

-in Li, Y., Sundararajan, N., Saratchandray, P., “Stable neuro-flight-controller using fully tuned radial basis function neural networks,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 4, pp. 665-674, Jul.-Aug. 2001.

-in Durrant-Whyte, H. F., Rao, B. Y. S., Hu, H., “Toward a Fully Decentralized Architecture for Multisensor Fusion,” Proceedings of 1990 Conference on Robotics and Automation, pp. 1331-1336, Cincinnati, OH, 13-18 May 1990.

-in Blackman, S. S., Broida, T. J.,  “Multiple-Sensor-Data-Association and Fusion in Aerospace Applications,” Journal of  Robotic Systems, Vol. 7, No. 3, pp. 445-485, Jun.  1990.

-in Roy, S., Hashemi, R. H., and Laub, A. J., “Square Root Parallel Filtering Using Reduced-Order Local Filters,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 27, No. 2, pp. 276-289, Mar. 1991.

-in Hong, L., “Centralized and Distributed Multisensor Integration with Uncertainties in Communication Networks,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 27, No. 2, pp. 370-379, Mar. 1991.

-in Makhoul, J., “Toeplitz Determinants and Positive Semidefiniteness,” IEEE Trans. on Signal Processing, Vol. 39, No. 3, pp. 743-746, Mar. 1991 (in particular, please see page 744, footnote and acknowledgement on page 748 for references to T. H. Kerrs professionally benign comments and positively supportive and cooperative interactions with the author of this work).

-in Brumback, B. D., Srinath, M. D., “A Fault-Tolerant Multisensor Navigation System-Design,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 23, No. 6, pp. 738-756, 1987.

-in Brumback, B. D., Srinath, M. D., “A Chi-Square Test for Fault-Detection in Kalman Filters,” IEEE Trans. on Automatic Control, Vol. 32, No. 6, pp. 532-554, June 1987.

-in Uwe D. Hanbeck, “Recursive Nonlinear Set-Theoretic Estimation Based on Pseudo-Ellipsoids,” Proceedings of the IEEE Conference on Multisensor Fusion and Integration for Intelligent Systems, pp. 159–164 (MFI2001), Baden–Baden.
Their patent abandoned by Siemens AG (perhaps because of prior art: me): https://patents.google.com/patent/US20060234722A1/en

(Other citations appear within our “Consulting Services” section of this website under our “Recent Clients”. . . . 

Additional citations to my publications occurred within earlier decades: the 1970’s and 1980’s. A search performed 20 years ago revealed that each of the above references cited at least one of my prior published papers. 

Click this link here to see a more comprehensive list of our publications.

Current searches use a Web of Science Researcher ID that is evidently incorrect as is the associated "Publons" ID through no fault of my own although I am actively trying to have it fixed by them.)

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Dr. Kerr has guided TeK Associates, an engineering consulting company, in developing their main software product TK-MIP™ (please click on TK-MIP v.2.0 for PC button at top of this screen for specifics and a free software demo download) and in pursuing Small Business Innovation Research (SBIRs) and sub-contracts in the evolving areas of Kalman filter and Control applications for Navigation, Target Tracking, and for Image Processing and Sensor Fusion. He has taught Optimal Control in the graduate Electrical and Computer Engineering (E.C.E.) Department at Northeastern University in the evenings for four years in the 1990s and has TeK consultant affiliations there and at UCLA. We have followed the development of optimal and sub-optimal estimation technology for over 40 years (since his first year long course in Kalman Filtering in 1968-'69 and a 2 week 8 hr/day Short Course at UCLA in the summer of 1969 and continued to do so from the entirety of his work experience) so that TK-MIP users can immediately reap the benefits of our expertise and experience (without our users having to be experts in these areas themselves).  Go to Primary Table of Contents

He is versed in FORTRAN77\90\95, PL/1, IBM Assembly Language, GW BASIC, BASICA, HTML, VBA, VBScript, and PC MatLab®\Simulink® (16-bit ver. 4.2.c and 32-bit ver. 6.5 MatLab and ver. 5.0 Simulink and for the later 64-bit versions up to the present), COMSOL Multiphysics® vers. 3.5a and 4.1, and also has some experience with Neural Networks (NN) for pattern recognition applications. TeK Associates has MatLab and Simulink along with the following MatLab toolboxes and/or Blocksets (and has experience in using them, as first obtained for his graduate students at Northeastern University in the 1990s and later during TeK Associates’ software development projects for National Missile Defense [NMD] for MITRE [1997], XonTech [1999], and Raytheon [1999, 2000] and for U. S. Navy AROSS Littoral Surveillance Program [2003], specifically, Kalman filter covariance analysis of INS/GPS for Arête); and for Goodrich ISR (now UTC Flight Services, later purchasing Rockwell Collins then merging with Raytheon to become Raytheon Technologies Coporation) for certain critical 2 state Kalman filter analysis and simulation (Oct. 2011-May 2012) for camera pointing; and, more recently, for Kalman filter implementations in MatLab for OKSI (Nov. 2012-Mar. 2013) and Aurora Flight Sciences (2014) [now part of Boeing in 2018].

* Fixed Point Blockset * Real-Time Workshop ver. 5.0 * MatLab Compilier ver. 3.0
* Control Systems ver. 5.2 * Data Acquisition* ver. 2.2 * Symbolic Math (Maple) ver. 2.1.3
* Statistics ver. 4.0 * Neural Network ver. 4.0.2 * Extended Symbolic Math ver. 2.1.3
* Image Processing ver. 3.2 * Robust Control ver. 2.0.9 * Mu-Analysis and Synthesis ver. 3.0.7
* Signal Processing ver. 6.0 * System Identification ver. 5.0.2 * SB2SL ver. 2.5 (which converts models to Simulink)

*Unfortunately, according to an October 2009 meeting at The MathWorks, their Data Acquisition Toolbox above currently lacks the ability to handle measurements using the older VME and PCI protocols, PCI, nor the ability to handle the recent PCIe protocol. In 2010, the Data Acquisition Toolbox does support PCIe protocol but still not VME.

and with Simulink® Real-Time Workshop (ver. 5.0) and the associated Fixed Point Blockset. He is becoming more familiar with C and C++ (as a prelude to his using the more straight-forward C#  [with automatic garabage collection] of Microsoft Studio.NET) and WindowsNT out of necessity since TeK Associates has developed and continues to refine and update a low cost PC-based Kalman filter\smoother\ simulator\optimal feedback regulator LQG\LTR software package: TK-MIP (first demonstrated at IEEE Electro95 in Boston, MA). TK-MIP is for sale commercially along with the accompanying on-line prompters and built-in tutorials included as lucrative aspects of the software (where the tutorials are unloaded from memory during actual signal processing to avoid being a CPU burden at that critical time, but still present and available on the hard drive to appear when needed and invoked). TK-MIP does not use anything from MatLab or Simulink since its main objective is to be extremely efficient in order to be sufficiently real-time and to still run in a small footprint requiring a host PC with no more than 16 Megs of RAM. Using a processor with more than 16 Megabytes of RAM is therefore not a constraint on TK-MIP. Please click on the TK-MIP ver. 2.0 for PC button at top of this screen to proceed to a free demo download representative of our TK-MIP® software. If any potential customer has further interest in purchasing our TK-MIP® software, a detailed order form for printout (to be sent back to us via surface mail or fax) is available within the free demo by clicking on the obvious Menu Item appearing at the top of the primary demo screen (which is the Tutorials Screen within the actual TK-MIP® software). We also include representative numerical algorithms (fundamental to our software) for users to test for numerical accuracy and computational speed to satisfy themselves regarding its efficacy and efficiency before making any commitment to purchase. We also have experience with National Instruments LabView® ver. 8.1, with COMSOL Multiphysics® versions 3.5a and 4.1, and likewise with MathSofts S-Plus® version 4.5 and Latent Gold® statistical software, with Mathsofts MathCad® version 13, with Mathematica®, and with Microsoft’s Zing® (at http://research.microsoft.com/zing); all of which we possess except for LabView® and COMSOL Multiphysics). We also have InstallShield Express version 2.01 and InstallShield PackageForTheWeb version 1.3 and both Wise Installer version 8.12 and PC-Install version 7.

Since 1992, his new forte is Visual Basic™ (vers. 3, 4, 5, 6 and .NET) for truly compiled executables, *.exes (ever since ver. 5), using VBXs\OCXs, DLLs, DDE, OLE, COM\DCOM\COM+, CAPICOM, and the Windows API for snappier performance on the PC under both Windows 9x\ME and WindowsNT\2000\XP and the use of associated third party tools. He is also involved in aspects of data acquisition for PCs (e.g., DMA and PCI databuses and DAQ data acquisition cards and signal conditioning). He documents his research findings either in Microsoft Word or in LaTeX. He owns all the above mentioned software tools (including a Simulink-to-C compiler 3.0) and a wide variety of MatLab toolboxes, which he has demonstrated to his students at Northeastern University. (He was at Intermetrics, Inc. as Ada was developed there for the Air Force in the 1980s, so he has some exposure to Ada® as well [but limited to just attending classes in it]. However, Tucker Taff at SofCheck (sofcheck.com, and previously at Intermetrics, Inc. and long standing local Ada guru) and Bard Crawford ( Ada Essentials: Overview, Examples and Glossary [Learnada, Vol. 1] by Bard Crawford Published in 19 June 2000, Trafford Publishing, British Columbia, Canada,  ISBN 10: 1552123715, ISBN 13: 9781552123713, also as a Kindle Edition, and originally from Barnes and Noble) are minutes away from our location in the center of Lexington. (Also see www.AdaCore.com for current status and recent developments and Tucker Taft, as reported by this originally New York, NY company.) Dr. Crawford is currently two blocks away (until September 2009) and is known for his automated Ada teaching materials. However, it is merely a stepping stone since another version of Ada evolved later as Ada 95. Ada 95 Textbooks: Brief Reviews, January 2001, http://www.seas.gwu.edu/faculty/mfeldman/ada95books.htmMichael B. Feldman, Education Working Group Chair, ACM Special Interest Group on Ada (SIGAda), Department of Computer Science, The George Washington University, Washington, DC 20052, (202) 994-5919 (voice) -- (202) 994-4875 (fax), mfeldman@seas.gwu.edu http://www.seas.gwu.edu/faculty/mfeldmanFor additional information and other useful links pertaining to Ada 95, visit Ada Programming Language Resources for Educators and Students (http://www.acm.org/sigada/education) and AdaPower (http://www.adapower.com). SofCheck is also known for expertise in JAVA and in tools for JAVA support. TeK Associates version of Simulink accommodates Ada modules within an S-Box and likewise for Fortran code and C code. Fortran is not dead but lives on (in some of us, especially since U.S. Government laboratories and FFRDCs received a waiver allowing them to be exempted from required use of Ada in the 1980s). Fortran was the first computer language to meet the challenges of exploiting parallel processing machines, as Fortran 90/95. A version of Fortran was also early to support Interval Analysis, where unknown scalar parameters (perhaps many) are contained between known lower and upper bounds. [For more information on this interval analysis topic, please contact Northeastern University ECE Department Prof. Bahram Shafai, shafai@ece.neu.edu; phone: 617.373.2984]  This Interval Analysis, Interval Matrices,  and Interval Computing approach has already been applied in 1997 to radar target tracking by George Siouris (AFIT-retired) in Dayton, OH. See: . See: Siouris, G. M., Chen, G.-R., Wang, J.-R., Tracking an Incoming Ballistic Missile using an Extended Interval Kalman Filter, IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1, pp. 232-240, Jan. 1997.

Dr. Kerr has developed a complete methodology consisting of a catalog of analytic closed-form test cases for verifying general purpose control and estimation related software code implementations and has previously participated (through the Boston area IEEE Control Systems Society as chairman for six years and as chairman of the Steering Committee for two years) in a run off competition\comparison which occurred in September 1993 between four local, but nationally known, Computer-Aided Control System Design (CACSD) vendors. The benefits of using these recommended or similarly justified test cases are the reduced computational expense incurred during software debug by using such low-dimensional test cases and the insight gained into software performance (as gauged against test problems of known closed-form solution behavior).  

Click here to see a copy of the software benchmark test handout that we sought to compare to the computed outputs at this IEEE meeting.

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Having validated software that one is confident of is a necessary prerequisite before venturing into mission-critical Navigation applications, sonobuoy target tracking, radar target tracking, and novel research areas such as applications of decentralized Kalman filters, or sophisticated algorithms for further post-processing and massaging the outputs of a Kalman filter, as occurs in certain approaches to signal detection in statistically nonstationary systems and in NAV system failure detection and in radar and optics-based maneuver detection. Explicit analytic closed-form examples or counterexamples are also useful for exposing existing problems or weaknesses in other areas of control and estimation theory so that these unfortunate holes may be shored up in a timely fashion before any damage is done in actual application mechanizations.       Go to Top        Go to Primary Table of Contents

Professional Affiliations: Institute of Electrical and Electronics Engineers  (IEEE) Life Senior Member (Automatic Control, Aerospace and Electronic Systems, Information Theory, Signal Processing, Computer Systems), American Institute of Aeronautics and Astronautics (AIAA) Guidance, Control and Dynamics (AIAA Senior Member/AIAA Associate Fellow: https://www.aiaa.org/docs/default-source/uploadedfiles/membership-and-communities/recognition/member-advancement/aiaa-associate-fellows.pdf?sfvrsn=dbf7e9f9_0), Institute of Navigation (ION), life member of American Defense Preparedness Association (ADPA) now renamed NDIA, National Defense Industrial Association, Society of  Optical Engineering (SPIE), American Association for the Advancement of Science (AAAS), Mathematical Association of America (MAA), American Statistical Association (ASA), Association for Computing Machinery (ACM), Visual Basic Users Group, Microsoft Developers Network (MSDN) [Level 2], and the Instrumentation, Systems, and Automation Society (ISA), and in New England Chinese Information & Networking Association (NECINA) [2005-2007].    Go to Top        Go to Primary Table of Contents

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Honors: Junior High Rensselaer (RPI) Medal in 1960 for Mathematics and Science proficiency, High School Honor Society in 1962, High School Mathematics and Science Award in 1963, High School Musician Award (and one year membership in professional musicians union) in 1963, Tau Beta Pi, Pi Mu Epsilon (president of student chapter in his senior year 66-67), Eta Kappa Nu, Sigma Pi Sigma, Western Electric Award (66), Douglas Aircraft Award (67), Whos Who in American Schools and Colleges (67), $340 Student Prize Paper Contest Sponsored by the Federal Power Commission (67), Engineers Wives Award (67), National Science Foundation Traineeship (68-70), Acting chairman of Stochastic Control Session of IEEE Conf. on Decision & Control (75) [originally, was only assistant chairman but the chairman, Prof. David Kleinman, had to leave beforehand because of a family emergency], won 1987 M. Barry Carlton Award and $3,000 honorarium for Outstanding Paper to appear in IEEE Aerospace and Electronic Systems Transactions in 87 [for further confirmation, please see page 822 of Vol. 24, No. 6, Nov. 1988 of the aforementioned journal and see: https://ieee-aess.org/media/decentralized-filtering-and-redundancy-management-multisensor-navigation], delivered invited lecture at University of Iowa (1988), joined Sigma Xi (in 90), delivered Distinguished Engineer Lecture at University of Maryland (UMBC on Feb. 1990), delivered invited lecture at University of Connecticut (1995). Listed in Marquis Whos Who in the East (92) and in Technology (93), and in the World (98), and in the USA (03), and in Finance and Business (05), and in America (06), and in Science and Engineering (06), and in Whos Who (10). Listed in Global Registers Whos Who of Executives and Professionals (05). Chairman of local Boston section of IEEE Control Systems 90-92, 01-04; chairman of the Steering Committee 92-94, 04-06; vice-chairman of the section 95-96, 98-00. Co-chairman of Sensors, Components, and Algorithms for Navigation session at the Institute of Navigation (ION) Annual Summer Conference  (99) in Cambridge, MA., Life Senior Member of IEEE (10). Member of SPIE: https://spie.org/profile/Thomas.KerrIII-2982?SSO=1 Over 130+ publications in the open peer-reviewed literature and as company reports. Thomas H. Kerr IIIs 2019 Nomination for IEEE Computer Societys Harry H. Goode Award.

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From (year) to (year) Name of Company  Position Held  
1992-Present TeK Associates (Lexington, MA, now in Woburn, MA) CEO/Sr. Systems Engineer/Chief Programmer/Web Master
06/21/2022-07/14/2023 Exclusively for Zivaro, Inc.(Partnered with JACOBS) in Colorado Springs, CO Algorithm Engineer (Performing Strategic Consulting for SpaceForce Office of the Chief Scientist)
06/17/2019-11/01/2019 GCR at Draper Laboratory (Cambridge, MA) Contractor: Senior GNC Analyst
10/2012-5/2013 Adecco at Goodrich ISR (Westford, MA) Contractor: Systems Engineer for U-2S SYERS Camera Pointing accuracy
04/09/07-04/08/2009 Kelly Services at Google Books (Lexington, MA) Contractor: Quality Assurance  (QA)  operator for 2-D images
1992-6/21/2022 TeK Associates (Lexington, MA, now in Woburn, MA) CEO/Principal Investigator/Chief Programmer/Owner  
1990-1995 (evenings) Northeastern University Graduate ECE Department (Boston) Instructor in Optimal Control and Kalman Filtering (for 4 yrs)
1986-1992 Lincoln Laboratory of MIT (Lexington, MA) Member of the Technical Staff  
1979-1986 Intermetrics, Inc.  (Cambridge, MA) Senior Systems Analyst/Systems Engineer  
1973-1979 The Analytic Sciences Corporation (TASC) (Reading, MA) Member of the Technical Staff  
1971-1973 General Electric Corporate R&D Center (Schenectady, NY) Control Engineer
1969-1971 University of Iowa (Iowa City, IA) Research Assistant/Teaching Assistant (as a graduate student, obtaining M.S.E.E. and Ph.D.)
1967 Howard University (Washington, D.C.) Research Assistant (part of senior year and summer after graduating  with B.S.E.E.)







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Tom has been nominated to become an IEEE Fellow (but not yet completed): For contributions to Kalman filter-based failure detection/system reconfiguration theory and to decentralized Kalman filter and nonlinear filtering applications.

Our SSBN submarines can launch while submerged; while those of many other countries must surface first before they can launch.

Publications constituting significant development in submarine navigation trade-off considerations between frequency of external navaid usage (to maintain sufficient navigation accuracy in case a launch is ordered) versus exposure to enemy surveillance:

  1. Kerr, T. H., Preliminary Quantitative Evaluation of Accuracy/Observables Trade-off in Selecting Loran/NAVSAT Fix Strategies,” TASC Technical Information Memorandum TIM-889-3-1, Reading, MA, December 1977 (Confidential).

  2. Kerr, T. H., Improving C-3 SSBN Navaid Utilization,” TASC TIM-1390-3-1, Reading, MA, August 1979 (Secret).

  3. Kerr, T. H., Modeling and Evaluating an Empirical INS Difference Monitoring Procedure Used to Sequence SSBN Navaid Fixes,” Proceedings of the Annual Meeting of the Institute of Navigation, U.S. Naval Academy, Annapolis, Md., 9-11 June 1981 (reprinted in Navigation: Journal of the Institute of Navigation, Vol. 28, No. 4, pp. 263-285, Winter 1981-82).

  4. Kerr, T. H., Sensor Scheduling in Kalman Filters: Evaluating a Procedure for Varying Submarine Navaids,” Proceedings of 57th Annual Meeting of the Institute of Navigation, pp. 310-324, Albuquerque, NM, 9-13 June 2001 (an update).

Publications wherein he developed the Two Confidence Region Failure Detection Approach§ (used in INS submarine navigation):

Kerr, T. H., “Poseidon Improvement Studies: Real-Time Failure Detection in the SINS/ESGM,” TASC Report TR-418-20, Reading, MA, June 1974 (Confidential).

Kerr, T. H., “Failure Detection in the SINS/ESGM System,” TASC Report TR-528-3-1, Reading, MA, July 1975 (Confidential).

Kerr, T. H., “Improving ESGM Failure Detection in the SINS/ESGM System (U),” TASC Report TR-678-3-1, Reading, MA, October 1976 (Confidential).

Kerr, T. H., “Failure Detection Aids for Human Operator Decisions in a Precision Inertial Navigation System Complex,” Proceedings of Symposium on Applications of Decision Theory to Problems of Diagnosis and Repair, Keith Womer (editor), Wright-Patterson AFB, OH: AFIT TR 76-15, AFIT/EN, Oct. 1976, sponsored by Dayton Chapter of the American Statistical Association, Fairborn, Ohio, June 1976.

Kerr, T. H., “Real-Time Failure Detection: A Static Nonlinear Optimization Problem that Yields a Two Ellipsoid Overlap Test,” Journal of Optimization Theory and Applications, Vol. 22, No. 4, pp. 509-535, August 1977.

Kerr, T. H., “Statistical Analysis of a Two Ellipsoid Overlap Test for Real-Time Failure Detection,” IEEE Transactions on Automatic Control, Vol. 25, No. 4, August 1980.

Kerr, T. H., “False Alarm and Correct Detection Probabilities Over a Time Interval for Restricted Classes of Failure Detection Algorithms,” IEEE Transactions on Information Theory, Vol. 28, No. 4, pp. 619-631, July 1982.

Kerr, T. H., “Examining the Controversy Over the Acceptability of SPRT and GLR Techniques and Other Loose Ends in Failure Detection,” Proceedings of the American Control Conference, San Francisco, CA, 22-24 June 1983.  (an expose)

Kerr, T. H., “Comments on ‘A Chi-Square Test for Fault Detection in Kalman Filters’,” IEEE Transactions on Automatic Control, Vol. 35, No. 11, pp. 1277-1278, November 1990.

Kerr, T. H., “A Critique of Several Failure Detection Approaches for Navigation Systems,” IEEE Transactions on Automatic Control, Vol. 34, No. 7, pp. 791-792, July 1989. (an expose of sorts)

Kerr, T. H., “On Duality Between Failure Detection and Radar/Optical Maneuver Detection,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 4, pp. 581-583, July 1989.

Kerr, T. H., “Comments on ‘An Algorithm for Real-Time Failure Detection in Kalman Filters’,” IEEE Trans. on Automatic Control, Vol. 43, No. 5, pp. 682-683, May 1998. (an expose of sorts)

Kerr, T. H., “Integral Evaluation Enabling Performance Trade-offs for Two Confidence Region-Based Failure Detection,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 3, pp. 757-762, May-Jun. 2006.

Publications addressing Decentralized Kalman Filtering-a theoretical basis for networked sensors:

Kerr, T. H., Stability Conditions for the RelNav Community as a Decentralized Estimator-Final Report,” Intermetrics, Inc. Report No. IR-480, Cambridge, MA, 10 August 1980

Kerr, T. H., and Chin, L., A Stable Decentralized Filtering Implementation for JTIDS RelNav,” Proceedings of IEEE Position, Location, and Navigation Symposium, Atlantic City, NJ, 8-11 December 1980.

Kerr, T.H., and Chin, L., The Theory and Techniques of Discrete-Time Decentralized Filters,” in Advances in the Techniques and Technology in the Application of Nonlinear Filters and Kalman Filters, edited by C.T. Leondes, AGARDograph No. 256, Noordhoff International Publishing, Lieden, 1981.

Carlson, N. A., Kerr, T. H., Sacks, J. E., Integrated Navigation Concept Study,” Intermetrics Report No. IR-MA-321, 15 June 1984. 

His publications that combine the ideas of failure detection with those of decentralized Kalman Filtering to yield a breakthrough rigorous basis for system reconfiguration and redundancy management:

Kerr, T. H., “Decentralized Filtering and Redundancy Management Failure Detection for Multi-Sensor Integrated Navigation Systems,” Proceedings of the National Technical Meeting of the Institute of Navigation (ION), San Diego, CA, 15-17 January 1985. (an expose)

Kerr, T. H., “Decentralized Filtering and Redundancy Management for Multi-sensor Navigation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 23, No. 1, pp. 83-119, Jan. 1987.   (which spawned 11 patents, as can be confirmed by viewing this paper in IEEExplore, or merely click here: "View Paper": , none of which personally benefited me financially except for favorable publicity.)


Personally trailblazing R&D development of the Kalman filter-based Two Confidence Region Failure Detection proceeding from first principles and carrying it elegantly to fruition.

He surveyed many historical approaches to decentralized filtering and narrowed down to identify those few that rigorously satisfied reasonableness constraints possessed by the Joint Tactical Information and Distribution System (JTIDS) and Integrated Communications Navigation and Identification in Avionics (ICNIA) applications that motivated his investigation.

Ground breaking insight was exhibited in his leaping to realize the utility of combining his earlier “failure detection methodologies” with the results of his later investigation into “decentralized estimation”, thus reaping a satisfying firm theoretical foundation for “redundancy management” for navigation applications.

He has published the following three book chapters:

  1. Kerr, T.H., and Chin, L., “The Theory and Techniques of Discrete-Time Decentralized Filters,” in Advances in the Techniques and Technology in the Application of Nonlinear Filters and Kalman Filters, edited by C. T.  Leondes, AGARDograph No. 256, Noordhoff International Publishing, Lieden, 1981.

  2. Kerr, T. H., “Computational Techniques for the Matrix Pseudoinverse in Minimum Variance Reduced-Order Filtering and Control,” in Control and Dynamic Systems-Advances in Theory and Applications, Vol. XXVIII: Advances in Algorithms and computational Techniques for Dynamic Control Systems, Part 1 of 3, C. T. Leondes (Ed.), Academic Press, NY, 1988; (an expose and illustrative use of counterexamples)

  3. Kerr, T. H., “Numerical Approximations and Other Structural Issues in Practical Implementations of Kalman Filtering,” a chapter in Approximate Kalman Filtering, edited by Guanrong Chen, World Scientific, NY, 1993;

where all three of the above discussions specifically pertain to different aspects of Kalman filters.

He has several publications relating to underlying numerical computational details, as arise in implementing Kalman filters:

  1. Kerr, T. H., An Invalid Norm Appearing in Control and Estimation,” IEEE Transactions on Automatic Control, Vol. 23, No. 1, Feb. 1978.  (counterexamples and a correction)

  2. Kerr, T. H., Testing Matrices for Definiteness and Application Examples that Spawn the Need,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 10, No. 5, pp. 503-506, Sept.-Oct., 1987.

  3. Kerr, T. H., “Three Important Matrix Inequalities Currently Impacting Control and Estimation Applications,” IEEE Trans. on Automatic Control, Vol. AC-23, No. 6, pp. 1110-1111, Dec. 1978.

  4. Kerr, T. H., Rationale for Monte-Carlo Simulator Design to Support Multichannel Spectral Estimation and/or Kalman Filter Performance Testing and Software Validation/Verification Using Closed-Form Test Cases,” MIT Lincoln Laboratory Report No. PA-512, Lexington, MA, 22 December 1989 (BSD).

  5. Kerr, T. H., Multichannel Shaping Filter Formulations for Vector Random Process Modeling Using Matrix Spectral Factorization,” MIT Lincoln Laboratory Report No. PA-500, Lexington, MA, 27 March 1989.

  6. Kerr, T. H., Status of CR-Like Lower bounds for Nonlinear Filtering,”  IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 5, pp. 590-601, Sep. 1989. (an expose)

  7. Kerr, T. H., On Misstatements of the Test for Positive Semidefinite Matrices,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, pp. 571-572, May-Jun. 1990. (as occurred in Navigation & Target Tracking software in the 1970’s & 1980’s using counterexamples)

  8. Kerr, T. H., Fallacies in Computational Testing of Matrix Positive Definiteness/Semidefiniteness,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 2, pp. 415-421, Mar. 1990. (Lists fallacious algorithms that the author found to routinely exist in U.S. Navy submarine navigation and sonobuoy software in the late 1970’s and early 1980’s using explicit counterexamples to point out the problems that “lurk under the surface”.)

  9. Kerr, T. H., A Constructive Use of Idempotent Matrices to Validate Linear Systems Analysis Software,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 6, pp. 935-952, Nov. 1990. (closed-form analytic solutions)

  10. Kerr, T. H., Emulating Random Process Target Statistics (Using MSF),” IEEE Transactions on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 556-577, Apr. 1994. (closed-form analytic solutions)

  11. Kerr, T. H., Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic Results,” Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 142-168, San Diego, 29 July-3 Aug. 2001. (as above, more closed-form analytic solutions to be used as test cases for comparison to numerically computed solutions for software IV&V)

  12. Kerr, T. H., “ADA70 Steady-State Initial-Value Convergence Techniques,” General Electric Class 2 Report, Technical Information Series No. 72 CRD095, 1972.   Click here for More...

and as encountered in several diverse applications:

  1. Kerr, T. H., Angle-Only Tracking,” slide presentation for Reentry Systems Program Review, Lincoln Laboratory, Lexington, MA, 10 Jan. 1989.

  2. Kerr, T. H., Streamlining Measurement Iteration for EKF Target Tracking,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 2, pp. 408-421, Mar. 1991.  One may confirm that, at the end of section 4.3 on page 17 of this paper:

  3. Kerr, T. H., “Assessing and Improving the Status of Existing Angle-Only Tracking (AOT) Results,” Proceedings of the International Conference on Signal Processing Applications & Technology, Boston, pp. 1574-1587, 24-26 Oct. 1995. (an expose)
    At the end of Sec. 4.3 of my previous 1995 AOT paper just cited above, I advocated for or suggested use of the E-M Algorithm instead of GLR within some applications of Extended Kalman Filters (EKF) back then.
    (See the following 2018 IEEE AES Barry Carlton Award winning paper: Yulong Huang; Yonggang Zhang; Bo Xu; Zhemin Wu; Jonathon A. Chambers,
    “A New Adaptive Extended Kalman Filter for Cooperative Localization,"
    IEEE Transactions on Aerospace and Electronic Systems, Vol. 54, No. 1, pp. 353-368, Feb. 2018. They follow-up and utilize the E-M Algorithm within their EKF!)

  4. Kerr, T. H., Use of GPS/INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),” the Institute of Navigation Proceedings of GPS-94, Salt Lake City, pp. 1173-1188, 20-23 Sep. 1994.

  5. Kerr, T. H., Extending Decentralized Kalman Filtering (KF) to 2-D for Real-Time Multisensor Image Fusion and/or Restoration,” Proceedings of SPIE Conference, Vol. 2755, Orlando, pp. 548-564, 8-10 Apr. 1996.

  6. Kerr, T. H., Extending Decentralized Kalman Filtering (KF) to 2D for Real-Time Multisensor Image Fusion and/or Restoration: Optimality of Some Decentralized KF Architectures,” Proceedings of the International Conference on Signal Processing Applications & Technology, Boston, MA, 7-10 Oct. 1996.

  7. Kerr, T. H., Developing Cramér-Rao Lower Bounds to Gauge the Effectiveness of UEWR Target Tracking Filters(U),” Proceedings of AIAA/BMDO Technology Readiness Conference and Exhibit, Colorado Springs, 3-7 August 1998  (Unclassified).

  8. Kerr, T. H., UEWR Design Notebook-Section 2.3: Track Analysis, TeK Associates: XonTech Report No. D744-10300, 29 March 1999.

  9. Kerr, T. H., Considerations in whether to use Marquardt Nonlinear Least Squares vs. Lambert Algorithm for NMD Cue Track Initiation (TI) calculations,” TeK Associates Technical Report No. 2000-101, Lexington, MA, (for Raytheon, Sudbury, MA), 27 September 2000.

  10. Satz, H. S., Kerr, T. H., Comparison of Batch and Kalman Filtering for Radar Tracking,” Proceedings of 10th Annual AIAA/BMDO Conference, Williamsburg, VA, 25 July 2001. (Unclassified).   Also see: https://apps.dtic.mil/dtic/tr/fulltext/u2/p011192.pdf 

  11. Kerr, T. H., Novel Variations on Old Architectures/Mechanizations for New Miniature Autonomous Systems,” Web-Based Proceedings of GNC Challenges of Miniature Autonomous Systems Workshop, Session E1: Controlling Miniature Autonomous Systems, sponsored by Institute of Navigation (ION), Fort Walton Beach, FL, 26-28 October 2009.

He has sufficient breadth to analyze other issues besides just those relating to Kalman Filtering such as GPS integration, Sonobuoy passive and active target tracking, Surveillance sweeprates, and Neural Networks:

  1. Kerr, T. H., Impact of Navigation Accuracy in Optimized Straight-Line Surveillance/Detection of Undersea Buried Pipe Valves,” Proceedings of National Marine Meeting of the Institute of Navigation, Cambridge, MA, 27-29 Oct. 1982. (Importance of surveillance sweeprates and closed-form analytic solutions)

  2. Kerr, T. H., Phase III GPS Integration; Volume 1: GPS U.E. Characteristics,” Intermetrics Report IR-MA-177, Cambridge, MA, Jan. 1983.

  3. Kerr, T.H., GPS/SSN Antenna Detectability,” Intermetrics Report No. IR-MA-199, Cambridge, MA, 15 Mar. 1983

  4. Kerr, T. H., “Functional and Mathematical Structural Analysis of the Passive Tracking Algorithm (PTA),” Intermetrics Report No. IR-MA-208, Cambridge, MA, 25 May 1983, for NADC.

  5. Kerr, T. H., Assessment of the Status of the Current Post-Coherent Localization Algorithm,” Intermetrics Report No. IR-MA-319, 31 May 1984. (Sonobuoy target tracking and counterexamples)

  6. Kerr, T. H., “Update to and Refinement of Aspects of Pattern Recognition Principles Used in the Missile Warning System (AN/AAR-47),” Intermetrics Report No. IR-MA-362, Cambridge, MA, for Honeywell Electro-Optical, Lexington, MA, 15 Sep. 1984.

  7. Kerr, T. H., An Analytic Example of a Schweppe Likelihood Ratio Detector,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 4, pp. 545-558, Jul. 1989. (closed-form analytic solution)

  8. Kerr, T. H., Critique of Some Neural Network Architectures and Claims for Control and Estimation,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 34, No. 2, pp. 406-419, Apr. 1998. (an expose)

  9. Kerr, T. H., Further Critical Perspectives on Certain Aspects of GPS Development and Use,” Proceedings of 57th Annual Meeting of the Institute of Navigation, pp. 592-608, Albuquerque, NM, 9-13 Jun. 2001. (an expose of several loose ends in GPS development that needed [and have now received] further attention before unabated and unabashed reliance upon GPS, as had been the plan and goal for Battlefield 2000)

  10. Kerr, T. H., New Lamps for Old: a shell game for generalized likelihood use in radar? Or this isn’t your father’s GLR!,” Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 476-483, San Diego, CA, 29 July-3 Aug. 2001. (an expose)

  11. Kerr, T. H., Vulnerability of Recent GPS Adaptive Antenna Processing (and all STAP/SLC) to Statistically Non-Stationary Jammer Threats,” Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 62-73, San Diego, CA, 29 July-3 Aug. 2001.  (an expose)

  12. Kerr, T. H., “Comments on ‘Determining if Two Solid Ellipsoids Intersect, AIAA Journal of Guidance, Control, and Dynamics, Vol. 28, No. 1, pp. 189-190, Jan.-Feb. 2005. (Offers a simpler implementation and reminds readers that real-time embedded applications do not usually have MatLab algorithms available, as otherwise required for implementing the algorithm without the simplification that we provide.)

  13. Kerr, T. H., Comment on Precision Free-Inertial Navigation with Gravity Compensation by an Onboard Gradiometer’,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4, pp. 1214-1215, Jul.-Aug. 2007.  (This provides two closed-form counterexamples to demonstrate the problem with this new result. Since the procedure proposed by Prof. C. Jekeli is offered for numerical data only, it would be difficult or impossible to reveal the flaw that exists in the new methodology offered without resorting to closed-form analytical solutions, which I did. Prof. Jekeli strongly denied that he had this problem when my article was first published in this Journal even though it had been critically reviewed by others before publication, as is standard procedure yet Prof. Jekeli denied it and merely repeated the exact same flawed conditions for applicability that he had previously stated in the hypothesis of conditions for the applicability of his newly proposed technique. I went back to the fundamentals of random variables and Realization Theory, which are well-known to Control Theorists, in order to create these fairly obvious counterexamples. I would not expect him to know this since it is not his bailiwick but it is mine, which is why I immediately responded. My old coworker at Intermetrics, Inc., (the late) David Antonitis, would likely have wanted me to help his prior client from the High Altitude Balloon project in the 1980's, back when Dr. Jekeli was at The Air Force Geophysical Laboratory at Hanscomb AFB [before they changed their name to Phillips Laboratory and moved to Albuquerque, NM].)

  14.  Kerr, T. H., “Comment on ‘Low-Noise Linear Combination of Triple-Frequency Carrier Phase Measurements’,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 2, pp. 161, 162, Summer 2010.  (provides a simpler more direct solution)

  15. Click this link here to see a more comprehensive list of our publications.


1975 Vice-Chairman of Stochastic Control Session at Conference on Decision and Control (CDC);

1988 M. Barry Carlton Award from IEEE Aerospace and Electronics Systems for Outstanding Paper in 1987 (which spawned 11 patents, as can be confirmed, none of which personally benefited me financially);
For confirmation, merely click here: "View Paper" to see the number of patents spawned on the upper left hand side within the gray box.

1990-1992 Chairman of local Boston section of Control Systems Society;

1992-1994 Chairman of Steering Committee of local Boston section of Control Systems Society;

1995-1996 Vice-Chairman of local Boston section of Control Systems Society;

1997-1998 At-large member of Steering Committee of local Boston section of Control Systems Society;

2000-2004 Chairman of local Boston section of Control Systems Society (again);

Has served as paper reviewer numerous times for IEEE Transactions on AC, IT, AES, SMC, SP, Computer Science and for AIAA Journal of Guidance, Control, and Dynamics over the years;

Made a  Life Senior Member of IEEE in 2011.


Qualified for and joined honor societies: Tau Beta Pi, Eta Kappa Nu, Sigma Pi Sigma, Pi Mu Epsilon (student president), Sigma Xi;

1967 Whos Who in American Schools and Colleges;

1967 $340 Student Prize Paper Award sponsored by Federal Power Commission for local engineering schools in the Washington D.C. area;

1966-1969 Tutored Statics, Dynamics, Calculus, and Strength of Materials at Howard Univ. & Circuit Theory at Univ. of Iowa;

1971-1973 Tutored mathematics at Union College and at Schenectady, NY Community Center;

1973 -1975 Tutored mathematics at Union Methodist Church in Boston, MA;

In 1990’s, gave invited lectures at University of Iowa (Iowa City), University of Connecticut, University of Maryland (Baltimore), and West Virginia University (Morgantown);

AIAA GNC Senior Member (and became an AIAA GNC Associate Fellow in January 2012); 

Member of Institute of Navigation (ION) since 1981 (served as interim ION Journal editor in 1985-1986);

Served as Co-chairman of Sensors, Components, and Algorithms for Navigation session at the Institute of Navigation (ION) Annual Summer Conference (1999) in Cambridge, MA;

Member of American Association for the Advancement of Science, Association of Computing Machinery, SPIE, National Defense Preparedness Association (life member), Mathematical Association of America, American Statistical Association, Microsoft Developer Network (MSDN) level 2; 

Whos Who in the East (92), in Technology (93), in the World (98), in the USA (03), in Finance and Business (05), and in Science and Engineering (06). Listed in Global Registers Whos Who of Executives and Professionals in 05;

Received AIAA 25 year plaque (2005);

Became an Associate Fellow of AIAA GNC (January 2012);

Ride leader for Charles River Wheelmen (90-97), long distance cycling club. (Member: 77-Present).

§The CR2 failure detection approach, developed by Tom and summarized above, is independently endorsed in: Brumback, B. D., Srinath, M. D., “A Chi-Square Test for Fault-Detection in Kalman Filters,” IEEE Trans. on Automatic Control, Vol. 32, No. 6, pp. 532-554, June 1987.

Please notice the high ratings of relevance and importance ascribed to the publications listed above, when they are obtained from the Citation Index associated with the on-line “Web of Science” at any good research library.   

Also see:  




(click comments to see my entries) They can always be found by clicking here.

While we sometimes serve as a watch dog; evidently, more watch dogs are badly needed!

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From left to right, Ed Bristol (Foxboro, now retired), "Larry" Y.-C. Ho (Harvard, now retired), George Kovatch (Volpe Transportation Systems center, now retired), unidentified (Volpe Transportation Systems center), Tom Kerr (TeK Associates, retiring personality)   Go to Top


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