KF for Nav &Tracking
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Kalman Filtering for Navigation and Target Tracking:

U.S. Navy Submarine applications related to Kalman filtering 

We have prior experience for over 40+ years in a variety of defense areas including Submarine Inertial Navigation (compare the prior hyperlink to our clearer discussion below) [and an understanding and a 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; Antenna Radar Cross-Section Detectability; NavSat (a.k.a. Transit), LORAN-C (both hyperbolic and phase-shift rho-rho circular), Bathymetry (bottom sounding sonar map-matching) and GPS analysis and usage on Submarines; and GPS analysis and usage in test aircraft (along with test plans and procedures for many 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). Thanks to John Rommelfanger (MITRE, retired), we have a copy of Modern Navigation Systems, a short course by (the late) Walter R. Fried (Hughes Aircraft Company), 10-12 June 1992. Of course, we at TeK Associates already had both editions of Walter R. Frieds book but having access to his slide-based concise summary is priceless. Thomas Kerr knew Walter Fried personally and when Tom last saw him in 1994, based on Tom’s rather aggressive questions and comments from the audience, Walter Fried seemed pleased that Tom had evidently become a watchdog for navigation since they had first met back in 1980, when Tom made his first technical Navigation presentation at Position, Location, and Navigation Symposium (PLANS) in Atlantic City and Walter Fried was there as his session chairman.

Familiarity with historical application constraints and specs for many platforms (especially including C-3 Poseidon, C-4 Poseidon-back-fit, and D-1 Trident SSBN\SSN submarine mission objectives, scenarios, and countermeasures). We have had first hand shipboard experience in San Diego in the 1980s and earlier weapons system and fire control training in the 1970s (regarding numbers and mixes of RVs) at Dam Neck, VA. We have also been aboard the Compass Island (sister ship of Cobra Judy used for strategic radar target tracking) in the 1970s, where components being planned for use within the SSBN Navigation Room are tested beforehand (in a room that was identical to but bass-ackwards from how it is oriented within actual SSBNs). The U.S.S. Compass Island was replaced in this role in the late 1970s by the U.S.S. Vanguard (as obtained from NASA). We are aware of vintage 1970s vibration tests for submarine INS components using Big Bertha and the Little Chipperson the deck above it. Present day barge tests with submerged C-4 plastic explosives emulating depth charges and use of 300 pound swinging hammers, capable of impacting at up to 100 gs, now reveal weaknesses or non-compliance of electronics within the expected dangerous environments is just as important today (even if their names are no longer as colorful). We have also performed GPS testing, both dockside and at sea, onboard the SSN-701 LaJolla in the 1980s at the San Diego, CA submarine base (for NADC).

We have participated in several Independent Verification and Validation (IV&V) programs for sonar\sonobuoy target tracking (PTA and LOFAR/DIFAR and LAMPS), and in analysis and development programs for integrated augmented INS navigation for Submarines (SSBNs) and in Joint Tactical Information and Distribution System (JTIDS) Relative Navigation (RelNav),  and in Development Testing and Evaluation for Operational Readiness [DT&E(OR)] for GPS navigation aboard submarines (SSNs). (To see a high level overview slide show on current status of GPS, please click here to obtain the main executable file stpete.exe. In order to view the slideshow, user must first download this associated .DLL file, then this .DLL file, then this VBX file, all to the same location on their local computer. Our Web Site host requires temporary conversion to exclusively lower case spellings. A constraint in running it is that a Windows host Operating System is required. Those typical OSs that allow this are Windows 9X/2000/NT/Millenium/XP and Vista. It also runs on older OSs like Windows 3.1 and 3.11 For Workgroups.) 

Other interesting precedents (to set the stage):

Emeritus Prof. Thomas Kailath (Stanford Univ.) alerted the estimation community to a precedent by some Japanese researchers that posed linear estimation within a Krein Space instead of within a Hilbert Space and apparently obtained faster convergence as a consequence. While Matrix Positive definiteness plays a prominent role within all the analytic proofs supporting the usual Hilbert Space-based derivation of Kalman filters, the Krein Space approach frequently involves matrices that are indefinite. The tool in common is still  projections onto linear subspaces.
Hassibi, B., Ali H. Sayed,A/ H., and Kailath, T., Linear Estimation in Krein Spaces-Part I: Theory, IEEE Trans. on Autom. Contr., Vol. 41, No. 1, pp. 18-33, Jan. 1996.

In the early 1970s, many researchers from Washington University in St. Louis, MO (e.g., Alfred S. Gilman, K-P. Dunn, Prof. Ian B. Rhodes) investigated approximate nonlinear estimation in the presence of so-called Cone Bounded nonlinearities so that the resulting mechanizations are tractable. Dunn and Gilman went to work at Lincoln Laboratory after obtaining their Ph.D.'s but, unfortunately, these nice results apparently were not deemed directly relevant to EWR target tracking at that time.

Lest we forget, Emeritus Prof. Ronald L. Klein (UWV) published many articles on estimation Theory using Gaussian Quadrature formulas [in order to improve the accuracy of the Propagate Step integration of the system dynamics within an EKF]. Here and in what follows below, Thomas H. Kerr IIIs comments and annotations are in a different color font to make it easier for readers to distinguish (and, perhaps, to ignore).

Click here to obtain a detailed 128Kilobyte resume for Thomas H. Kerr III emphasizing only his Navigation experience.

Click here to download a 214KByte pdf file which conveys our view on the problems with Covariance Intersection

Click here to obtain a detailed 266Kilobyte resume for Thomas H. Kerr III emphasizing only Target Tracking for strategic Updated Early Warning Radar (UEWR).

Also see or click on http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADP011192 or please click on http://www.dtic.mil/dtic/tr/fulltext/u2/p011192.pdf 

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 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.] and by Wally Vander Velde [MIT Aero. & Astro.].)

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 elapses.  Click here to obtain the corresponding 1.40 MByte PowerPoint presentation.

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

Please click here for information on jamming vulnerability of STAP.

Key Benefits:

We are knowledgeable about various historical approaches, their assumptions, their derivation, and their evolution [such as the INS analysis conventions of Peter Grundy and William Widnall (Intermetrics, Inc.) vs. that of the late Ken Brittings (Northrup) and of that of the missing minus sign in that of the late Prof. Itzhack Bar-Itzhacks (Technion Univ.)  vs. Don Bensons (Delco AC Electronics, TASC, Dynamics Research Corporation, and now at MITRE): Benson, D. O., `The Psi-Angle Error Equation in Strapdown Inertial Navigation Systems’, IEEE Trans. on Aerospace and Electronic Systems, Vol. 15, No. 1, pp. 168-170, Jan. 1979., where Donald Benson was correct all along; or on issues of intentionally and actively maintaining the small angle approximation for INS analysis to ensure the validity of the associated analysis that relies on this assumption being correct]. A sad commentary is that in one of Prof. Bar-Itzacks later publications, he notices that the underlying navigation coordinate systems appear to move in a direction opposite from what he previously expects but he still fails to recognize this quirk as merely a consequence of his prior failure to recognize and adhere to the sign convention that Don Benson tried unsuccessfully to alert him to 20 years earlier as being in error. It was rather sad and disappointing that no one from a recognized navigation analysis house (like C. S. Draper Laboratory [James Potter?], Rockwell International-Autonetics [James Lowery III?, J. S. Stambaugh?], Rockwell Collins, Singer-Kerfott [Dr. Bernard Friedland?], Honeywell, Northrup Grumman, Sperry Systems Management at Sperry Univac - Unisys [e.g., Dr. Hy Strell or the late Norman Zabb or the many other navigation analysts there], Magnavox, Motorola, TASC, General Dynamics, Teledyne Brown, JHU/APL, JPL, Air Force Institute of Technology (AFIT) [Peter S. Maybeck?], MIT Aeronautics & Astronautics [Prof. Wally VanderVelde or Prof. Richard Battin], Stanford Univ. [Prof. Arthur Bryson or Prof. Charles Hutchinson, who received his Ph.D. from Stanford Univ. and was a TASC navigation consultant at the time], Stanford Telecommunications, or anyone else from Dynamics Research Corporation [DRC] like Al Dushman? Al Kleinman?) entered into the fray to back up Don Bensons view. At the ION 57th Annual Meeting & CIGTF 20th Biennial Guidance Test Symposium, 11-13 June  2001, Albuquerque, NM, Tom found out that Don faults Tom for not doing so back then since Tom described how he recognized the problem but did not say anything at the time (but Tom has always had to pick his battles carefully and wait his turn since Tom is frequently critical and does not want to be labeled as just another Nay Sayer) and, moreover, Tom was not yet a recognized authority in this particular area of specifying navigation error models from first principles even though Tom had seen it done and understood it, including its underlying principles and assumptions. Besides, at the time, Tom worked for TASC, which was a direct competitor of DRC (where Don Benson then worked), so it would have been extremely politically incorrect for Tom to have entered the fray back then and endorse our competition (especially since Itzhack Bar-Ithzach was on sabatical and was working at TASC at the time). As the Happy Warrior, Tom certainly has not shied away from controversial technical battles. However, he can disagree without being disagreeable (most times, unless he has to return fire in like kind).
 
On a more positive note, the late Prof. Itzhack Bar-Itzhack proved the observability and controllability of the linear error models that represent navigation systems so Kalman filtering may be rigorously applied in this application domain. (It had already been successfully applied to navigation for more than 10 years without this analytical nicety having been supplied to shore up the hole in the analysis that everyone recognized was present but just had not bothered to clean up since they were busy actually implementing Navigation solutions using Kalman filtering in a somewhat cavalier fashion without this rigorous analytical stepping stone yet officially being in place.)
We are somewhat familiar with the historical HAD/HAP procedure, developed by the late William Zimmerman in the 1960s while he was at DRC, for computationally calibrating biases within the SSBN submarine Ships Inertial Navigation System (SINS), in those days consisting of only single-degree-of-freedom conventional gyros (but with two SINS present with one as a warm standby system with the other one being in the path of primary navigation reliance) with mechanical spinning rotator gyros. We also know about the Carousel navigation system INS that is constantly rotated to average out the adverse effect of the biases that are present (where William Zimmerman and Robert Ship [along with several others] hold a patent on this important concept). 
 
We have gone through the rigorous supporting mathematics, yet we summarize the results in a clear straightforward manner, expressed as simply as possible.
We are familiar with the application constraints associated with utilizing these algorithms and are aware of what application constraints are usually actively in force.

Capabilities:

Knowledge of operational principles and behavior of INS gyros and accelerometers and likewise for GPS: Familiar with their underlying state variable error models and INS calibration procedures and typical failure modes and interactions.

We follow novel INS developments and relative INS accuracies: Familiar with Electro-statically supported Gyro (ESG) such as the airborne Micro, the SSBN ESG, as well as that in the Gravity-Probe satellite), Laser Gyros, Fiber Optics Gyros, Wine glass\tuning fork gyros, Microelectromechanical systems (MEMS) Gyroscopes as well as conventional mechanical spinning rotor gyros and their analysis.

We follow evolving procedures for moving platform shipborne and  in-air alignment gyro-compassing and alternative mechanizations: Local Level, Space-Stable, Wander-Azimuth, Strapdown and associated transformations (and typical frequency of re-calculation sample rates).  Surprisingly, new insights have recently been offered that much of the technology harkens back to analog gyro behavior more than is currently necessary in this digital age of extremely high processing speeds which can now support relatively high external GPS updates within strapdown gyroscope implementations. Previous notions of coning, sculling, the dynamics of Schuler loop oscillations being activated, or 24 hour diurnal oscillations are no longer necessary in Navigation systems mechanized with MEMS throughout and with GPS or differential GPS updates on the order of seconds or minutes because the gyros no longer need to go open loop without a compensating and ameliorating external  navaid fix for anything that approaches a significant fraction of the ~hour and a half Schuler period [30].

We are familiar with typical operational constraints and weapon system accuracies of several military platforms as well: e.g., Ships Submersible Ballistic Nuclear (SSBNs) submarines (a.k.a. Boomers), Ships Submersible Nuclear (SSN) submarines (a.k.a., attack subs), which allied countrys submarines use degaussing coils and which use flash, deperm procedures,  etc. We are also familiar with the tenets, details, and history of Search and Screening: e.g., detection range, worse case detection threats, observables-in-the-military-sense, countermeasures and counter-countermeasures for various sensors, etc. See [1] to [7] for perspectives on our early experience in this area. We are also knowledgeable in the associated terminology such as that of alertness levels: 1SQ,..., Operation Sanguine, Take Charge and Move Out (TACAMO), long trailing wire antenna, pig tail antenna, whip antenna, Blue-green laser, Counter Value vs. Counter Force, Mid-course star fix, firing keys, etc.

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

We are cognizant of the Society of Old Crows, of the Countermeasures Handbook (we possess several back issues), and Paladin Press publications over the years (that should never have been allowed to appear). CV motion models, Lamps helicopters and ships, use of  ship-borne winch and cables dropped from helicopters seeking to land onboard in rough seas (where cable is secured to winch and helicopter pulls cable taught and is reeled in slowly so that Helicopter motion automatically matches that of the deck of the ship as both pitch, roll, and yaw together (to avoid damaging the helicopter with a nasty unexpected impact with the deck of the much more massive ship capable of preserving inertia by inflecting a severe impulse force as a big crushing blow over the short period of time-BANG!) We know about historical pipe dreams that failed miserably as well as alternative more robust approaches (using older technology) that was good enough without being vulnerable to a myriad of difficulties associated with other things going wrong (one example being trying to use a laser-based reflection system to guide the helicopter to land on the deck in rough seas-obvious vulnerabilities being: fog, battle smoke, electronic failures at an extremely critical time ala Murphys law, laser orientation capability for interacting with surface ships deck-in-motion possibly falling out of sufficient calibration [as needed to retrieve the necessary reflection close to perpendicular to the moving deck for instantaneous round trip timing-so you cant solve the problem until you have already solved the problem] and needing additional INS components with their additional costs and vulnerabilities and operational procedures). Thank Michael Athans and AlphaTech for the less practical approach, described above. Example 2: What about the attempt to align several (two or more) surface ships at sea in tandem to create an effective landing strip for those super-sized carrier air craft to take-off and land for re-supply at sea. Although some of their numerous computer studies demonstrated feasibility, please just think about being in the North Atlantic with typical winter weather conditions involving very high sea states and then try to pull off this stunt. We have Raman Mehra and Scientific Systems to thank for this second one. Both examples were funded by the U.S. Navy and further reported in an open unclassified forum but my critical ear hears all and I dont soon forget these apparent technical boondoggles but do continue to wonder how they ever got pass other watchdogs. I guess it pays to be well connected. Its not my cup of tea though. I have to say what I see and what I smell. We Kerr's (curs) are well known watchdogs too. We try to avoid stepping in it as our predecessors did! Sometimes we mark our territory as a good alpha dog. Arrrooooo! Better to lead than to follow since the scenery is much better and more interesting (as every sled dog knows).

Rodriguez, J. J., Aggarwal, J. K., “Matching Aerial Images to 3D Terrain Maps,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 12, No. 12, pp. 1138-1149, Dec. 1990: Sparse terrain profile data are stored onboard and direct measurement of relative shifts between images are used to estimate position and velocity; however, an EKF is deemed superior here to use of merely a Kalman filter that uses altitude estimates in order to estimate aircraft position and velocity. 

Heeger, D. J., Jepson, A. D., “Subspace Methods for Recovering Rigid Motion I: Algorithm and Implementation,” International Journal of Computer Vision, Vol. 7, No. 2, pp. 95-117, Jan. 1992: Terrain matching methods are also used to estimate platform position and orientation via comparisons to an on-board digital elevation map. 

Soatto, S., Frezza, R., Perona, P., “Motion Estimation via Dynamic Vision,” IEEE Trans. on Automatic Control, Vol. 41, No. 3, pp. 95-117, Mar. 1996: A least squares formulation is used to recover user's 3D motion (3 translation variables and 6 rotation variables or 4 if quaternions are utilized). 

Goyurfil, P., Rotstein, H., “Partial Aircraft State Estimation from Visual Motion Using the Substate Constraint Approach,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 5, pp. 1016-1025, Sep.-Oct. 2001: What is called an implicit EKF is used here to estimate aircraft states-aircraft velocities, angular rates, angle of attack, and angle of sideslip but not aircraft Euler angles nor inertial location. Measurements available are the image points of N featured objects, which are tracked from one frame to another. 

Craig Lawson, John F. Raquet, Michael J. Veth, “The Impact of Attitude on Image-Based Integrity,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 4, pp. 249-292, Winter 2010: Being aware of the historical importance of having good satellite geometry when seeking to utilize GPS for positioning and for timing (characterized by HDOP, VDOP, TDOP, and GDOP), they analogously extrapolate these ideas to the geometry of their airborne image collecting and refer to this as image integrity (similar to how researchers endeavor to associate sufficient Integrity to GPS measurements). Also see: Dennis Milbert, “Dilution of Precision Revisited,” Navigation: Journal of The Institute of Navigation (ION), Vol. 55, No. 1, pp. 67-81, Spring 2008.

Hoshizaki, T., Andrisani, D., Braun, A. W., Mulyana, A. K., and Bethel, J. S., “Performance of Integrated Electro-Optical Navigation Systems,” Navigation: Journal of the Institute of Navigation, Vol. 51, No. 2, pp. 101-122, Summer 2004: Contains good modeling and they have a “tightly coupled system consisting of INS, GPS, and EO” all working together to simultaneously benefit both navigation and photogrammetry (estimates platform states, sensor biases, and unknown ground object coordinates using a single Kalman filter).

Kyungsuk Lee, Jason M. Kriesel, Nahum Gat, "Autonomous Airborne Video-Aided Navigation," Navigation: Journal of the Institute of Navigation, Vol. 57, No. 3, pp. 163-173, Fall 2010: ONR-funded discussion utilizes (1) “digitally stored georeferenced landmark images” (altimeter/DTED), (2) video from an onboard camera, and (3) data from an IMU. Relative position and motion are tracked by comparing simple mathematical representations of consecutive video frames. A single image frame is periodically compared to a landmark image to determine absolute position and to correct for possible drift or bias in calculating the relative motion.
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Crassidis, J. L., Markley, F. L., Cheng, Y., “Survey of Nonlinear Attitude Estimation Methods,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 1, pp. 12-28, Jan. 2007: An excellent survey on the subject of attitude estimation. It provides insights into what is important in estimation algorithms. It is a more practical and rigorous addendum to their many earlier NASA surveys, concerned with utilizing alternative EKF's or Nonlinear Luenberger Observers (as alternatives to Extended Kalman filter-based approaches). Compare to [152] below. (Thomas H. Kerr III comment: This version is more concise.)

Maji, M., Junkins, J. L., Turner, J. D., “Jth Moment Extended Kalman Filtering for Estimation of Nonlinear Dynamic Systems,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Honolulu, HI, Paper No. AIAA 2008-7386, pp. 1-18, 18-21 Aug. 2008: Explores two variations on JMEKF formulations that properly handle higher order moments (that lurk in the background while trying to get good estimates and covariances from EKF’s). Approximations utilized are acknowledged and properly handled (rather than ignored, as is usually the case). 

Scorse, W. T., Crassidis, A. L., “Robust Longitudinal and transverse Rate Gyro Bias Estimation for Precise Pitch and Roll Attitude Estimation in Highly Dynamic Operating Environments Utilizing a Two Dimensional Accelerometer Array,” AIAA Atmospheric Flight Mechanics Conference, Paper No. AIAA 2011-6447, Portland, OR, pp. 1-28, 8-11 Aug. 2011: Using the latest in rigorous real-time estimation algorithms (neither a particle filter nor an unscented/Oxford/Sigma-Point filter) for enabling accurate pointing (precise pitch and roll) within an aircraft within a high dynamics operating environment is reported. While it does utilize rate integrating gyros, as does SYERS-2C, it also utilizes 2D accelerometer arrays and compares to an onboard gravity map to achieve its accuracy.

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: Achieves a big breakthrough by providing a proof of this particular EKF’s global stability as a consequence by stating 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 claim. Author Jensen attains his results by utilizing appropriate Lyapunov functions. 

Discussing Gyroscopes (the heart of an INS)

The classical mechanical  gyroscope has a relatively massive rotor suspended within a framework of light supporting rings called gimbals which have nearly frictionless bearings (as the ideal that is sought) that are used to help isolate the central spinning rotor from all outside influences (i.e., torques). At high rotation speeds of the rotor, the gyroscope exhibits extraordinary stability of its balance and maintains the orientation of the direction of the high speed rotation axis of its central rotor in where it points in 3-dimensional space. The implication or consequence of the physical law known as the conservation of angular momentum is that the angular momentum of the rotor is constant and it maintains not only its magnitude or speed of spin, but also its direction in space of the spin axis in the absence of any external torques. The classical gyroscope finds application in gyro-compasses (as an alternative to using a magnetic compass) and in more sophisticated Inertial Navigation Systems (that reveal location and orientation of vehicles on the earth; and under and over the sea, respectively, in submarines and ships; and in space in aircraft, in rockets, and in missiles). However, there are many more common examples of gyroscopic motion and its associated stability: spinning tops  and their associated almost mysterious precession behavior, the spinning wheels of bicycles and motorcycles keeping them from falling over even in a severe leaning angle, the spin of the Earth in space as it orbits the sun, even the behavior of a boomerang as it is being hurled are all examples of gyroscopic motion.

Classical Inertial Navigation Systems:

 

The typical mechanical spinning-rotor gyroscope found within classical Inertial Navigation Systems (INS) is constructed by suspending a relatively massive spinning rotor inside three orthogonally mounted support rings called gimbals. Mounting each of these rotors on axes with high quality bearing surfaces with low friction insures that very little resisting torque is  exerted on the inside rotor as the rotor continues to spin. Electrical torquers (not shown here) are utilized to initially spin up the inner-most rotor to its nominal speed and to maintain its angular velocity, as continuously monitored by electrical or mechanical pick-offs (also not shown here). Modern day INS gyros take many different forms based on whatever other particular inherent physical principle is being exploited, such as that for wine glass acoustic frequency vibrating gyros, for electro-statically supported spherical gyros, for electro-magnetically supported spherical gyros, for ring laser gyros (RLG), for fiber optic gyros, for atomic quantum spin gyros, etc. Other important aspects are in exactly how the two or more gyros are implemented or bound together within an Inertial Navigation System (INS) such as in a Space Stable configuration, in a  Local-Level  configuration (as either Wander Azimuth, Free Inertial, or North Pointing), or in a Strap-Down configuration, and in its corresponding Navigation filter formulation, which can be implemented in three different alternative ways but with the differential feedback form being somewhat of a standard now. New insights have been recently revealed into how modern MEMS gyros may now be implemented in Strap Down configurations without the same hassles or operational constraints being present that were historically associated with handling the classical spinning rotor gyros depicted here. A Charles Stark Draper Laboratory study and report in the late 1960s had concluded that a preferred optimal configuration for redundant gyros (with a one-degree-of-freedom input axis) was being located in a certain prescribed way as placed along all the faces of a regular dodecahedron. It is indeed a pity that Draper seems to have forgotten this 40 year old conclusion of theirs as they now work with MEMS gyros for which  Draper should again appropriately invoke the very same solution (but they dont),

Gyroscopic Precession:

If a gyroscope is tipped away from its original orientation, the gimbals will try to reorient to keep the spin axis of the rotor aligned in the same original direction as conservation of momentum. If released after being tipped over in this new  orientation, the gyroscope will precess in the indicated direction depicted here due to the external torque exerted  on the gyroscope by gravity.

             

 

We are cognizant of the necessary interaction between the architectures associated with various alternative approaches to multi-target tracking and Kalman filter-based target tracking algorithms in use (alternative tracking algorithms hypothesized as possible modern replacements).

Our primary strength is having an in depth awareness of all the Kalman filter estimation-based approaches used to date for handling failure\fault detection in an INS or in GPS RAIM, or in a GPS/INS hybrid. We are analytic algorithm specialists. This is our area of greatest familiarity.

Historical Account of our experience therein:

[1] Kerr, T. H., “Poseidon Improvement Studies: Real-Time Failure Detection in the SINS\ESGM (U),” TASC Report TR-418-20, Reading, MA, June 1974 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
 
[2] Kerr, T. H., “Failure Detection in the SINS\ESGM System (U),” TASC Report TR-528-3-1, Reading, MA, July 1975 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
 
[3] Kerr, T. H., “Improving ESGM Failure Detection in the SINS\ESGM System (U),” TASC Report TR-678-3-1, Reading, MA, October 1976 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
 
[4] Kerr, T. H., “Preliminary Quantitative Evaluation of Accuracy\Observables Trade-off in Selecting Loran\NAVSAT Fix Strategies (U),” TASC Technical Information Memorandum TIM-889-3-1, Reading, MA, December 1977 (Confidential) for Navy, SP-2413 (Jerome “Jerry” Katz).
 
[5] Kerr, T. H., “Improving C-3 SSBN Navaid Utilization (U),” TASC Technical Information Memorandum TIM-1390-3-1, Reading, MA, August 1979 (Secret) for Navy, SP-2413 (Jerome Jerry Katz).

[6] 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. (Selected for reprinting in Navigation: Journal of the Institute of Navigation, Vol. 28, No. 4, pp. 263-285, Winter 1981-82).

[7] 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 (ION), Cambridge, MA, 27-29 October 1982.

[8]  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, for NADC (Warminster, PA).

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

[10] 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, NATO Advisory Group for Aerospace Research and Development, AGARDograph No. 256, Noordhoff International Publishing, Lieden, 1981.

[11] Kerr, T. H., and Rogers, R., Report on PINS Filter Design Review (of Magnavox), Intermetrics Memo, Cambridge, MA, 11 August 1983, for NOSC (San Diego, CA). (Minesweeper Navigation)

[12] Kerr, T. H., “GPS\SSN Antenna Detectability,” Intermetrics Report No. IR-MA-199, Cambridge, MA, 15 March 1983, for NADC (George Lowenstein).

[13] 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. (LAMPS Sonobuoy algorithms.)

[14] Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Magnavox Modification Center (Mod Center) Test Report,” 1 June 1985, for NADC Code 4022 (George Lowenstein).

[15] Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Rockwell-Collins Modification Center (Mod Center) Test Report,” 1 June 1985, for NADC Code 4022 (George Lowenstein).

[16] Kerr, T. H., “Navy GPS\SSN Phase II User Equipment DT&E Rockwell-Collins Developmental Test and Evaluation (Operational Readiness) [DT&E (OR)] Test Report,” 10 June 1985, for NADC Code 4022 (George Lowenstein).

[17] Kerr, T. H., “Magnavox Military Utility Test Report,” 10 June 1985, for NADC Code 4022 (for George Lowenstein).

[18] Kerr, T. H., “Phase III GPS Integration; Volume 1: GPS U.E. Characteristics,” Intermetrics Report IR-MA-177, Cambridge, MA, January 1983, for Navair and for NOSC (Richard Akita).

[19] 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.

[20] 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, UT, pp. 1173-1188, 20-23 Sept. 1994.

[21] Kerr, T. H., “Further Comments on ‘Optimal Sensor Selection Strategy for Discrete-Time Estimators’,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 31, No. 3, pp. 1159-1166, June 1995.

[22] 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.  

[23] Kerr, T. H., Sensor Scheduling in Kalman Filters: varying navaid fixes for trading-off submarine NAV accuracy vs. ASW exposure,” Proceedings of The Workshop on Estimation, Tracking, and Fusion: A Tribute to Yaakov Bar-Shalom (on the occasion of his 60th Birthday) following the Fourth ONR/GTRI Workshop on Target Tracking and Sensor Fusion, Naval Postgraduate School, Monterey, CA, pp. 104-122, 17 May 2001.

[24] Kerr, T. H., Further Critical Perspectives on Certain Aspects of GPS Development and Use,” Proceedings of 57th Annual Meeting of the Institute of Navigation, 9-13 June 2001.

(To see a high level overview slide show associated with the topics of the preceding paper, please click here to obtain the main executable file stpete.exe. In order to view the slideshow, user must first download this associated .DLL file, then this .DLL file, then this VBX file, all to the same location on their local computer. Our Web Site host required temporary conversion to exclusively lower case spellings.)

[25] Biezad, D. J., Integrated Navigation and Guidance Systems, AIAA Education Series, Reston, VA, 1999.

[26] Sofir, I., “Improved Method for Calculating Exact Geodetic Latitude and Attitude-Revisited, AIAA Journal of Guidance, Control, and Dynamics, Vol. 23, No. 2, ff. 369, 2000.

[27] Siouris, G. M., “Navigation: Inertial,” Encyclopedia of Physical Science and Technology, 2nd Edition, V. 10, pp. 595-647, Academic Press, NY, 1992.

[28] Jordan, J. F., Wood, L. J., “Navigation: Space Missions,” Encyclopedia of Physical Science and Technology, 2nd Edition, Vol. 10, pp. 649-673, Academic Press, NY, 1992.

[29] Ward, P., “Navigation: Satellites,” Encyclopedia of Physical Science and Technology, 2nd Edition, Vol. 10, pp. 675-702, Academic Press, NY, 1992.

[30] Farrell, J. L., “Strapdown at the Crossroads, Navigation, Journal of the Institute of Navigation, Vol. 51, No. 4, pp. 249-257, Winter 2004. (A good modern perspective! Correction in Vol. 52, No. 1, page iii, Spring 2005. Strong conclusions in this paper should be viewed  as being somewhat controversial.)

[31] 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, July-Aug. 2007.

[32] Felter, S. C., Wu, N. E., “A Relative Navigation System for Formation Flight,IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 958-967, July 1997.

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[37] Luo, N., “Multiple Moving Platform, GPS, Relative Positioning,IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 7, pp. 936-948, July 2003.

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[39] Qi, H., “GPS/INS Integration: Direct Kalman Filtering Approach,IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 1, pp. 687-693, Jan. 2002.

[40] Shin, D.-H., “TOA and TDOA Positioning Error,IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 1, pp. 307-308, Jan. 2002.

[41] Pervan, B., “Sigma Inflation for Local Area Augmentation of GPS,IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 10, pp. 1301-1311, Out. 2001.

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[43] Ray, J. K., “Carrier Multipath Mitigation, Multiantenna System,IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 1, pp. 183-195, Jan. 2001.

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[45] Jardak, N., Samama, N., “Indoor Positioning Based on GPS-Repeators: Performance Enhancement using an Open Code Loop Architecture,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 347-359, Jan. 2009.

[46] “Noncoherrent Integrations for GNSS Detection: Analysis and Comparisons,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 360-375, Jan. 2009.

[47] Chiang, K.-W., Noureldin, A., El-Sheimy, N., “Constructive Neural-Networks-Based MEMS/GPS Integration Scheme,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 582-594, April 2008.

[48] Farrell, W. J., “Interacting Multiple Model Filter for Tactical Ballistic Missile Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 418-426, April 2008.

[49] Borio, D., Camoriano, L., Lo Presti, L., Fantino, M., “DTFT-Based Frequency Lock Loop for GNSS Applications,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 595-612, April 2008.

[50] Kaplan, L. M., “Assignment Costs for Multiple Sensor Track-to-Track Association,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 655-675, April 2008.

[51] Bon, N., Khenchaf, A., Garello, R., “GLRT Subspace Detection for Range and Doppler Distributed Targets,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 678-695, April 2008.

[52] Juang, J.-C., “Multi-Objective Approach to GNSS Code Discrimination Design,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 481-492, April 2008.

[53] Geren, W. P., Murphy, T., Pankaskif, T. A., “Analysis of Airborne GPS Multipath Effects using High-Fidelity EM Models,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 2, pp. 711-723, April 2008.

[54] Jan, S.-S., Gebre-Egziabher, D., Walter, T., Enge, P., “Improving GPS-Based Landing System Performance using an Empirical Barometric Altimeter Confidence Bound,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 127-146, Jan. 2008.

[55] Lambert, H. C., “Tracking Filter for the Mitigation of the Ionospheric Range Bias,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 339-348, Jan. 2008.

[56] Tudoroiu, N., Khorasani, K., “Satellite Fault Diagnosis using a Bank of Interacting Kalman Filters,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 43, No. 4, pp. 1334-1350, Oct. 2007.

[57] Musicki, D., La Scala, B., “Multi-Target Tracking in Clutter Without Measurement Assignment,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 877-896, July 2008.

[58] Blanch, J., Walter, T., Enge, P., “Position Error Bound Calculation for GNSS Using Measurement Residuals,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 977-984, July 2008.

[59] Musicki, D., “Multi-Target Tracking using Multiple Passive Bearings-Only Asynchronous Sensors,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1151-1160, July 2008.  Also see: http://www.gallup.unm.edu/~smarandache/NATOASI_ATJDTSPK.pdf 

[60] Foster, C. C., Elkaim, G. H., “Extension of a Two-Step Calibration Methodology to Include Nonorthogonal Sensor Axes,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1070-1078, July 2008.

[61] Borio, D., Camoriano, L., Lo Presti, L., “Impact of GPS Acquisition Strategy on Decision Probabilities,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 996-1011, July 2008.

[62] Lee, J., Pullen, S., Enge, P., “Sigma-Mean Monitoring for the Local Area Augmentation of GPS,IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 625-635, Apr. 2006.

[63] Bednarz, S., Misra, P., “Receiver Clock-Based Integrity Monitoring for GPS Precision Approaches,IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 636-643, Apr. 2006.

[64] Heo, M.-B., Pervan, B., “Carrier Phase Navigation Architecture for Shipboard Relative GPS,IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 670-679, Apr. 2006.

[65] Pacher, M., Porter, A., Polat, M., INS-Aiding Using Bearings-Only Measurements of an Unknown Ground Object,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 1-20, Spring 2006.

[66] Wendel, J., Metzger, J., Moenikes, R., Maier, A., Trommer, G. F., A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems Based on Extended and Sigma Point Kalman Filters,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 21-31, Spring 2006.

[67] Farrell, J. L., Full Integrity Testing for GPS/INS,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 33-40, Spring 2006.

[68] Hwang, P. Y., Brown, R. G., RAIM-FDE Revisited: A New Breakthrough in Availability Performance with nioRAIM (Novel Integrity-Optimized RAIM),Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 41-51, Spring 2006.

[69] Alves, D. B. M., Monico, J. F. G., Mitigating Systematic Errors for Single Frequency GPS Receivers Employing A Penalized Least Squares Methodology,Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 53-60, Spring 2006.

[70] Fante, R. L., Vaccaro, J. J., “Cancellation of Jammers and Jammer Multipath in a GPS Receiver,IEEE AES Systems Magazine, Vol. 13, No. 11, pp. 25-28, Nov. 1998.

[71] Fante, R. L., Vaccaro, J. J., “Wideband Cancellation of Interference in a GPS Receive Array,IEEE Trans. on Aerospace and Electronic Systems, Vol. 36, No. 2, pp. 549-564, April 2000.

[72] Counselman, C. C., “Array Antennas for DGPS,IEEE Systems Magazine, Vol. 13, No. 12, pp. 15-19, Dec. 1998.

[73] Rabideau, D. J., “Clutter and Jammer Multipath Cancellation in Airborne Adaptive Radar,IEEE Trans. on Aerospace and Electronic Systems, Vol. 36, No. 2, pp. 565-583, April 2000.

[74] Myers, L., Improved Radio Jamming Techniques: Electronic Guerilla Warfare, ISBN 0873645200, Paladin Press, Boulder, CO, 1989.

[75] Daher, J. K., Harris, J. M., Wheeler, M. L., “An Evaluation of the Radio Frequency Susceptibility of Commercial GPS Receivers,IEEE AES Systems Magazine, Vol. 9, No. 10, pp. 21-25, October 1994.

[76] White, N. A., “Detection of Interference/Jamming and Spoofing in DGPS-aided Inertial Systems,IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 5, pp. 1208-1217, Oct. 1998.

[77] White, N. A., Maybeck, P. S., DeVilbiss, S. L., “Detection of Interference/Jamming and Spoofing in a DGPS-Aided Inertial System,IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 4 pp. 1208-1217, Oct. 1998.

[78] Pinker, A., Smith, D., Walker, D., “Jamming the GPS Signal,Proceedings of the 55th Annual Meeting of the ION, Cambridge, MA, 28-30 June 1999.

[79] Littlepage, R. S., “The Impact of Interference on Civil GPS,Proceedings of the 55th Annual Meeting of the ION, Cambridge, MA, 28-30 June 1999. (He warned us early on! His presentation was more explicit than his paper. He was truly concerned.)

[80] Goldstein, J. S., “Multistage partially adaptive STAP CFAR detection algorithm,IEEE Trans. on Aerospace and Electronic Systems, Vol. 35, No. 2, pp. 645-669,  April 1999.

[81] Saha, R. K., “Effect of Common Process Noise on Two-Sensor Track Fusion,AIAA Journal of Guidance, Control, and Dynamics, Vol. 19, No. 4, pp. 829-835, July-August 1996.

[82] Fitzgerald, R. J., “Effects of Range-Doppler Coupling on Chirp Radar Tracking  Accuracy,IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-10, No. 4, pp. 528-532, July 1974.

[83] Brennan, L. E., Reed, I. S., “Theory of Adaptive Radar,IEEE Trans. on Aerospace and Electronic Systems, Vol. 9, No., pp. 237-252, March 1973.

[84] Brennan, L. E., Mallett, J. D., Reed, I. S., “Adaptive Arrays in Airborne MTI Radar,IEEE Trans. on Antennas and Propagation, Vol. 24, No. 5, pp. 607-615, September 1978.

[85] Arregui, F. J. (ed.), Sensors Based on Nanostructured Materials, Springer Science & Business Media LLC, 2009.

[86] Righini, G. C., Tajani, A., Cutolo, A., An Introduction to Optoelectronic Sensors, World Scientific, NY, 2009.

[87] Vladimir Cherkassky and Filip Mulier, Learning from Data: Concepts, Theory, and Methods, John Wiley & Sons, Inc., NY, 1998.

[88] Gupta, S. N., “An Extension of Closed-Form Solutions of Target-Tracking Filters with Discrete Measurements,IEEE Trans. on Aerospace and Electronic Systems, Vol. 20, No. 6, pp. 839-840, Nov. 1984.

[89] Junichiro Toriwaki, Hiroyuki Yoshida, Fundamentals of Three-Dimensional Digital Processing, Springer-Verlag, London, 2009.

[90] Julien Bourgeois, Wolfgang Minker, Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car Environment, Springer Science + Business Media, NY, 2009.

[91] Jekeli, C., “Navigation Error Analysis of Atom Interferometer Inertial Sensing, Navigation: Journal of the Institute of Navigation, Vol. 52, No. 1, pp. 1-14, Spring 2005.

[92] Another intriguing wrinkle is conveyed in Fernandez-Alcada, R., Navarro-Moreno, Ruiz-Molina, J. C., Oya, A., “Recursive Linear Estimation for Doubly Stochastic Poisson Processes,” Proceedings of the World Congress on Engineering (WCE), Vol. II, London, UK, pp. 2-6, 2-4 July 2007.

[93] Huddle, J.R., “Inertial Navigation System Error Model Considerations in Kalman Filter Applications,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 294-340, Part 2 of 3, 1983.

[94] Lechner, W., “Application of Model Switching and Adaptive Kalman Filtering for Aided Strapdown Navigation Systems,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 155-185, Part 2 of 3, 1983.

[95] Chien, T. T., “An Adaptive Technique for a Redundant-Sensor Navigation System,” Report No. T-560, C. S. Draper Laboratory, Cambridge, MA, 1972.

[96] Salazar, M. R., “State Estimation of Ballistic Trajectories with Angle-Only Measurements,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 21, Academic Press, NY, pp. 117-175, Part 3 of 3, 1984.

[97] Hsiao, C.- Y., “Computational Techniques in Angle-Only Tracking Filtering,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 29, Academic Press, NY, pp. 101-134, Part 2 of 3, 1988.

[98] Liang, D. F., “Comparisons of Nonlinear Recursive Filters for Systems with Non-negligible Nonlinearities,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 20, Academic Press, NY, pp. 341-402, Part 2 of 3, 1983.

[99] Yannis A. Phillis, “Algorithms for Systems with Multiplicative Noise,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 30, Academic Press, NY, pp. 65-83, Part 3 of 3, 1989.

[100] Yannis A. Phillis and Vassilis S. Kouikoglou, “Minimax Estimation and Control of Multiplicative Systems,” Control and Dynamic Systems: Advances in Theory and Applications - Nonlinear and Kalman Filtering Techniques, Vol. 31, Academic Press, NY, pp. 93-124, Part 1 of 3, 1989.

[101] Ahn, B.-H., Regan, R., et al, “Inertial Technology for the Future,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 20, No. 4, pp. 414-444, Jul. 1984.

[102] Jayawardhana, B., Logemann, H., and Ryan, E. P., “The Circle Criterion and Input-to-State Stability: new perspectives on a classical result,” IEEE Control System Magazine, pp. 32-67, Vol. 31, No. 4, August 2011.

[103] Yan, J., Hoagg, J. B., Hindman, R. E., Bernstein, D. S.,  “Longitudinal Aircraft Dynamics and the Instantaneous Acceleration Center of Rotation: the case of the vanishing zeros,” IEEE Control System Magazine, pp. 68-92, Vol. 31, No. 4, August 2011.

[104] Bergin, J., Guerci, J. R., MIMO Radar: Theory and Practice, Artech House, Boston, 2018.

[105] Son, J. S., Thomas, G., Flores, B. C., Range-Doppler Radar Imaging and Motion Compensation, Artech House, Boston, 2001.

[106] Guerci, J. R., Space-Time Adaptive Processing for Radar, Artech House, Boston, 2003.

[107] Hudson, J. E., Adaptive Array Principles, Peter Peregrinus, Ltd., London, U. K., 1981, reprinted 1989, 1991. 

[108] Copps, E. M., “An aspect of the role of the clock in a GPS receiver,” Navigation, Journal of The (U.S.) Institute of Navigation, Vol. 31, No. 3, pp. 233-242, 1986. Also in Global Positioning System, papers published in Navigation, reprinted by The (U.S.) Institute of Navigation, Vol. III,  pp. 44-53, 1986. 

[109] Copps, E. M.,  Geier, G. J.,  Fidler, W. C. and Grundy, P. A. , “Optimal processing of GPS signals,” Proceedings of the Thirty-Sixth Annual Meeting of The (U.S.) Institute of Navigation, Monterey, CA, 23- 26 June, pp. 17-24, 1980. Also in Navigation, Journal of The (U.S.) Institute of Navigation, Vol. 27, No. 3, pp. 171-182, 1984. Also in Global Positioning System, papers published in Navigation, reprinted by The Institute of Navigation, Vol. II, pp. 13-24, 1984.

[110] Kashyap, S. K., Naidu, V. P. S., Singh, J., Girija, G., Rao, J. R., “Tracking of Multiple Targets Using Interactive Multiple Model and Data Association Filter,” Journal of Aerospace Science and Technologies, Vol. 58, No. 1, pp. 66-74, 2006.

NAVIGATION via Visual Cues Using Only Imaging Sensors:
[111] Rodriguez, J. J., Aggarwal, J. K., “Matching Aerial Images to 3D Terrain Maps,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 12, No. 12, pp. 1138-1149, Dec. 1990: Sparse terrain profile data are stored onboard and direct measurement of relative shifts between images are used to estimate position and velocity; however, an EKF is deemed superior here to use of merely a Kalman filter that uses altitude estimates in order to estimate aircraft position and velocity. 
[112] Heeger, D. J., Jepson, A. D., “Subspace Methods for Recovering Rigid Motion I: Algorithm and Implementation,” International Journal of Computer Vision, Vol. 7, No. 2, pp. 95-117, Jan. 1992: Terrain matching methods are also used to estimate platform position and orientation via comparisons to an on-board digital elevation map. 
[113] Soatto, S., Frezza, R., Perona, P., “Motion Estimation via Dynamic Vision,” IEEE Trans. on Automatic Control, Vol. 41, No. 3, pp. 95-117, Mar. 1996: A least squares formulation is used to recover user's 3D motion (3 translation variables and 6 rotation variables or 4 if quaternions are utilized). 
[114] Goyurfil, P., Rotstein, H., “Partial Aircraft State Estimation from Visual Motion Using the Substate Constraint Approach,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 5, pp. 1016-1025, Sep.-Oct. 2001: What is called an implicit EKF is used here to estimate aircraft states-aircraft velocities, angular rates, angle of attack, and angle of sideslip but not aircraft Euler angles nor inertial location. Measurements available are the image points of N featured objects, which are tracked from one frame to another. 
[115] Hoshizaki, T., Andrisani, D., Braun, A. W., Mulyana, A. K., and Bethel, J. S., “Performance of Integrated Electro-Optical Navigation Systems,” Navigation: Journal of the Institute of Navigation, Vol. 51, No. 2, pp. 101-122, Summer 2004: Contains good modeling and they have a “tightly coupled system consisting of INS, GPS, and EO” all working together to simultaneously benefit both navigation and photogrammetry (estimates platform states, sensor biases, and unknown ground object coordinates using a single Kalman filter).Use of control points avoided pre-stored terrain. 
[116] Kyungsuk Lee, Jason M. Kriesel, Nahum Gat, “Autonomous Airborne Video-Aided Navigation,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 3, pp. 163-173, Fall 2010: ONR-funded discussion utilizes (1) “digitally stored georeferenced landmark images” (altimeter/DTED), (2) video from an onboard camera, and (3) data from an IMU. Relative position and motion are tracked by comparing simple mathematical representations of consecutive video frames. A single image frame is periodically compared to a landmark image to determine absolute position and to correct for possible drift or bias in calculating the relative motion. 
[117] Craig Lawson, John F. Raquet, Michael J. Veth, “The Impact of Attitude on Image-Based Integrity,” Navigation: Journal of the Institute of Navigation, Vol. 57, No. 4, pp. 249-292, Winter 2010: Being aware of the historical importance of having good satellite geometry when seeking to utilize GPS for positioning and for timing (characterized by HDOP, VDOP, TDOP, and GDOP), they analogously extrapolate these ideas to the geometry of their airborne image collecting and refer to this as image integrity (similar to how researchers endeavor to associate sufficient Integrity to GPS measurements). Known a/c attitude significantly beats unknown attitude (altitude-indexed). Also see: Dennis Milbert,
Likely comparable Classified DoD Pointing Improvements: Cobra Ball/Cobra Eye & other airborne Laser developments.
Rigorous updates in airborne estimation for attitude determination:
[118] Crassidis, J. L., Markley, F. L., Cheng, Y., “Survey of Nonlinear Attitude Estimation Methods,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 1, pp. 12-28, Jan. 2007: An excellent survey on the subject of attitude estimation. It provides insights into what is important in estimation algorithms. It is a more practical and rigorous addendum to their many earlier surveys, concerned with utilizing alternative EKF's or Nonlinear Luenberger Observers (as alternatives to Extended Kalman filter-based approaches). They admonish to “stick with EKF”.
[119] Majji, M., Junkins, J. L., Turner, J. D., “Jth Moment Extended Kalman Filtering for Estimation of Nonlinear Dynamic Systems,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Honolulu, HI, Paper No. AIAA 2008-7386, pp. 1-18, 18-21 Aug. 2008: Explores two variations on JMEKF formulations that properly handle higher order moments (that lurk in the background while trying to get good estimates and covariances from EKF’s). Approximations utilized are acknowledged and properly handled (rather than ignored, as is usually the case). Errors reduced by several orders of magnitude within 5 sec., but results in normalized units (for comparisons to ordinary EKF approach, which it beat by a wide margin). Down side is its larger CPU burden yet to be completely quantified.
[120] Scorse, W. T., Crassidis, A. L., “Robust Longitudinal and transverse Rate Gyro Bias Estimation for Precise Pitch and Roll Attitude Estimation in Highly Dynamic Operating Environments Utilizing a Two Dimensional Accelerometer Array,” AIAA Atmospheric Flight Mechanics Conference, Paper No. AIAA 2011-6447, Portland, OR, pp. 1-28, 8-11 Aug. 2011: Using the latest in rigorous real-time estimation algorithms (neither a particle filter nor an unscented/Oxford /Sigma-Point filter) for enabling accurate pointing (precise pitch and roll) within an aircraft within a high dynamics operating environment is reported. While it does utilize rate integrating gyros. It also utilizes 2D accelerometer arrays and compares to an onboard gravity map to achieve its accuracy. Following reasonably large offsets, got back to within 0.1 degree pointing error within 10 seconds but results much worse with turbulence present. 
[121] 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: Achieves a big breakthrough by providing a proof of this particular EKF’s global stability as a consequence by stating 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 claim. Author Jensen attains his results by utilizing appropriate stochastic Lyapunov functions (proper handling of such due to Prof. Emeritus Harold J. Kushner, Brown Univ.).
[122] La Scala, B. F., Bitmead, R. R., James, M. R., “Conditions for stability of the Extended Kalman Filter and their application to the frequency tracking problem,” Math. Control, Signals Syst. (MCSS), vol. 8, No. 1, pp. 1-26, Mar. 1995: Proof of Stability for yet another EKF. Now worries about EFK divergence evaporate for this application.
[123] Reif, K., Gunther, S., Yaz, E., Unbehauen, R., “Stochastic stability of the continuous-time extended Kalman filter,” Proc. Inst. Elect. Eng., Vol. 147, p. 45, 2000: Proof of Stability for yet another EKF. Now worries about EFK divergence evaporate for this application
[124] Salcudean, S., “A globally convergent angular velocity observer for rigid body motion,” IEEE Trans. on Autom. Control, Vol. 36, No. 12, pp.1493-1497, Dec. 1991: Proof of Stability for Luenberger Observer use too (~EKF). 
Rigorous Matrix Kalman Filter (MKF) updates in airborne estimation for attitude determination (Cont.’d):
 

In anticipation of later success, I have explored some possibilities offered by the following novel Kalman filter variants that use matrix sensor (allowing simultaneous angle) measurements in lieu of the more familiar version of a Kalman filter involving only vector sensor (one-direction-at-a-time) measurements. 
(JTIDS RelNav used multilateration and only ordinary Kalman filters with vector sensors on each platform but had many participants in the net who automatically responded at regular short intervals!)
[125] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Kalman Filtering for Matrix Estimation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 147-159, Jan. 2006: A linear Matrix Kalman filter for DCM. DCM Refinement #1 
[126] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Direction Cosine Matrix Estimation from Vector Observations Using a Matrix Kalman Filter,” AIAA Guidance, Navigation, and Control Conference and Exhibit, pp. 1-11, Aug. 2003: A linear Matrix Kalman Filter for DMC using either vector or matrix measurement updates. DCM Refinement #2 . 
[127] Choukroun, D., “A Novel Quaternion Kalman Filter using GPS Measurements,” Proceedings of ION GPS, Portland, OR, pp. 1117-1128, 24-27 Sep. 2002: An alternative viewpoint: Quaternion Refinement #1.
[128] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Kalman Filtering for Matrix Estimation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 147-159, Jan. 2006: Quaternion Refinement #2.
[129] Choukroun, D., Bar-Itzhack, I. Y., Oshman, “Novel Quaternion Kalman Filter,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 174-190, Jan. 2006: Quaternion Refinement #3.
[130] Choukroun, D., Weiss, H., Bar-Itzhack, I. Y., Oshman, “Direction Cosine Matrix Estimation From Vector Observations Using A Matrix Kalman Filter,” Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, TX, pp. 1-11, 11-14 August 2003: DCM Refinement #3 
[131] Choukroun, D., “Ito Stochastic Modeling for Attitude Quarternion Filtering,”
Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P. R. China, pp. 733-738, 16-18 Dec. 2009: Quaternion Refinement #4.

In the above,  DCM = Direction Cosine Matrix; and for the Quaterion Matrices, the quaterions are to be normalized. One can convert from quaternions to DCM and vice versa. For the Matrix KF material, above, a major contributor was Daniel Choukroun, B. S. (Summa cum Laude), M.S., Ph.D. (1997, 2000, 2003), post-doc (UCLA), currently an Assistant Professor at Delft University of Technology, Netherlands.

In Thomas H. Kerr III's humble opinion, Angle Only Tracking (AOT) can also be accommodated within the above structure by updating from two (or more) different time-synchronized (via sorted time-tags) noncolocated sensors (with lever arms appropriately accounted for) simultaneously (thus used as a matrix measurement). The optimal estimator retains a linear syructure and is finite dimensional. This is the benefit of this novel approach. 
NASA updates in Spaceborne estimation for attitude determination:
[132] Cheng, Y., Landis Markley, F., Crassidis, J. L. Oshman, Y., “Averaging Quaternions,” Advances in the Astronautical Sciences series, Vol. 127, American Astronautical Society, AAS paper No. 07-213, 2007: Will eventually Summarize!
[133] Landis Markley, F., “Attitude Filtering on SO(3),” Advances in the Astronautical Sciences series, Vol. 122, American Astronautical Society, AAS paper No. 06-460, 2006: Will eventually Summarize!
[134] Cheng, Y., Crassidis, J. L., and Landis Markley, F., “Attitude Estimation for Large Field-of-View Sensors,” Advances in the Astronautical Sciences series, Vol. 122, American Astronautical Society, AAS paper No. 06-462, 2006: Will eventually Summarize!
[135] Landis Markley, F., “Attitude Estimation or Quaternion Estimation?,” Advances in the Astronautical Sciences series, Vol. 115, American Astronautical Society, AAS paper No. 03-264, 2003: Critical and thorough Analysis of 3 different EKF’s vs. Technion MKF. MKF was ultimately improved by this investigation..
[136] Reynolds, R., Landis Markley, F., Crassidis, J. L., “Asymptotically Optimal Attitude and Rate Bias Estimation with Guaranteed Convergence,” Advances in the Astronautical Sciences series, Vol. 132, American Astronautical Society, AAS paper No. 08-286, 2008: Will eventually Summarize!
Estimation Results for Bilinear Systems (to tie into the MKF results above):
[137] Halawani, T. U., Mohler, R. R., and Kolodziej, W. J., “A two-step bilinear filtering algorithm,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 32, 344-352, 1984: Will eventually Summarize! 
[138] Glielmo, L., Marino, P., Setola, R., Vasca, F., “Parallel Kalman Filter Algorithm for State Estimation in Bilinear Systems,” Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, pp. 1228-1229, Dec. 1994: Will eventually Summarize!
[139] Wang, Z., Qiao, H., “Robust Filtering for Bilinear Uncertain Stochastic Discrete-Time Systems,” IEEE Trans. on Signal Processing, Vol. 50, No. 3, pp. 560-567, Mar. 2002: In general, “Robust” approaches usually have a sluggish response time.
[140]] Lopes dos Santos, P., Ramos, J. A., Frias, R., “Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs,” Proceedings of the 46th Conference on Decision and Control, New Orleans, LA, pp, 6196-6202, 12-14 Dec. 2007: Structure similar to what above Technion MKF exhibits.

While linear systems are very tractable, general nonlinear systems are less so. Bilinear systems are close to being linear systems and so are somewhat more tractable, and likewise for their associated Optimal estimators.
Prof. Roger W. Brockett (Harvard-Emeritus) discusses how to handle bilinear systems in:
[141] Brockett, R. W., "Finite Dimensional Linear Systems," SIAM Classics in Applied Mathematics, 2015 (original in 1970).

We can provide 17 more examples of practical estimators for bilinear systems, as have been reported in the technical literature by others over the last 40+ years, (some involving Lie Algebras and Lie Brackets such as those provided by A. S. Wilsky and J. T.-H. Lo for SO(2) and by many others later).

[142] H. C. Lambert, “Tracking filter for the mitigation of the ionospheric range bias,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 1, pp. 339–348, Jan. 2008.

[143] S. Blackman and R. Popoli, Design and Analysis of Modern Tracking Systems, Artech House, Boston, MA, 1999.

[144] B. D. Tapley, M. M. Watkins, J. C. Ries, G. W. Davis, R. J. Eanes, S. R. Poole, H. J. Rim, B. E. Schutz, and C. K. Shum, “The joint gravity model 3,” Journal of Geophysical Research, Vol. 101, No. B12, pp. 28 029–28 049, Dec. 1996.

[145] N. Bergman, “Recursive Bayesian estimation: Navigation and tracking applications,” Ph.D. dissertation, Linkoping University, SE-581 83 Linkoping, Sweden, April 1999.

[146] N. Bergman, Sequential Monte Carlo Methods in Practice, New York: Springer, New York, 2001 (Chapter: Posterior Cramér-Rao Bounds for Sequential Estimation, pp. 321–338).

[147] Vytas B. Gylys, Kalman Filters and Nonlinear Filters, Texas Instruments Inc.

[148] Wasim Huleihel, Joseph Tabrikian, and Reuven Shavit, “Optimal Adaptive Waveform Design for Cognitive MIMO Radar,”
IEEE Transactions on Signal Processing, Vol., 61, No. 20, pp. 5075-, Oct. 2013. [Assumes fixed, known target range and Doppler information and only in the conclusion do they sketch how it may, perhaps, be successfully extended to a more realistic situation where the target is actually moving with respect to the radar. Did anyone actually follow-up and see whether it resolves as they speculated? No wonder Dr. Eli Brookner is up in arms about MIMO practicioners either doing what can already be done conventionally or about overstepping or overstating what MIMO can actually do!]
http://www.ee.bgu.ac.il/~rshavit/Papers/p52.pdf

[149] M. Morf, J.R. Dobbins, B. Friedlander, T. Kailath, “Square-root algorithms for parallel processing in optimal estimation,” Automatica, Vol. 15, No. 3, pp. 299-306, 1979.

[150] H. H. Afshari, S. A. Gadsden, S. Habbi, “Gaussian Filters for parameter and state estimation: a general review of the theory and recent trends,” Signal Processing, Vol. 135, pp. 218-238, 2017.

[151] http://www.gallup.unm.edu/~smarandache/NATOASI_ATJDTSPK.pdf 

[152] F. Landis Markley, John L. Crassidis, Yang Cheng, “Nonlinear Attitude Filtering Methods,” American Institute of Aeronautics and Astronautics, pp. 1-32,  2007. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050212421.pdf    Landis.Markley@nasa.gov   AIAA Fellow
I. Introduction (from the above [152], as copied verbatim, as follows next)
The extended Kalman (EKF) is the workhorse of real-time spacecraft attitude estimation. Since the group SO(3) of rotation matrices has dimension three, most attitude determination EKFs use lower-dimensional attitude parameterizations than the nine-parameter attitude matrix itself. The fact that all three-parameter representations of SO(3) are singular or discontinuous for certain attitudes has led to extended discussions of constraints and attitude representations in EKF & 719-11 These issues are now well understood, however, and the EKF, especially in the form known as the multiplicative extended Kalman filter5-7 (MEKF), has performed admirably in the vast majority of attitude determination applications. Nevertheless, poor performance or even divergence arising from the linearization implicit in the EKF has led to the development of other filters. Several of these approaches retain the basic structure of the EKF, such as additive EKF a backwards-smoothing EKF,l8 and deterministic EKF-like estimators. ”-” In particular, the backwards-smoothing EKF solves a nonlinear smoothing problem for the current and past sample intervals using iterative numerical techniques. The numerical iteration retains all of the nonlinearities of a fixed number of stages that precede the terminal stage of interest, and it processes information from earlier stages in an approximate manner. l5 Deterministic EKF-like estimators are closely related to H_infinity control design.” Usually an upper bound is derived first, and then the bound is minimized based on approaches such as Riccati equations and linear matrix inequalities. The nonlinear problem is much more difficult; which requires the solution of the Hamilton-Jacobi-Isaacs partial differential inequality. For attitude estimation, small-error approximations are used to developed a filter. 19i20 Other designs use various assumptions to derive simplified filters. These generally provide suboptimal performance characteristics in relation to the EKF, but involve linear or pseudo-linear equations that are used to estimate the states of a nonlinear dynamical system. Therefore, linear design and analysis tools can be used to construct the filter and to assess its overall performance. Some of these use a deterministic solution of the attitude] e.g. methods that are based on the QUEST attitude determination solution.23 Simple filter designs based on QUEST include filter QUEST24 and recursive QUEST.25 A more complicated but far more robust approach] called extended uses a full nonlinear propagation along with a novel measurement update. This approach can be used to estimate attitude and additional parameters as well. Interlaced filters that replace a nonlinear filter with two or more linear filters have been used for rate estimation] but not for attitude e~timation.~~-~’ Several new alternatives to the standard EKF have been recently introduced] such as sigma point or unscented filter^^'-^^ and particle filter^.^^-^^ Unscented filters (UFs) have been shown to exhibit several advantages over the EKF, including: 1) the expected error is lower than the EKF, 2) they can be applied to non-differentiable functions, 3) no Jacobian matrix calculations are required] and 4) they provide higher- order expansions than the standard EKF. Unscented filters work on the premise that with a fixed number of parameters it should be easier to approximate a Gaussian distribution than to approximate an arbitrary nonlinear function. They typically use the standard Kalman form in the post-update, but use a different propagation of the covariance and pre-measurement update with no local iterations. The attitude estimation UF derived in Ref. 33 is based on a quaternion representation of the attitude kinematics. However, straightforward implementation of the standard UF equations derives a predicted quaternion mean from an averaged sum of quaternions. Therefore, no guarantees can be made that the resulting quaternion will have unit norm. This was overcome by using a generalized unconstrained three-component vector to represent the attitude error-quaternion] leading to an unconstrained formulation in the UF design. Unscented filters are essentially based on second or higher order approximations of nonlinear functions, which are used to estimate the mean and covariance of the state vector. Though the mean and covariance are the sufficient statistics of a Gaussian distribution, they are not sufficient to represent a general probability distribution. When UF methods are applied to strongly nonlinear and non-Gaussian estimation problems] where the a posteriori distribution of the state vector may be multi-peaked, heavily-tailed, or skewed, desired performance characteristics may not be obtained. This may be overcome by using particle filter^^^-^^ (PFs). Like other approximate approaches to optimal filtering] the ultimate objective of PFs is to construct the a posteriori probability density function (PDF) of the state vector, or the PDF of the state vector conditional on all the available measurements. However, the approximation of PFs is vastly different from that of conventional nonlinear filters. The central idea of a PF approximation is to represent a continuous distribution of interest by a finite (but large) number of weighted random samples of the state vector, or particles. A PF does not assume the a posteriori distribution of the state vector to be a Gaussian distribution or any other distribution of known form. In principle,it can estimate probability distributions of arbitrary form and solve any nonlinear and/or non-Gaussian system. Reference 36 presents a PF for attitude estimation based on the bootstrap filter.35 The optimal solution of the nonlinear estimation problem requires the propagation of the conditional PDF of the state given the observation history.37 All practical nonlinear filters are approximations to this ideal. Exact finite dimensional filters38 can be found that solve some nonlinear problems by using the Fokker-Planck equation2l3’ to propagate a non-Gaussian PDF between measurements and Bayes’ formula‘? to incorporate measurement information. A recently proposed filter4’ follows this pattern, but does not solve the nonlinear attitude filtering problem exactly. We refer to it as an orthogonal filter, because it represents the attitude by an orthogonal rotation matrix, rather than by some parameterization of the rotation matrix. The PDF is a non-Gaussian function defined on the Cartesian product of S0(3), the group of rotation matrices, and the Euclidean space Rn of bias parameters. This filter entirely avoids questions about singularities of representations or covariance matrices arising in EKFS~-~~ and UFS,~~ and has the additional advantage of providing a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space. Nonlinear observers often exhibit global convergence, which is to say that they can converge from any initial guess.41 Several applications of observers for attitude control have been proposed Refs. 42-48. A nonlinear observer and controller using only measurements of roll, pitch and yaw has been developed in Ref. 43. Local asymptotic stability is ensured under mild hypotheses. A globally convergent, nonlinear full- order observer using quaternions and Euler’s equations for the dynamics has been derived in Ref. 44. The observer structure contains a discontinuous term, which is often associated with “sliding mode” observers. The error-quaternion is defined using a multiplicative approach and stability is proven using a Lyapunov function. A simpler, robust smoothed sliding mode observer that avoids quaternion error differentiation noise and eliminates the necessity of measuring angular rate is derived in Ref. 45. Although an additive approach is used to define the quaternion error, global stability is still provided through a Lyapunov function. Algrain and Lee develop a nonlinear observer to estimate angular rates along the third axis of a spinning spacecraft using only two-axis measurement^.^^ A pseudo-linear model is developed by decomposing the nonlinear system into linear and nonlinear parts. BoSkoviC, Li and Mehra use angular rate measurements with quaternion kinematics to derive a nonlinear bias observer, which is coupled with an adaptive sliding mode ~ontroller.~~ Stability is proven as long as the attitude never passes through f180 rotations. Thienel and Sanner develop an exponentially convergent nonlinear observer given a constant gyro bias with identification of the bias proven through a persistency of excitation argument.48 An analysis is also shown that includes gyro noise. Adaptive approaches generally fall into two categories. One category encompasses approaches that adap- tively tune the Kalman filter through the identification of either the process noise covariance or measurement noise covariance, or both simultaneously. In practice “tuning” a Kalman filter can be arduous and very time- consuming. Usually, the measurement-error covariance is fairly well known, derived from statistical inferences of the hardware sensing device. However, the process noise covariance is usually not well known and is of- ten derived from experiences gained by the design engineer based on intimate knowledge of the particular system. The approach is based on “residual whitening.” 49 Unfortunately, most noise adaptive techniques are applicable only for linear systems,’ which creates problems for attitude estimation due to the nonlinear equations involved. Still, it is possible to use these techniques with linearized equations, as demonstrated in Ref. 50. Lam and Wu further develop adaptive filters that address both colored and white noise ~tatistics.~~ The former noise is identified using a non-parametric neural network approach, while the latter noise is identified using an a-P filter. An adaptive filter is also proposed in Ref. 17 to account for inaccuracy in the knowledge of the process noise statistical model, which uses a linear pseudo-measurement model. Other adaptive approaches use adaptive methods for fault tolerant estimation 53 The other category includes approaches that adaptively estimate unknown system parameters, such as the inertia matrix. These generally fall into two basic categories: 1) parameter estimation or filter-based methods, and 2) nonlinear adaptive techniques. Least squares methods to determine the inertia matrix and other constant parameters, such as disturbance model parameters and biases, are shown in Refs. 54-56. A disturbance accommodation technique that models the unknown disturbance angular rate using a power set of time as basis functions is shown in Ref. 57. Nonlinear adaptive techniques are similar to nonlinear observers in that they usually provide global stability proofs that guarantee convergence of the estimated parameter^.^^-^' This paper will review the basic assumptions of these filters, presenting enough mathematical detail to give a general orientation. First, reviews of the quaternion parameterization and gyro model equations are given. Then, attitude estimation methods based on the EKF are shown, followed by QUEST-based approaches. Next, the two-step estimator is shown. The UF and PF approaches are then shown, followed by the orthogonal filter. Then, the predictive filter, as well as nonlinear observers and adaptive approaches are reviewed. The paper concludes with a discussion of the strengths and weaknesses of the various filters. 
(Thomas H. Kerr comment: Also see item [168] below for a 1971 precedent to handling estimation on a circle, SO(2),  and on a sphere, SO(3) .)

Other topics that I routinely follow:

[153] Niu, X., Nassar, S., El-Sheimy, N., “An Accurate Land-Vehicle MEMS IMU/GPS Navigation System Using 2D Auxiliary Velocity Updates,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 3, pp. 177-188, Fall 2007.

[154] Soloviev, A., van Graas, F., “Batch-Processing of Inertial Measurements for Mitigation of Sculling and Commutation Errors,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 4, pp. 265-276, Winter 2007.

[155] Soloviev, A., van Graas, F., “Enhancement of Integrated GPS/INS Performance Utilizing Frequency Domain Implementation of INS Calibration,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 2, pp. 87-98, Summer 2007.

[156] Lee, Y. C., “Two New RAIM Methods Based on the Optimally Weighted Average Solution (OWAS) Concept,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 4, ff. 333, Winter 2007.

[157] Farrell, J. L., “Inertial Instrument Error Characterization,” Navigation: Journal of the Institute of Navigation, Vol. 54, No. 3, pp. 169-176, Fall 2007.

[158] Farrell, J. L., “Full Integrity Testing for GPS/INS,” Navigation: Journal of the Institute of Navigation, Vol. 53, No. 1, pp. 33-40, Spring 2006.

[159] Milbert, D., “Dilution of Precision Revisited,” Navigation: Journal of the Institute of Navigation, Vol. 55, No. 1, pp. 67-81, Spring 2008.

[160] Pulford, G. W., “A Proof of the Spherically Symmetric Overbounding Theorem for Linear Systems,” Navigation: Journal of the Institute of Navigation, Vol. 55, No. 4, pp. 283-292, Winter 2008.

[161] Li, Y., Rizos, C., Wang, J., Mumford, P., Ding, W., “Sigma-Point Kalman Filtering for Tightly Coupled GPS/INS Integration,” Navigation: Journal of the Institute of Navigation, Vol. 55, No. 3, pp. 167-177, Fall 2008.

[162] “Algorithm Aligns Gyrocompass in Twisting and Swaying Vehicle,” NASA Tech Briefs MFS-28671, George C. Marshall Space Flight Center, Alabama 35812, Gyrocompass FDR Version 6.0.6/MO (from Specification CP-830100A, Appendix 1, Rev. A, 28 July 1989 for TOS on Titan), pp. 1-87, 18 June 1991.

[163] Shively, C. A., Hsio, T. T., “Error and Availability Analysis of CAT IIIb LAAS Augmented by Radar Altimetry,” Navigation: Journal of the Institute of Navigation, Vol. 52, No. 3, pp. 155-162, Fall 2005.

[164] Mason, J., “Algebraic Two-Satellite TOA/FOA Position Solution on an Ellipsoidal Earth,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 40, No. 7, pp. 1087-1092, July 2004. 

[165] Mason, J., Romero, L., “TOA/FOA Geolocation Solutions Using Multivariate Resultants,” Navigation: Journal of the Institute of Navigation, Vol. 52, No. 3, pp. 163-177, Fall 2005.

[166] Jekeli, C., “Navigation Error Analysis of Atom Interferometer Inertial Sensing,” Navigation: Journal of the Institute of Navigation, Vol. 52, No. 1, pp. 1-14, Spring 2005.

[167] Ristic, B., Arulampalam, S., Gordon, N., Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House, Boston, MA, 2004. [One of the clearest discussions of both historical and recent estimation algorithms (including EKF, UKF, MMM, INN, and Particle Filters), their underlying assumptions/mechanization equations and that also provides extremely useful insight into important aspects and distinctions in their implementations is offered in Chapters 1-3.]

[168] Li, J. T.-H. Lo and A. S. Wilsky, “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. [They explicitly handle estimation on a circle, SO(2), rather than estimation on a sphere, SO(3), as NASA's F. Landis Markley, et all deal with above in their extensive survey and comparison between approaches and techniques in [152]. However, Wilsky 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  

[169] Lo, J. T.-H. and Wilsky, A. S., “Stochastic Control of Rotational Processes with One Degree of Freedom,” SIAM Journal on Control, Vol. 13, No. 4, 886ff, July 1975.

USS Cobra Judy Radar Ship is the sister ship of the U.S.S. Compass Island. The Compass Island had been used in the early and mid 1970s as a test suite for demonstration and shake down of SSBN Navigation changes and upgrades before deploying within the submarine fleet. Both sister ships had little lateral fins on the bottom of the hull below the water line that could be extended out horizontally from the hull to stabilize the platform in rough seas (of a high sea state). A complete SSBN Navigation Room was present on the Compass Island, but intentionally installed backwards from its orientation aboard SSBNs. A prior NASA observation ship, the U.S.S. Vangard, replaced the Compass Island in this role in the late 1970s.

Pre- (and post-)GPS Relative Navigation (RelNav) enabled networks of different platforms to reference both friendlies and enemy targets with respect to a single common (virtual) grid using the L-band JTIDS (time-slotted and frequency hopped from 960 MHz to 1215 MHz, with gaps imposed for TACAN and IFFN). This capability was especially useful when all participants were at sea and far from any geographic landmarks of absolute location. The grid tended to move and rotate slightly. Its location was dictated by the Navigation Controller (NC), the platform having the best navigation accuracy (as a self-assessment), but in lieu of the demise of the original NC, the NC was replaced by the next best platform in this role to avoid possessing a single point vulnerability. JTRS (pronounced Jitters) is slated to replace JTIDS as an entirely software radio system (with its own unique set of problems yet to be solved). JTIDS included NTDS/ATDS. Air Force JTIDS used DTDMA protocol without RelNav. Navy version was TDMA with RelNav. Marine version of JTIDS was PLRS. Reed Solomon Code throughout. GPS uses Gold Code in two flavors or cycle lengths (to be upgraded).

Hybrid High-Rate Output Candidate Design for JTIDS/GPS/INS Integration and INS Navaid Selection.

Sam Blackman (Raytheon/Hughes), the (late) Oliver Drummond, Yaakov Bar-Shalom (UCONN), and Rabinder Madan.

http://www.ieee.org/about/awards/bios/picard_recipients.html

Blazers of the exciting area of multi-sensor\multi-target tracking (sometimes pursued even in clutter) [related to optimal resource allocation and solved by invoking Munkres or the Hungarian or Jonker- Volgenent- Castanons (J-V-C) or Murtys (1968) or Sam Blackman's Multi- Hypothesis Testing (MHT) algorithms. The first 3 techniques are all from the Operations Research area; the last is based on Bayesian Statistical analysis.

Not shown here: Prof. David Castanon (Boston University) and Charles Morefield (originally of Aerospace Corporation in the 1970s when he posed multi-target tracking as a 0-1 Integer Programming Problem, more recently Chairman of the Board at Alphatech (after Michael Athans stepped down and went to Portugal) before Alphatech became part of BAE in Burlington, MA), and Thomas Kurien (Raytheon). Also see Particle Filter variations in: Vermaak, J., Godsill, S. J., Perez, P., Monte-Carlo Filtering for Multi-Target Tracking and Data Association, IEEE Trans. on Aerospace and Electronic Systems, Vol. 41, No. 1, pp. 309-331, Jan. 2005. Also see Miller, M. L., Stone, H, S., Cox, I. J., Optimizing Murtys Ranked Assignment Method, IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 7, pp. 851-862, July 1997. Another: Frankel, L., and Feder, M., Recursive Expectation-Maximizing (EM) Algorithms for Time-Varying Parameters with Applications to Multi-target Tracking, IEEE Trans. on Signal Processing, Vol. 47, No. 2, pp. 306-320, February 1999. Yet another: Buzzi, S., Lops, M., Venturino, L., Ferri, M., Track-before-Detect Procedures in a Multi-Target Environment, IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1135-1150, July 2008.

Fourth ONR/GTRI Workshop on Target Tracking and Sensor Fusion, Naval Postgraduate School, Monterey, CA, 17 May 2001.Notice the guy (i.e., THK III) apparently in sun glasses (actually transitions) in the back row there (left of center, as always).

Lockheed Martins Paveway II Dual Mode Laser-Guided Bomb (DMLGB), which uses both laser-guided and inertial/GPS guidance, has achieved the U.S. Navy's initial operational capability and is now preparing for operational employment.

http://mg.gpsworld.com/gpsmg/data/articlestandard/gpsmg/032009/575729/lockheed.jpg

The DMLGB is designed to execute precision strike missions against stationary and mobile targets in all stationary and mobile targets in all weather conditions, according to Lockheed. The kits can operate in laser only, inertial/GPS, or dual-mode to provide pilots with flexibility to engage various types of targets in a single mission, says Lockheed Martin.

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Extra! Extra! Read all about it!

JAVAD GNSS has announced that its customers with JAVAD GNSS triple-frequency type OEM boards (TR-G2T, TR-G3T, TRE-G2T, TRE-G3T, TRE-G3TAJ) and receivers (TRIUMPH-1, Alpha TR-G2T/TR-G3T, DeltaS TRE-G2T/TRE-G3T/TRE-G3TAJ, SigmaS TRE-G2T/TRE-G3T/TRE-G3TAJ) can now track the L5 demonstration signal.

The first GPS satellite with the L5 signal [Block IIR-20(M)] was successfully launched on 24 March 2009 and its L5 = 1176.45 MHz payload activated on 10 April 2009.

The signal characteristics clearly indicate that JAVAD GNSS receivers allow high-quality code and carrier-phase measurements of the L5 signal. The signal-to-noise ratio typically varies from about 30 dB*Hz at low elevations up to 57 dB*Hz at zenith (see figures below: top is SNR for L5; bottom is SNR for GPS PRN 1).

The white-noise and multipath tracking errors are comparable to what is normally seen for the L1 and L2 signals.

Those interested in sample raw data with the triple-frequency(L1-L2-L5) code and carrier phase measurements from IIR-20(M), can download sample data from GNSS Almanac Archive (see the ADVANCED section on www.javad.com). Note that these sample raw data are available in the JAVAD GNSS proprietary binary format as well as Rinex 3.0. http://sc.gpsworld.com/gpssc/data/articlestandard/gpssc/182009/595183/javad-1.jpg

http://sc.gpsworld.com/gpssc/data/articlestandard/gpssc/182009/595183/javad-2.jpg

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Air Force Successfully Transmits an L5 Signal From GPS IIR-20(M) Satellite

4/13/2009 - LOS ANGELES AIR FORCE BASE, Calif. -- The U.S. Air Force GPS IIR-20(M) satellite successfully transmitted for the first time a GPS signal in the L5 frequency band today. L5, the third civil GPS signal, will eventually support safety-of-life applications for aviation and provide improved availability and accuracy.

This broadcast brings into use the GPS International Telecommunication Union filing at 1176.45 MHz in the highly protected and co-allocated Radio Navigation Satellite Service and Aeronautical Radio Navigation Service band. A joint team consisting of the GPS Wing, Lockheed Martin, ITT and The Aerospace Corporation developed the L5 Demonstration signal payload and integrated it onto the GPS IIR-20(M) spacecraft, which launched March 24, 2009.

The initial broadcast of the L5 Demonstration signal was monitored and validated by SRI International in Menlo Park, Calif, in cooperation with the GPS Wing, 2nd Space Operations Squadron, Lockheed Martin, Draper Laboratory and The MITRE Corporation.

Thanks to the men and women of the Air Force, our industry partners and national research institute, this mornings successful L5 transmission marks an important milestone in GPS civilian applications. This new third civil signal will make possible the research and development of safety-of-life applications for the commercial transportation sector, and in the future, will play a vital role in improving safety, fuel efficiency, and capacity in our airspace, waterways, highways, and railroads. Todays event marks another important step in the ongoing effort to maintain and modernize GPS as the global standard for space-based positioning, navigation, and timing, said Joel Szabat, Deputy Assistant Secretary for Transportation Policy, U.S. Department of Transportation.

The L5 demonstration payload effort shows the can-do spirit and dedication of all who work in this industry and is an example of a government/industry team working together to meet a significant challenge in a very short time. Development of a solid plan and schedule, adherence to that plan, and consistently looking ahead allowed for a timely and successful completion of the L5 effort, said Col. Dave Madden, Commander, and Global Positioning Systems Wing.

Air Force Space Command
s Space and Missile Systems Center, located at Los Angeles Air Force Base, Calif., is the U.S. Air Forces center of acquisition excellence for developing, acquiring, fielding and sustaining the worlds best space and missile systems for the joint warfighter and the nation.

L5 Signal

Time series and power spectrum of the L5 demonstration signal

New GPS Satellite’s Problems Indicated on 4 May 2009

Lt Col David Goldstein, chief engineer for the GPS Wing, told the plenary session at the European Navigation Conference in Naples, Italy, that the Wing is experiencing some out of family measurements from the recently launched IIRM (20) satellite. This appears to corroborate some unofficial rumors that have circulated recently about problems with legacy signals from the satellite, that is, L1 and L2. The April 10 broadcast of the first L5 signal secured that frequency for the U.S. GPS program; since that signal contains no navigation message at present, it is presumably not affected by these problems.

Goldstein told the ENC opening session, Monday 4 May 2009, that the Air Force will not launch any further satellites until this issue is resolved. IIR(M) 21, the last of the IIR(M) series, is currently scheduled to rise sometime in August, with the first of the IIF generation to follow in late 2009 or early 2010.

Normally, a satellite is set healthy within 28 days of launch, after extensive testing, but this has not occurred with the satellite launched on 24 March 2009. The U.S. Air Force has formed a response team and is working nearly round the clock to resolve the problem, but according to Goldstein is not rushing the issue, seeking a thorough solution since the overall constellation is robust at 30 satellites.

We are currently examining data from the satellite that is not consistent with data from the other IIR(M)s, he stated, characterizing the variances as measurements with larger than expected pseudorange errors that are elevation-dependent, and that we have not seen before. We have experimented with a few fixes and it looks very promising.

He described the response team’s approach as making a fishbone diagram of all potential failure mechanisms, and working through them methodically. We think we have identified the failure but it may be several more months before the analysis is complete, and the situation is fully resolved.

The big delay in preventing GPS from being completed by the planned date of 1984 was the Space Shuttle Challenger disaster. Most GPS satellites were planned to be inserted from a Space Shuttle but instead had to be inserted from Delta rockets as a fall back that delayed a full GPS satellite constellation from existing until 1994.

The open literature discussion of L3 in the early 1980s for GPS was that like L2 (=1227.5 MegaHertz) and L1 (=1575.42 MegaHertz), it was also an integer multiple of a single onboard clock frequency being L3 (= 1381 MegaHertz). It was speculated that L3 was used to cross-communicate between GPS satellites like a JTIDS RelNav network in the sky. Some have speculated that it had related to autonomously maintaining proper satellite ephemeris of the network since in the bad old days of Mutually Assured Destruction (MAD) as a policy strategy, he who had the last accurate weapon fired won. Land-based Minuteman ICBMs (with AIRS navigation systems) utilized GPS for a midcourse nav fix. Ship launched SLBMs did not. GPS supposedly had sufficient untended (by human intervention) ephemeris to last for 6 months unaided, according to NADC in the early 1980s. 

L3  is now both known by the private sector and is controversial in the civilian Radio Astronomy community, as seen below.

The Global Positioning Satellite system has a mode, L3 at 1381 MHz, which is used for global alarm. If it is within your observing band, then all astronomical signal gets swamped. With advanced notice, the observatory is in a position to alert the responsible authorities and request rescheduling GPS L3 transmission. 

As circulated in unclassified literature in the 1980s, L3 is a part of NUGET, GPS satellites monitor and report on whether they have detected a nuclear blast anywhere in the world.

GPS L3 Interference and Radio Astronomy

European radio astronomy stations operating in the frequency band 1330 - 1400 MHz are experiencing harmful interference at a frequency of about 1381 MHz, which is so strong that it ruins the observations in this frequency range when it occurs. This interference is generated by transmissions from the GPS L3 channel.

An example of this type of interference observed with the Westerbork Synthesis Radio Telescope, WSRT, in the Netherlands is shown in Figure 1 for the amplitude and Figure 2 for the phase of the observed signal. The radio astronomical observation concerns a radio source at 23h36m35.20s right ascension and 26o40’36.00” declination (epoch J2000). The absolute scale for the amplitude of the interference signal is not calibrated since the antenna gain into the direction of the satellite, which was emitting in the far sidelobes of the antennas, is not known.

The indicated level of detrimental interference for the observations presented in the figures below is -239 dB(W/m2/Hz), which was determined using the methodology of Recommendation ITU-R RA.769. This methodology includes the assumption that the interference is received through the far antenna sidelobes, where an antenna gain of 0 dBi applies.


Fig.1: Intensity of the interference signal from GPS L3 observed through the far sidelobes at the WSRT on August 25/26, 2002. The figure shows a detailed spectrum in two linear polarization channels (noted as XX and YY) for an integration time of 0.8 minutes. The amplitude scale is in arbitrary units (see text); the astronomical signal of interest occurs at a level of 0.005 (!) only on this scale. Note that the signal rings throughout the entire 20 MHz band that is displayed.


Fig.2: Signal phase corrupted by GPS L3 interference at the WSRT during the same observation as for Figure 1. The spiky comb in the phase is due to the interfering signal, again in two polarizations.

The L3 spread spectrum transmissions centered at 1381 MHz also transgresses into the frequency range 1400 - 1427 MHz, a spectral band where the radio astronomy has a primary allocation to which RR footnote 5.340 applies, which states that “all emissions are prohibited”. Using a band-stop filter the signal could be suppressed to a level of -252 dB(W/m2/Hz), i.e. still 3 dB above the level of interference detrimental to radio astronomy continuum observations as given in Recommendation ITU-R RA.769.

The fundamental problem remains that the GPS L3 emission is intentionally produced in the band 1400 - 1427 MHz and is therefore in conflict with footnote 5.340 of the ITU-R Radio Regulations.

It should be noted that in the ITU Radio Regulations for Region 1 the band 1300 - 1350 MHz includes a primary allocation to RADIONAVIGATION-SATELLITE (Earth-to-space) and no allocation to a space service in the band 1350-1400 MHz. Thus no space-to-Earth transmissions are allowed according to these Regulations. For the frequency band 1330-1400 MHz footnote 5.149 applies, which states that administrations are urged to take all practicable steps to protect the radio astronomy service from harmful interference. Emissions from spaceborne or airborne stations can be particularly serious sources of interference to the radio astronomy service (...).

CRAF considers that a regulatory solution for this issue is required, in order to avoid the creation of an undesirable regulatory precedent, where the operation of an application is allowed in conflict with the ITU Radio Regulations.

On this matter CRAF is currently in the process of negotiation with concerned Administrations and expects that it can be solved in due course.

Recent solutions to GNSS incursions into frequencies reserved for Radio Astronomy have been advertised (but the band of concern apparently differs from what is complained about above): Julien, O., Issler, J.-L., "Mitigating the Impact of GNSS Signals in the Radio Astronomy Band 1610.6-1613.8 MHz,"  Navigation: Journal of the Institute of Navigation, pp. 229-240, Vol. 56, No. 4, Winter 2009.

In 1957, Walter Marrow (Lincoln Laboratory of MIT), who later became its head but retired from that position early in the new millennium, launched a missile full of thousands of small metal space needles into LEO, which took about six months to decay out of orbit and burn up in the atmosphere. The entire event was viewed by Lincolns Haystack radar. Radio Astronomers were livid since reception was impossible during that time period. 

The activation of the L2C signal in January 2006 will be of great benefit to the civil community, said Colonel Jester, Chief, Space Operations Branch, Air Force Space Command. But they will be using this signal at their own risk until the command and control of L2C is realized in the Fiscal Year 2013 timeframe. Receivers able to fully utilize the L2C signal will be the responsibility of the civil community. The military will build receivers focused on the new M-code signal.

L2C is stronger than L1.

The premiere civilian GPS manufacturer (TomTom GPS internationally headquartered in the Netherlands, US headquarters in Concord, MA) had been stiffed by ~ $8 million when Circuit City went out of business. Negotiations between Microsoft and TomTom GPS about licensing Microsoft patents broke off around March  2009 and Microsoft was starting to sue TomTom GPS. TomTom GPS subsequently formed a collective with other European companies that held a number of patents similar to Microsofts in order to counter-sue Microsoft over the same issue. It will be interesting to see how this one plays out....

GPS at Risk: Doomsday 2010

The United States Government Accountability Office (GAO) issued on 7 May 2009 an alarming report on the future of GPS, characterizing ongoing modernization efforts as shaky. The agency appears to single out the IIF program as the weak link between current stability and ensured future capability, calling into doubt whether the Air Force will be able to acquire new satellites in time to maintain current GPS service without interruption. It asserts the very real possibility that in 2010, as old satellites begin to fail, the overall GPS constellation will fall below the number of satellites required to provide the level of GPS service that the U.S. government commits to. read more»

L5 and Rorschach Shock

“There is a very minor problem with the L1, L2, and M-code navigation signals. Any causes would be pure speculation at this point, but the issue is the satellite will not be set healthy until these problems are fixed…. The ITT, LMCO and GPS Wing teams are working the problem hard. It may be a few weeks before the satellite is set healthy, but when that time comes I am sanguine that all the signal issues will be mitigated and the navigation message will be on par with the other IIR(M) payloads.” — Colonel Mark Crews

BY DON JEWELL | djewell@questex.com

I am sure that many of you remember Colonel Mark Crews when he served with distinction as the chief engineer for the GPS Wing at SMC. Mark made some legendary and landmark contributions to the future of the GPS constellation as we know it, nationally and internationally. After you read what Dr. Crews has to say about the L5 payload, I will launch into an issue concerning user equipment that has been on mind for sometime — with a trip to the shrink’s couch. read more»

 

 

Parkinson Prescribes Remedy for GAO Report Alarm

Brad Parkinson, the first GPS Program Office director, chief architect and advocate for GPS, submitted written testimony to Congress on mitigation options for possible GPS brownouts. His presentation comes in reference to the recent GAO report highlighting the risk that the GPS constellation may fall below the minimum level of 24 satellites required for full operational capability. In his opening, Parkinson states that ”GAO correctly points out the possibility that the GPS constellation will be reduced to less than the current number of 30 to 32 satellites. In fact, it is possible that the constellation will be at a level of less than 24 satellites. I would like to focus on the options that would help reduce this risk." read more»  Click here to download a 91KByte pdf file conveying Sir Brad Parkinsons excellent 10 side PowerPoint presentation to Congress.                    Prof. Parkingsons original 228KByte PowerPoint is here, including his speaker's notes as prompters.

Calling the Real Race in GNSS

Andrew Sage, a director of UK-based transport consultancy Helios, delivered a presentation at the European Navigation Conference entitled: The race to be the partner of choice for GPS. read more» 

Analyses of a Drop in GPS Satellite Numbers 

Professor Richard Langley of the University of New Brunswick (also GPS World Innovation editor) has done several analyses to see how the use of GLONASS satellites could help compensate for a potential reduction in the number of available GPS satellites. These studies came in response to a warning from the U.S. Government Accountability Office about the potential drop in the number of healthy satellites in the GPS constellation as a result of delays in both the Block IIF and Block III modernization programs. read more>>

The SVN-49 Story: What Went Wrong, How It Got Found, and Fixed 
During a very reassuring teleconference today with Colonel David Madden (GPSW/CC) and Colonel David Buckman (AFSPC - GPS Command Lead), we learned the true story of exactly what happened to SVN-49 , aka IIR-20(M), launched March 24, and why it has not been set to a healthy status. This teleconference should put an end to all the speculation concerning SVN-49 and its future status. In sum, there is nothing wrong with the L1, L2, or L5 signal transmitters, and they will not have to undergo expensive re-testing. 

read more>>

Latest GPS Satellite Early Orbit Checkout Extended 
The U.S. Air Force is investigating the cause and effects of signal distortions observed from the GPS IIR-20(M) spacecraft launched on March 24, 2009. Routine early orbit checkout procedures determined that GPS IIR-20(M) signals were inconsistent with the performance of other GPS IIR-M satellites. The signal distortion was initially observed as an elevation-dependent bias in ranging measurements from GPS monitor stations. read more>>

Coast Guard Directed to Maintain and Upgrade Loran
The U.S. Senate, in a Coast Guard Authorization Act for Fiscal Years 2010 and 2011 currently before the Committee on Commerce, Science, and Transportation, directs the Secretary of Transportation to maintain the current Loran-C navigation system and prepare for modernization to eLoran, and authorizes $37 million per year for 2010 and 2011 towards that purpose. Similar action is also currently pending in the House. 

read more>> 

Resource for Comparing Precise Point Positioning (PPP) Solutions
GNSS researchers at the University of New Brunswick, Canada, have created a Precise Point Positioning (PPP) Software Centre website to offer an easy means of comparing solutions from online PPP applications. Users are invited to send a RINEX observation file that will be simultaneously processed by three online PPP applications. 

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Final Modernized GPS IIR Satellite to Lift off from Cape Canaveral The last in a series of eight modernized Global Positioning System Block IIR (GPS IIR-M) satellites built by Lockheed Martin for the U.S. Air Force is set to launch aboard a Delta II rocket on Aug. 17 from Cape Canaveral Air Force Station, Florida. More...

Summary of SDI

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GPS IIR-21(M) Satellite Declared Operational

The last in the series of eight modernized Global Positioning System IIR satellites, GPS IIR-21(M), was declared operational Thursday for military and civilian users worldwide, just 10 days after launching from Cape Canaveral Air Force Station. More...

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PRN01/SVN49: Another GPS Satellite Anomaly

From monitoring at the University of New Brunswick and elsewhere around the globe, it appears that normal signals from the L1 and L2 transmitters on the GPS satellite PRN01/SVN49 were unavailable for more than two hours on the morning of September 4. More...

More problems with GPS and the end for Loran (not too wise since redundant navaids enable easy detection by comparison when GPS is being interfered with) can be found at the following link: http://www.gpsworld.com/gnss-system/out-front-rocky-road-robustness-9424  .

http://www.gpsworld.com/gnss-system/augmentation-assistance/expert-advice-remembering-and-resolving-10268

An INS-basaed Tracking device the size of a pin head:

http://www.ecnmag.com/News/2010/10/A-tracking-device-that-fits-on-the-head-of-a-pin/

Please click here to see the future of GNSS and the current status (as of August 2012) of the LightSquared Controversy, which had threatened GPS reception if it had been allowed to proceed.

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