|
§AGI also provides their
HTTP/IP-based CONNECT® API methodology to enable cross-communication with
other external software programs (as well as providing the more recent
COM/ActiveX option) and AGI promises to continue to support CONNECT® in order
to have complete backwards compatibility with what older versions of STK could
do.
Linux
Operating Systems can
also be accommodated using
Mono®, a program that allows
Linux Operating Systems to run
.NET® applications (i.e., Microsoft products developed in
Studio.NET normally require at least WindowsXP or Windows2000 or Vista or Windows 7 to Windows
11 to be the host Operating Systems for .NET applications). Version 1 Mono® was
released by 29 October 2005.
(By
July 2007, two other software products,
Mainsoft®
and
Wine®,
have also emerged for providing compatibility of Window’s-based software to a
Linux
Operating System.)
| While we vigorously vouch for the
veracity of our TK-MIP software, for routine legal reasons, we must
invoke the standard “shrink-wrap” software disclaimers and other
prudent limitations on any possible liability exposure of TeK
Associates. |
Go
to Top
Go to Primary Table of Contents
We also have experience investigating numerical analysis aspects such as:
“What intermediate
algorithms should be used?”,
“What will be the effect of round-off, register size,
possible numerical sensitivities, convergence, and convergence rates?” We have performed
tallies of operations
counts incurred, assessed how amenable algorithms are to decentralization or to parallelization
(as, say, separate threads in embedded processors, as cordic algorithms, as
systolic arrays, as neural networks, or, alternatively, as analog-based
Monolithic
Microwave Integrated Chips [MMIC]). We
routinely apply the principles and techniques of modern mathematical analysis
and appreciate the insights availed through its use.
We also routinely track and use new developments in statistics and random
process theory. To be cognizant of aspects related to countermeasures, we have
worked in Search and Screening exercises in the past (and also published
our results in the open, peer-reviewed professional literature) and so we are aware
of sweep-rate characterizations of platform or antenna exposure to enemy
surveillance as well as the adverse impact of increasing the duration of such
exposure (as this also relates to Moving Target Indicators [MTI] and to
“stop-move-stop”
strategies of radar or optical detection avoidance). We are aware that C3I
system principles of operation must be well understood before one can figure out
countermeasures (i.e., how to break it: C4I) or how to prevent having
it broken (i.e., counter-countermeasures or C5I). We are cognizant of
Old Crows’ Countermeasures Handbook
and The Wild Geese (LORAN Association). While “birds
of a feather flock together”,
sometimes birds of different interest areas cross-breed and, as a consequence,
have offspring where both interests/talents are combined within one individual!
Go
to Top
Go to Primary Table of Contents
TeK Associates’ Mission:
Our strong track record of participating in both evolutionary and revolutionary developments by historically trailblazing significant new results in estimation theory and in its practical applications stands on its own merits. We continue
along this same course that we find so stimulating, lucrative, gratifying, and rewarding.
We have innovative ideas (in our fields of specialization) and we first prove
their utility theoretically and then confirm it in simulation and finally in
implementation. Our commercial product TK-MIP for the PC is but one
instantiation of our particular philosophical approach to software development, based on our novel insights
(and extensive background in mathematical analysis, familiarity with other
developments in the field, and our overwhelming desire to satisfy our users’
needs by
making steps associated with its use crystal clear). Recapitulating,
in the estimation arena for a variety of platforms involving navigation or target
tracking:
 | Can provide detailed rigorous technical analyses and supporting
rationale based on principles in mathematics, probability & statistics
(and stochastic or random processes), physics, and practical
engineering concerns; |
| Can provide system performance evaluations (via adequately detailed
Monte-Carlo computer simulations); |
| Can provide critical insights into current
status of the field (without hype); |
| Can provide new theoretical and technical developments in our
specialties (where we have already done so many times before in proving that
we have the necessary background and insight); |
| Can provide development and implementation of our own tested software
(conventional or embedded) in several alternative computer languages (please
click here for insights into our capabilities for embedded)  , or... |
| Can provide Independent Verification and Validation (IV&V) of software developed by
others (using our existing exhaustive repertoire of simple test problems
with analytically known and theoretically justified closed-form solutions
that should be the computed outcome of any new software under test) and cross-check the clarity of the
associated documentation supplied by the developers and veracity of the
developers’ supporting theoretical claims and associated supporting rationale. |
All of the above are in line with our prior experience (since 1971) in a
variety of defense areas including Submarine Inertial Navigation (and an
understanding and facility with the underlying navigation error models
constituting a psi-angle analysis of an Inertial Navigation System [INS], consisting of
accelerometers
and gyroscopes
in an integrated whole); Air Force Aircraft Navigation and Radio Multi-lateration Relative Navigation
(JTIDS RelNav) and communication (JTIDS/MUFBARS/ICNIA);
Sonobuoy DIFAR/LOFAR target tracking; Search and Screening; (dielectric
AN/BRA-34) Antenna Radar
Cross-Section Detectability (and vulnerability to enemy jamming, spoofing, and
other interference); NavSat (now defunct), LORAN-C
(now defunct but due to return as eLORAN to strengthen against enemy spoofing of
GPS/GNSS), Bathymetry
(i.e., bottom sounding sonar map-matching using acoustic sensors in the Janus
configuration [i.e., 2 pointing forwards and 2 pointing backwards]) and GPS analysis and usage on Submarines; and GPS analysis and
usage in test aircraft (along with test plans and procedures for most of the
above); and Early Warning Radar Target tracking considerations relating to the
target tracking filters and estimation concerns (and the underlying mathematical
models of all of the above and more). We are cognizant and capable
in many other analytic areas (e.g., Reliability/Availability) as a consequence of our existing proficiency
in Failure detection and in
mathematics, physics, systems engineering, and software development involving
challenging mathematics-based algorithms; especially regarding distributed or
decentralized parallelization of such algorithms and in data fusion using
either a single Kalman filter or decentralized Kalman filters, while being wary and observant
of existing application constraints.
Go to Top Go to Primary Table of Contents
TeK Associates (registered by that name in Lexington, Massachusetts, USA
back in 1992)
has absolutely NO affiliation with other companies
with similar names that have subsequently sprouted up, such as:
|
· A-Tek Associates
|
· M-TeK Associates
|
· T E K Associates in
Oxford, UK
|
· V-TEK Associates
|
|
· B-Tek Associates
|
· S-TEK Associates
|
· Tek Search Associates
|
· Q-Tek Associates
|
|
· C-TEK Associates
|
· H-TeK Associates
|
· STAR TEK Associates
|
· W-TeK Associates
|
|
· Hybrid-Tek Associates
|
· TeK Associates, Ltd.
|
· L-Tek Associates
|
· TEK Associates, L.L.C.
|
|
· Arpan Tek Associates
|
· KRAF Tek Associates
|
· Hi-Tek Associates
|
· TEK Associates, Inc.
|
|
|
· TEK Associates
|
|
|
We suppose that “imitation (as has evidently occurred above) is the sincerest form
of flattery”. However, it
is our company that has performed the milestone research, has the results, and
accompanying peer-reviewed open literature publications reporting (some of) our
results.
Go to Top Go to
Primary Table of Contents
Profile of Critical Company Personnel:
Thomas H. Kerr III, the founder and CEO of TeK
Associates since 1992
(until June, 2022), was born in Washington, DC. He received the B.S.E.E.
in electronics (magna cum laude) from Howard University in 1967 and
the M.S. and Ph.D. degrees (via a National Science Foundation traineeship) in
the electrical engineering specialty of control and estimation from the University
of Iowa, Iowa City, IA in 1969 and 1971, respectively.
Click here to view his Entrepreneurial Elevator Speech.Click
here too! [Thomas H. Kerr III is NO LONGER open
or available to outside requests and assignments (except for those
officially and explicitly sanctioned by his current employer, Zivaro, Inc.).]
  
Greek: “αρετή” Icelandic: “Fyrsta
flokks. Af alefli.” “Hann
er sinn eigin herra.” German: “Ich
mache viele Uberstunden.” Please
click on the above picture for more.
Dr. Thomas H. Kerr III’s practical industrial experience since 1971, as a mathematically-oriented R&D Algorithm Specialist, Systems
Engineer, and Software Developer, has encompassed various Kalman filter theoretical evolutionary
developments for DoD applications in submarine and aircraft Inertial Navigation
Systems (INS), in Global Position Satellite System (GPS) receiver
characterization and validation and in the incorporation of GPS receiver data (in weak,
medium, and strong configurations) within an Inertial Navigation
System (INS), in Lamps Difar Sonar/Sonobuoy target tracking, in
Joint Tactical Information Distribution System (JTIDS) Relative
Navigation (RelNav), in Integrated Communication, Navigation, and
Identification for Avionics (ICNIA) [a combination of almost the exact
same radio systems, as a precedent twenty five years earlier for the Advanced
Tactical Fighter (ATF) F-22 Raptor, as was subsequently pursued by JTRS],
and in radar target tracking for strategic reentry vehicles versus decoys [e.g.,
Strategic Defense Initiative (SDI), National Missile Defense/Upgraded Early
Warning Radar (NMD/UEWR)], and support software issues for implementing promising
algorithms-with particular emphasis by TeK Associates on novel state variable model-based
Kalman filter (KF) applications. He also worked on critiquing the Honeywell Electro-Optical
Missile Warning System (MWS) for helicopters and on critiquing an early (Magnavox)
version of PINS navigation for Minesweepers while serving on a team representing
U.S. Government interests. He has
an awareness of current target “observables”, countermeasures,
counter-countermeasures (e.g., Old Crow-related), sweeprate exposure to
enemy surveillance, pattern recognition classification procedures, Neural
Network (NN) limitations [some that he has not yet sufficiently publicized,
other than here NOW, regarding
warnings about improper use of feed-forward
control since some people actually argue that feed-forward control laws
(nowadays, frequently availed through use of a NN) were the same as or equivalent to
use of feedback control laws! Historically, the class of feed-forward controls is a much smaller subset of controls than those adaptive ones
offered or availed via a more conventional feedback implementation (involving negative feedback and/or positive
feedback https://www.electronics-tutorials.ws/systems/feedback-systems.html),
as recognized by others more
than 45 years ago [as discussed by W. M. Wonham, "Random Differential Equations in Control Theory," a chapter within Vol. 2 of the three volume set: Probabilistic Methods in Applied Mathematics, Vol. I (1968), Vol. 2 (1970), Vol. 3 (1973) by A. T.
Bharucha-Reid (ed.). https://ntrs.nasa.gov/search.jsp?R=19700065159] before there was any financially motivated “axe to grid” and before the
subsequent and consequential application “stakes were so high” regarding
possible use of NN's in control applications. Feedback laws arose much
earlier and properly accommodate “aging” of components and the associated “changes
in parameter values” that subsequently occurred without needing to make any
other accommodations other than, perhaps, ocassionally slightly changing the scalar gain constant “K”].
He was involved in Security aspects of
World Wide Military
Command and Control System (WWMCCS) during its epoch
as a WWMCCS Improvement
System (WIS). [WWMCCS was decommissioned in 1996 and
replaced by Global
Command and Control System.] For WIS, he was involved only in the
multi-level Computer Security aspects and some vulnerability precedents of a networked distributed system,
some hardware triaxial cable issues, some fiber-optic vulnerability issues, and
use of encryption versus check-sum issues. He possesses expertise in the following
Research and Development (R&D) areas:
| Decentralized
or Distributed (or as sometimes referred to as parallel) Kalman filters. |
| Various
novel approximate approaches for handling nonlinear filtering by being alert
to possible improvements to supplant, replace, or augment Extended Kalman
Filters or Iterated Extended Kalman Filters,
such as (please excuse the somewhat critical view point that I
initially convey below as I get my “licks in”
[after waiting for ~20 years by intentionally delaying my critical responses
until
early 2019 so that I could not be accused of interfering with or attempting to block any potentially competitive algorithm developments
or its subsequent evolution after encountering
normal, likely
temporary roadblocks to later be circumvented]). My criticisms being conveyed here
now for the specialists are both from my own past experience and that of others, as identified.
My tone will be more mellow further below (beyond this color)
at the end of this critique of the 3 different current and prevalent alternative estimation approaches,
as I later also discuss
Fred Daum’s very nice and clear tutorial and summary of
these same 3 competitive
alternative estimation algorithms within his own overview “status-of-the-field” discussion that is
generally accessible to all,
including the non-specialists. While I have the highest regard for Fredrick E. Daum and his
accomplishments, I don't always agree entirely with everything. My own criticisms precede Daum’s
discussion below (but Daum’s comments are not
criticisms) while mine are definitely criticisms and follow next: |
-Particle Filtering
(PF)-(only if they live up to their hype
[which has not completely happened yet]) with careful assessment of their associated respective
computational burdens. (PF provides very good tracking
accuracy but can seldom be computed in real-time! Moreover, PF is not needed in
situations where good mathematical models already exist for the system dynamics [such as
objects acted upon solely by central forces, as with gravitational forces] and
the process or plant noise is merely a minor consideration [especially when it
is absent entirely, as is the case with radar tracking of RV’s in the midcourse phase
(where the RV’s are to be kinetically intercepted) and
for tracking all satellites, in general]. The strong suggestion that
“particle filters should only be used for difficult
nonlinear/non-Gaussian problems, when conventional methods fail” is
made within the Epilogue on page 287, next to the last sentence of the 1st paragraph of the book:
Ristic, Branko, Arulampalam, Sanjeev, Gordon,
Neil, Beyond the Kalman Filter: particle filters for tracking applications,
Artech House, Boston, 2004. (Moreover, pp. 271-283 in Section 12.5.2 discuss Rao-Blackwellized Particle Filters
(for additional speeding up of the computations) as well
and also discusses this topic further on page 287. Much benefit had already accrued by 2016 in use of
Rao-Blackwellized Particle Filters.) Many researchers, like
me, are somewhat suspicious when claims are made by other researchers
that they used a Particle
Filter for a particular application, when adequate linear Kalman Filters had been
successfully used for that same particular INS/GPS airborne application for
decades (prior to now being applied to an airborne drone, as recently claimed for a PF
used by MIT/Draper
Laboratory). I liked the older approach using conventional Kalman Filters for
airborne INS/GPS and even jointly with JTIDS, as discussed in GPS/JTIDS/INS Integration Study-Final Report, Vol. II of IV, Details, Technical Report
R-1151, C.S. Draper Laboratory, Inc., Cambridge, MA, Oct. 1977 to June
1978.
Since most recent so-called
ground-breaking results for PF’s claim
“orders-of-magnitude” improvements over prior
original PF implementation/ formulation, which itself increase exponentially in complexity
with dimension; so a several “orders-of-magnitude” improvement/reduction still leaves a net exponentially increasing
computational burden overall.
Richard Bellman
identified a “Curse-of-Dimensionally” relating to the computational burden
of his Dynamic Programming (DP) algorithm (a.k.a., a Viterbi algorithm
equivalent), but Bellman’s Dynamic Programming came first in 1953 Rand Report: http://www.dtic.mil/dtic/tr/fulltext/u2/074903.pdf
) and “Curse-of-Dimensionally” was not claimed back then for Particle Filtering per se since Particle
Filtering did not yet exist. Robert E. Larson (when he was a VP at Systems Control
Inc. in
Palo Alto, CA) published his approximate simplifications, in IFAC Automatica
circa 1976, that Larson invoked for taming the Dynamic Programming CPU burden in order that its
implementation would be tractable for practical applications. [R. E. Larson, A.
J. Korsak, "A dynamic programming successive approximations technique with convergence proofs," Automatica (Journal of IFAC), Vol. 6, No. 2,
pp 245-252, Mar. 1970 (https://doi.org/10.1016/0005-1098(70)90095-6).
Principles of Dynamic Programming (Part 1 Basic Analytic and Computational
Methods), by Robert E. Larson and John L. Casti, Marcel Dekker Inc., 1978; A Review of:
“Principles of Dynamic Programming, Part II, Advanced Theory and
Applications,” by Robert E. Larson and John L. Casti, Marcel Dekker Inc., 1982]. Since it was an
algorithm that differed considerably from that of Particle Filters in structure,
the same simplifications do not directly apply nor carry over and other simplifications for PF
were needed, as sought by others within the last 20 years. That distinction was not originally clarified by those who
were pursuing use of Particle Filters and sought to reduce the “Curse-of-Dimensionally”
but needed to do so in different ways since the precedents used in reducing the
computational burden for DP don’t strictly apply for PF’s.
When
process noise is present (as well as the usual sensor measurement noise), because of the “Central Limit Theorem” and especially
the “Central Limit Theorem (with weakened hypothesis but similar strong
conclusion)”, the corrupting noises are
usually Gaussian in general, and consequently don't require anything special
beyond an EKF for successful tracking. The methodology for determining what
measurements are needed, as availed from the full rank condition being satisfied
from an associated “Observability” analyses or the weaker “Detectability”
analysis routinely associated with KF (J. J. Deyst Jr., and C. F. Price, "Conditions for Asymptotic Stability of the
Discrete(-time), Minimum Variance, Linear Estimator," IEEE Trans. on Automatic Control, Vol. 13, No. 6, pp. 702-705, Dec.
1968 and J. J. Deyst , “Correction to 'conditions for the asymptotic stability of the discrete minimum-variance linear estimator',”
IEEE Trans. on Automatic Control , Vol. 18, No. 5, pp. 562-563,
Oct. 1973.)
and (somewhat by virtue of approximations but,
recently, now exactly for some special case EKF's using stochastic Lyapunov
functions) for EKF, apparently don’t exist
for PF since there is no system model specified beforehand for a PF for which
these conditions could be tested for compliance. Similarly, full rank conditions
for “Controllability” or the weaker “Stabilizibility” also cannot be tested
for compliance since there is no system model specified beforehand for a PF to be
used in such a test.) Without such conditions being satisfied, how can analyzers
and implementers be assured of the “stability” of a PF filter estimator to
be assured that it is not “diverging” from the “true state”. I have
appealed here to the very familiar ample framework that has existed for 4+
decades pertaining to use of available “Lyapunov functions” to demonstrate
stability of KF’s (even if the underlying system is unstable, the KF estimator
will still appropriately track it well) and approximately, through linearization, for EKF’s (and now exactly for some particular special case EKF’s
using “stochastic Lyapunov functions”), where such a useful framework apparently
does not yet exist for PF’s.
Unlike the
benign situation for a purely linear Kalman filter (KF) that allows use of a so-designated
separate “Covariance Analysis” (without any
system sensor measurements needing to be specified or collected nor any explicit KF estimates
needing to be specified or calculated) to set system “Error
Budgets” beforehand that serve as “specifications” on the actual hardware
to be implemented later along with the software algorithms under consideration
now so
that system accuracy goals may be met [as
discussed on pp. 260-266, Sec. 7.4 of Gelb, Arthur (ed.), Applied Optimal
Estimation, MIT Press, Cambridge, MA, 1974 and a view also confirmed in Maybeck,
P. S., Stochastic Models, Estimation and Control, Vol. 1, Academic Press, NY,
1979], the PF has no such capability since PF Covariances are
not available in that same way without PF estimates being simultaneously
calculated. However, for EKF’s,
the situation is similar to that for a PF since a linearization about an EKF estimate is
usually needed at each time step in order to calculate the approximate covariances to be used in a “Covariance Analysis” for an EKF
in order that an approximate “Error Budget” can be
obtained.
When having “real-time”
estimates is not an issue or constraint on the utility of estimator usefulness,
such as in some Data Analytics situations where underlying “financial models” may be completely unknown
and have a significant psychological component (sometimes related to seasons) and yet to be deciphered,
a PF may be the best approach to use since there is plenty of data and, perhaps, less of a pressing need to obtain the estimation results in real-time (at lest not initially when attempting to
reveal "cause and effect" for the first time in order to gain a better understanding of underlying relationships
that exist and actually explain underlying relationships that dictate what is going on).
Recall that Kalman smoothers (nowadays referred to as a Kalman “retrodiction”)
are of
three different forms: (1) “fixed interval” smoothing, (2) “single point (in time)”
smoothing, or (3) “fixed-lag” smoothing are also NOT “real-time”
algorithms but useful nonetheless such as in closely evaluating missile behavior
at the particular event time when a later stage ignites and separates for a multistage
rocket.
Sometimes a KF smoother is implemented using two Kalman filters, one running “forwards”
in time and the other running “backwards” in time (where initial conditions
for the first and final conditions for the second are made to corroborate
correctly (see “Backwards Markov Models” by Prof. George Verghese
[MIT], who obtained his Ph.D. at Stanford
University on this topic under Prof. Thomas Kailath, but the aggregate of these two
KF's being a smoothing solution that is still NOT real-time). As with PF's, the Kalman filter
has also been historically derived by James S. Meditch (Boeing) [Meditch,
J. S., Stochastic Optimal Linear Estimation and Control, McGraw-Hill, New
York, 1969] and A. V. Balakrishnan, Kalman Filtering Theory, Optimization Software, Inc., Publications Division, NY,
1987 using Bayesian arguments similar to those used
throughout for PF’s, as well as yielding the exact same KF form as independently derived and shown to simultaneously satisfy other
important optimality criteria, as discussed immediately below:
Paralleling #6 above:
My original Derivation of the Discrete-time Kalman filter using the Matrix Maximum Principle
(I followed what Prof. Michael Athans [MIT] and Edison Tse did for the continuous-time case in 1967).
(The
image inserted above [and its references cited therein] is a screen shot from TeK
Associates’ TK-MIP software product. Another missing detail is Ref. 29 Mendel, J. M., Lessons in Estimation Theory for Signal Processing,
Communication, and Control, Prentice-Hall PTR, Englewood Cliffs, NJ, 1996.)
IMPORTANT:
Use of Baysian statistical analysis is not a new tool for estimation applications developed specifically for handling derivations and implementation of Particle
Filters (PF). Bayesian statistics have been used for such estimation applications for over 50+ years.
The other new estimation candidates
discussed herein evidently do NOT satisfy any of the first 4 optimality properties (depicted in the above image) except if/when
they degenerate into a Kalman filter as an extreme case when system dynamics' description and measurement sensor observation description is exclusively linear and plant and measurement noises are
only additive and Gaussian and the initial conditions are properly from
a Gaussian distribution, independent of both the Gaussian plant and measurement
noises.
-with hopes for benefits to PF in
parallelization (multi-threaded parallel processing and/or embedded); I
continue to follow recent developments in use of Particle Filters but also
continue to have concerns about their failing to be real-time (except when they degenerate & essentially collapse into
being merely EKF’s or
KF’s [even if they are not explicitly acknowledged as being so]); I also noticed an incompatibility in current hopes for future parallel implementation of a Particle Filter as a further inherent barrier to PF ever being real-time: approaches currently being pursued to accomplish parallel implementation of pseudo-random number generators & maximizing the cycle before they repeat are based on
use of Linear Congruential Generator (LCG) algorithmic structures & Mersenne primes to generate variates from a uniform distribution before converting to
Gaussian, as needed for
PF’s to utilize within numerous
“mini-simulation” trials (that invoke use of a RNG within them) before each
“measurement incorporation” step, being a huge CPU burden, somewhat ameliorated by performing sophisticated variants of the
“Metropolis-Hastings-Gibbs” sampling/re-sampling. Donald Knuth only showed what tests LCG passes in
The Art of Computer Programming, Vol. 2, Addison-Wesley, 1969.
The late George Marsaglia (of Boeing)
(https://en.wikipedia.org/wiki/George_Marsaglia)
has warned for 30+ years that LCG yields variates that
“lie in planes”, a weakness that has been verified by Profs. Persi
Diaconis (Stanford Univ.), P. L’Ecuyer (Univ. of
Montreal, Quebec, Canada), and many
other current researchers in this area. Even if LCG were perfectly random (which it is not), by attempting a parallel implementation of it risks
inadvertent early repetition by a 2nd , 3rd, or 4th LCG, etc. of being somewhere within the
same sequence already
initiated by an earlier LCG invocation, thus preventing the maximum cycle length from being attained for the
following three integer parameters of the computer register: (a, b,
and T) involved
in the hardware implementation of an LCG [rigor regarding the proper selection
of the above mentioned parameters, (a, b,
and T), is provided near the bottom of the NEXT
screen that pops up after the USER clicks the navigation button at the TOP of
this screen labeled “TK-MIP for the PC”], before premature repetition of the series that
is sought to be generated. This is the same reason why, as observed in the rigorous simulations of the
1970’s and 1980’s, only one LCG should be invoked (but repeatedly) in the implementation of LCG for a standard serial von Neumann machine.
My long standing real-time PF concerns (stated above) are now somewhat mitigated in 2018:
https://www.linkedin.com/pulse/new-quantum-method-generates-really-random-numbers-alvin-lieberman-/
(This link is accessible only from LinkedIn by registered
LinkedIn users.) However, even this
last hypothesized potential path offered from the link immediately above
apparently does not yet exist as hardware (even though IBM [which
claims to have achieved a working quantum computer in early January 2019], Google, some
universities, and several smaller companies are working on it, as identified on the link
just offered).
Prof. P. L’Ecuyer
(Univ. of Montreal, Quebec, Canada) has proprietary improvements to eventual generation of
Gaussian variates as his approach to a pseudo random number (prn) generator.
(According to him, he has
ostensibly provided these to The MathWorks and to other software developers
for a hefty fee.) The conclusion to date is that the older approaches to generating Gaussian variates
are not as good as the more recent
approaches mentioned here.
Apparently missing so far in PF considerations is any attention to the effect of less-than-ideal prn generation
of uniformly distributed variates leading to less-than-ideal Gaussian generation. Since the Bayesian-based derivation of the PF
strongly utilizes the properties of conditional probability density functions at several critical places, and, all the more, those of
Gaussians; it is highly likely that the departure from ideal Gaussianess in what is actually used in implementing a PF will have
a
significant adverse affect in that PF’s performance.
One could postulate a type of sensitivity analysis that should be performed for this
situation in order to quantitatively gauge the effect on the expected
consequential PF performance associated with one or the other of the two less-than-ideal
approximate approaches to be used in PF
implementation. A more recent alternative approach to PRN generation, that apparently offers a considerably longer cycle before repeating, is availed in
Pei-Chi Wu, "Multiplicative, Congruential Random-Number Generators with Multiplier
± 2K1 ± 2K2 and Modulus [2p-1]," ACM Trans. on Mathematical
Software, Vol. 23, No. 23, pp. 255-265, Jun. 1997.
--See M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online
nonlinear/non-Gaussian Bayesian tracking,”
IEEE Trans. Signal Processing, vol. 50, pp. 174–188, Feb. 2002. https://www.irisa.fr/aspi/legland/ensta/ref/arulampalam02a.pdf
--See R. van der Merwe and E. Wan, “Gaussian mixture sigma-point particle filters for sequential probabilistic inference in dynamic state-space models,” in
Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Hong Kong, 2003, pp. 701–704.
https://www.gatsby.ucl.ac.uk/~byron/nlds/merwe2003a.pdf
--See
S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman Hall/CRC press, Boca Raton, 2003.
[Use of a homotopy in conjunction with Particle Flow is an existing method for solving PDE's that predates Particle Filters (and people who utilize it in a PF context should have said so unless they are attempting to take credit for this too).
Since a homotopy used here is a scalar function of the independent variable and
must be a continuous monotonely increasing function, taking the logarithm of a homotopy is again a continuous monotonely increasing function and
so is again a homotopy. The actual choice of the homotopy to be used is "up for grabs" for greatest convenience. Daum always emphasizes that he is using a log-homotopy function. It seems that there is no real difference between what Daum uses and what was standard in historically handling solutions of
PDE's using a homotopy. Different investigators can use different
scalar functions that exhibit the characteristics of a homotopy for gaining
insights into the nature of the solutions of PDE's.]
--Also see http://ieeecss.org/CSM/library/2010/june10/11-HistoricalPerspectives.pdf
--Please
see the excellent discussion of how a PF was implemented for their
application: Yozevitch, R., Ben Moshe, B., “A Robust Shadow
Matching Algorithm for GNSS Positioning,” Navigation: Journal of the
Institute of Navigation (ION), Vol. 66, No. 2, pp. 95-109, Summer 2015 [Notice
that they did not say that their PF was real-time] and some of their
pertinent references: (1) Crow, F. C., Shadow Algorithms for Computer
Graphics, ACM SIGGRAPH Computer Graphics, Vol. 11, No. 2, pp.
242-248, 1977; (2) Bourdeau, A., Sahmoudi, M., and Tourneret, J. Y., “Constructive
Use of GNSS NLOS-MUltipath: Augmenting the Navigation Kalman Filter with a
3D Model of the Environment,” 15th International Conference on
Information Fusion (FUSION), pp. 2271-2276, IEEE, 2012; (3) Thrun, S.,
Burgard, W., and Fox, D., Probabilistic Robotics, MIT Press, 2005;
(4) Muralidharan, K. Khan, A. J., Misra, A., Balan, R. K., and Agarwal, S., “Barametric
Phone Sensors: More Hype than Hope!,” Proceedings of the 15th Workshop
on Mobile Computing Systems and Applications, ACM, 2014, 12; (5) DeBerg,
M., Van Kreveld, M., Overmars, M., and Schwarzkopf, O. C., Computational Geometry,
Springer, NY, 2000.
--Please
consider that “Observability”
and Controllability” yea/nay tests for linear systems with time-varying “System
matrix”, “Obsevation matrix”, and “System Noise Gain matrix” are presented in
Bucy, R. S., Joseph, P. D., Filtering for
Stochastic Processes with Applications in Guidance, 2nd Edition, Chealsa,
NY, 1984 (1st Edition Interscience, NY, 1968).
--A
long view reveals that: tractable techniques for
handling “fractional derivatives” for applications have been around for over
40+ years based on Cauchy’s
integral theorem as a representation for derivatives in a Complex
Variables context (where the order of the derivative is generalized using Cauchy’s
theorem to no longer
be restricted to being merely an integer) or by being based on a Fourier
integral. Much of
the theory and practical applications of “fractional derivatives” were worked out back then (40+ years
ago), as pioneered and published in SIAM by Prof. Tom Osler: https://csm.rowan.edu/departments/math/facultystaff/math_full_part/osler.html. Another
useful more recent source on this topic is: Kenneth S. Miller and
Bertram Ross, An Introduction to the Fractional Calculus and Fractional
Differential Equations, A Wiley Interscience Publication, John Wiley
& Sons, Inc., NY, 1993.
--Other
more mundane practical considerations: What will the practical
challenges be for documenting Particle Filters for DoD applications in
Principles of Operation (POP’s)
rationale’s and later
in B1’s, B2’s,amd
B3’s or in C1’s,
C2’s and C3’s
without a clear delineation of what the system dynamics matrices and sensor
observation matrices and Noise Covariance Matrices are beforehand, as had
been established as historical precedents in documentation for Kalman filter or for EKF
tracking applications? [By the early 1980’s,
the aforementioned documentation for DoD tracking, Kalman filtering,
and EKF applications had already standardized on conventions for state
variable notation that TASC (as also utilized/adherred to by Peter Maybeck [AFIT] in his 3 Volume textbooks,
respectively, in 1979, 1980, and
1981, on this subject) had adopted and popularized as system: d[x(t)]/dt
= F x(t) + B u(t) + w(t) and sensor measurements: z(t)
= H x(t) + v(t), and independent zero mean white noise covariance
matrices corresponding to w(t) and v(t)
above, respectively, being: Q(t), R(t),
and Kalman gain: K(t); the familiar TASC
discrete-time notational conventions were also adopted.] Appropriate DoD
documentation was indeed a challenge for Neural Network (NN) applications that still had to be trained to obtain the necessary weights
for “Perceptrons” and multi-layer NN’s. DoD documentation was also challenging
for “Fuzzy Neural Networks”. Who or what organization is going to perform the
necessary associated “IV&V” of PF documentation? I
wish them good luck!
--The
excellent and extremely readable book: Gelb, Arthur (ed.), Applied Optimal
Estimation, MIT Press, Cambridge, MA, 1974 had
a few errors (beyond mere typos); however, corrections are provided in Kerr, T. H., “Streamlining Measurement Iteration for EKF Target Tracking,”
IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 2,
Mar.1991 and in Kerr,
T. H., “Computational Techniques for the Matrix Pseudoinverse in Minimum
Variance Reduced-Order Filtering and Control,” in Control and Dynamic
Systems-Advances in Theory and Applications, Vol. XXVIII: Advances in
Algorithms and computational Techniques for Dynamic Control Systems,
Part 1 of 3, C. T. Leondes (Ed.), Academic Press, NY, 1988
(as my expose and illustrative and
constructive use of counterexamples).
--See Section 12 of:
Kerr, T. H., “Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic
Results,” Proceedings of
SPIE, Session 4473:
Tracking Small Targets, pp. 142-168, San Diego, 29 July-3 Aug. 2001
for some warnings and concerns regarding the
direct applicability of Yaakov Bar-Shalom and William Dale Blair
(Editors), Multitarget-Multisensor Tracking: Applications and Advances,
Vol. III, Artech House Inc., Boston, 2000 for the
challenging case of a system with nonlinear dynamics. While
Section 12 of the above just cited Kerr paper above was true in 2001, my 7
item comparison then between what was possible for KF’s
for explicitly linear systems and what was possible for EKF’s
and IMM’s for nonlinear systems now
needs modification in 2018, since now a few special case EKF’s can be
shown to be stable using a stochastic Lyapunov function, as in:
Jensen, Kenneth J.,
“Generalized Nonlinear Complementary Attitude Filter,”
AIAA Journal of Guidance, Control, and Dynamics, Vol. 34, No. 5, pp. 1588-1593 , Sept.-Oct.
2011. [Jensen achieves the big stability breakthrough by providing a proof of this particular EKF’s global stability
but now states that it possesses “almost” global asymptotic stability; however, the term “almost” is required terminology to keep probability theorists and purists happy with the wording of his
new claim. Author Jensen attains his new results by utilizing appropriate stochastic Lyapunov functions (proper handling of such
is due to Prof. Emeritus Harold J. Kushner, Brown Univ.). I don’t know whether Jensen was the first to achieve this new result? I am aware of at least two others who also did it.] Please forgive me as I use the following two images to
explain and clarify
the technical term “almost” that Jensen was obligated to invoke:
(The
two images inserted above [and its references cited therein] are screen shots from TeK
Associates’ TK-MIP software product.)
--I
am aware that Fred Daum, Jim Huang, and Mike Hough (Raytheon) have jointly
published a recent paper on the use of a PF for Strategic Early Warning
Radar tracking of Reentry Vehicle targets but I
have not yet seen it! I look forward to
viewing it soon. Maybe it will “calm my qualms” (but, perhaps, maybe not).
-The solving of Partial Differential Equations
(PDE’s) has been described by
practitioners and others as
an infinite-dimensional problem because of its numerical and computational
complexity. It is reasonably well
known that PDE’s
describe the time evolution that is needed to specify the associated
probability density function underlying continuous-time optimal estimation for both linear
and nonlinear systems. The important fundamental PDE describing this is
known as the Kolmogorov equation
(where there
is, in general, a forwards (in time) and a backwards (in
time) Kolmogorov equation that describe the
statistical estimation situation in continuous-time) and the former is also known as the
Fokker-Planck equation arising in optimal statistical estimation for both the case of the system being linear and the noises being Gaussian (which
is very tractable
since it degenerates and simplifies
nicely to the standard Kalman Filter) and the general nonlinear case (usually very intractable and computationally tedious for
all except the simplest of problems that, frequently, are neither realistic nor
practical for most applications). Both of these PDE’s (of Parabolic type) deal with the time evolution of probability density functions (pdf’s) or, equivalently, the associated information flow.
These are Non-Polynomial (NP) algorithms in general. Also see Pavel
B. Bochev, Max G. Gunzburger, Least-Squares Finite Element Methods, Applied
Mathematical Sciences, Vol. 166, Springer Science + Business Media, LLC, NY,
2009. There is a PDE textbook that was published within the last 15 years
that routinely invokes use of scalar “homotopy” (but NOT log-homotopy since use of mere homotopy is sufficient, and use of log-homotopy in ultimately obtaining "particle flow" to characterize solution of the PDE appears to be a minor wrinkle similar to working with log-likelihood ratios in favor of likelihood ratios), and, further, has beautiful color images of associated “particle flows”, as are reminded there to be standard tools and methodologies for handling solutions of
PDE’s. However, in general,
PDE’s can not be solved in real-time! Sometimes speeded-up videos
are shown to convey the trend of the solution process to an audience. However, within the following
paper: Daum, F. E., “Exact
finite-dimensional nonlinear filters,”
IEEE Transactions on Automatic Control, Vol. 31, No. 7, pp. 616-622,
Jul. 1986, a novel, insightful, and
creative method was developed for decomposing the solution of the important PDE,
described above, into two parts: the 1st part was a large
computational burden to be solved off-line beforehand and stored until
needed; the 2nd part is to be solved on-line in real-time. The two parts,
when put together, constituted a solution to the PDE described in the preceding
paragraph and yields the exact optimal estimator or optimal filter for the nonlinear case.
However, a constraint on the 2nd part that, thankfully, is absent from the 1st part is a need for the times at which the measurements arrive beforehand too!
That is
usually only the case for navigation applications with periodic updates such
as by Omega (now defunct), Loran-C (now defunct but maybe
coming back as eLORAN to help GPS
recognize and
compensate for GPS spoofing”), or GPS and/or GNSS satellites in an
unjammed benign environment; otherwise, the aforementioned navigation aid
(i.e., are not deterministic in the time
at which they occur and the exact time of an external position fix is not
known beforehand because of complicating factors such as atmospheric interference
(e.g., atmospheric scintillation for EWR) ; thus computational calculation of
the 1st part beforehand is somewhat stymied! Radar applications seldom involve radar sensor
measurements arriving at a strictly periodic rate that is known beforehand since
targets are in motion and sometimes the radar platform is too, consequently, the round trip time of the radar
pulse varies from transmitter to receiver even if the transmitter rate is
periodic at a constant Pulse Repetition Frequency (PRF).
Moreover, there is an historical precedent in the 1960’s and early
1970’s to
avoid pre-calculated KF gains, as performed by Dr. Hy Strell and Norm
Zabb (Sperry Systems
Management as SSBN navigation work for SP-2413) which found pre-calculated KF gains satisfactory for simulations and
“test of concept” for the Ships Inertial Navigation
System (SINS) utilizing a 7-state STAtistical Reset (STAR)
Kalman filter on a surface ship used strictly for testing but not
satisfactory for the real world application for SSBN’s at sea because the external
position fixes were seldom available exactly as pre-planned in attempting to synchronize
to the pre-computed filter gains. Admittedly, this example is from a different
application area entirely but it is more benign in general than that for radar
applications. When there are problems within the more benign linear situation of
navigation, the same problems will likely plague the slightly more challenging nonlinear
situation of radar for the same reasons! However, more recent Boeing results:
Schmidt, G. C., "Designing nonlinear filters based on Daum's theory," AIAA Journal of Guidance, Control, and Dynamics, Vol. 16, No. 2, pp. 371-376,
Mar.-Apr.
1993, apparently
offer a way around the limitation that I mentioned (see Schmidt's admission
in his conclusion section of having obtained "mixed results", both good and bad). [It
is, perhaps, worth mentioning in passing that there are two special cases of nonlinear
filters that have an optimal estimator that is finite dimensional and the
mean and variance are sufficient statistics, as in the purely linear system
and Gaussian noises case: that of Benes and this other result of Daum (and subsequently by many others but there were some earlier investigations that served as analytic stepping stones that aided in this quest:
--Brockett, R., Finite Dimensional Linear Systems, Wiley, NY, 1970.
--M. Fujisaki, G. Kallianpur, H. Kunita, "Stochastic Differential Equations of Non-linéar filtering,"
Osaka J. of Mathematics, Vol. 9, pp. 19-40, 1972.
--Y. Sunahara, A. Ohsumi, K. Terashima, H. Akashi, and Y. Takeuchi, "On Lie Algebraic Solution of a Class of Vector Stochastic Differential Equations and its Application to Stability Analysis,"
10th JAACE Symposium on Stochastic Systems, Koyoto, pp. 17-20, 28-30 Nov.
1978.
--R. W. Brockett, "Remarks on Finite Dimensionai Non-linear Estimation,"
Asterisque, 1980 (Bordeaux 1978).
--Stephen I. Marcus and Alan S. Willsky, Algebraic Structure and Finite Dimensional Nonlinear Estimation,
SIAM J. MATH. ANAL., Vol. 9, No.2, pp. 312-327, April 1978. http://ssg.mit.edu/group/willsky/publ_pdfs/20_pub_SIAM.pdf
--Y.
Sunahara, A. Ohsumi, K. Terashima, H. Akashi, "Representation of Solutions and Stability of Linear Differential Equations with Random Coefficients via Lie Algebraic Theory,"
11th JAACE Symposium on Stochastic Systems, Koyoto, pp. 45-48, 27-29 Nov. 1979.
--Chikte, S. D., "Bilinear Systems with Nilpotent Lie Algebras: Least Squares Filtering,"
IEEE Trans. On Automatic Control, Vol. 25, No. 6, pp. 948-953, 1979.
https://apps.dtic.mil/dtic/tr/fulltext/u2/a062094.pdf
--R. W. Brockett and
J. M. C. Clark, "On the Geometry of the Conditional Density Equation," in
Analysis and Optimization of Stochastic Systems (eds. O. L. R. Jacobs et
al.), Acad. Press, 1980.
--Daum, F. E., "New Exact Nonlinear Filters,"
Bayesian Analysis of Time Series and Dynamic Models (edited by J. C. Spall), Chapt. 8, Marcel Dekker, New York, 1988.
--D.
Ocone, Topics in Nonlinear Filtering Theory, M.I.T. Ph.D. thesis, June 1980.
--S. Marcus, S. K. Mitter and D. Ocone, "Finite Dimensionai Non-linear Estimation in Continuous and Discrete Time," in
Analysis and Optimization of Stochastic Systems (eds. O.L.R. Jacobs et
al.), Acad. Press, 1980.
--V. E. Benes, "Exact Finite Dimensionai Filters for Certain Diffusions with Non-linear Drift,"
Stochastics, Vol. 5, pp. 65-92, 1981.
--Sanjoy K. Mitter, "Existence and Non-existence of Finite Dimensional Filters,"
publication date: indecipherable, but, perhaps,
1982; for reason for this ambiguity, please see last page, where the author doesn't explicitly state what the publication date is:
http://web.mit.edu/~mitter/www/publications/33_exist_nonexist_FSI.pdf
--S. K. Mitter, "On the Analogy between Mathematical Problems of Nonlinear Filtering and Quantum Physics,"
Ricerche di Automatica, Vol. 10, pp. 163-216, 1980.
--M. Hazewinkel and
S. I. Marcus, "On Lie Algebras and Finite Dimensional Filtering,"
Stochastics, Vol. 7, pp. 29-62, 1982.
--Daum, F. E., "Comments on 'Finite Dimensional Filters with Nonlinear Drift',"
IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 2, pp. 689-691, Apr. 1998.
--Yau, S.S.-T., and Yau, S. T., "Addendum to 'Finite Dimensional Filters with Nonlinear Drift': A Response to F. E. Daum's Comments,"
IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No. 2, pp. 691-692, Apr. 1998.),
but there are no realistic applications yet to which these results apply, as structurally revealed by MIT's Sanjoy K. Mitter within:
http://web.mit.edu/~mitter/www/publications/33_exist_nonexist_FSI.pdf
[Please notice that
neither navigation applications nor target tracking applications exhibit this
structure. Prof. Roger Brocket (Harvard
Univ.) had utilized
Lie algebras and associated
Lie Bracket when he handled
bilinear systems in the
late 1960's and early 1970's, as did Willsky and Ho, discussed further down here]. However, they are
all still useful for the valuable insights that they provide, possibly as test problems for performing IV&V of new software by cross-checking outputs against known closed-form output solutions beforehand
for confirmation prior to inserting the final models of the actual ultimate intended application.
-Unscented Kalman Filter [also known as
(a.k.a.),
the Oxford Filter, a.k.a. the Sigma-Point Filter]:
Our
historical apprehension regarding the Unscented Kalman Filter (UKF) is because
of the presence
of an unexplained factor (or unconstrained free real scalar parameter [not
necessarily an integer], possibly positive, negative, or time-varying, at the whim of the
analyst/implementer) that can serve as an expanding or contracting “twiddle factor” in the denominator of the gain expression that is consequentially inherited by the covariance
equations; which, for linear systems, still appropriately computes the exact
covariance associated with any approximate Gain that is used in an
accompanying estimation filter (even if it is not the optimal
“Kalman Gain”), as clearly explained on
page 234 in Eq. 5.4.18 and further emphasized
in the last sentence following Eq. 5.4.22 in: Brown, Robert Grover, Hwang, Patrick Y. C., Introduction to Random Signals and Applied Kalman
Filtering, 2nd Edition, John Wiley & Sons, Inc., New York, 1983.
The numerical comparison in Julier, S. J., Uhlmann, J. K., and
Durrant-Whyte, H. F., “A New Method for the Nonlinear Transformation of Means and Covariances in Filters and
Estimators,” IEEE Trans. on Automatic Control, Vol. 45, No. 8, pp. 477-482, May
2000 of UKF vs. EKF performance appears to be somewhat contrived since
actual EKF practitioners would either take more frequent measurement fixes
to supplement tracking the object’s trend and/or better pose the target model
in the first place to take into account its known anticipated planar motion about a circular track
of constant radius about the origin by merely posing the problem in
(rho,theta) polar coordinates [with known constant angular velocity] as the two states of interest,
or if the constant angular velocity is unknown beforehand, then including this
unknown parameter as an additional state to be estimated using parameter
identification techniques or by using an approach that came later:
Souris, G. M., Chen, G., Wang, J., “Tracking an Incoming Ballistic Missile Using an Extended Interval Kalman
Filter,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1, pp. 232-240, Jan.
1997, but Julier, S. J., Uhlmann, J. K., and
Durrant-Whyte, H. F. do
invoke conditions that are impossible to check beforehand e.g., [Julier, S.
J. et al, op.
cit., Eq. 2] since probability measure for x(k) is unknown); unconventional use of calculated covariance to account for nonlinear
measurement equation and associated unconventional assumption of mean being zero and
an unconventional proposed
handling if mean is not zero (by their saying “it can be
shifted”, but mean is in fact unknown so one can not know beforehand how much it should be shifted by, so
USER is thus stymied in trying to proceed
as they recommend [Julier, S. J. et al, op. cit., Sec. 4];
UKF also utilizes “mini-simulation” trials before each measurement incorporation step (but not as many as a PF would require).
From Unscented Kalman Filter discussion in Wikapedia: "The Unscented Kalman Filter (UKF) uses a deterministic sampling technique known as the unscented transformation (UT) to pick a minimal set of sample points (called sigma points) around the mean. ... For certain systems, the resulting UKF more accurately estimates the true mean and covariance."
To me, this is reminiscent of what Emeritus Prof. Ronald L. Klein (UWV)
had published
http://www.tekassociates.biz/serv04.htm#almosttop
in many articles on Estimation Theory using Gaussian Quadrature (i.e.,
integration) and other quadrature formulas [in order to improve the accuracy of the "Propagate Step" integration
(over the candidate time interval) of the system dynamics within an
EKF]. Recall that Gaussian quadrature does not use equispaced time steps for evaluating constituent pieces but requires that thae constituent pieces be evaluated at specially designated points (and weights) as provided in Sec. 25 of Abramowitz and Stegun’s 1964 book, Handbook of Mathematical Functions, National Bureau of Standards [now National Institute of Standards and Technology (NIST)], Washington, D.C.
The
above mentioned “Global Lipschitz condition” is much stronger in
contrast to the mere “continuity condition” of the system dynamics being a
sufficient condition on the nonlinear system dynamics for a deterministic
nonlinear differential equation to have a solution. For uniqueness of the
solution of the latter, only a “local Lipschitz condition” need be
satisfied. The need for a global Lipschitz condition is discussed in Bucy, R. S., Joseph, P. D., Filtering for
Stochastic Processes with Applications in Guidance, 2nd Edition, Chealsa,
NY, 1984 (1st Edition Interscience, NY, 1968) (and is also discussed in: Kerr, T. H., “Applying Stochastic Integral Equations to Solve a Particular Stochastic Modeling
Problem,” Ph.D. Thesis in the Department of Electrical Engineering, University of Iowa, Iowa City, Iowa, January
1971, where a
detailed proof is provided on pp. 188-213 utilizing Ito integrals for stochastic
integrands).
--R. F. Curtain
and, A. J. Pritchard, Infinite
Dimensional Linear Systems Theory, Springer, NY, 1978. (i.e.,
Systems described by Partial Differential Equations [ODE's] are infinite
dimensional systems.)
So
the numerical comparison between Julier, S. J., Uhlmann, J. K., and
Durrant-Whyte, H. F., “A New Method for the Nonlinear Transformation of Means and Covariances in Filters and
Estimators,” IEEE Trans. on Automatic Control, Vol. 45, No. 8, pp. 477-482, May
2000 is less of how well the UKF filter performed (as they
claimed) but more about how bad an EKF can perform if it uses an
inappropriate or bad model for the system. This should be NO
surprise! A more
appropriate posing of the estimation problem on a circle [SO(2)] is: Li, J. T.-H. Lo and A. S.
Willsky, “Estimation for Rotational Processes with One Degree of Freedom-Part 1,”
IEEE Trans. on Automatic Control, Vol. 20, No. 1, pp. 10-21, Feb.
1975. 5_pub_IEEE.pdf
Some space is allotted here now for
some views of others that are pro-use of Unscented Filter or Sigma-Point
Filters and even Particle Filters in specific applications:
-Sigma-Point Filtering for Integrated GPS and Inertial Navigation:
http://www.acsu.buffalo.edu/~johnc/gpsins_gnc05.pdf
-Sigma-Point Filters in Robotic Applications:
http://file.scirp.org/pdf/ICA_2015073115554557.pdf
-Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor-Fusion - Applications to Integrated Navigation:
https://pdfs.semanticscholar.org/18b6/1ef4351db50520df9173337aff1458fcd031.pdf
-Robot Mapping Unscented Kalman Filter:
http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/slam05-ukf.pdf
We are aware of the following Lockheed Martin Space Systems Company results and its references: Nima Moshtagh and Moses W. Chan,
"Multisensor Fusion Using Homotopy Particle Filter,"
Proceedings of 18th International Conference on Information Fusion, Washington, DC, pp. 1641-1648, 6-9 July, 2015.
As informative as this was (with a nice derivation of
how to use log-homotopy), it still ignored saying anything about the size of the computer burden incurred with respect to being able to calculate anything along these lines in
real-time. What else is new? They also use the trick of target motion in a circular track without
expressing it in offset polar coordinates, as was also absent with an early Unscented Filter versus Kalman Filter example, as already discussed above.
Also see references in Maciej Janowicz, Joanna Kaleta, Filip Krzy˙zewski, Marian Rusek, and Arkadiusz Orlowski, "Homotopy Analysis Method for Stochastic Differential Equations with Maxima,"
International Workshop on Computer Algebra in Scientific Computing, pp. 233-244, CASC 2015.
-Also see: plethora of references in Hariharan, G., "A homotopy analysis method for the nonlinear partial differential equations arising in engineering,"
International Journal for Computational Methods in Engineering Science and
Mechanics, Vol. 18, No. 2, 2017.
-Please
see: Daum, F. E., “Nonlinear filters: beyond the Kalman filter,” IEEE
AandE Magazine, Vol. 20, No. 8, pp. 57-69, Sept. 2005 for
an excellent, clear discussion of the three estimation algorithms that I
have just critiqued above. My only complaint here is that Daum seems to have
overlooked or missed the earlier Lie Algebra results of : Li, J. T.-H. Lo and A. S.
Willsky, “Estimation for Rotational Processes with One Degree of Freedom-Part 1,”
IEEE Trans. on Automatic Control, Vol. 20, No. 1, pp. 10-21, Feb.
1975 as a precedent.
[Willsky and Lo explicitly handle estimation on a circle, SO(2),
rather than estimation on a sphere, SO(3), as NASA’s
F. Landis Markley, et al deal with
in
their extensive NASA survey and comparison between approaches and techniques.
However, Willsky and Lo are particularly lucid in their development and
exposition and, moreover, within the last sentence of their conclusion, provide specifics of
their
suggested generalization to estimation results on arbitrary
Abelian Lie groups, such as SO(3).] 5_pub_IEEE.pdf Also
see: Lo, J. T.-H. and Willsky, A. S., “Stochastic Control of Rotational Processes with One Degree of
Freedom,” SIAM Journal on Control, Vol. 13, No. 4, 886ff, July 1975. Another
aspect that Daum may have, perhaps, overlooked is the strong applicability of Lie Algebras
well beyond mere separation-of-variables for PDE’s or ODE’s, as in: Wu, Y.,
Hu, X., Hu, D., Li, T., and Liam, J., “Strapdown Inertial Navigation System Algorithms Based on Dual
Quaternions,”
IEEE Trans. on Aerospace and Electronic Systems, Vol. 41, No. 1, pp. 110-132, Jan.
2005 and Savage, P. G., “A Unified Mathematical Framework for Strapdown Algorithm Design,”
AIAA Journal of Guidance, Control, and Dynamics, Vol. 29, No. 2, pp. 237-249, March-April 2006
and Bernard Friedland, “Analysis of Strapdown Navigation Using
Quaternions,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 14 , No. 5, pp. 764-768, Sept. 1978
and Bell, D. J., “Manifolds and Lie Algebras,” in Mathematics of
Linear and Nonlinear Systems: for Engineers and Applied Scientists,
Clarendon Press, Oxford, UK, 1990.
Warning
again:
Precedents in use of “speeded up videos” to depict computational solution of PDE's
have occurred frequently in the past so that the solutions “appear” to be proceeding in real-time (even though
that is NOT the case)!
About 35+ years ago, there were claims
from others that one was now able to computationally solve the Navier–Stokes equations (PDE's) in real-time for flow around an aircraft wing! What happened to this braggadocious claim? Seems as though it was not true either!
My immediately posted retort (in the middle
of the night) to a Vice
President of a Fortune 500 Defense firm [who had just claimed, in a public post on
Linkedin,
that their firm provided excellent tracking, as computed in
“almost
real-time”!] was that
his admitting that such information was being computed by
them in “almost real-time” is tantamount to
“almost” avoiding a collision
(for FAA/ARINC navigation applications) and “almost” intercepting the
designated threatening enemy target (for DoD applications)! My point being that navigation information and target tracking results
are needed in “real-time” and,
to date, are only available for exact Kalman filter constructs (for the linear case with
Gaussian noises or, at worse, noises from an Exponential family of
distributions, where marginal and/or conditional distributions are still Gaussians) and
also available for Extended
Kalman
Filter
(EKF)
constructs as well (as an approximate estimator
for the
nonlinear case).
The VP immediately retracted it before it could be viewed by a larger audience and
was thus able to save face. (I actually did him a favor by my responding in this
manner "for his trial run in the middle of the night" before anybody else saw it.)
For both navigation applications and target tracking applications, there are always specifications indicating the frequency of computed output estimates to be provided by the estimation algorithm. For navigation, for the short time between
when estimates are available, the platform is proceeding using “Dead Reckoning”, https://www.google.com/search?source=hp&ei=U8B5XqyLD7OrytMPgveyEA&q=dead+reckoning&oq=Drad+Recon&gs_l=psy-ab.1.0.0i13l10.6322.14766..26055...0.0..0.199.851.8j2......0....1..gws-wiz.......0i131j0j0i10j0i13i10j0i13i5i30.9ANUljaMMYU
https://en.wikipedia.org/wiki/Dead_reckoning, which is usually adequate. However, if there is a density of other maneuvering platforms in the same vicinity, there
may be a problem relying only on Dead Reckoning (even for a short time epoch) and other further compensating techniques may be needed (such as use of
VOR/DME, ILS, Tacan, altimeter, compass, etc.)
For target tracking, there can also be additional processing needed by other
augmenting algorithms to associate estimates with particular tracks in a multi-target tracking environment and, perhaps, also classification of the nature or identity of the targets using
pattern recognition or discrimination/classification techniques-maybe as part of IFFN (Identification: Friend, Foe, or Neutral). So
timeliness of computed estimates is of the essence before the further
computations (just indicated here as being beyond mere Kalman Filter-like
estimation) can proceed!
The overall performance of
sigma-point filters, Oxford filters (a.k.a., Unscented Kalman
Filters) is not terrible. They are merely not quite as good as a Kalman-based
filter in the application role. This aspect was analytically proved in
Andrew Jazwinski's textbook beyond a shadow of a doubt. That these two
filtering schemes work reasonably well is expected, as established in even
earlier research results associated with so-designated "model
following" in using the output of one linear system as input to another
linear system even when the internal states of both don't correspond exactly
yet still behave similarly.
An interesting article that also invokes a Genetic
Algorithm approach: Xiyuan
Chen, Chong Shen, and Yuefang Zhao, “Study on GPS/INS System Using Novel Filtering Methods for Vessel Attitude Determination,” in
Special Issue
of Marine Engineering and Applications, Research Article | Open Access, Volume 2013 |Article ID 678943 | 8 pages |
https://doi.org/10.1155/2013/678943.
Especially see the extensive references listing interesting alternative hybrid approaches to estimation.
“JUST
BECAUSE APPROACHES ARE NEW AND DIFFERENT FROM BEFORE DOES
NOT MEAN THAT THEY ARE BETTER !”
| Investigating new Markov Chain Monte-Carlo techniques (Metropolis-Hastings and
Metropolis-Gibbs sampling and re-sampling) and associated supporting
pseudo-random number and quasi-random number generation techniques so
germane to PF (and quasi-random number generation techniques also relevant to encryption). |
| Angle-only
tracking (AOT) or Bearings-0nly filtering (for passive sonar or range-denied
jammed radar tracking)-all being highly nonlinear and also relevant to
interceptor guidance laws (and fire control). |
| Kalman
filter tracking accoutrements like the handling of multiple target tracks
(e.g., through use of the Hungarian algorithm, or Munkres algorithm, or J-V-C algorithm,
or Murty’s
algorithm, or Multiple Hypotheses Testing, or distributed Auction algorithm,
or new wrinkle using Generalized Likelihood Ratios [GLR] for recent modern
update to use of Track-before-Detect algorithms, or any other approaches to solving the Assignment Problem of Operations
Research);
Matrix Spectral Factorization; and Cramer-Rao Lower Bound (CRLB) analysis
& evaluation. |
| Event
detection (e.g., through use of Generalized Likelihood Ratio [GLR] or other
comparable algorithms), which utilizes the
outputs associated with Kalman filters or statistical estimation, to
identify faulty navigation components (i.e., INS components, GPS receivers,
Receiver Autonomous Integrity Monitoring [RAIM]) or target maneuvers within
radar target tracking applications. |
| Self-assembling
or self-organizing networked sensors (perhaps exploiting different
sections of the electromagnetic spectrum for multi-spectral or
hyper-spectral assessments or determinations), perhaps based on Kalman
filter constructs or other comparable technologies. |
| Employing tactics
for improving target observables such as engaging in certain sensor-host platform
maneuvers to improve passive sonar observability, using aircraft maneuvers to
eliminate ambiguity associated with several different candidate INS
component sources of owncraft INS failure or to reveal the presence of such
failures during early stages of a mission before they have deleterious
impacts. (E.g., enemy use of decoy wooden gun barrels were eventually
distinguished from actual metal ones using Infrared (IR) at sun down during first Iraq
war, where “Bud-Light” of flashing
InfraRed (IR) lights, only visible to those with IR goggles,
were heroically developed by others over an extremely short schedule for aiding in
Identification Friend or Foe [IFF] task). |
| Investigations
into probability one convergence arguments for assessing estimator
convergence to true targets instead of relying on mere
mean-square-convergence arguments inappropriately extrapolated from
multitudinous Monte-Carlo trials (especially since successful National
Missile Defense (NMD) interception is a single sample event). Such
developments would enable a more realistic design of experiments for
NMD/GMD. |
| Partial
Differential Equations (PDE-based) Kalman filter constructs for chemical or thermal
conduction (not convection nor radiation) for thermal diffusion (expertise in
parabolic PDE’s also extends to understanding methodology in
proper use of Kolmogorov equation (a.k.a. the Fokker-Planck equation)
arising for the underlying conditional probability density function
underlying nonlinear filtering [and in
similar PDE’s arising in Electromagnetic theory for the hyperbolic wave equation
for transmission lines, wave guides, and antennas]). |
| 2-D
Kalman filters for image processing resolution enhancements (with these
Kalman filter constructs, along with Decentralized Kalman filters &
image registration being likely basis for multi-sensor fusion). |
| Multi-channel (approximate) generalizations to scalar Maximum Entropy spectral estimation (similarly
model-based). |
| Use of a Kalman filter in “sensor
fusion”
applications. |
He is
enthusiastic about novel
ideas from the above list (and elsewhere) that further network centric warfare
(i.e., use of decentralized Kalman filters to obtain different complementary
perspectives of the same targets by viewing from different aspect angles
simultaneously from GPS-derived known locations of the sensors; perhaps also
likely synchronized by GPS time; however, he is well aware that
other more robust time standards and navigation standards are currently being
pursued in 2018 and beyond for PNT, where DOT has taken over the reins from DoD
in spearheading solutions for civilian applications while DoD is still pursuing
solutions for military applications). He encourages using Kalman Filter-related technology to
replace Matrix Spectral Factorization (MSF) in Space-Time Adaptive
Processing (STAP) to achieve more robustness in STAP by perhaps accommodating some nonstationarity (in the statistical sense). He seeks to be aware of the
emergence of disruptive technologies that may revolutionize certain critical
areas related to national defense (but at the same time maintains a healthy
skepticism until they actually prove themselves) and he tends to warn others if any
perceived fraud
is being perpetrated in any form (even if it takes the form of over zealous researchers
perhaps overstating the capabilities of a new technique or ignoring its apparent
limitations). He discourages invoking unwarranted hype in R&D endeavors.
He is
an algorithm specialist who is heavy on the analysis, having taken Advanced
Calculus, Complex Variables, Operational Mathematics (from Churchill ’s
textbook), Point Set Topology, Modern Algebra, Real Analysis
I, II and Measure and Integration Theory I, II from the mathematics department in graduate
school well before it was in vogue to do so within an engineering curriculum (as
it is now). He took the Graduate Record Exam and its mathematics specialty test in
October 1967
and scored in the 98th percentile upon entering graduate school.
However, he does not overly dwell on this aspect of his past. However, being
mathematically oriented does help him to keep up with changes in technology
since mathematics, although pervasive throughout technology, generally, has a
longer time constant than the other areas of technology but, of course, it
evolves too as new discoveries are made and interconnections revealed. He also
follows through with “down to earth”
practical considerations. One of
his goals is to help prevent engineers from going astray with the mathematics
and getting hurt (or hurting anybody else and therefore to possibly avoid the
usual finger pointing and “blaming the programmer when things go wrong” because someone’s theoretically
supporting mathematics was in error). Tom also took extra courses in physics
too, like Modern Physics/Quantum Mechanics, Physical/Celestial Mechanics.
As a Research & Development
Engineer, Systems Engineer, and Software Developer, specializing in digital algorithms,
he has worked in the estimation, simulation, and digital implementation area continuously since
1971. This includes 6 years on U.S. DoD
(Poseidon\Trident) C-3 and C-4 back-fit submarines [which, in those days, used
multiple Univac CP-890/YUK computers in the Navigation Room] and 6 years on Navy and Air Force aircraft Navigation
(failure detection and reconfiguration in Navigation systems within own-craft
position and attitude determination). He has some experience with sonar target tracking
software algorithm evaluation Independent Verification and
Validation (IV&V) and has performed Global Positioning Satellite (GPS)
System integration Development Test and Evaluation [DT&E(OR)] Operational
Readiness in attack submarines (specifically,
on the SSN-701 LaJolla as a typical representative) and cross-checked their Department of
Defense (DoD) spec compliance in monitoring performance in the GPS
Phase II receiver
competition between Magnavox and Rockwell Collins in the early 1980’s
and has investigated use of INS/GPS in other novel applications
of airborne mapping in the 1990’s
and in 2003 for the
Navy AROSS airborne Littoral surveillance program (under subcontract for Arête)
by performing a quantitative analysis of the relative
pointing accuracy provided by each of several alternative candidate INS
platforms of varying quality (and cost) by using high quality GPS [P(Y)-code,
differential, or kinematic] fixes at a high rate to enhance the INS with
frequent updates to compensate for degradations incurred with time due to
inherent gyro drift rate characteristics of each less expensive INS candidate. He has also worked in strategic Radar target-tracking; and in some
aspects of tactical and strategic Electronic Warfare (EW)
pattern recognition applications for Honeywell Electro-Optical’s
helicopter Missile Warning System (MWS) in the early 1980’s
and on Updated
Early Warning Radar (UEWR) in 2000 (please click on Consulting Services
button at top of this screen for specifics). The common thread is that almost all of the above
projects involve Kalman
filter signal processing or related estimation theory considerations. An
exception was the work he did on security for the WIS program, which
stands for WWMCCS Improvement System, and WWMCCS itself stands for
World Wide Military Command and Control System (WWMCCS was decommissioned in
1996 and replaced by Global
Command and Control System). He draws heavily from his prior experience at General Electric Corporate R&D Center
(’71-’73),
The Analytical Science Corporation: TASC (’73-’79), Intermetrics, Inc. (’79-’86), and the Lincoln Laboratory of the Massachusetts
Institute of Technology (’86-’92), and at TeK Associates (’92-present) and from work he performed on his client’s projects. At Intermetrics, Inc., he
also served
as Interim Technical Editor of Navigation, The journal of the Institute of Navigation
(standing in for his previous supervisor, Stephen Gilbert, for a year: 1985-86)
during the transition period between Paul M. Janiczek (after Paul Janiczek got married and
relinquished the position of editor) and years before the next full
time editor was installed. Click here to
see the numerous Continuing Education Courses Tom has taken to keep up with
evolving technology.
As
an algorithm and signal processing specialist, he generally focuses on system
aspects related to optimal and sub-optimal estimation and Kalman filtering and in the underlying
models and, in particular, to requisite further statistical processing of state estimates
and covariances related to incident detection and tracking. He also has interests in GIS and enjoys
developing Windows-based PC software and GUI’s to prompt and
constructively aid the user. He recognizes that GUI’s
can be implemented in interpretive software languages and still be faster than a
human’s
response while numerical calculations are always to be implemented in truly
compiled software languages to reap the benefit of speed, timeliness, and
possibly parallelization. At General
Electric Corporate Research & Development Center in
the early 1970’s,
Tom was a protégée of his fellow coworkers in corporate software development
of Automated Dynamic Analyzer (ADA) [but not the WPAFB-funded
1980’s computer
language known as Air Force Ada (discussed much further below), where both
software approaches were named to honor the first computer programmer, Ada
Lovelace]: being Joe Watson, Hal Moore, and Dr.
Glen Roe (the degree to which this early exposure benefited Tom has only
recently been fully realized, as that early experience continues to unexpectedly influence
him over the 4+ decades that ensued).
Tom’s work and research experience has encompassed:
estimation applications with standard Gaussian white noises or with non-standard
Poisson or other point-process noises present (primarily in NAVIGATION and in
RADAR and IR target tracking); spectral estimation in analyzing and emulating
RADAR primary polarization (PP) and orthogonal polarization (OP) target
signatures; decentralized and multi-rate filters; mathematical modeling and
parameter identification for stochastic systems; team theory and zero-sum and
nonzero-sum differential
games (Stackelberg strategies and Nash equilibrium, signaling, coalitions); optimal search and screening;
angle-only (a.k.a. bearings-only) tracking; fault\ failure detection in dynamical
systems (and the mathematically identical areas of maneuver detection, change
detection and\or incident detection); optimal-sensor-usage-alternation with a
Kalman filter; determining Pareto-optimal strategies using the
method-of-linear-combinations (for multi-criteria optimization); optimal
control; algorithm convergence; engineering analyses; trade-off analyses\trade
studies; computational techniques; control theory (modern state-space
based and classical frequency-domain based approaches including Matrix Spectral
Factorization, Proportional-Integral-Derivative (PID)
control compensation, calculus-of-variations,
Pontryagin’s
Maximum Principle); and the supporting
underlying systems theory. His publications are frequently cited by other
independent authors and researchers;
explicit examples (a partial list obtained from Citation Index associated with the on-line “Web of Science” at any good research library [Ostensibly, my current Web of Science Researcher ID: K-4879-2019] (or from the PC-based relatively new “Publons”) by searching under “Kerr, T. H.”) being:
-Skog, I., Handel, P.,
“In-Car Positioning and Navigation Technologies-A Survey,”
IEEE Transactions on Intelligent Transportation Systems, Vol. 10, No. 1, pp. 4-21, Mar. 2009.
-Smith, M. A.,
“On Doppler Measurements for Tracking,”
International Conference on
Radar, Adelaide, Australia, Vol. 1 and 2, pp. 309-314, 2-5 Sep. 2008.
-Shi, Y., Han, C. Z., Lian, F.,
“The Iterated divided difference filter,”
IEEE International Conference on Automation and
Logistics, 1-3 Sep. 2008, Qingdao, Peoples Republic of China, Vols. 1-6, pp. 1799-1802, 2008.
-Banani, S. A., Masnadi-Shirazi, M. A.,
“A New Version of Unscented Kalman Filter,”
Proceedings of Conference of the World Academy of Science, Engineering, and
Technology, Barcelona, Spain, Vol. 20, pp. 192-197, 25-27 Apr. 2007.
-Petsios, M. N., Alivizatos, E. G., Uzunoglu, N. K.,
“Solving the association problem for a multistatic range-only radar target
tracker,”
Signal Processing, Vol. 88, No. 9, pp. 2254-2277, Sep. 2008.
-Xu, B. L., Chen, Q. L., Wu, Z. Y., et al,
“Analysis and approximation of performance bound for two-observer bearings-only
tracking,”
Information Sciences, Vol. 178, No. 8, pp. 2059-2078, 15 Apr. 2008.
-Hovareshti, P., Gupta, V., Baras, J. S.,
“Sensor scheduling using smart sensors,”
Proceedings of 46th IEEE Conference on Decision and Control, New Orleans,
LA, Vols. 1-14, pp. 6083-6088, 12-14 Dec. 2007.
-Gadzhiev, C. M.,
“Determining the operating conditions of floating marine platforms based on the predicted motion control under conditions of wind and wave
disturbances,”
Measurement Techniques, Vol. 51, No. 1, pp. 28-33, Jan. 2008.
-Choudhury, D. R.,
“Shifted power method for positive semi-definite matrices using
Gerschgorin,”
Proceedings of 10th World Multi-Conference on Systemics, Cybernetics and Informatics/12th International Conference on Information Systems Analysis and
Synthesis, Orlando, FL, WMSCI 2006, Vol. IV, pp. 251-253, 16-19 Jul. 2006.
-Fong, K. F., Loh, A. P., Tan, W. W.,
“A frequency domain approach for fault detection,”
International Journal of Control, Vol. 81, No. 2, pp. 264-276, 2008.
-Xu, B. L., Wu, Z. Y., Wang, Z. Q.,
“Theoretic performance bound for bearings-only tracking,”
Proceedings of 6th International Conference on Machine Learning and
Cybernetics, Hong Kong, Peoples Republic of China, Vols. 1-7, pp. 2300-2305, 19-22 Aug. 2007.
-Duan, F. Y., Wang, H., Zhang, L. J., et al,
“Study on fault-tolerant filter algorithm for integrated navigation
system,”
Proceedings of IEEE International Conference on Mechatronics and Automation, 5-8 Aug. 2007, Harbin, Peoples Republic of China, 2007,
Vols. I-V, pp. 2419-2423, 2007.
-Tong, Z. M., Tang, W. Y.,
“The application of data fusion in optical theodolite coordinate measurement
system,”
art. no.
659510, Proceedings of Conference on Fundamental Problems of Optoelectronics and Microelectronics III, 12-14 Sep. 2006, Harbin, Peoples Republic of China, Pts. 1 and 2, Proceedings of the Society of Photo-Optical Instrumentation Engineers
(SPIE), Vol. 6595, pp. 5951-5951, Parts 1-2, 2007.
-Kramer, K. A., Stubberud, S. C., Geremiam, J. A.,
“Sensor calibration using the neural extended Kalman filter in a control
loop,”
Proceedings of IEEE International Conference on Computational Intelligence for Measurement Systems and
Applications, 27-29 Jun. 2007, Ostuni, Italy, pp. 19-24, 2007
-Xu, B. L., Wu, Z. Y., Wang, Z. Q.,
“On the Cramér-Rao lower bound for biased bearings-only maneuvering target
tracking,”
Signal Processing, Vol. 87, No. 12, pp. 3175-3189, Dec. 2007.
-Mironovskii, L. A.,
“The use of analytical redundancy in navigational measuring systems,,”
Proceedings of 4th International Seminar on Mathematical, Statistical, and Computer Support of Measurement
Quality, 28-30 Jun. 2006, St. Petersburg, Russia, Measurement Techniques, Vol. 50, No. 2, pp. 142-148, Feb. 2007.
-Li, X. R., Jilkov, V. P., “Survey of maneuvering target tracking. Part V: Multiple-model
methods,” IEEE
Trans. on Aerospace and Electronic Systems, Vol. 41, No. 4, pp. 1255-1321,
Oct. 2005.
-Li, X. R., Jilkov, V. P.,
“A survey of maneuvering target tracking: Approximation techniques for nonlinear
filtering,” 16th Conference on Signal and Data Processing of Small Targets, 13-15 Apr. 2004 Orlando, FL,
Signal and Data Processing of Small Targets 2004, Proceedings of the Society
of Photo-Optical Instrumentation Engineers (SPIE), Vol. 5428, pp. 537-550, 2004.
-Koutsoukos, X. D.,
“Estimation of hybrid systems using discrete sensors,”
Proceedings of 42nd IEEE Conference on Decision and Control, Maui, HI, Vols. 1-6,
Dec. 09-12, 2003.
-Rapoport, I., Oshman, Y.,
“A Cramér-Rao type lower bound for the estimation error of systems with measurement
faults,” Proceedings of 42nd IEEE Conference on Decision and
Control, 9-12 Dec. 2003, Maui, HI, Vols. 1-6, pp. 4853-4858, 2003.
-Bessell, A., Ristic, B., Farina, A., et al.,
“Error performance bounds for tracking a maneuvering target,”
Proceedings of 6th International Conference on Information Fusion, 8-11 Jul. 2003, Cairns,
Australia, FUSION 2003, Vols. 1-2, pp. 903-910, 2003.
-Xiong, W., He, Y., Zhang, J. W.,
“Centralized multisensor nonlinear filter method,”
Proceedings of 3rd International Symposium on Instrumentation Science and
Technology, 18-22 Aug. 2004, Xian, People's Republic China, Vol. 2, pp. 526-530, 2004.
-Ristic, B., Farina, A., Hernandez, M.,
“Cramér-Rao lower bound for tracking multiple targets,” IEE Proceedings-Radar, Sonar, and
Navigation, Vol. 151, No. 3, pp. 129-134, Jun. 2004.
-Behazin, F., Nabavi, B., Fesharaki, M. N.,
“The reformulation and modification on iterated EKF for applications with large-dimension
measurement,” Proceedings of 6th International Conference on Signal
Processing, 26-30 Aug. 2002, Beijing, People's Republic of China, Vols. I and II, pp. 756-759, 2002.
-Simandl, M., Straka, O.,
“Seting sample size in particle filters using Cramér-Rao
bound,” Proceedings of 5th IFAC Symposium on Nonlinear Control
Systems, 4-6 Jul. 2001, St. Petersburg, Russia, Nonlinear Control Systems 2001, Vols. 1-3, IFAC Symposia Series, pp. 681-686, 2002.
-Ning, X. L., Fang, J. C.,
“A new method of autonomous navigation for deep space explorer based on information
fusion,” Proceedings of 6th International Conference on Electronic Measurement and
Instruments, 18-21 Aug. 2003, Taiyuan, People's Republic of China, Vols. 1-3, pp. 220-224, 2003.
-Li, X. R., Jilkov, V. P.,
“A survey of maneuvering target tracking - Part II: Ballistic target
models,” Proceedings of 13th Conference on Signal and Data Processing of Small
Targets, 30 Jul.-2 Aug. 2001, San Diego, CA, Proceedings of The Society of Photo-Optical Instrumentation Engineers
(SPIE), Vol. 4473, pp. 559-581, 2001.
-Li, X. R., Jilkov, V. P.,
“A survey of maneuvering target tracking - Part III: Measurement
models,” Proceedings of 13th Conference on Signal and Data Processing of Small
Targets, 30 Jul.-2 Aug. 2001, San Diego, CA, Proceedings of The Society of Photo-Optical Instrumentation Engineers
(SPIE), Vol. 4473, pp. 423-446, 2001.
-Li, X. R., Jilkov, V. P.,
“A survey of maneuvering target tracking - Part IV: Decision-based
methods,” Proceedings of 14th Conference on Signal and Data Processing of Small
Targets, 2-4 Apr. 2002, Orlando, FL, Proceedings of The Society of Photo-Optical Instrumentation Engineers
(SPIE), Vol. 4728, pp. 511-534, 2002.
-El-Mahy, M. K.,
“Efficient satellite orbit determination algorithm,” Proceedings of 18th National Radio Science Conference
(NRSC 2001), 27-29 Mar. 2001, Mansoura, Egypt, Vols. 1
and 2, pp. 225-232, 2001.
-Parra-Michel, R., Kontorovitch, V.Y., Orozco-Lugo, A. G.,
“Simulation of wide band channels with nonseparable scattering
functions,” Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing
(ICASSP), 13-17 MAY 2002 ORLANDO, FL, Vols. I-IV, pp. 2829-2832, 2002
-Hanebeck, U. W. D.,
“Recursive nonlinear set-theoretic estimation based on pseudo
ellipsoids,” Proceedings of International Conference on Multisensor Fusion and Integration for Intelligent
Systems, 20-22 Aug. 2001, Baden Baden, Germany, pp. 159-164, 2001.
-Mosavi, M. R., Mohammadi, K.,
“Improve the position accuracy on low cost GPS receiver with adaptive neural
networks,” Proceedings of Student Conference on Research and Development-Globalizing Research and Development in Electrical and Electronics
Engineering, 16-17 Jul. 2002, Shah Alam, Malaysia,, pp. 322-325, 2002.
-Campa, G., Fravolini, M. L., Napolitano, M, et al.,
“Neural networks-based sensor validation for the flight control system of a B777 research
model,” Proceedings of 20th Annual American Control Conference (ACC), 8-10 May 2002, Anchorage, AK, Vols. 1-6, pp. 412-417, 2002.
-Vershinin, Y. A.,
“A data fusion algorithm for multisensor systems,” Proceedings of 5th International Conference on Information Fusion (FUSION 2002), 8-11 Jul. 2002 Annapolis, MD, Vol. I, pp. 341-345, 2002.
-Chetouani, Y., Mouhab, N., Cosmao, J. M., et al.,
“Application of extended Kalman filtering to chemical reactor fault
detection,” Chemical Engineering Communications, Vol. 189, No. 9, pp. 1222-1241, Sep. 2002.
-Stentz, A., Dima, C., Wellington, C., et al.,
“A system for semi-autonomous tractor operations,” Autonomous Robots, Vol. 13, No. 1, pp. 87-104, Jul. 2002.
-Carpenter, J. R.,
“Decentralized control of satellite formations,” International Journal of Robust and Nonlinear
Control, Vol. 12, No. 2-3, pp. 141-161, Feb.-Mar. 2002.
-Mirabadi, A., Mort, N., Schmidt, F.,
“A fault tolerant train navigation system using multi-sensor,
multi-filter integration
techniques,” Proceedings of International Conference on Multisource-Multisensor Information Fusion (FUSION '98), 6-9 Jul. 1998 Las Vegas, NV, Vols. 1 AND 2, pp. 340-347, 1998.
-Degen, U.,
“Operations research of tracking algorithms for air surveillance
system,” Proceedings of International Conference on Multisource-Multisensor Information Fusion (FUSION '98), 6-9 Jul. 1998 Las Vegas, NV, Vols. 1 and 2, pp. 850-855, 1998.
-Fravolini, M. L., Campa, G., Napolitano, M., et al.,
“Minimal resource allocating networks for aircraft SFDIA,” Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM '01), 8-12 Jul. 2001, Como, Italy, Vols. I and II, pp. 1251-1256, 2001.
-Hasan, K., Hossain, J.,
“Multichannel autoregressive spectral estimation from noisy
observations,” Proceedings of 10th International IEEE Tencon
Conference, 24-27 Sep. 2000, Kuala Lumpur, Malaysia, Vols. I-III, Intelligent
Systems and Technologies for the New Millennium, pp. 327-332, 2000.
-Simandl, M., Kralovec, J., Tichavsky, P.,
“Filtering, predictive, and smoothing Cramér-Rao bounds for discrete-time nonlinear dynamic
systems,” Proceedings of 14th IFAC World
Congress, 5-9 Jul. 1999, Beijing, Peoples Republic of China, Automatica, Vol. 37, No. 11, pp. 1703-1716, Nov. 2001.
-Leung, H., Zhu, Z. W.,
“Performance evaluation of EKF-based chaotic synchronization,” IEEE Transactions on Circuits and System I-Fundamental Theory and
Applications, Vol. 48, No 9, pp. 1118-1125, Sep. 2001.
-Sivananthan, S., Kirubarajan, T., Bar-Shalom, Y.,
“Radar power multiplier for acquisition of low observables using an ESA
radar,” IEEE Transactions on Aerospace and Electronic Systems
Systems, Vol. 37, No. 2, pp. 401-418, Apr. 2001.
-Li, Y., Sundararajan, N., Saratchandran, P.,
“Stable neuro-flight-controller using fully tuned radial basis function neural
networks,” Journal of Guidance, Control, and
Dynamics, Vol. 24, No. 4, pp. 665-674, Jul.-Aug. 2001.
-Niu, R. X., Willett, P., Bar-Shalom, Y.,
“Matrix CRLB scaling due to measurements of uncertain origin,” IEEE Transactions on Signal
Processing, Vol. 49, No. 7, pp. 1325-1335, Jul. 2001.
-Bergman, N., Doucet, A., Gordon, N.,
“Optimal estimation and Cramér-Rao bounds for partial
non-gaussian state space
models,” Proceedings of International Symposium on the Frontiers of Time Series
Modeling, 14-16 Feb. 2000, Annals of the Institute of Statistical
Mathematics, Tokyo, Japan, Vol. 53, No. 1, Special Issue, pp. 97-112, Mar. 2001.
-Mahapatra, P. R., Mehrotra, K.,
“Mixed coordinate tracking of generalized maneuvering targets using acceleration and jerk
models,” IEEE Transactions on Aerospace and Electronic
Systems, Vol. 36, No. 3, pp. 992-1000, Jul. 2000.
-Mirabadi, A., Schmid, F., Mort, N.,
“Fault detection and isolation in a multisensor train navigation
system,” Proceedings 6th International Conference on Computer Aided Design, Manufacture, and Operation in the Railway and Other Advanced Mass Transit
Systems, 2-4 Sep. 1998, Lisbon, Portugal, Computers in Railways VI, Advances in
Transportation, Vol. 2, pp. 1025-1035, 1998.
-Jayakumar, M., Banavar, R. N.,
“Risk-sensitive filters for recursive estimation of motion from images,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, Vol. 20, No. 6, pp. 659-666, Jun. 1998.
-Tichavsky, P., Muravchik, C. H., Nehorai, A.,
“Posterior Cramér-Rao bounds for discrete-time nonlinear filtering,” Proceedings of 1st European Conference on Signal Analysis and Prediction (ECSAP-97), 24-27 Jun. 1997 Prague, Czech Republic,
IEEE Transactions on Signal Processing, Vol. 46, No. 5, pp. 1386-1396, May 1998.
-Koshaev, D. A.,
“A comparison of lower bounds of accuracy in problems of nonlinear
estimation,” Journal of Computer and Systems Sciences
International, Vol. 37, No. 2, pp. 222-225, Mar.-Apr. 1998.
-Mazor, E., Averbuch, A., Bar-Shalom, Y., et al.,
“Interacting multiple model methods in target tracking: A survey,” IEEE Transactions on Aerospace and Electronic
Systems, Vol. 34, No. 1, pp. 103-123, Jan. 1998.
-Koshaev, D. A., Stepanov, O. A.,
“Application of the Rao-Cramér inequality in problems of nonlinear
estimation,” Journal of Computer and System Sciences
International, Vol. 36, No. 2, pp. 220-227, Mar.-Apr. 1997.
-on page 208 in Bevly, D. M., Parkinson, B., “Cascaded Kalman Filters for Accurate Estimation of Multiple Biases, Dead-Reckoning Navigation, and Full State Feedback Control of Ground Vehicles,”
IEEE Trans. on Control Systems Technology, Vol. 15, No. 2, pp. 199-208, Mar.
2007.
-Lee, H. K., Lee, J. G., “Fault-Tolerant
Compression Filters by Time-Propagated Measurement Fusion,” Automatica, Vol.
43, No. 2, pp. 355-361, Feb.
2007.
-Xu, B. L., Wu, Z. Y., Wu, Wang, Z. Q., “On the
Cramér-Rao
Lower Bound for Biased Bearings-Only Maneuvering Target Tracking,”
IEEE Trans. on Signal Processing, Vol. 87, No. 12, pp. 3175-3189, Dec. 2007.
-Mironovskii, L. A., “The Use of Analytical
Redundancy,” Measurement Techniques, Vol. 50, No. 6, pp. 142-148, Feb.
2007.
-Aloi, D. N.,
Alsliety, M., Akos, D. M., “A
Methodology for the Evaluation of a GPS Receiver in Telematics Applications,”
IEEE Trans. on Instrumentation and Measurement, Vol. 56, No. 1, pp.
11-24, Feb.
2007.
-Petsios, M. N.,
Alivizatos, E. G., Uzunoglu, N. K., “Manuvering
Target Tracking Using Multiple Bistatic Range and Range-Rate Measurements,”
IEEE Trans. on Signal Processing, Vol. 87, No. 4, pp. 665-686, Apr.
2007.
-on page 48 of Hue, C., Le Cadre, J.-P., Perez, P., “Posterior Cramér-Rao Bounds for Multi-Target Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 37-49, Jan. 2006.
-Chetouani, Y., “Fault Detection in a Chemical
Reactor by Using the Standardized Innovation,” Process Safety and
Environmental Protection, Vol. 84, No. B1, pp. 27-32, Jan. 2006.
-Gupta, V., Chung, T. H.,
Hassibi, B., Murray, R. M., “On
a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling
and Sensor Coverage,” Automatica, Vol. 42, No. 2, pp. 251-260, Feb.
2006.
-Hwang, D. H., Oh, S. H., Lee, S. J., Park, C.,
Rizos,
C., “Design of a Low-Cost Attitude Determination GPS/INS Integrated Navigation
System,” GPS Solutions, Vol. 9, No. 4, pp. 294-311, Nov. 2006.
-Pulford, G. W., “Taxonomy of Multiple Target
Tracking Systems,” IEE Proceedings-Radar, Sonar, and Communications, Vol.
151, No. 5, pp. 291-304, Oct. 2005.
-Ristic,
B., “Cramér Rao Bounds for Target Tracking,” International
Conference on Sensor Networks and Information Processing, 6
Dec. 2005.
-Lee, T. H., Ra, W. S., Yoon, T. S., Park, J. B., “Robust
Extended Kalman Filtering via Krein Space Estimation,” IEICE Transactions
on Fundamentals of Electronics Communications and Computer Sciences, Vol.
E87A, No. 1, pp. 243-250, Jan. 2004.
-Hagan, M. T.,
Demuth, H. B., De Jesus, O., “An
Introduction to the Use of Neural Networks in Control Systems,” International
Journal of Robust and Nonlinear Control, Vol. E87A, No. 1, pp. 243-250, Jan.
2004.
-on page 2369 of Hernandez, M.,
Ristic, B., Farina, A., Timmoneri,
L., “A Comparison of Two Cramér-Rao Bounds for Nonlinear Filtering with Pd <
1,” IEEE Trans. on Signal Processing, Vol. 52, No. 9, pp. 2361-2370, Sept. 2004.
-on page 81 of Ristic, B., Arulampalam, S., Gordon, N., Beyond the Kalman Filter: Particle Filters for Tracking
Applications, Artech House, Boston, MA, 2004.
-in references of Mutel, L. H., Speyer, J. L.,
“Fault-Tolerant GPS/INS Navigation System with Application to Unmanned Aerial
Vehicles,” Navigation: Journal of the Institute of
Navigation, Vol. 49, No. 1, Spring 2002.
-in references of Tichavsky, P., Muravchik, C. H., Nehorai, A.,
“Posterior Cramér-Rao Bounds for Discrete-Time Nonlinear
Filtering,”
IEEE Trans. on Signal Processing, Vol. 46, No. 5, pp. 1386-1396, May 1998.
-in Siouris, G. M., Chen, G.-R., Wang, J.-R.,
“Tracking an Incoming Ballistic Missile using an Extended Interval Kalman
Filter,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1, pp. 232-240, Jan. 1997.
-in Napolitano, M. R., Chen, C. L., Naylor, S.,
“Aircraft Failure Detection and Identification using Neural
Networks,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 16, No. 6, pp. 999-1009, 1998.
-in Napolitano, M. R., Neppach, C., Casdorph, V., Naylor, S., Innocenti, M.,
Silventri, G.,
“Neural-Network-based Scheme for Sensor Failure
Detection,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 18, No. 6, pp. 1280-1286, Nov.-Dec. 1995.
-in
Grejner-Brzezinska, D. A., Da, R., Toth, C., “GPS error
modeling and OTF ambiguity resolution for high-accuracy GPS/INS integrated
system,” Journal of Geodesy, Vol. 72,
pp. 626-638, 1998.
-in
Farina, A., “Target Tracking with Bearings-Only
Measurements,” IEEE Trans. on Signal Processing, Vol.
78, No. 1,
pp. 61-78, Oct. 1999.
-in
Ristic, B., Farina, A., Hernandez, M., “Cramér-Rao lower bound for Tracking Multiple Targets,”
IEE Proceedings-Radar, Sonar, and Navigation, Vol. 151, No. 3, pp.
129-134, Jun. 2004.
-in
Simandl, M., Kralovec, J., Tichavsky, P., “Filtering,
Prediction, and Smoothing Cramér-Rao
Bounds for Discrete Time Nonlinear
Dynamic Systems,” Automatica, Vol. 37, No.
11, pp. 1703-1716, Nov. 2001.
-in
Spall, J. C., Garner, J. P., “Parameter-Identification for
State-Space Models with Nuisance Parameters,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 26, No.
6,
pp. 992-998, Nov. 1990.
-in
Da, R., Lin, C. F., “A New Failure-Detection Approach and
its Application to GPS Autonomous Integrity Monitoring,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 31, No. 1,
pp. 499-506, Jan. 1995.
-in
Da, R., “Failure-Detection of Dynamical Systems with the
State Chi-Square Test,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 17, No. 2,
pp. 271-277, Mar.-Apr. 1994.
-in
Leung, H., Zhu, Z. W., “Performance Evaluation of EKF-based
Chaotic Synchronization,” IEEE Trans. on Circuits and Systems, Vol. 48, No. 9,
pp. 1118- 1125, Sep. 2001.
-in
Bergman, N, Doucet, A., Gordon, N., “Optimal estimation and Cramér-Rao
Bounds for Partial Non-Gaussian State Space Models,” Annals of the Institute of Statistical Mathematics, Vol. 53, No.
1,
pp. 97-112, Iss S I Mar. 2001.
-in
Mahapatra, P. R., Mehrotra, K., “Mixed coordinate tracking
of generalized maneuvering targets using acceleration and jerk models,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 36, No. 3,
pp. 992-1000, Jul. 2000.
-in Park, S. T., Lee, J. G.,
“Improved Kalman Filter
design for three-dimensional radar tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 2,
pp. 727-739, Apr. 2001.
-in
Reece, S., “Nonlinear Kalman filtering with semi-parametric
Biscay distributions,” IEEE Trans. on Signal Processing, Vol. 49, No. 11,
pp. 2445-2453, Nov. 2001.
-in
Sivananthan, S., Kirubarajan, T., and Bar-Shalom, Y., “Radar
Power Multiplier for Acquisition of Low Observables using an ESA Radar,” IEEE Trans. on Aero- space and Electronic Systems, Vol. 37, No.
2,
pp. 401-418, Jan. 2001.
-in
Lee, T. H., Ra, W. S., Jin, S. H., et al, “Robust extended
Kalman filtering via Krein space estimation,” IEICE Transactions
on Fundamentals of Electronics Communications and Computer Sciences, No. 1,
pp. 243-250, Jan. 2004.
-in
Niu, R. X., Willett, P., Bar-Shalom, Y., “Matrix CRLB
Scaling due to measurements of uncertain origin,” IEEE Trans. on Signal Processing, Vol. 49, No. 7,
pp. 1325-1335, Jun. 2001.
-in
Nabaa, N., Bishop, R. H., “Solution
to a Multisensor Tracking Problem with Sensor Registration Errors,” IEEE Trans. on Aerospace and Electronic Systems, Vol.
35, No.
1,
pp. 354-365, Jan. 1999.
-in
Rizos, Chris, “Quality Issues in Real-Time GPS Positioning,” International
Association of Geodesy SSG 1.154, IUGG Congress, Birmingham, U.K., 18-29
July 1999.
-in
Jayakumar, M., Banavar, R. N., “Risk-sensitive filters for
recursive estimation of motion from images,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.
20, No. 6,
pp. 659-666, Jun. 1998.
-in
Mazor, E., Averbuch, A., Bar-Shalom, Y., et al, “Interacting
multiple model methods in target tracking: A Survey,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 34, No.
1,
pp. 103-123, Jan. 1998.
-in
Benhaim, Y., “Optimizing Multi-hypothesis Diagnosis of
Control-Actuator Failures in Linear Systems,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 4,
pp. 744-750, Jul.-Aug. 1990.
-in
Li, X. -R., Bar-Shalom, Y., “Performance Prediction
of the Interacting Multiple Model Algorithm,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 29, No. 3,
pp. 755-771, Jul. 1993.
-in
Campa, G., Fravdini, M. L., Seanor, B., et al, “On-line
learning neural networks for sensor validation for flight control system of
a B777 research scale model,” International Journal of Robust and Nonlinear Control, Vol. 12, No.
11,
pp. 987-1007, Sep. 2002.
-in
Korbicz, J., Fathi, Z., Ramirez, W. F., “State Estimation
Schemes for Fault-Detection and Diagnosis in Dynamic-Systems,” International Journal of System Science, Vol. 24, No. 5,
pp. 985-1000, May 1993.
-in
Ghil, M., Malanotterizzoli, P., “Data Assimilation in
Meteorology and Oceanography,” Advances in Geophysics, Vol. 33, pp. 141-266, 1991.
-in
Hanan, K., Yahagi, T., “An iterative method for the
identification of multi-channel autoregressive processes with additive
observation noise,” IEICE Transactions
on Fundamentals of Electronics Communications and Computer Sciences, No.
5,
pp. 674-680, May 1996.
-in
Liggins, M. E., Chong, C. Y., Kadar, I., et al, “Distributed
fusion architectures and algorithms for target tracking,” Proceedings of the IEEE, Vol. 85, No. 1,
pp. 95-107, Jan. 1997.
-in
Doerschuk, P. C., “Cramér-Rao Lower Bounds for Discrete-Time Nonlinear Filters,”
IEEE Trans. on Automatic Control, Vol. 40, No. 8,
pp. 1465-1469, Aug. 1995.
-in
Lu S., Doerschuk, P. C., “Performance Bounds for Nonlinear Filters,” IEEE
Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1,
pp. 316-319, Jan. 1995.
-in
Zolghadri, A., Bergeon, B., Monison, M., “A Two Ellipsoid Overlap Test for
On-line Failure Detection,” Automatica, Vol. 29, No. 6,
pp. 1517-1522, 1993.
-in
Zolghadri, A., “An Algorithm for Real-Time Failure Detection in Kalman
Filters,” IEEE
Trans. on Automatic Control, Vol. 41, No. 1,
pp. 232-240, Oct. 1996.
-in
Wahnon, E., “A Min-Max Testing Approach to
Failure-Detection and Identification,” Lecture Notes in Control and Information Sciences, Vol. 144, pp.
487-496, 1990.
-in
Golovan, A. A., Mironovskii, L. A., “An
Algorithmic Control of Kalman Filters,” Automation and Remote Control, Vol. 54, No. 7,
pp. 1183-1194, Jul. 1993.
-in
Gadzhiev, C. M., “Prediction of failures in linear-systems
with the use of tolerance ranges,” Measurement Techniques, Vol. 35, No. 8,
pp. 851-896, Aug. 1992.
-in
Gadzhiev, C. M., “Prediction the Technical State of Dynamic
Systems by a Kalman Filter Updating Sequence,” Automation and Remote Control-Part 2, Vol. 54, No. 5,
pp. 851-854, May 1993.
-in
Mertikas, S. P., Rizos, C., “On-line Detection of Abrupt
Changes in the Carrier-Phase measurement of GPS,” Journal of Geodesy, Vol. 71,
pp. 469-482, 1997.
-in
Hagan, M. T., Demuth, H. B., De Jesus, O., “An introduction
to the use of neural networks in control systems,” International Journal of Robust and Nonlinear Control, Vol. 12, No.
11,
pp. 959-985, Sep. 2002.
-in
Li, Y., Sundararajan, N., Saratchandray, P., “Stable neuro-flight-controller
using fully tuned radial basis function neural networks,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 4,
pp. 665-674, Jul.-Aug. 2001.
-in
Durrant-Whyte, H. F., Rao, B. Y. S., Hu, H., “Toward a Fully Decentralized
Architecture for Multisensor Fusion,” Proceedings of 1990 Conference on
Robotics and Automation, pp. 1331-1336, Cincinnati, OH, 13-18 May 1990.
-in
Blackman, S. S., Broida, T. J., “Multiple-Sensor-Data-Association and
Fusion in Aerospace Applications,” Journal of Robotic Systems,
Vol. 7, No. 3, pp. 445-485, Jun. 1990.
-in
Roy, S., Hashemi, R. H., and Laub, A. J., “Square Root Parallel Filtering
Using Reduced-Order Local Filters,” IEEE Trans. on Aerospace and Electronic
Systems, Vol. 27, No. 2,
pp. 276-289, Mar. 1991.
-in
Hong, L., “Centralized and Distributed Multisensor Integration with
Uncertainties in Communication Networks,” IEEE Trans. on Aerospace and
Electronic Systems, Vol. 27, No. 2,
pp. 370-379, Mar. 1991.
-in
Makhoul, J., “Toeplitz Determinants and Positive Semidefiniteness,” IEEE
Trans. on Signal Processing, Vol. 39, No. 3, pp. 743-746, Mar. 1991 (in
particular, please see page 744, footnote and acknowledgement on page 748
for references to T. H. Kerr’s
professionally benign comments and positively supportive and cooperative interactions
with the author of this work).
-in
Brumback, B. D., Srinath, M. D., “A Fault-Tolerant
Multisensor Navigation System-Design,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 23, No. 6,
pp. 738-756, 1987.
-in
Brumback, B. D., Srinath, M. D., “A Chi-Square Test for Fault-Detection in
Kalman Filters,” IEEE Trans. on Automatic Control, Vol. 32, No. 6,
pp. 532-554, June 1987.
-in
Uwe D. Hanbeck, “Recursive Nonlinear
Set-Theoretic Estimation Based on Pseudo-Ellipsoids,” Proceedings of the IEEE Conference on
Multisensor Fusion and Integration for Intelligent Systems, pp. 159–164 (MFI’
2001), Baden–Baden.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.8080
https://www.researchgate.net/publication/3955109_Recursive_nonlinear_set-theoretic_estimation_based_on_pseudo_ellipsoids
https://core.ac.uk/display/22665895
https://core.ac.uk/display/24506648
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.3779
Their patent abandoned by Siemens AG (perhaps because of prior art: me): https://patents.google.com/patent/US20060234722A1/en
(Other citations appear within our “Consulting Services” section of this website under our “Recent Clients”. . . .
Additional citations to my publications occurred within earlier decades: the 1970’s and 1980’s.
A search performed 20 years ago revealed that each of the above references cited at least one of my
prior published papers.
Click this link here to see a more
comprehensive
list of our publications.
Current searches use a Web of Science Researcher ID that is evidently incorrect as is the associated
"Publons"
ID
through no fault of my own although I am
actively trying to have it fixed by them.)
Go
to Top
Go to Primary Table of Contents
Dr. Kerr has guided TeK
Associates, an engineering consulting company, in developing their main
software product TK-MIP™ (please click on
TK-MIP v.2.0 for PC
button at top of this screen for specifics and a free software demo download) and in pursuing Small Business Innovation Research
(SBIR’s)
and sub-contracts in the evolving areas of Kalman filter and Control
applications for Navigation, Target Tracking, and for Image Processing and
Sensor Fusion. He has taught Optimal Control in the graduate Electrical
and Computer Engineering (E.C.E.)
Department at Northeastern University in the evenings for four years in the 1990’s and has TeK
consultant affiliations there and at UCLA. We have followed
the development of optimal and sub-optimal estimation technology for over 40 years
(since his first year long course in Kalman Filtering in 1968-'69 and a 2 week 8
hr/day Short Course at UCLA in the
summer of 1969 and continued to do so from the entirety of his work experience) so that
TK-MIP users can immediately reap the
benefits of our expertise and experience (without our users having to be experts in these areas themselves). Go
to Primary Table of Contents
He is versed in FORTRAN77\90\95, PL/1, IBM Assembly Language, GW BASIC,
BASICA, HTML, VBA,
VBScript, and PC MatLab®\Simulink®
(16-bit ver. 4.2.c and 32-bit ver. 6.5 MatLab and ver. 5.0 Simulink and for the later 64-bit versions up to the present),
COMSOL Multiphysics® vers. 3.5a and 4.1, and also has some experience with Neural Networks (NN) for pattern
recognition applications. TeK Associates
has
MatLab and Simulink along with the following MatLab toolboxes
and/or Blocksets (and has experience in using them, as first obtained for his
graduate students at Northeastern University in the 1990’s
and later during TeK Associates’ software development projects for National
Missile Defense [NMD] for MITRE [1997], XonTech [1999], and Raytheon [1999,
2000] and for U. S.
Navy AROSS
Littoral
Surveillance Program [2003],
specifically, Kalman filter covariance analysis of INS/GPS for Arête);
and for Goodrich ISR (now UTC Flight Services, later purchasing Rockwell Collins then merging with Raytheon to become Raytheon Technologies Coporation) for
certain critical 2 state Kalman filter analysis and
simulation (Oct. 2011-May 2012) for camera pointing; and, more recently, for
Kalman filter implementations in MatLab for OKSI (Nov. 2012-Mar. 2013) and
Aurora Flight Sciences (2014) [now part of Boeing in 2018].
|
* Fixed Point Blockset |
* Real-Time Workshop ver. 5.0
|
* MatLab Compilier
ver. 3.0
|
|
* Control
Systems ver. 5.2
|
* Data
Acquisition* ver. 2.2
|
* Symbolic
Math (Maple) ver. 2.1.3
|
|
* Statistics ver. 4.0
|
* Neural
Network ver. 4.0.2
|
* Extended
Symbolic Math ver. 2.1.3
|
| * Image
Processing ver. 3.2
|
* Robust
Control ver. 2.0.9
|
* Mu-Analysis
and Synthesis ver. 3.0.7
|
| * Signal
Processing ver. 6.0
|
* System
Identification ver. 5.0.2
|
* SB2SL ver. 2.5 (which converts models to Simulink)
|
*Unfortunately, according to an October 2009 meeting at
The MathWorks, their Data Acquisition Toolbox above currently lacks the ability to handle measurements using the older
VME and PCI protocols, PCI, nor the ability to handle the recent
PCIe protocol. In 2010, the Data Acquisition Toolbox does support
PCIe protocol but still not VME.
and
with Simulink®
Real-Time Workshop (ver. 5.0) and the associated Fixed Point Blockset.
He is becoming more familiar with C and C++ (as a prelude
to his using the more straight-forward C# [with automatic garabage
collection] of Microsoft Studio.NET) and WindowsNT
out of necessity since TeK Associates
has developed and continues to refine and update a low cost PC-based
Kalman filter\smoother\ simulator\optimal feedback regulator LQG\LTR software package:
TK-MIP (first demonstrated at IEEE Electro’95 in Boston,
MA). TK-MIP
is for sale commercially along with the accompanying
on-line prompters and built-in tutorials included as lucrative aspects of the
software (where the tutorials are unloaded from memory during actual signal processing to
avoid being a
CPU burden at that critical time, but still present and available on the hard
drive to appear when needed and invoked). TK-MIP
does not use anything from MatLab or Simulink since its main
objective is to be extremely efficient in
order to be sufficiently real-time and to still run in a small footprint
requiring a host PC with no more than 16
Megs of RAM. Using a processor with more than 16 Megabytes of RAM is therefore not a
constraint on TK-MIP.
Please click on
the “TK-MIP
ver. 2.0 for PC”
button at top of this screen to proceed to a free demo download
representative of our TK-MIP®
software. If any potential customer has further interest in purchasing our TK-MIP®
software, a detailed order form for printout (to be sent back to us via surface
mail or
fax) is
available within the free demo by clicking on the obvious Menu Item appearing at
the top of the primary demo screen (which is the Tutorials Screen within the
actual TK-MIP®
software). We also include representative numerical algorithms (fundamental to
our software) for users to test for numerical accuracy and computational speed
to satisfy themselves regarding its efficacy and efficiency before making any
commitment to purchase. We also have experience with National Instruments’
LabView® ver. 8.1, with COMSOL Multiphysics® versions 3.5a and 4.1, and likewise with MathSoft’s S-Plus®
version 4.5
and Latent Gold® statistical software, with Mathsoft’s
MathCad® version 13, with Mathematica®, and with Microsoft’s Zing®
(at http://research.microsoft.com/zing);
all of which we possess except for LabView® and COMSOL Multiphysics). We also have InstallShield Express version 2.01 and InstallShield PackageForTheWeb
version 1.3 and both Wise Installer version 8.12 and PC-Install version 7.
Since 1992, his new forte
is Visual Basic™ (vers. 3, 4, 5, 6 and .NET) for truly compiled executables,
*.exe’s (ever since
ver. 5), using
VBX’s\OCX’s,
DLL’s, DDE, OLE,
COM\DCOM\COM+, CAPICOM, and the
Window’s API for snappier
performance on the PC under both Windows 9x\ME and WindowsNT\2000\XP and the use of associated
third party tools. He is also involved in aspects of data acquisition for PC’s
(e.g., DMA and PCI databuses and DAQ data acquisition cards and signal
conditioning). He documents his research findings either in Microsoft Word or in
LaTeX. He owns all the above mentioned software tools (including a Simulink-to-C compiler 3.0) and a wide variety of MatLab
toolboxes, which he has demonstrated to his students at Northeastern University.
(He was at Intermetrics, Inc. as Ada was developed there for the Air
Force in the 1980’s,
so he has some exposure to Ada® as well [but limited to just attending classes in
it]. However, Tucker Taff at SofCheck (sofcheck.com,
and previously at Intermetrics, Inc. and long standing local Ada guru) and Bard Crawford
( Ada
Essentials: Overview, Examples and Glossary [Learnada, Vol. 1] by Bard
Crawford Published in 19 June 2000, Trafford Publishing, British Columbia,
Canada, ISBN 10: 1552123715, ISBN 13: 9781552123713,
also as a Kindle Edition, and originally from Barnes and Noble)
are minutes away from our location
in the center of Lexington. (Also see www.AdaCore.com
for current status and recent developments and Tucker Taft, as reported by this
originally New York, NY
company.) Dr. Crawford is currently two blocks away (until September 2009) and is known for his
automated Ada teaching materials. However, it is merely a stepping stone
since another version of Ada evolved later
as Ada 95. Ada 95 Textbooks: Brief Reviews, January 2001, http://www.seas.gwu.edu/faculty/mfeldman/ada95books.htmMichael
B. Feldman, Education Working Group Chair, ACM Special Interest
Group on Ada (SIGAda), Department of Computer Science, The George Washington
University, Washington, DC 20052, (202) 994-5919 (voice) -- (202) 994-4875
(fax), mfeldman@seas.gwu.edu http://www.seas.gwu.edu/faculty/mfeldmanFor
additional information and other useful links pertaining to Ada 95, visit Ada
Programming Language Resources for Educators and Students (http://www.acm.org/sigada/education) and AdaPower
(http://www.adapower.com). SofCheck is also known for expertise in
JAVA and in tools for JAVA support. TeK
Associates’
version of Simulink accommodates Ada modules within an S-Box and likewise for Fortran code and C code.
Fortran is not dead but lives on (in some of us, especially since U.S.
Government laboratories and FFRDC’s
received a waiver allowing them to be exempted from required use of Ada in the
1980’s). Fortran was the first computer language to meet the challenges
of exploiting parallel processing machines, as Fortran 90/95. A version of
Fortran was also early to support Interval Analysis, where unknown scalar
parameters (perhaps many) are contained between known lower and upper bounds.
[For more information on this interval analysis topic, please contact
Northeastern University ECE Department Prof. Bahram Shafai, shafai@ece.neu.edu;
phone: 617.373.2984] This Interval Analysis, Interval Matrices, and Interval Computing
approach has already been applied in
1997
to
radar target tracking by George Siouris (AFIT-retired) in Dayton, OH.
See:
.
See:
Siouris, G. M., Chen, G.-R., Wang, J.-R.,
“Tracking an Incoming Ballistic Missile using an Extended Interval Kalman
Filter,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 33, No. 1, pp. 232-240, Jan. 1997.
Dr. Kerr has developed a complete methodology
consisting of a catalog of analytic closed-form test cases for verifying general
purpose control and estimation related software code implementations and has
previously participated (through the Boston area IEEE Control Systems Society as
chairman for six years and as chairman of the Steering Committee for two years) in a run off competition\comparison which
occurred in September 1993 between four local, but nationally known,
Computer-Aided Control System Design (CACSD) vendors. The benefits of using
these recommended or similarly justified test cases are the reduced
computational expense incurred during software debug by using such
low-dimensional test cases and the insight gained into software performance (as
gauged against test problems of known closed-form solution behavior).
Click
here to see a copy of the software benchmark test handout that we sought to
compare to the computed outputs at this IEEE meeting.
Go
To Top
Go to Primary Table
of Contents
Having validated software that one is confident
of is a necessary prerequisite before venturing into mission-critical Navigation
applications, sonobuoy target tracking, radar target tracking, and novel
research areas such as applications of decentralized Kalman filters, or
sophisticated algorithms for further post-processing and massaging the outputs
of a Kalman filter, as occurs in certain approaches to signal detection in
statistically nonstationary systems and in NAV system failure detection and in
radar and optics-based maneuver
detection. Explicit analytic closed-form examples or counterexamples are also
useful for exposing existing problems or weaknesses in other areas of control
and estimation theory so that these unfortunate holes may be shored up in a
timely fashion before any damage is done in actual application mechanizations. Go to Top
Go to Primary Table of Contents
Professional
Affiliations: Institute of Electrical and
Electronics Engineers (IEEE) Life Senior
Member (Automatic Control, Aerospace and Electronic Systems, Information Theory,
Signal Processing, Computer Systems), American Institute of Aeronautics and
Astronautics (AIAA) Guidance, Control and Dynamics (AIAA Senior Member/AIAA
Associate Fellow: https://www.aiaa.org/docs/default-source/uploadedfiles/membership-and-communities/recognition/member-advancement/aiaa-associate-fellows.pdf?sfvrsn=dbf7e9f9_0), Institute of
Navigation (ION), life member of American Defense Preparedness Association (ADPA)
now renamed NDIA, National Defense Industrial Association, Society
of Optical
Engineering (SPIE), American Association for the Advancement of Science
(AAAS),
Mathematical Association of America (MAA), American Statistical Association (ASA),
Association for Computing Machinery (ACM), Visual Basic User’s Group, Microsoft
Developers’ Network (MSDN) [Level
2], and the Instrumentation, Systems, and Automation Society (ISA), and in New
England Chinese Information & Networking Association (NECINA) [2005-2007].
Go
to Top
Go to Primary Table of Contents
Go
to Top
Go to Primary Table of Contents
Honors:
Junior High Rensselaer (RPI) Medal in 1960 “for
Mathematics and Science proficiency”,
High School Honor Society in 1962, High School Mathematics and Science Award in
1963, High School Musician Award (and one year membership in professional
musician’s
union) in 1963, Tau Beta Pi, Pi Mu Epsilon (president of student chapter in his senior year ’66-’67), Eta Kappa
Nu, Sigma Pi Sigma, Western Electric Award
(’66), Douglas Aircraft Award
(’67),
Who’s Who in American Schools and
Colleges (’67),
$340 Student Prize Paper Contest Sponsored by the Federal Power
Commission (’67),
Engineers Wives’
Award (’67),
National Science Foundation Traineeship
(’68-’70), Acting
chairman of Stochastic Control Session of IEEE Conf. on Decision & Control (’75)
[originally, was only assistant chairman but the chairman, Prof. David Kleinman,
had to leave beforehand because of a family emergency], won 1987
M. Barry Carlton Award and
$3,000 honorarium for
Outstanding Paper to
appear in IEEE Aerospace and Electronic Systems Transactions in
’87
[for further confirmation, please see page 822 of Vol. 24, No. 6,
Nov. 1988 of the aforementioned journal and see:
https://ieee-aess.org/media/decentralized-filtering-and-redundancy-management-multisensor-navigation], delivered invited lecture at
University of Iowa (1988), joined
Sigma Xi (in ’90),
delivered Distinguished Engineer Lecture at University of
Maryland (UMBC on Feb. 1990), delivered invited lecture at University of Connecticut
(1995). Listed in Marquis’
Who’s Who
in
the East
(’92) and
in Technology (’93), and
in the World (’98), and
in
the USA (’03), and
in Finance and Business (’05),
and in America (’06),
and in Science and Engineering (’06),
and in Who’s
Who (’10).
Listed
in Global Register’s
Who’s Who
of Executives and Professionals (’05).
Chairman of local Boston section of
IEEE Control Systems ’90-’92,
’01-’04; chairman of the Steering Committee
’92-’94,
’04-’06; vice-chairman of the section
’95-’96,
’98-’00. Co-chairman
of Sensors, Components, and Algorithms for Navigation session at the
Institute of Navigation (ION) Annual Summer Conference (’99) in Cambridge, MA.,
Life Senior Member of IEEE (’10).
Member of SPIE: https://spie.org/profile/Thomas.KerrIII-2982?SSO=1
Over
130+
publications in the open peer-reviewed literature and as company reports. Thomas H. Kerr
III’s 2019 Nomination for IEEE Computer
Society’s Harry H. Goode Award.
Go to Top
Go to Primary Table of Contents
PROFESSIONAL
HISTORY:
| From
(year) to (year) |
Name
of Company |
Position
Held
|
|
1992-Present
|
TeK Associates (Lexington,
MA, now in Woburn, MA)
|
CEO/Sr. Systems Engineer/Chief Programmer/Web Master |
| 06/21/2022-07/14/2023 |
Exclusively
for Zivaro,
Inc.(Partnered with JACOBS) in Colorado Springs, CO |
Algorithm
Engineer (Performing Strategic Consulting for SpaceForce
Office
of the Chief Scientist) |
| 06/17/2019-11/01/2019 |
GCR
at Draper Laboratory (Cambridge, MA) |
Contractor:
Senior GNC Analyst |
| 10/2012-5/2013 |
Adecco
at
Goodrich
ISR (Westford, MA) |
Contractor:
Systems Engineer for U-2S SYERS Camera Pointing accuracy |
| 04/09/07-04/08/2009 |
Kelly
Services at Google Books (Lexington, MA) |
Contractor: Quality Assurance (QA)
operator for 2-D images |
| 1992-6/21/2022 |
TeK Associates (Lexington,
MA, now in Woburn, MA) |
CEO/Principal Investigator/Chief Programmer/Owner
|
| 1990-1995 (evenings) |
Northeastern
University Graduate ECE Department (Boston) |
Instructor in Optimal Control and Kalman Filtering (for 4
yrs) |
| 1986-1992 |
Lincoln Laboratory of MIT (Lexington, MA) |
Member of the Technical Staff
|
| 1979-1986 |
Intermetrics, Inc. (Cambridge, MA) |
Senior Systems Analyst/Systems Engineer
|
| 1973-1979 |
The Analytic Sciences Corporation (TASC) (Reading,
MA) |
Member of the Technical Staff
|
| 1971-1973 |
General Electric Corporate R&D Center
(Schenectady, NY) |
Control Engineer |
| 1969-1971 |
University of Iowa (Iowa City, IA) |
Research Assistant/Teaching Assistant (as a
graduate student, obtaining M.S.E.E. and Ph.D.) |
| 1967 |
Howard
University (Washington, D.C.) |
Research Assistant (part of senior year and summer
after graduating with B.S.E.E.) |
Go to Primary Table of
Contents
Tom
has been nominated to become an IEEE Fellow (but not yet completed): For contributions to Kalman
filter-based failure detection/system reconfiguration theory and to
decentralized Kalman filter and nonlinear filtering applications.
Our SSBN submarines can launch while submerged;
while those of many other countries must surface first before they can launch.
|
Publications
constituting significant development in submarine navigation trade-off
considerations between frequency of external navaid usage (to maintain
sufficient navigation accuracy in case a launch is ordered) versus exposure to
enemy surveillance:
-
Kerr, T. H., “Preliminary Quantitative Evaluation of
Accuracy/Observables Trade-off in Selecting Loran/NAVSAT Fix Strategies,”
TASC Technical Information Memorandum TIM-889-3-1, Reading, MA, December 1977 (Confidential).
-
Kerr, T. H., “Improving C-3 SSBN Navaid
Utilization,”
TASC TIM-1390-3-1, Reading, MA, August 1979 (Secret).
-
Kerr, T. H., “Modeling and Evaluating an Empirical INS Difference Monitoring Procedure Used to Sequence SSBN Navaid
Fixes,”
Proceedings of the Annual Meeting of the Institute of Navigation, U.S. Naval Academy, Annapolis, Md., 9-11 June 1981 (reprinted in
Navigation: Journal of the Institute of Navigation, Vol. 28, No. 4, pp. 263-285, Winter
1981-82).
-
Kerr, T. H., “Sensor Scheduling in Kalman Filters: Evaluating a Procedure for Varying Submarine
Navaids,”
Proceedings of 57th Annual Meeting of the Institute of Navigation, pp. 310-324, Albuquerque, NM, 9-13 June
2001 (an update).
|
|
Publications
wherein he developed the Two Confidence Region Failure Detection Approach§ (used
in INS submarine navigation):
|
Kerr,
T. H., “Poseidon Improvement Studies: Real-Time Failure Detection in the
SINS/ESGM,” TASC Report TR-418-20, Reading, MA, June 1974 (Confidential).
|
|
Kerr,
T. H., “Failure Detection in the SINS/ESGM System,” TASC Report
TR-528-3-1, Reading, MA, July 1975 (Confidential).
|
|
Kerr,
T. H., “Improving ESGM Failure Detection in the SINS/ESGM System (U),”
TASC Report TR-678-3-1, Reading, MA, October 1976 (Confidential).
|
|
Kerr,
T. H., “Failure Detection Aids for Human Operator Decisions in a Precision
Inertial Navigation System Complex,” Proceedings of Symposium on
Applications of Decision Theory to Problems of Diagnosis and Repair,
Keith Womer (editor), Wright-Patterson AFB, OH: AFIT TR 76-15, AFIT/EN, Oct.
1976, sponsored by Dayton Chapter of the American Statistical Association,
Fairborn, Ohio, June 1976.
|
|
Kerr, T. H., “Real-Time Failure Detection: A Static Nonlinear
Optimization Problem that Yields a Two Ellipsoid Overlap Test,” Journal of
Optimization Theory and Applications, Vol. 22, No. 4, pp. 509-535, August
1977.
|
|
Kerr,
T. H., “Statistical Analysis of a Two Ellipsoid Overlap Test for Real-Time
Failure Detection,” IEEE Transactions on Automatic Control, Vol. 25, No. 4, August
1980.
|
|
Kerr,
T. H., “False Alarm and Correct Detection Probabilities Over a Time
Interval for Restricted Classes of Failure Detection Algorithms,” IEEE
Transactions on Information Theory, Vol. 28, No. 4, pp. 619-631, July 1982.
|
|
Kerr,
T. H., “Examining the Controversy Over the Acceptability of SPRT and GLR
Techniques and Other Loose Ends in Failure Detection,” Proceedings of
the American Control Conference, San Francisco, CA, 22-24 June 1983.
(an expose)
|
|
Kerr,
T. H., “Comments on ‘A Chi-Square Test for Fault Detection in Kalman
Filters’,” IEEE Transactions on Automatic Control, Vol. 35, No. 11, pp.
1277-1278, November 1990.
|
|
Kerr,
T. H., “A Critique of Several Failure Detection Approaches for Navigation
Systems,” IEEE Transactions on Automatic Control, Vol. 34, No. 7, pp. 791-792,
July 1989. (an expose of sorts)
|
|
Kerr,
T. H., “On Duality Between Failure Detection and Radar/Optical Maneuver
Detection,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 4, pp. 581-583,
July 1989.
|
|
Kerr,
T. H., “Comments on ‘An Algorithm for Real-Time Failure Detection in
Kalman Filters’,” IEEE Trans. on Automatic Control, Vol. 43, No. 5, pp. 682-683,
May 1998. (an expose of sorts) |
|
Kerr,
T. H., “Integral Evaluation Enabling Performance Trade-offs for Two
Confidence Region-Based Failure Detection,” AIAA Journal of Guidance,
Control, and Dynamics, Vol. 29, No. 3, pp. 757-762, May-Jun. 2006.
|
|
|
Publications
addressing Decentralized Kalman Filtering-a theoretical basis for networked
sensors:
|
Kerr, T. H.,
“Stability Conditions for the RelNav Community as a Decentralized Estimator-Final
Report,”
Intermetrics, Inc. Report No. IR-480, Cambridge, MA, 10 August 1980 |
|
Kerr, T. H., and Chin, L.,
“A Stable Decentralized Filtering Implementation for JTIDS RelNav,”
Proceedings of IEEE Position, Location, and Navigation Symposium, Atlantic City, NJ, 8-11 December 1980. |
|
Kerr,
T.H., and Chin, L., “The Theory and Techniques of Discrete-Time Decentralized
Filters,”
in
Advances in the Techniques and Technology in the Application of Nonlinear Filters and Kalman
Filters, edited by C.T. Leondes, AGARDograph No. 256, Noordhoff International Publishing, Lieden, 1981. |
|
Carlson, N. A., Kerr, T. H., Sacks, J. E.,
“Integrated Navigation Concept
Study,”
Intermetrics Report No. IR-MA-321, 15 June 1984.
|
|
|
His
publications that combine the ideas of failure detection with those of
decentralized Kalman Filtering to yield a breakthrough rigorous basis for system
reconfiguration and redundancy management:
|
Kerr, T. H., “Decentralized Filtering and Redundancy Management Failure Detection for Multi-Sensor Integrated Navigation
Systems,”
Proceedings of the National Technical Meeting of the Institute of Navigation
(ION), San Diego, CA, 15-17 January 1985. (an expose) |
| Kerr, T. H., “Decentralized Filtering and Redundancy Management for
Multi -sensor
Navigation,”
IEEE Trans. on Aerospace and Electronic Systems, Vol. 23, No. 1, pp. 83-119, Jan.
1987.
(which spawned 11
patents, as can be confirmed by viewing this paper in IEEExplore, or merely click
here: "View Paper":
, none of which personally benefited me
financially except for favorable publicity.) |
|
|
EVIDENCE
OF TECHNICAL ACCOMPLISHMENT:
|
Personally
trailblazing R&D development of the Kalman filter-based Two Confidence
Region Failure Detection proceeding from first principles and carrying it
elegantly to fruition. |
|
He
surveyed many historical approaches to decentralized filtering and narrowed
down to identify those few that rigorously satisfied reasonableness
constraints possessed by the Joint Tactical Information and Distribution
System (JTIDS) and Integrated Communications Navigation and Identification
in Avionics (ICNIA) applications that motivated his investigation. |
|
Ground
breaking insight was exhibited in his leaping to realize the utility of
combining his earlier “failure detection methodologies” with the results
of his later investigation into “decentralized estimation”, thus reaping
a satisfying firm theoretical foundation for “redundancy management” for
navigation applications.
|
|
|
He
has published the following three book chapters:
-
Kerr,
T.H., and Chin, L., “The Theory and Techniques of Discrete-Time
Decentralized Filters,” in Advances in the Techniques and Technology in
the Application of Nonlinear Filters and Kalman Filters, edited by C. T.
Leondes, AGARDograph No. 256, Noordhoff International Publishing, Lieden,
1981.
-
Kerr,
T. H., “Computational Techniques for the Matrix Pseudoinverse in Minimum
Variance Reduced-Order Filtering and Control,” in Control and Dynamic
Systems-Advances in Theory and Applications, Vol. XXVIII: Advances in
Algorithms and computational Techniques for Dynamic Control Systems,
Part 1 of 3, C. T. Leondes (Ed.), Academic Press, NY, 1988; (an
expose and illustrative use of counterexamples)
-
Kerr,
T. H., “Numerical Approximations and Other Structural Issues in Practical
Implementations of Kalman Filtering,” a chapter in Approximate Kalman
Filtering, edited by Guanrong Chen, World Scientific, NY, 1993;
where all three of the above discussions
specifically pertain to different aspects of Kalman filters.
|
|
He
has several publications relating to underlying numerical computational details,
as arise in implementing Kalman filters:
-
Kerr, T. H., “An Invalid Norm Appearing in Control and
Estimation,”
IEEE Transactions on Automatic Control, Vol. 23, No. 1, Feb. 1978.
(counterexamples
and a correction)
-
Kerr, T. H., “Testing Matrices for Definiteness and Application Examples that Spawn the
Need,”
AIAA Journal of Guidance, Control, and Dynamics, Vol. 10, No. 5, pp. 503-506, Sept.-Oct., 1987.
-
Kerr, T. H., “Three Important Matrix Inequalities Currently Impacting Control and Estimation Applications,”
IEEE Trans. on Automatic Control, Vol. AC-23, No. 6, pp. 1110-1111, Dec. 1978.
-
Kerr, T. H., “Rationale for Monte-Carlo Simulator Design to Support Multichannel Spectral Estimation and/or Kalman Filter Performance Testing and Software Validation/Verification Using Closed-Form Test
Cases,”
MIT Lincoln Laboratory Report No. PA-512, Lexington, MA, 22 December 1989
(BSD).
-
Kerr, T. H., “Multichannel Shaping Filter Formulations for Vector Random Process Modeling Using Matrix Spectral
Factorization,”
MIT Lincoln Laboratory Report No. PA-500, Lexington, MA, 27 March 1989.
-
Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear
Filtering,”
IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 5, pp. 590-601, Sep.
1989.
(an expose)
-
Kerr, T. H., “On Misstatements of the Test for Positive Semidefinite
Matrices,”
AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, pp. 571-572, May-Jun.
1990.
(as occurred in Navigation & Target Tracking software in
the 1970’s & 1980’s using counterexamples)
-
Kerr, T. H., “Fallacies in Computational Testing of Matrix Positive
Definiteness/Semidefiniteness,”
IEEE Transactions on Aerospace and
Electronic Systems, Vol. 26, No. 2, pp. 415-421, Mar. 1990.
(Lists fallacious algorithms that the author found to routinely exist in
U.S. Navy submarine navigation and sonobuoy software in the late 1970’s and
early 1980’s using explicit counterexamples to point out the problems that “lurk under the
surface”.)
-
Kerr, T. H., “A Constructive Use of Idempotent Matrices to Validate Linear Systems Analysis
Software,”
IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 6, pp. 935-952, Nov. 1990.
(closed-form
analytic solutions)
-
Kerr, T. H., “Emulating Random Process Target Statistics (Using
MSF),”
IEEE Transactions on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 556-577, Apr. 1994.
(closed-form
analytic solutions)
-
Kerr, T. H., “Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic
Results,” Proceedings of
SPIE, Session 4473: Tracking Small Targets, pp. 142-168, San Diego, 29 July-3 Aug. 2001.
(as
above, more closed-form
analytic solutions to be used as test cases for comparison to numerically
computed solutions for software IV&V)
-
Kerr, T. H., “ADA70 Steady-State Initial-Value Convergence Techniques,” General Electric Class 2 Report, Technical Information Series No. 72 CRD095, 1972.
Click here for More...
and
as encountered in several diverse applications:
-
Kerr, T. H.,
“Angle-Only Tracking,”
slide presentation for Reentry Systems Program Review, Lincoln Laboratory, Lexington, MA, 10 Jan. 1989.
-
Kerr, T. H.,
“Streamlining Measurement Iteration for EKF Target
Tracking,”
IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 2,
pp. 408-421, Mar. 1991.
One may confirm that, at the end of section 4.3 on page 17 of this paper:
-
Kerr, T. H., “Assessing and Improving the Status of Existing Angle-Only Tracking (AOT) Results,” Proceedings of the International Conference on Signal Processing Applications & Technology, Boston, pp. 1574-1587, 24-26 Oct. 1995.
(an expose)
At the end of
Sec. 4.3 of my previous 1995 AOT paper just cited above, I advocated for or suggested use
of the E-M Algorithm
instead of
GLR
within some applications of
Extended Kalman Filters (EKF)
back then.
(See the following 2018 IEEE AES Barry Carlton Award winning paper:
Yulong Huang; Yonggang Zhang; Bo Xu; Zhemin Wu; Jonathon A. Chambers,
“A New Adaptive Extended Kalman Filter for
Cooperative Localization,"
IEEE Transactions on Aerospace and Electronic Systems, Vol. 54, No. 1, pp. 353-368, Feb. 2018.
They follow-up and utilize the E-M
Algorithm within their EKF!)
-
Kerr, T. H.,
“Use of GPS/INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning
NN-based ATR
algorithms),”
the Institute of Navigation
Proceedings of GPS-94, Salt Lake City, pp. 1173-1188, 20-23 Sep. 1994.
-
Kerr, T. H.,
“Extending Decentralized Kalman Filtering
(KF) to 2-D for Real-Time Multisensor Image Fusion and/or
Restoration,”
Proceedings of SPIE Conference, Vol. 2755, Orlando, pp. 548-564, 8-10 Apr. 1996.
-
Kerr, T. H.,
“Extending Decentralized Kalman Filtering
(KF) to 2D for Real-Time Multisensor Image Fusion and/or Restoration: Optimality of Some Decentralized KF
Architectures,”
Proceedings of the International Conference on Signal Processing Applications &
Technology, Boston, MA, 7-10 Oct. 1996.
-
Kerr, T. H.,
“Developing Cramér-Rao
Lower Bounds to Gauge the Effectiveness of UEWR Target Tracking
Filters(U),”
Proceedings of AIAA/BMDO Technology Readiness Conference and Exhibit, Colorado Springs, 3-7 August
1998 (Unclassified).
-
Kerr, T. H., UEWR Design Notebook-Section 2.3: Track Analysis, TeK Associates: XonTech Report No. D744-10300, 29 March 1999.
-
Kerr, T. H.,
“Considerations in whether to use Marquardt Nonlinear Least Squares vs. Lambert Algorithm for NMD Cue Track Initiation (TI)
calculations,”
TeK Associates Technical Report No. 2000-101, Lexington, MA, (for Raytheon, Sudbury, MA), 27 September 2000.
-
Satz, H. S., Kerr, T. H.,
“Comparison of Batch and Kalman Filtering for Radar
Tracking,”
Proceedings of 10th Annual AIAA/BMDO Conference, Williamsburg, VA, 25 July 2001. (Unclassified).
Also see: https://apps.dtic.mil/dtic/tr/fulltext/u2/p011192.pdf
-
Kerr, T. H.,
“Novel
Variations on Old Architectures/Mechanizations for New Miniature Autonomous
Systems,”
Web-Based Proceedings of GNC Challenges of
Miniature Autonomous Systems Workshop,
Session E1: Controlling Miniature Autonomous Systems, sponsored by Institute
of Navigation (ION), Fort Walton Beach, FL, 26-28 October 2009.
|
|
He
has sufficient breadth to analyze other issues besides just those relating to
Kalman Filtering such as GPS integration, Sonobuoy passive and active target tracking,
Surveillance sweeprates, and Neural Networks:
-
Kerr, T. H.,
“Impact of Navigation Accuracy in Optimized Straight-Line Surveillance/Detection of Undersea Buried Pipe
Valves,”
Proceedings of National Marine Meeting of the Institute of Navigation, Cambridge, MA, 27-29 Oct. 1982.
(Importance of surveillance sweeprates and closed-form analytic
solutions)
-
Kerr, T. H.,
“Phase III GPS Integration; Volume 1: GPS
U.E.
Characteristics,”
Intermetrics Report IR-MA-177, Cambridge, MA, Jan. 1983.
-
Kerr, T.H.,
“GPS/SSN Antenna Detectability,”
Intermetrics Report No. IR-MA-199, Cambridge, MA, 15 Mar. 1983
-
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.
-
Kerr, T. H.,
“Assessment of the Status of the Current Post-Coherent Localization
Algorithm,”
Intermetrics Report No. IR-MA-319, 31 May 1984.
(Sonobuoy target tracking and counterexamples)
-
Kerr, T. H., “Update to and Refinement of Aspects of Pattern Recognition Principles Used in the Missile Warning System (AN/AAR-47),” Intermetrics Report No. IR-MA-362, Cambridge, MA, for Honeywell Electro-Optical, Lexington, MA, 15 Sep. 1984.
-
Kerr, T. H.,
“An Analytic Example of a Schweppe Likelihood Ratio
Detector,”
IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 4, pp. 545-558, Jul.
1989.
(closed-form analytic solution)
-
Kerr, T. H.,
“Critique of Some Neural Network Architectures and Claims for Control and
Estimation,”
IEEE Transactions on Aerospace and Electronic Systems, Vol. 34, No. 2, pp. 406-419, Apr. 1998.
(an expose)
-
Kerr, T. H.,
“Further Critical Perspectives on Certain Aspects of GPS Development and
Use,”
Proceedings of 57th Annual Meeting of the Institute of Navigation, pp. 592-608, Albuquerque, NM, 9-13 Jun. 2001.
(an expose of several loose ends in GPS
development that needed [and have now received] further attention before unabated
and unabashed reliance upon GPS, as had been the plan and goal for
Battlefield 2000)
-
Kerr, T. H.,
“New Lamps for Old: a shell game for generalized likelihood use in radar? Or this
isn’t your father’s GLR!,”
Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 476-483, San Diego, CA, 29 July-3 Aug. 2001.
(an expose)
-
Kerr, T. H.,
“Vulnerability of Recent GPS Adaptive Antenna Processing (and all
STAP/SLC) to Statistically Non-Stationary Jammer
Threats,”
Proceedings of SPIE, Session 4473: Tracking Small Targets, pp. 62-73, San Diego, CA, 29 July-3 Aug. 2001.
(an expose)
-
Kerr, T. H., “Comments on ‘Determining if Two Solid Ellipsoids
Intersect’,” AIAA Journal of Guidance, Control, and
Dynamics,
Vol. 28, No. 1, pp. 189-190, Jan.-Feb. 2005.
(Offers a simpler implementation and reminds readers that real-time embedded
applications do not usually have MatLab algorithms available, as otherwise
required for implementing the algorithm without the simplification that we
provide.)
-
Kerr, T. H.,
“Comment on
‘Precision Free-Inertial Navigation with Gravity Compensation by an Onboard
Gradiometer’,”
AIAA Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4, pp.
1214-1215, Jul.-Aug.
2007.
(This
provides two closed-form counterexamples to demonstrate the problem with this
new result. Since the procedure proposed by Prof. C. Jekeli is offered for numerical
data only, it would be difficult or impossible to reveal the flaw that
exists in the new methodology offered without
resorting to closed-form analytical solutions, which I did. Prof. Jekeli strongly denied
that he had this problem when my article was first published in this Journal
even though it had been critically reviewed by others before publication, as is
standard procedure yet Prof. Jekeli denied it and merely repeated the exact same
flawed
conditions for applicability that he had previously stated in the hypothesis of conditions for the applicability of his
newly proposed technique. I went back to the fundamentals of random variables
and Realization Theory, which are well-known to Control Theorists, in order
to create these fairly obvious counterexamples. I would not expect him to know this since it is not his
bailiwick but it is mine, which is why I immediately responded. My old coworker at Intermetrics, Inc., (the late)
David Antonitis, would likely have wanted me to help his prior client from the High
Altitude Balloon
project in the 1980's, back when Dr. Jekeli was at The Air Force Geophysical Laboratory at
Hanscomb AFB [before they changed their name to Phillips Laboratory and moved to
Albuquerque, NM].)
-
Kerr,
T. H., “Comment on ‘Low-Noise Linear Combination of Triple-Frequency
Carrier Phase Measurements’,” Navigation: Journal of the Institute of
Navigation, Vol. 57, No. 2, pp. 161, 162, Summer 2010.
(provides
a simpler more direct solution)
-
Click this link here to see a more
comprehensive
list of our publications.
|
|
IEEE
ACTIVITIES – AWARDS, OFFICES HELD, COMMITTEE MEMBERSHIPS:
|
1975 Vice-Chairman of Stochastic Control Session at Conference on Decision and Control
(CDC); |
| 1988
M. Barry Carlton Award from IEEE Aerospace and Electronics Systems for
Outstanding Paper in 1987 (which spawned 11 patents, as can be
confirmed, none of which personally benefited me financially);
For confirmation, merely click here:
"View Paper"
to
see the number of patents spawned on the upper left hand side within the gray
box. |
|
1990-1992 Chairman of local Boston section of Control Systems Society; |
|
1992-1994 Chairman of Steering Committee of local Boston section of Control Systems Society; |
|
1995-1996 Vice-Chairman of local Boston section of Control Systems Society; |
|
1997-1998 At-large member of Steering Committee of local Boston section of Control Systems Society; |
|
2000-2004 Chairman of local Boston section of Control Systems Society (again); |
| Has served as paper reviewer numerous times for IEEE Transactions on AC, IT, AES, SMC,
SP, Computer Science and for AIAA Journal of Guidance, Control, and Dynamics over the
years; |
|
Made
a Life Senior Member of IEEE in 2011. |
|
|
NON-IEEE
ACTIVITIES AWARDS, PROFESSIONAL SOCIETY MEMBERSHIPS, COMMITTEE
MEMBERSHIPS:
|
Qualified
for and joined honor societies: Tau Beta Pi, Eta Kappa Nu, Sigma Pi Sigma, Pi Mu Epsilon (student president), Sigma
Xi; |
|
1967
Who’s Who in American Schools and Colleges; |
|
1967 $340 Student Prize Paper Award sponsored by Federal Power Commission for local engineering schools in the Washington D.C. area; |
| 1966-1969
Tutored Statics, Dynamics, Calculus,
and Strength of Materials at Howard Univ. &
Circuit Theory at
Univ. of Iowa; |
|
1971-1973 Tutored mathematics at Union College and at Schenectady, NY Community Center; |
|
1973 -1975 Tutored mathematics at Union Methodist Church in Boston, MA; |
|
In
1990’s, gave invited lectures at University of Iowa (Iowa City), University of Connecticut, University of Maryland (Baltimore), and West Virginia
University (Morgantown); |
|
AIAA
GNC Senior Member (and became an AIAA
GNC Associate Fellow in January 2012); |
|
Member of Institute of Navigation (ION) since 1981 (served as interim ION Journal editor in 1985-1986); |
|
Served as Co-chairman of
“Sensors, Components, and Algorithms for
Navigation”
session at the Institute of Navigation (ION) Annual Summer Conference (1999) in Cambridge, MA; |
|
Member of American Association for the Advancement of Science, Association of Computing Machinery, SPIE, National Defense Preparedness Association (life member), Mathematical Association of America, American Statistical Association, Microsoft Developer Network (MSDN) level 2; |
|
Who’s Who in the East
(’92), in Technology
(’93), in the World
(’98), in the USA
(’03), in Finance and Business
(’05), and in Science and Engineering
(’06). Listed in Global
Register’s
Who’s Who of Executives and Professionals in
’05; |
| Received AIAA 25 year plaque
(2005); |
| Became
an Associate Fellow of AIAA GNC (January 2012);
|
| Ride leader for Charles River Wheelmen
(’90-’97),
long distance cycling club. (Member:
’77-Present). |
|
§The
CR2 failure detection approach, developed by Tom and summarized above, is independently endorsed in:
Brumback, B. D., Srinath, M. D., “A
Chi-Square Test for Fault-Detection in Kalman Filters,” IEEE Trans. on
Automatic Control, Vol. 32, No. 6,
pp. 532-554, June 1987.
Please
notice the high ratings of relevance and importance ascribed to the publications
listed above, when they are obtained from the Citation Index associated with the on-line “Web
of Science” at any good research library.
Also
see:
-https://scicomp.stackexchange.com/users/27180/thomas-h-kerr-iii?tab=profile
-https://scholar.google.com/citations?user=UjaYY4EAAAAJ&hl=en
-https://academic.microsoft.com/#/detail/2424976702
-https://www.researchgate.net/profile/Thomas_Kerr_Iii
-https://blogs.mathworks.com/headlines/2016/09/08/this-56-year-old-algorithm-is-key-to-space-travel-gps-vr-and-more/
(click comments to see my entries)
They can always be found by clicking
here.
While we sometimes serve as a watch dog;
evidently, more watch dogs are badly needed!
Go
To Top
Go to Primary Table
of Contents
From left to right, Ed Bristol (Foxboro,
now retired), "Larry" Y.-C. Ho (Harvard, now retired), George Kovatch (Volpe Transportation Systems
center, now retired),
unidentified (Volpe Transportation Systems center), Tom Kerr (TeK Associates,
retiring personality)
Go to Top
Links
TeK Associates’ website
sometimes contains links to other sites. TeK Associates assumes no
responsibility for the content or the privacy policies and practices of such
websites. TeK Associates encourages you to read the privacy statements of
these linked sites; their privacy practices may differ from ours. However, we
are always rather conservative in what we link to.
Contact Information:
- Telephone:
 - FAX:
 - Postal address:
- TeK Associates
- 21
Cummings Park Dr., Suite 230
- Woburn,
Massachusetts 01801, USA
-
Click
here for TeK Associates’
brick and mortar
physical location and how to get there. [It was still there even
when I was NOT, while I was was working in Colorado Springs, CO at Zivaro, Inc.
until August 2023.]
Electronic mail:
General Information, Sales, Customer Support, Webmaster:
(If you wish to print information from Websites with black backgrounds, we recommend that
you first invert colors unless you are interested in the original graphics.
Click on: http://word.mvps.org/FAQs/Formatting/PrintWhiteOnBlack.htm
The present website is optimized for viewing from a Microsoft Internet Explorer 5.0 or
later browser.) For some reason (unknown to us), the spacing is
better when viewed using a Firefox browser. Go
to Primary Table of Contents
|
(Our
navigation buttons are at the TOP of each screen.) 
