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Thomas Henderson Kerr III

Thomas Henderson Kerr III
TeK Associates · TK-MIP R&D Software Development Department

BSEE magna cum laude, MSEE, Ph.D. in EE Modern Control & Estimation

About

98
Publications
3,479
Reads
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1,062
Citations
Introduction
I am an R&D Algorithm Engineer in DSP & in Extended Kalman Filter & Estimation Theory-related apps. I have supplemented my formal education with 95+ continuing education courses. I developed a failure detection algorithm for an SSBN Inertial Navigation System. I understand navigation and GPS & have also been involved in Kalman-like filters for Early Warning Radars to track enemy RV's. I am proficient in many computer languages but now use Matlab/Simulink and my own TK-MIP s/w for Monte-Carlo simulation.
Additional affiliations
June 2019 - November 2019
Draper Laboratory
Position
  • Senior GNC Analyst
Description
  • As GCR Contractor, used LaTeX to document Covariance Analysis approach to gauging effect of angle random walk on errors associated with existing Kalman filter for Trident submarines.
January 1990 - June 1995
Northeastern University
Position
  • Instructor
Description
  • Instructor teaching Optimal Control & LQG with Kalman Filter (evenings only)
October 1986 - July 1992
Massachusetts Institute of Technology
Position
  • Member of the Technical Staff
Description
  • Representing an RV's wake using multi-channel maximum entropy spectral estimation & other approaches. Numerical studies of EKF tracking of enemy RV's for several cases. NAV analysis to specify grooming procedures for multi-sensor airborne data collection
Education
September 1967 - February 1971
University of Iowa
Field of study
  • Optimal and Stochastic Control and Estimation/Kalman Filters
September 1963 - June 1967
Howard University
Field of study
  • Electrical Engineering: Electronics

Publications

Publications (98)
Article
Full-text available
Elucidating the nature of a familiar closed-form solution arising in the optimization of [1].
Article
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New methodologies for target tracking and for evaluating its efficacy have recently emerged, all potentially being a "magic bullet". The questionable accuracy benefits, missing rigor (in some cases), and definitely large CPU-time computer loading drawbacks of the new estimation approaches are discussed as compared to a conventional Extended Kalman...
Article
Full-text available
The integral evaluations enabling performance tradeoffs for two-confidence-region approach (CR2) for detection of failure are discussed. Failure detection requires continuous vigilant monitoring of the observable output variables of the system. The CR2 approach to failure detection places one ellipsoidal confidence region about the nominally unfill...
Article
Full-text available
Use of the Generalized Likelihood Ratio or of Inter-active Multiple Model-Based filters have been historically posed as solutions to certain event detection problems such as for failure detection in navigation systems and for maneuver detection in radar target tracking. This critical survey discusses specific drawbacks, barriers, and limitations en...
Article
Full-text available
The clarification regarding the anticipated computational load and numerical sensitivity of the overlap test of two solid ellipsoids is presented. The act of computing eigenvalues is the act of computing the zeros of the characteristic polynomial. The overlap test needs matrix positive definiteness/semidefiniteness tests along with an implied eigen...
Article
Full-text available
We alert the reader here to a variety of structural properties associated with idempotent matrices that make them extremely useful in the verification/validation testing of general purpose control and estimation related software. A rigorous general methodology is provided here along with its rationale to justify use of idempotent matrices in conjun...
Article
We alert the reader here to an apparent vulnerability in recent adaptive antenna processing that claims increased GPS jammer resistance via use of lucrative new approaches to adaptive beamforming and/or null-steering, but unfortunately, presumes only simplistic unsophisticated wideband barrage WGN jammers as threats. When jammers are less cooperati...
Article
Full-text available
We alert the reader here to a discrepancy between what has recently been referred to as the Generalized Likelihood Ratio (GLR) approach to radar target detection and what has historically been used as the GLR approach to this same problem in detection theory. Despite these identified discrepancies, the recent version is tractable and has desirable...
Article
Full-text available
Radar tracking performance was compared among two choices of statistical filtering algorithms for the noisy measurements of exo-atmospheric objects in ballistic motion. Such motion is characteristic of satellites and missiles. Object position and velocity were governed by the nonlinear dynamics of body motion in a central force field, and measureme...
Article
In the above-mentioned paper by Zolghadri (ibid. vol.41 (1996)) the commenter objects to claims made of providing simpler implementation complexity or computational burden without an explicit mechanization for obtaining a solution ever actually being offered (and operations counts being tallied).
Article
Full-text available
While there is great potential for successful use of neural network (NN) algorithms in automatic target recognition (ATR) and other pattern identification/classification applications, significant barriers have been encountered that, to date, defy rigorous use of NNs within feedback control designs. The status of several problems and contradictions...
Conference Paper
While we offered the first link between idempotent matrices and expedient easy calculation of the matrix exponential for pre-validation software testing in 1989, there have been several interesting closed-form expressions subsequently offered by others for the matrix exponential exp(F) under special cases of the system matrix F being merely 2×2 or...
Conference Paper
We seek to clarify a few problems associated with GPS use in order to propel their resolution by clearly elucidating the nature of these problems. We express our concerns about (1) certain aspects of prescribed GPS availability augmentation that currently calls for heavy supplemental reliance on (apparently risky) baro-altimeters, (2) the difficult...
Article
Full-text available
We pursue the idea that recent 'decentralized' Kalman filter (KF) technology, by outfitting each participating imaging sensor with its own dedicated 2-D Kalman filter can be used as the basis of a sensor fusion methodology that allows a final collating filter to assemble the data from diverse imaging sensors of various resolutions into a single res...
Article
The fundamental TPBVP usually underlying true “optimal sensor selection strategy” is revisited to obtain practical real-time mechanizations as a solution to an exclusively initial value problem
Article
The commenter analyses the four main contributions of the article by Y. Oshman (see ibid., vol.30, no.2, p.307-314 (Apr. 1994)). The author's reply is also presented.< >
Article
Full-text available
The topics of matrix spectral factorization (MSF) in conjunction with results from realization theory are applied here in simulating a stationary multi-input/multi-output (MIMO) linear system from a specified power spectral density matrix. MSF provides the appropriate transfer function matrix and realization theory specifies the corresponding param...
Chapter
Full-text available
Getting incorrect results at the output of a Kalman filter (KF) simulation or hardware implementation can be blamed on (1) use of faulty approximations in the implementation, or (2) on faulty coding/computer programming or (3) may actually be due to theoretical details of what should be implemented in the application being incorrectly specified by...
Article
Full-text available
The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A stre...
Article
In seeking to verify various computer implementations of Kalman filters, the extended Kalman filter (EKF), or other algorithms that rely on the same fundamental computations in a variety of different applications, it is useful to first validate software performance using low-dimensional test problems of known solution. Besides reporting the state-o...
Article
A few errors of omission in the failure-detection application of the above-titled paper by Brumback and Srinath (ibid., vol.AC-32, p.552-4, June 1987) are corrected by the commenter. The commenter points out that what the authors claim is an original alternate (chi-square) test for the failure detection as a possible noniterative replacement for th...
Article
Full-text available
Some prevalent misconceptions on how to test matrices for positive semidefiniteness (both theoretically and computationally are reviewed. A simple counterexample revealed that a recently offered partitioned test for demonstrating the positive semidefiniteness of a matrix (with the potential of being applied stagewise to the higher dimensional matri...
Article
Full-text available
The status of computational tests for establishing matrix positive semidefiniteness and positive definiteness is reviewed. Two pervasive real-time tests that have been used for many years in varied applications to ensure that computed covariances encountered in Kalman filter applications are positive definite and discussed. Structural representatio...
Article
The motivation and mechanics of utilizing Cramer-Rao (CR) -type lower bounds to gauge the performance of filters being evaluated in nonlinear estimation applications such as in sonar, sonobuoy, and radar target tracking are reviewed. The status of several similar alternative CR-type lower bounds that have been considered or used for this purpose an...
Article
Full-text available
The two distinct technical specialty areas of failure detection in stochastic dynamical systems and the detection and tracking of target maneuvers by radar or optics are identified as two separate disciplines that have achieved results by using modeling techniques. These techniques can be cross-applied to the other specialty area, which is revealed...
Article
Full-text available
A low-dimensional test problem with a known solution is used to verify various computer implementations of F.C. Schweppe's likelihood detector (1965). In this case a closed-form solution is provided for a Schweppe likelihood detector in terms of an intermediate Kalman filter, as utilized in its implementation, for detecting the presence of a two-st...
Article
Full-text available
Additional references relating to the work of J.E. White and J.L. Speyer (ibid., vol.AC-32, p.593-603, July 1987) are reported and commented on. White and Speyer discussed predecessor studies that dealt with failure detection in navigation applications described by stochastic time-invariant linear system with additive Gaussian white process and mea...
Article
The present author offers precedents for use of the Bar-Itzhack filter formulation, as recently recast in a multirate parallel Kalman filter framework discussed by D. Andrisani, II and C.-F. Gau (see ibid., vol.AC-32, p.653-6, Jul. 1987).< >
Article
The 'principal minor test' for matrix positive semidefiniteness was re-examined here and pointers were provided to both correct and incorrect published versions of it as a cautionary reminder of what expert opinions to, respectively, either embrace or avoid on this subject. A brief review was provided of how important such tests are in applications...
Article
Full-text available
Failure detection and redundancy management is discussed for avionics applications of integrated navigation involving coordinated use of multiple simultaneous sensor subsystems such as GPS, JTIDS, TACAN, VOR/DME, ILS, an inertial navigation system (INS), and possibly even Doppler AHRS. A brief high level survey is provided to assess the status of t...
Article
Full-text available
There have been two new algorithms of fairly recent origin offered for the calculation of the matrix pseudoinverse. Unfortunately, nonpathological counterexamples can be constructed, as offered herein, that demonstrate the questionable nature of these two algorithms; however, a resolution is offered here to help prevent possible uncritical propagat...
Article
Full-text available
While reformulations of Sequential Probability Ratio Tests (SPRT) and Generalized Likelihood Ratio (GLR) tests have been used within the last ten years for failure detection and other event or incident detection applications, several problems underlying SPRT and GLR for these applications have yet to be resolved. For this reason, results and critic...
Article
Full-text available
The statistical analysis of failure detection decisions in terms of the instantaneous probabilities of false alarm and correct detection for a specified failure magnitude at each check-time have previously been performed for several different failure detection techniques that utilize a Kalman filter. By performing a discrete-time specialization of...
Article
Full-text available
Ballistic missile equipped, nuclear powered submarines, denoted as Ships Submersible Ballistic Nuclear (SSBN), have to take navigation fixes in connection with a deterioration in the navigation accuracy provided by their Inertial Navigation System (INS). Such a degradation is related to gyro drift-rate and other sources. An SSBN utilization of the...
Article
Full-text available
Real-time failure detection for systems having linear stochastic dynamical truth models has been posed in terms of two confidence region sheaths in [1]-[3]. One confidence region sheath is about the expected nominal no-failure trajectory; the other is about the Kalman estimate of the state(s) being monitored for failures. The implementation of a ne...
Article
Full-text available
Eight alternative decentralized linear estimation schemes are surveyed to find the mechanization most appropriate for stable community relative navigation in the JTIDS RelNav tactical scenario. Advantages, disadvantages and caveats are identified for each. The paper also outlines an analytic proof of asymptotic stability for both SPA and SLU. The c...
Article
This correspondence traces the origin of three simple but powerful matrix inequalities that have arisen in many diverse control and estimation studies. The purpose of this slightly critical discussion is to stimulate an awareness of the variety of applications for these inequalities and by so doing, hopefully, to reduce the period for their reappea...
Article
Two counterexamples are presented in the above correspondence [1] to demonstrate that |A|_{3} ,the minimum of the standard column-sum norm (|A|_{1}) and the row-sum norm (|A|_{2}) , is not a valid norm. While these observations are correct, there is an error in [1] in the argument used to justify the use of |A|_{3} as a convergence test. This error...
Article
Full-text available
This correspondence calls attention to a so-called norm that has appeared and reappeared in the estimation and modern control theory literature. By means of a simple counterexample, the properties that a valid norm should satisfy are shown to be violated by this bogus norm.
Article
Full-text available
Real-time failure detection for systems having linear stochastic dynamical truth models is posed in terms of two confidence region sheaths. One confidence region sheath is about the expected no-failure trajectory; the other is about the Kalman estimate. If these two confidence regions of ellipsoidal cross section are disjoint at any time instant, a...
Conference Paper
Full-text available
Real time failure detection for systems having a linear stochastic dynamical truth model is posed in terms of two confidence region sheaths. One confidence region sheath is about the expected no failure trajectory, the other is about the Kalman estimate. If these two confidence regions of ellipsoidal cross-section are disjoint at any time instant,...
Article
Full-text available
A new form of the Cramer-Rao inequality for the estimator of vector parameter constants is presented. For a scalar Cramer-Rao inequality of the form of the one derived, the so-called Cramer-Rao lower bound does not have a denominator that must be maximized over all components of some matrix as was required in previous multivariate derivations. For...
Article
In this paper a method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper i...
Article
A method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenolog...
Article
Full-text available
New approaches to the practice of medicine and to food production have arrived on the technolo-gical scene as a consequence of the knowledge gained through modern genome sequencing. Now Scientists and genetic engineers can modify and manipulate the fundamental genetic code of cer-tain crops and animals to benefit mankind. Although the stated goals...
Article
Full-text available
A counterexample is presented to a result claimed in a proof in (1), pertaining to using this new approach to Covariance Intersection (CI). Other researchers have already demonstrated certain problems that exist with earlier versions of CI, as summarized in a survey (7) of the previous CI approaches encountered in Target tracking applications. We a...
Article
Full-text available
A derivation is provided herein of the fundamental Integral and its evaluation using the Cauchy Residue Theorem to enable a rigorous setting of decision thresholds for the Two Confidence Region (CR2) approach to failure detection. This CR2 approach (for 1-D and 2-D) was historically used on board US Submarines in monitoring the SINS/ESGM Inertial N...

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Projects

Projects (6)
Archived project
Fundamentally, problem is cast as a “cat-and-mouse” game of “sensor schedule optimization” within a natural Kalman Nav filter context/framework (utilizing bicriteria optimization to yield a Pareto-optimal solution set as a lower bound on "close" practical operational approximations). One criteria is sweeprate exposure to enemy surveillance while using various navaids. The sweeprate exposure is from the official worse-case detection threat (identified through official channels but threat and quantifications NOT divulged NOR identified here). The other criteria is miss distance incurred by submarine (if called upon to launch a missile at a pre-assigned enemy target). Explicit quantification of SSBN observables associated with use of various alternative (vintage 1979) navaids which had already been tabulated via a standard methodology utilized by JHU/APL. SSBN missile miss distances were available by multiplying available analytical sensitivity matrices by the SBBN's position accuracy at launch. NO classified information is revealed here.
Project
My main motivation was for Navigation Applications.
Project
Providing an assortment of application examples to make life easier for other practitioners seeking to build upon these results in implementations.