Thomas Henderson Kerr III

TeK Associates · TK-MIP R&D Software Development Department

Elucidating the nature of a familiar closed-form solution arising in the optimization of [1].

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...

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...

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...

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...

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...

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...

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...

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...

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).

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...

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...

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...

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...

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

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.< >

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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).< >

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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,...

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...

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...

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...

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...

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...

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...

Thesis (Ph. D.)--University of Iowa.