TeK Service 2

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Preparation of proposals and reports on mathematically-based estimation methodologies and pertinent algorithmic topics

Key Benefits:

	We are knowledgeable about various historical approaches, their assumptions, their derivation, and their historical evolution.
	We have gone through the rigorous supporting mathematics, yet we summarize the results in a clear straightforward manner, expressed as simply as possible.
	We are familiar with typical applications utilizing these algorithms and are aware of what application constraints are usually actively in force as being typically encountered.
	Experience writing Company technical reports for General Electric, TASC, Intermetrics, Lincoln Laboratory of MIT, MITRE, XonTech, Raytheon, and TeK Associates (exclusively for Department of Defense projects, with one commercial exception at GE in 1972 for internal use only).
	Participated in proposal preparation at General Electric CRD (Schenectady, NY), at The Analytic Sciences Corporation (TASC) now part of Grumman Aerospace, and at Intermetrics, Inc.
	Even more experience writing proposals at TeK Associates proper and in partnership with others.

Capabilities:

We have a facility with analytic manipulations that enabled the following:: construction of instructive simple numerical counter-examples of low dimension that point out fallacies in the theory that existed at the time, as representatively conveyed below in references [4], [7]-[12], [17], [20], [24], [30]. Constructive fixes were offered afterwards.
We have a facility with analytic manipulations that enabled the following:: construction of instructive simple closed-form numerical examples that illustrate a theoretical result (and which may be used to cross-check the outputs of software code that ostensibly implements it), as conveyed below in references [4], [6], [8], [13]-[15], [18], [19], [28], [30].
We have a facility with analytic manipulations that enabled the following:: insights into obtaining new theoretical results at the point where they are needed to expand and improve the existing theory, as conveyed below in references [1]-[3], [5], [16], [20]-[23], [25]-[27], [29]-[31].

Historical Account of some of our selected experience therein (as reflected by our corresponding peer-reviewed open literature publications):

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

[2] Kerr, T. H., Eyman, E. D., and Loh, N. K., “Modeling a Particular Class of Multiple-Input/ Multiple-Output Black Boxes with Stochastic Integral Equations and Specifying the Required Parameters,” Proceedings of the I.F.A.C. Symposium on Modeling and Identification, Hague, Netherlands, 1973.

[3] Kerr, T. H., “A Simplified Approach to Obtaining the Steady-State Initial Conditions for Linear System Simulations,” Proceedings of the Fifth Annual Pittsburgh Conference on Modeling and Simulation, 1003 ff, 1974.

[4] Kerr, T. H., “An Invalid Norm Appearing in Control and Estimation,” IEEE Transactions on Automatic Control, Vol. AC-23, No. 1, pp. 73-74, Feb. 1978 (correction in No. 6, p. 1117-118, Dec. 1978).

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

[6] Kerr, T. H., “The Proper Computation of the Matrix Pseudo-Inverse and Its Impact in MVRO Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-21, No. 5, pp. 711-724, Sept. 1985.

[7] 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 (reply to and rebuttal by author in Vol. 12, No. 5, p. 767, Sept.-Oct. 1989 issue).

[8] Kerr, T. H., “Computational Techniques for the Matrix Pseudoinverse in Minimum Variance Reduced-Order Filtering and Control,” a chapter 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, N.Y., pp. 57-107, 1988.

[9] Kerr, T. H., “Comments on ‘Estimation Using a Multirate Filter’,” IEEE Transactions on Automatic Control, Vol. AC-34, No. 3, p. 384, Mar. 1989.

[10] Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-25, No. 5, pp. 590-601, Sept. 1989 (Author’s reply in Vol. AES-26, No. 5, pp. 896-898, Sept. 1990).

[11] 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.

[12] Kerr, T. H., “Fallacies in Computational Testing of Matrix Positive Definiteness\Semi- definiteness,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-26, No. 2, pp. 415-421, Mar. 1990.

[13] 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 Dec. 1989 (BSD [previously BMO] limited distribution).

[14] 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.

[15] 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 (minor correction appears in Nov. 1991 issue).

[16] Kerr, T. H., “Streamlining Measurement Iteration for EKF Target Tracking,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 2, Mar. 1991 (minor correction appears in Nov. 1991 issue).

[17] Kerr, T. H., “Comments on ‘Federated Square Root Filter for Decentralized Parallel Processes’,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 27, No. 6, Nov. 1991.

[18] 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, 1993.

[19] 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.

[20] 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 (ICSPAT), Boston, MA, pp. 1574-1587, 24-26 Oct. 1995.

[21] Kerr, T. H., “Extending Decentralized Kalman Filtering (KF) to 2-D for Real-Time Multisensor Image Fusion and\or Restoration,” Signal Processing, Sensor Fusion, and Target Recognition V, Proceedings of SPIE Conference, Vol. 2755, Orlando, FL, pp. 548-564, 8-10 Apr. 1996.

[22] 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 (ICSPAT96), Boston, MA, 7-10 Oct. 1996.

[23] Kerr, T. H., and Satz, H., S., “Applications of Some Explicit Formulas for the Matrix Exponential in Linear Systems Software Validation,” Proceedings of 16th Digital Avionics System Conference, Vol. I, pp. 1.4-9 to 1.4-20, Irvine, CA, 26-30 Oct. 1997.

[24] Kerr, T. H., “Critique of Some Neural Network Architectures and Claims for Control and Estimation,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-34, No. 2, pp. 406-419, Apr. 1998.

[25] Kerr, T. H., UEWR Design Notebook-Section 2.3: Track Analysis, TeK Associates, Lexington, MA, (for XonTech, Hartwell Rd, Lexington, MA), XonTech Report No. D744-10300, 29 Mar. 1999.

[26] 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 Sept. 2000.

[27] 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 Jul. 2001 (Unclassified paper but Conference Proceedings are SECRET).

[28] 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, CA, 29 July-3 Aug. 2001.

[29] Kerr, T. H., “A Critical View of Some New and Older approaches to EWR Target Tracking: A Summary and Endorsement of Kalman Filter-Related Techniques,” a tutorial submitted to IEEE Aerospace and Electronic Systems, Ed. by Peter Willett (in review and expected to appear in 2005).

[30] Kerr, T. H., “Apparent Drawbacks that Exist in the Underlying Structure of Covariance Intersection,” submitted to IEEE Transactions on Aerospace and Electronic Systems in 2004 (still in review).

[31] 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.

[32] 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.

[33] Kerr, T. H., “Comments 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.

[34] Kerr, T. H., “Novel Variations on Old Architectures/Mechanizations for New Miniature Autonomous Systems,” Online Proceedings of GMC MAS 2009 Conference, Session E1: Controlling Miniature Autonomous Systems, Ft. Walton Beach, FL, 28 October 2009.

[35] 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.

[36] How to Calculate an Ensemble of Neural Network Model Weights in Keras (Polyak Averaging) https://lnkd.in/gmVUr7W

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