Computational Techniques for the Matrix Pseudoinverse in Minimum Variance Reduced-Order Filtering and Control

Kerr, T. H.

doi:10.1016/b978-0-12-012728-3.50005-6

Cited by 9 publications

(4 citation statements)

References 97 publications

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“…3 for specifying a decision threshold using random process level-crossing theory so that a particular probability of false alarm exists over an entire specified time interval and not just instantaneously at each discrete check time k.) Realtime online mechanization of CR2 for one dimensions uses only Eqs. (16), (18), and (19) and the two comparison tests of Eq. (14).…”

Section: A Cr2 P Fa (K) Calculations Simplify Nicely For the Scaler mentioning

confidence: 99%

“…The system is assumed to be outfitted or equipped with an adequate, perhaps reduced-order, Kalman filter 18 matched to a linearized version of the system. For INS involving a constellation of gyros and accelerometers, even though the mechanization itself is nonlinear (e.g., space stable, local level, or strapdown), the underlying error model is linear, 19 and, as such, possesses an optimal estimator that can be obtained as the output of a linear Kalman filter, usually implemented in indirect feedback form (Ref.…”

Section: Introductionmentioning

confidence: 99%

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Integral Evaluations Enabling Performance Tradeoffs for Two-Confidence-Region-Based Failure Detection

Kerr¹

2006

Journal of Guidance, Control, and Dynamics

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Engineering Notes ENGINEERING NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes should not exceed 2500 words (where a figure or table counts as 200 words). Following informal review by the Editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover).

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Section: A Cr2 P Fa (K) Calculations Simplify Nicely For the Scaler mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integral Evaluations Enabling Performance Tradeoffs for Two-Confidence-Region-Based Failure Detection

Kerr¹

2006

Journal of Guidance, Control, and Dynamics

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“…On-line tutorials and extensive application examples are also available for TK-MIP including an on-line sell-contained professional level textbook and short course complete with lectures, tests, corresponding answers, and a guest lecturer. This software runs on 80386 or later Personal Computer (PC) processor with hardware math co-processor chip under Microsoft Windows 95/98/NT/ME/2000 (32-bit) operating systems and does not presume the presence or require use of MatLab or Simulink TK-MIP is a software product for the PC (without needing to have or use MatLab) that we recently developed for teaching others about the theory and practice of KF simulation {13}- [14] , [16] [69] , [73] , [75] and for actually implementing KF technology and its many variations on-line for linear and nonlinear estimation and tracking. It makes modest demands on the amount of RAM a platform need have to run TK-MIP.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Vulnerability of recent GPS adaptive antenna processing (and all STAP/SLC) to statistically nonstationary jammer threats

Kerr¹

2001

SPIE Proceedings

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We alert the reader here to an apparent vulnerability in recent adaptive antenna processing that claims increased cPs jammer resistance via use of lucrative new approaches to adaptive beamforming and/or null-steering hut, unfortunately, presumes only simplistic unsophisticated wideband barrage WGN jammers as threats. When jammers are less cooperative by being statistically non-stationary (e.g., by exhibiting time-varying means or biases, by beiiig synchronized blmkmg jammer pairs, or by varying the total power output with time), then statistics on the jammers can apparently no longer be successfully extracted from the time-averages (even in post-processing mode using long blocks of I(CCiVe(I data that was saved) because ergodicity of the underlying intermediate covariance estimate is lost. This unpleasant situation arises or exists for abstracted, idealized STAP or SLC algorithms making use of the, by now, iamiliar fundaixiental STAP-related equation: R where this necessary intermediate covariance estimate R = R1 + '2 + 113 has the three indicated constituent components due to thermal/environmental noise, clutter, arid jammers, resJ)ectively. Without an ability to accurately estimate R3 , the appropriate jammer nullings apparently can no longer be activated successfully. Such systems susceptil)le to jamming can be revealed by in-situ tests with simple equipmeiit. rfopics herein include updates to PRN generation, updates to statistical tests in general and to CLT in particular and all three updates being new to most engineers.

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“…22 is of the form [7, Eq. 9.2-12}: (23) idempotent matrices can again be used to an advantage with F =A and the entire transient solution is revea'ed (via the result of Eq. 20) to be of the form:…”

Section: What About Its Use As Solutions To Matrix Lyapunov and Riccatimentioning

confidence: 99%

Exact methodology for testing linear system software using idempotent matrices and other closed-form analytic results

Kerr¹

2001

SPIE Proceedings

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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 conjunction with other tests (for expedient full functional coverage) as the basis of a coherent general strategy of software validation for these particular types of applications. The techniques espoused here are universal and independent of the constructs of particular computer languages and were honed from years of experience in crosschecking Kalman filter implementations in several diverse commercial and military applications. While standard Kalman filter implementation equations were originally derived by Rudolf E. Kalman in 1960 using the Projection Theorem in a Hubert Space context (with prescribed inner product related to expectations), there are now comparable Kalman filter results for systems described by partial differential equations (e.g., arising in some approaches to image restoration or with some distributed sensor situations for environmental toxic effluent monitoring) involving a type of Riccati-like PDE equation to be solved for the estimation error. The natural framework for such infinite dimensional PDE formulations is within a Banach Space (being norm-based) and there are generalizations of idempotent matrices similar to those offered herein for these spaces as well that allow closed-form test solutions for infinite dimensional linear systems to verify and confirm proper PDE implementations in S/W code. Other closed-form test case extensions discussed earlier by the author have been specifically tailored for S/W verification of multichannel maximum entropy power spectral estimation algorithms and of approximate nonlinear estimation implementations of Extended Kalman filtering and for Batch Least Squares (BLS) filters, respectively.

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Computational Techniques for the Matrix Pseudoinverse in Minimum Variance Reduced-Order Filtering and Control

Cited by 9 publications

References 97 publications

Integral Evaluations Enabling Performance Tradeoffs for Two-Confidence-Region-Based Failure Detection

Integral Evaluations Enabling Performance Tradeoffs for Two-Confidence-Region-Based Failure Detection

Vulnerability of recent GPS adaptive antenna processing (and all STAP/SLC) to statistically nonstationary jammer threats

Exact methodology for testing linear system software using idempotent matrices and other closed-form analytic results

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