Title Factorization methods for discrete sequential estimation / Gerald J. Bierman

Published New York : Academic Press, 1977

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Description 1 online resource (xvi, 241 pages) Series Mathematics in science and engineering series ; v. 128 Mathematics in science and engineering ; v. 128. Contents Front Cover; Factorization Methods for Discrete Sequential Estimation; Copyright Page; Contents; Preface; Acknowledgments; List of Symbols; Chapter I. lntroductlon; I.1 Introduction; I.2 Prerequisites; I.3 Scope and Objectives; I.4 Historical Perspectives; I.5 Chapter Synopses; References; Chapter II. Review of Least Squares Data Processing and the Kalman Filter Algorithm; II. 1 Introduction; II. 2 Linear Least Squares; II. 3 Statistical Interpretation of the Least Squares Solution; II. 4 Inclusion of a Priori Statistics; II. 5 Recursions for the Least Squares Information Processor II. 6 Kalman Filter Data ProcessingII. 7 Potter's Mechanization of the Kalman Algorithm; II. 8 Computational Considerations Associated with Covariance Data Processing; Appendix II. A Proof that an Overdetermined System with Full Rank Has a Nonsingular Normal Matrix; Appendix II. B A Matrix Inversion Lemma; Appendix II. C Data Processing Using the Information Matrix; Appendix II. D Data Processing Using the Kalman Algorithm; Appendix II. E Data Processing Using the Potter Algorithm; References; Chapter III. Positive Definition Matrices, the Cholesky Decomposition, and Some Applications III. 1 Positive Definite MatricesIII. 2 Properties of PD Matrices; III. 3 Matrix Square Roots and the Cholesky Decomposition Algorithm; III. 4 Rank One Modification of the Cholesky Factorization; III. 5 Whitening Observation Errors; III. 6 Observation Errors That Are Pairwise Correlated; III. 7 Construction of Random Samples Having a Given Covariance; Appendix III. A Upper Triangular Matrix Factorization Algorithm; Appendix III. B FORTRAN Mechanization of the Lower Triangular Cholesky Factorization; Appendix III. C FORTRAN Mechanization of the UDUT Update; References Chapter IV. Householder Orthogonal TransformationsIV. 1 Review of Orthogonal Transformations; IV. 2 Application of Orthogonal Matrices to the Least Squares Problem; IV. 3 The Householder Transformation; Appendix IV. A Annihilating the First Column of a Matrix Using the Householder Transformation; Appendix IV. B Solution of the Triangular System Rx = y and Inversion of a Triangular Matrix; References; Chapter V. Sequential Square Root Data Processing; V.l Introduction; V.2 The SRIF Data Processing Algorithm; V.3 Data Processing Using the U-D Covariance Factorization v. 4 Sequential Data Processing Algorithm Computation Counts and ComparisonsV. 5 Filter Algorithm Numerical Deterioration; Some Examples; Appendix V.A U-D and Upper Triangular P 1/2 FORTRAN Mechanizations; Appendix V.B Arithmetic Operation Counts for Various Data Processing Algorithms; References; Chapter VI. Inclusion of Mapping Effects and Process Noise; VI. 1 Introduction; VI. 2 Mapping and the Inclusion of Process Noise into the SRIF; VI. 3 Mapping and the Inclusion of Process Noise into the Kalman Filter; VI. 4 Mapping and the Inclusion of Process Noise into the U-D Covariance Filter Summary Factorization methods for discrete sequential estimation Bibliography Includes bibliographical references (pages 233-236) and index Notes Print version record Subject Control theory. Estimation theory. Digital filters (Mathematics) Matrices. MATHEMATICS -- Probability & Statistics -- General. Control theory Digital filters (Mathematics) Estimation theory Matrices Form Electronic book ISBN 9780120973507 0120973502 9780080956374 0080956378

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