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

Format:

Book

Author/Creator:

Bierman, Gerald J.

Series:

Mathematics in science and engineering ; v. 128.

Mathematics in science and engineering series ; v. 128

Language:

English

Subjects (All):

Control theory.

Digital filters (Mathematics).

Estimation theory.

Matrices.

Physical Description:

1 online resource (259 p.)

Place of Publication:

New York : Academic Press, 1977.

Language Note:

English

Summary:

Factorization methods for discrete sequential estimation

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

VI.5 Duality Relationships between Information and Covariance Algorithms

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 233-236) and index.

ISBN:

1-282-28933-0

9786612289330

0-08-095637-8

OCLC:

316568484