Factorization Methods for Discrete Sequential Estimation

by Bierman, Gerald J.

• ISBN13: 9780486785882
• ISBN10: 0486785882
• Format: Hardcover
• Copyright: 2013-12-10
• Publisher: Dover Publications

Summary

This estimation reference text thoroughly describes matrix factorization methods successfully employed by numerical analysts, familiarizing readers with the techniques that lead to efficient, economical, reliable, and flexible estimation algorithms.
Topics include a review of least squares data processing and the Kalman filter algorithm; positive definite matrices, the Cholesky decomposition, and some of their applications; Householder orthogonal transformations; sequential square root data processing; mapping effects and process noise; biases and correlated process noise; and covariance analysis of effects due to mismodeled variables and incorrect filter a priori statistics. The concluding chapters explore SRIF error analysis of effects due to mismodeled variables and incorrect filter a priori statistics as well as square root information smoothing. Geared toward advanced undergraduates and graduate students, this pragmatically oriented and detailed presentation is also a useful reference, featuring numerous helpful appendixes throughout the text.

Table of Contents

1. Introduction
2. Review of Least Squares Data Processing and the Kalman Filter Algorithm
3. Positive Definite Matrices, the Cholesky Decomposition, and Some Applications
4. Householder Orthogonal Transformations
5. Sequential Square Root Data Processing
6. Inclusion of Mapping Effects and Process Noise
7. Treatment of Biases and Correlated Process Noise
8. Covariance Analysis of Effects Due to Mismodeled Variables and Incorrect Filter a Priori Statistics
9. SRIF Error Analysis of Effects Due to Mismodeled Variables and Incorrect Filter a Prior Statistics
10. Square Root Information Smoothing
Bibliography
Index