(Not in A Kalman Filter Primer
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$37.95$34.16 - Hardback: 200 pages
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- Published: November 2005
- ISBN: 978-0-8247-2365-1
- Publisher: Chapman and Hall/CRC
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- By Randall L. Eubank.
- Series Edited by William Shucany.
Series: Statistics: A Series of Textbooks and Monographs.
System state estimation in the presence of noise is critical for control systems, signal processing, and many other applications in a variety of fields. Developed decades ago, the Kalman filter remains an important, powerful tool for estimating the variables in a system in the presence of noise. However, when inundated with theory and vast notations, learning just how the Kalman filter works can be a daunting task.
With its mathematically rigorous, “no frills” approach to the basic discrete-time Kalman filter, A Kalman Filter Primer builds a thorough understanding of the inner workings and basic concepts of Kalman filter recursions from first principles. Instead of the typical Bayesian perspective, the author develops the topic via least-squares and classical matrix methods using the Cholesky decomposition to distill the essence of the Kalman filter and reveal the motivations behind the choice of the initializing state vector. He supplies pseudo-code algorithms for the various recursions, enabling code development to implement the filter in practice. The book thoroughly studies the development of modern smoothing algorithms and methods for determining initial states, along with a comprehensive development of the “diffuse” Kalman filter.
Using a tiered presentation that builds on simple discussions to more complex and thorough treatments, A Kalman Filter Primer is the perfect introduction to quickly and effectively using the Kalman filter in practice.
Table of Contents
Signal-Plus-Noise Models
Introduction
The Prediction Problem
State-Space Models
What Lies Ahead
The Fundamental Covariance Structure
Introduction
Some Tools of the Trade
State and Innovation Covariances
An Example
Recursions for L and L−1
Introduction
Recursions for L
Recursions for L−1
An Example
Forward Recursions
Introduction
Computing the Innovations
State and Signal Prediction
Other Options
Examples
Smoothing
Introduction
Fixed Interval Smoothing
Examples
Initialization
Introduction
Diffuseness
Diffuseness and Least-Squares Estimation
An Example
Normal Priors
Introduction
Likelihood Evaluation
Diffuseness
Parameter Estimation
An Example
A General State-Space Model
Introduction
KF Recursions
Estimation of β
Likelihood Evaluation
Appendix A: The Cholesky Decomposition
Appendix B: Notation Guide
References
Index
