Eubank A Kalman Filter Primer

Erscheinungsjahr 2010
ISBN: 978-1-4200-2867-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 200 Seiten

Reihe: 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.

Zielgruppe

Statisticians in time series analysis, Bayesian analysis, and computational statistics; process and control engineers; engineers and researchers in adaptive signal processing, signal processing, radar tracking and navigational systems, and avionics; students in these areas.

Autoren/Hrsg.

Eubank, Randall L.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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 ß

Likelihood Evaluation

Appendix A: The Cholesky Decomposition

Appendix B: Notation Guide

References

Index