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Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises, 4th Edition

Name: Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises, 4th Edition
ISBN: 9780470609699

by Robert Grover Brown, Patrick Y. C. Hwang

February 2012

Intermediate to advanced

400 pages

11h 15m

English

Wiley

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Cover Page
Title Page
Copyright
Preface To The Fourth Edition
Brief Contents
Contents
PART 1: Random Signals Background
Chapter 1: Probability and Random Variables: A Review
1.1 RANDOM SIGNALS1.2 INTUITIVE NOTION OF PROBABILITY1.3 AXIOMATIC PROBABILITY1.4 RANDOM VARIABLES1.5 JOINT AND CONDITIONAL PROBABILITY, BAYES RULE, AND INDEPENDENCE1.6 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DENSITY FUNCTION1.7 EXPECTATION, AVERAGES, AND CHARACTERISTIC FUNCTION1.8 NORMAL OR GAUSSIAN RANDOM VARIABLES1.9 IMPULSIVE PROBABILITY DENSITY FUNCTIONS1.10 JOINT CONTINUOUS RANDOM VARIABLES1.11 CORRELATION, COVARIANCE, AND ORTHOGONALITY1.12 SUM OF INDEPENDENT RANDOM VARIABLES AND TENDENCY TOWARD NORMAL DISTRIBUTION1.13 TRANSFORMATION OF RANDOM VARIABLES1.14 MULTIVARIATE NORMAL DENSITY FUNCTION1.15 LINEAR TRANSFORMATION AND GENERAL PROPERTIES OF NORMAL RANDOM VARIABLES1.16 LIMITS, CONVERGENCE, AND UNBIASED ESTIMATORS1.17 A NOTE ON STATISTICAL ESTIMATORS
Chapter 2: Mathematical Description of Random Signals
2.1 CONCEPT OF A RANDOM PROCESS2.2 PROBABILISTIC DESCRIPTION OF A RANDOM PROCESS2.3 GAUSSIAN RANDOM PROCESS2.4 STATIONARITY, ERGODICITY, AND CLASSIFICATION OF PROCESSES2.5 AUTOCORRELATION FUNCTION2.6 CROSSCORRELATION FUNCTION2.7 POWER SPECTRAL DENSITY FUNCTION2.8 WHITE NOISE2.9 GAUSS–MARKOV PROCESSES2.10 NARROWBAND GAUSSIAN PROCESS2.11 WIENER OR BROWNIAN-MOTION PROCESS2.12 PSEUDORANDOM SIGNALS2.13 DETERMINATION OF AUTOCORRELATION AND SPECTRAL DENSITY FUNCTIONS FROM EXPERIMENTAL DATA2.14 SAMPLING THEOREM
Chapter 3: Linear Systems Response, State-Space Modeling, and Monte Carlo Simulation
3.1 INTRODUCTION: THE ANALYSIS PROBLEM3.2 STATIONARY (STEADY-STATE) ANALYSIS3.3 INTEGRAL TABLES FOR COMPUTING MEAN-SQUARE VALUE3.4 PURE WHITE NOISE AND BANDLIMITED SYSTEMS3.5 NOISE EQUIVALENT BANDWIDTH3.6 SHAPING FILTER3.7 NONSTATIONARY (TRANSIENT) ANALYSIS3.8 NOTE ON UNITS AND UNITY WHITE NOISE3.9 VECTOR DESCRIPTION OF RANDOM PROCESSES3.10 MONTE CARLO SIMULATION OF DISCRETE-TIME PROCESSES

PART 2: Kalman Filtering And Applications
Chapter 4: Discrete Kalman Filter Basics
4.1 A SIMPLE RECURSIVE EXAMPLE4.2 THE DISCRETE KALMAN FILTER4.3 SIMPLE KALMAN FILTER EXAMPLES AND AUGMENTING THE STATE VECTOR4.4 MARINE NAVIGATION APPLICATION WITH MULTIPLE-INPUTS/MULTIPLE-OUTPUTS4.5 GAUSSIAN MONTE CARLO EXAMPLES4.6 PREDICTION4.7 THE CONDITIONAL DENSITY VIEWPOINT4.8 RE-CAP AND SPECIAL NOTE ON UPDATING THE ERROR COVARIANCE MATRIX
Chapter 5: Intermediate Topics on Kalman Filtering
5.1 ALTERNATIVE FORM OF THE DISCRETE KALMAN FILTER–THE INFORMATION FILTER5.2 PROCESSING THE MEASUREMENTS ONE AT A TIME5.3 ORTHOGONALITY PRINCIPLE5.4 DIVERGENCE PROBLEMS5.5 SUBOPTIMAL ERROR ANALYSIS5.6 REDUCED-ORDER SUBOPTIMALITY5.7 SQUARE-ROOT FILTERING AND U-D FACTORIZATION5.8 KALMAN FILTER STABILITY5.9 RELATIONSHIP TO DETERMINISTIC LEAST SQUARES ESTIMATION5.10 DETERMINISTIC INPUTS
Chapter 6: Smoothing and Further Intermediate Topics
6.1 CLASSIFICATION OF SMOOTHING PROBLEMS6.2 DISCRETE FIXED-INTERVAL SMOOTHING6.3 DISCRETE FIXED-POINT SMOOTHING6.4 DISCRETE FIXED-LAG SMOOTHING6.5 ADAPTIVE KALMAN FILTER (MULTIPLE MODEL ADAPTIVE ESTIMATOR)6.6 CORRELATED PROCESS AND MEASUREMENT NOISE FOR THE DISCRETE FILTER—DELAYED-STATE FILTER ALGORITHM6.7 DECENTRALIZED KALMAN FILTERING6.8 DIFFICULTY WITH HARD-BANDLIMITED PROCESSES6.9 THE RECURSIVE BAYESIAN FILTER
Chapter 7: Linearization, Nonlinear Filtering, and Sampling Bayesian Filters
7.1 LINEARIZATION7.2 THE EXTENDED KALMAN FILTER7.3 “BEYOND THE KALMAN FILTER”7.4 THE ENSEMBLE KALMAN FILTER7.5 THE UNSCENTED KALMAN FILTER7.6 THE PARTICLE FILTER
Chapter 8: The “Go-Free” Concept, Complementary Filter, and Aided Inertial Examples
8.1 INTRODUCTION: WHY GO FREE OF ANYTHING?8.2 SIMPLE GPS CLOCK BIAS MODEL8.3 EULER/GOAD EXPERIMENT8.4 REPRISE: GPS CLOCK-BIAS MODEL REVISITED8.5 THE COMPLEMENTARY FILTER8.6 SIMPLE COMPLEMENTARY FILTER: INTUITIVE METHOD8.7 KALMAN FILTER APPROACH—ERROR MODEL8.8 KALMAN FILTER APPROACH—TOTAL MODEL8.9 GO-FREE MONTE CARLO SIMULATION8.10 INS ERROR MODELS8.11 AIDING WITH POSITIONING MEASUREMENTS—INS/DME MEASUREMENT MODEL8.12 OTHER INTEGRATION CONSIDERATIONS AND CONCLUDING REMARKS
Chapter 9: Kalman Filter Applications To The GPS And Other Navigation Systems
9.1 POSITION DETERMINATION WITH GPS9.2 THE OBSERVABLES9.3 BASIC POSITION AND TIME PROCESS MODELS9.4 MODELING OF DIFFERENT CARRIER PHASE MEASUREMENTS AND RANGING ERRORS9.5 GPS-AIDED INERTIAL ERROR MODELS9.6 COMMUNICATION LINK RANGING AND TIMING9.7 SIMULTANEOUS LOCALIZATION AND MAPPING (SLAM)9.8 CLOSING REMARKS
APPENDIX A: Laplace and Fourier Transforms
A.1 THE LAPLACE TRANSFORMA.2 THE FOURIER TRANSFORM
APPENDIX B: The Continuous Kalman Filter
B.1 TRANSITION FROM THE DISCRETE TO CONTINUOUS FILTER EQUATIONSB.2 SOLUTION OF THE MATRIX RICCATI EQUATION
Index

Overview

The Fourth Edition to the Introduction of Random Signals and Applied Kalman Filtering is updated to cover innovations in the Kalman filter algorithm and the proliferation of Kalman filtering applications from the past decade. The text updates both the research advances in variations on the Kalman filter algorithm and adds a wide range of new application examples. Several chapters include a significant amount of new material on applications such as simultaneous localization and mapping for autonomous vehicles, inertial navigation systems and global satellite navigation systems.

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