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Summary Table of Contents

Includes new and updated theory on the basic Kalman filter algorithm in line with recent advancements in the subject. Many new applications and examples have been added in this new edition.

Introduction to Two-Dimensional Design, Second Edition provides a solid foundation in timeless design principles.

The 4th 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 filterin... MORE

Preface	p. v
Random Signals Background	p. 1
Probability and Random Variables: A Review	p. 3
Random Signals	p. 3
Intuitive Notion of Probability	p. 4
Axiomatic Probability	p. 5
Random Variables	p. 8
Joint and Conditional Probability, Bayes Rule and Independence	p. 9
Continuous Random Variables and Probability Density Function	... MOREp. 13
Expectation, Averages, and Characteristic Function	p. 15
Normal or Gaussian Random Variables	p. 18
Impulsive Probability Density Functions	p. 22
Joint Continuous Random Variables	p. 23
Correlation, Covariance, and Orthogonality	p. 26
Sum of Independent Random Variables and Tendency Toward Normal Distribution	p. 28
Transformation of Random Variables	p. 32
Multivariate Normal Density Function	p. 37
Linear Transformation and General Properties of Normal Random Variables	p. 40
Limits, Convergence, and Unbiased Estimators	p. 43
A Note on Statistical Estimators	p. 46
Mathematical Description of Random Signals	p. 57
Concept of a Random Process	p. 57
Probabilistic Description of a Random Process	p. 60
Gaussian Random Process	p. 62
Stationarity, Ergodicity, and Classification of Processes	p. 63
Autocorrelation Function	p. 65
Crosscorrelation Function	p. 68
Power Spectral Density Function	p. 70
White Noise	p. 75
Gauss-Markov Processes	p. 77
Narrowband Gaussian Process	p. 81
Wiener or Brownian-Motion Process	p. 83
Pseudorandom Signals	p. 86
Determination of Autocorrelation and Spectral Density Functions from Experimental Data	p. 90
Sampling Theorem	p. 95
Linear Systems Response, State-Space Modeling, and Monte Carlo Simulation	p. 105
Introduction: The Analysis Problem	p. 105
Stationary (Steady-State) Analysis	p. 106
Integral Tables for Computing Mean-Square Value	p. 109
Pure White Noise and Bandlimited Systems	p. 110
Noise Equivalent Bandwidth	p. 111
Shaping Filter	p. 113
Nonstationary (Transient) Analysis	p. 114
Note on Units and Unity White Noise	p. 118
Vector Description of Random Processes	p. 121
Monte Carlo Simulation of Discrete-Time Processes	p. 128
Summary	p. 130
Kalman Filtering and Applications	p. 139
Discrete Kalman Filter Basics	p. 141
A Simple Recursive Example	p. 141
The Discrete Kalman Filter	p. 143
Simple Kalman Filter Examples and Augmenting the State Vector	p. 148
Marine Navigation Application with Multiple-Inputs/Multiple-Outputs	p. 151
Gaussian Monte Carlo Examples	p. 154
Prediction	p. 159
The Conditional Density Viewpoint	p. 162
Re-cap and Special Note On Updating the Error Covariance Matrix	p. 165
Intermediate Topics on Kalman Filtering	p. 173
Alternative Form of the Discrete Kalman Filter - the Information Filter	p. 173
Processing the Measurements One at a Time	p. 176
Orthogonality Principle	p. 178
Divergence Problems	p. 181
Suboptimal Error Analysis	p. 184
Reduced-Order Suboptimality	p. 188
Square-Root Filtering and U-D Factorization	p. 193
Kalman Filter Stability	p. 197
Relationship to Deterministic Least Squares Estimation	p. 198
Deterministic Inputs	p. 201
Smoothing and Further Intermediate Topics	p. 207
Classification of smoothing Problems	p. 207
Discrete Fixed-Interval Smoothing	p. 208
Discrete Fixed-Point Smoothing	p. 212
Discrete Fixed-Lag Smoothing	p. 213
Adaptive Kalman Filter (Multiple Model Adaptive Estimator)	p. 216
Correlated Process and Measurement Noise for the Discrete Filter-Delayed-State Filter Algorithm	p. 226
Decentralized Kalman Filtering	p. 231
Difficulty with Hard-Bandlimited Processes	p. 234
The Recursive Bayesian Filter	p. 237
Linearization, Nonlinear Filtering, and Sampling Bayesian Filters	p. 249
Linearization	p. 249
The Extended Kalman Filter	p. 257
"Beyond the Kalman Filter"	p. 260
The Ensemble Kalman Filter	p. 262
The Unscented Kalman Filter	p. 265
The Particle Filter	p. 269
The "Go-Free" Concept, Complementary Filter, and Aided Inertial Examples	p. 284
Introduction: Why Go Free of Anything?	p. 284
Simple GPS Clock Bias Model	p. 285
Euler/Goad Experiment	p. 287
Reprise: GPS Clock-Bias Model Revisited	p. 289
The Complementary Filter	p. 290
Simple Complementary Filter: Intuitive Method	p. 292
Kalman Filter Approach-Error Model	p. 294
Kalman Filter Approach-Total Model	p. 296
Go-Free Monte Carlo Simulation	p. 298
INS Error Models	p. 303
Aiding with Positioning Measurements-INS/DME Measurement Model	p. 307
Other Integration Considerations and Concluding Remarks	p. 309
Kalman Filter Applications to the GPS and Other Navigation Systems	p. 318
Position Determination with GPS	p. 318
The Observables	p. 321
Basic Position and Time Process Models	p. 324
Modeling of Different Carrier Phase Measurements and Ranging Errors	p. 330
GPS-Aided Inertial Error Models	p. 339
Communication Link Ranging and Timing	p. 345
Simultaneous Localization and Mapping (SLAM)	p. 348
Closing Remarks	p. 352
Laplace and Fourier Transforms	p. 365
The Continuous Kalman Filter	p. 371
Index	p. 379
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