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

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  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2011-09-01
  • Publisher: Wiley

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Introduction to Two-Dimensional Design, Second Edition provides a solid foundation in timeless design principles. With the help of more than 200 revealing illustrations, the book explores both the qualitative and quantitative aspects of 2D design, interweaving historical accounts with penetrating analyses of visual principles and issues found in important contemporary examples. This new edition demonstrates how competing approaches to 2D design--including those based on intuition, play, chance, and empirical research--can be used successfully, either alone or in combination.

Table of Contents

Prefacep. v
Random Signals Backgroundp. 1
Probability and Random Variables: A Reviewp. 3
Random Signalsp. 3
Intuitive Notion of Probabilityp. 4
Axiomatic Probabilityp. 5
Random Variablesp. 8
Joint and Conditional Probability, Bayes Rule and Independencep. 9
Continuous Random Variables and Probability Density Functionp. 13
Expectation, Averages, and Characteristic Functionp. 15
Normal or Gaussian Random Variablesp. 18
Impulsive Probability Density Functionsp. 22
Joint Continuous Random Variablesp. 23
Correlation, Covariance, and Orthogonalityp. 26
Sum of Independent Random Variables and Tendency Toward Normal Distributionp. 28
Transformation of Random Variablesp. 32
Multivariate Normal Density Functionp. 37
Linear Transformation and General Properties of Normal Random Variablesp. 40
Limits, Convergence, and Unbiased Estimatorsp. 43
A Note on Statistical Estimatorsp. 46
Mathematical Description of Random Signalsp. 57
Concept of a Random Processp. 57
Probabilistic Description of a Random Processp. 60
Gaussian Random Processp. 62
Stationarity, Ergodicity, and Classification of Processesp. 63
Autocorrelation Functionp. 65
Crosscorrelation Functionp. 68
Power Spectral Density Functionp. 70
White Noisep. 75
Gauss-Markov Processesp. 77
Narrowband Gaussian Processp. 81
Wiener or Brownian-Motion Processp. 83
Pseudorandom Signalsp. 86
Determination of Autocorrelation and Spectral Density Functions from Experimental Datap. 90
Sampling Theoremp. 95
Linear Systems Response, State-Space Modeling, and Monte Carlo Simulationp. 105
Introduction: The Analysis Problemp. 105
Stationary (Steady-State) Analysisp. 106
Integral Tables for Computing Mean-Square Valuep. 109
Pure White Noise and Bandlimited Systemsp. 110
Noise Equivalent Bandwidthp. 111
Shaping Filterp. 113
Nonstationary (Transient) Analysisp. 114
Note on Units and Unity White Noisep. 118
Vector Description of Random Processesp. 121
Monte Carlo Simulation of Discrete-Time Processesp. 128
Summaryp. 130
Kalman Filtering and Applicationsp. 139
Discrete Kalman Filter Basicsp. 141
A Simple Recursive Examplep. 141
The Discrete Kalman Filterp. 143
Simple Kalman Filter Examples and Augmenting the State Vectorp. 148
Marine Navigation Application with Multiple-Inputs/Multiple-Outputsp. 151
Gaussian Monte Carlo Examplesp. 154
Predictionp. 159
The Conditional Density Viewpointp. 162
Re-cap and Special Note On Updating the Error Covariance Matrixp. 165
Intermediate Topics on Kalman Filteringp. 173
Alternative Form of the Discrete Kalman Filter - the Information Filterp. 173
Processing the Measurements One at a Timep. 176
Orthogonality Principlep. 178
Divergence Problemsp. 181
Suboptimal Error Analysisp. 184
Reduced-Order Suboptimalityp. 188
Square-Root Filtering and U-D Factorizationp. 193
Kalman Filter Stabilityp. 197
Relationship to Deterministic Least Squares Estimationp. 198
Deterministic Inputsp. 201
Smoothing and Further Intermediate Topicsp. 207
Classification of smoothing Problemsp. 207
Discrete Fixed-Interval Smoothingp. 208
Discrete Fixed-Point Smoothingp. 212
Discrete Fixed-Lag Smoothingp. 213
Adaptive Kalman Filter (Multiple Model Adaptive Estimator)p. 216
Correlated Process and Measurement Noise for the Discrete Filter-Delayed-State Filter Algorithmp. 226
Decentralized Kalman Filteringp. 231
Difficulty with Hard-Bandlimited Processesp. 234
The Recursive Bayesian Filterp. 237
Linearization, Nonlinear Filtering, and Sampling Bayesian Filtersp. 249
Linearizationp. 249
The Extended Kalman Filterp. 257
"Beyond the Kalman Filter"p. 260
The Ensemble Kalman Filterp. 262
The Unscented Kalman Filterp. 265
The Particle Filterp. 269
The "Go-Free" Concept, Complementary Filter, and Aided Inertial Examplesp. 284
Introduction: Why Go Free of Anything?p. 284
Simple GPS Clock Bias Modelp. 285
Euler/Goad Experimentp. 287
Reprise: GPS Clock-Bias Model Revisitedp. 289
The Complementary Filterp. 290
Simple Complementary Filter: Intuitive Methodp. 292
Kalman Filter Approach-Error Modelp. 294
Kalman Filter Approach-Total Modelp. 296
Go-Free Monte Carlo Simulationp. 298
INS Error Modelsp. 303
Aiding with Positioning Measurements-INS/DME Measurement Modelp. 307
Other Integration Considerations and Concluding Remarksp. 309
Kalman Filter Applications to the GPS and Other Navigation Systemsp. 318
Position Determination with GPSp. 318
The Observablesp. 321
Basic Position and Time Process Modelsp. 324
Modeling of Different Carrier Phase Measurements and Ranging Errorsp. 330
GPS-Aided Inertial Error Modelsp. 339
Communication Link Ranging and Timingp. 345
Simultaneous Localization and Mapping (SLAM)p. 348
Closing Remarksp. 352
Laplace and Fourier Transformsp. 365
The Continuous Kalman Filterp. 371
Indexp. 379
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