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

**by**Robert Grover Brown (Iowa State Univ.)

4th

### 9780470609699

0470609699

Hardcover

9/1/2011

Wiley

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## Summary

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

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 | p. 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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