EBOOK - Introduction to random signals and applied kalman filtering (Robert Grover Brown & Patrich Y. C. Hwang)


EBOOK - Giới thiệu các tín hiệu ngẫu nhiên và áp dụng vào bộ lọc Kalman (Robert Grover Brown và Patrich Y. C. Hwang) - 397 Trang.

We are happy to report that Kalman filtering is alive and well after 50 years of existence. New applications keep appearing regularly which broadens the interest throughout engineering. This, of course, has all been made possible by the fantastic advances in computer technology over the past few decades. If it were not for that, the neat recursive solution for the Wiener filter problem that R. E. Kalman introduced in 1960 would probably only be remembered as an interesting academic curiosity, in engineering literature at least.

Enough of the history; clearly, Kalman filtering is here to stay. It is eminently practical, and it has withstood the test of time. This text is a revision of the Third Edition ofIntroduction to Random Signals and Applied Kalman Filtering with MATLAB Exercises. Kalman filtering has now reached a stage of maturity where a variety of extensions and variations on the basic theory have been introduced since the Third Edition was published in 1997. We have included some of these developments, especially those that deal with nonlinear systems. The extended Kalman filter is included because it is used widely and it is still the preferred solution to many integrated navigation systems today, just as it was a few decades ago.

CONTENTS:

PART 1 RANDOM SIGNALS BACKGROUND 1

1 Probability and Random Variables: A Review 3
1.1 Random Signals 3
1.2 Intuitive Notion of Probability 4
1.3 Axiomatic Probability 5
1.4 Random Variables 8
1.5 Joint and Conditional Probability, Bayes Rule and Independence 9
1.6 Continuous Random Variables and Probability Density Function 13
1.7 Expectation, Averages, and Characteristic Function 15
1.8 Normal or Gaussian Random Variables 18
1.9 Impulsive Probability Density Functions 22
1.10 Joint Continuous Random Variables 23
1.11 Correlation, Covariance, and Orthogonality 26
1.12 Sum of Independent Random Variables and Tendency Toward Normal Distribution 28
1.13 Transformation of Random Variables 32
1.14 Multivariate Normal Density Function 37
1.15 Linear Transformation and General Properties of Normal Random Variables 40
1.16 Limits, Convergence, and Unbiased Estimators 43
1.17 A Note on Statistical Estimators 46
2 Mathematical Description of Random Signals 57
2.1 Concept of a Random Process 57
2.2 Probabilistic Description of a Random Process 60
2.3 Gaussian Random Process 62
2.4 Stationarity, Ergodicity, and Classification of Processes 63
2.5 Autocorrelation Function 65
2.6 Crosscorrelation Function 68
2.7 Power Spectral Density Function 70
2.8 White Noise 75
2.9 Gauss–Markov Processes 77
2.10 Narrowband Gaussian Process 81
2.11 Wiener or Brownian-Motion Process 83
2.12 Pseudorandom Signals 86
2.13 Determination of Autocorrelation and Spectral Density Functions from Experimental Data 90
2.14 Sampling Theorem 95
3 Linear Systems Response, State-Space Modeling, and Monte Carlo Simulation 105
3.1 Introduction: The Analysis Problem 105
3.2 Stationary (Steady-State) Analysis 106
3.3 Integral Tables for Computing Mean-Square Value 109
3.4 Pure White Noise and Bandlimited Systems 110
3.5 Noise Equivalent Bandwidth 111
3.6 Shaping Filter 113
3.7 Nonstationary (Transient) Analysis 114
3.8 Note on Units and Unity White Noise 118
3.9 Vector Description of Random Processes 121
3.10 Monte Carlo Simulation of Discrete-Time Processes 128
3.11 Summary 130

PART 2 KALMAN FILTERING AND APPLICATIONS 139

4 Discrete Kalman Filter Basics 141
4.1 A Simple Recursive Example 141
4.2 The Discrete Kalman Filter 143
4.3 Simple Kalman Filter Examples and Augmenting the State Vector 148
4.4 Marine Navigation Application with Multiple-Inputs/Multiple-Outputs 151
4.5 Gaussian Monte Carlo Examples 154
4.6 Prediction 159
4.7 The Conditional Density Viewpoint 162
4.8 Re-cap and Special Note On Updating the Error Covariance Matrix 165
5 Intermediate Topics on Kalman Filtering 173
5.1 Alternative Form of the Discrete Kalman Filter – the Information Filter 173
5.2 Processing the Measurements One at a Time 176
5.3 Orthogonality Principle 178
5.4 Divergence Problems 181
5.5 Suboptimal Error Analysis 184
5.6 Reduced-Order Suboptimality 188
5.7 Square-Root Filtering and U-D Factorization 193
5.8 Kalman Filter Stability 197
5.9 Relationship to Deterministic Least Squares Estimation 198
5.10 Deterministic Inputs 201
6 Smoothing and Further Intermediate Topics 207
6.1 Classification of smoothing Problems 207
6.2 Discrete Fixed-Interval Smoothing 208
6.3 Discrete Fixed-Point Smoothing 212
6.4 Discrete Fixed-Lag Smoothing 213
6.5 Adaptive Kalman Filter (Multiple Model Adaptive Estimator) 216
6.6 Correlated Process and Measurement Noise for the Discrete Filter—DelayedState Filter Algorithm 226
6.7 Decentralized Kalman Filtering 231
6.8 Difficulty with Hard-Bandlimited Processes 234
6.9 The Recursive Bayesian Filter 237
7 Linearization, Nonlinear Filtering, and Sampling Bayesian Filters 249
7.1 Linearization 249
7.2 The Extended Kalman Filter 257
7.3 “Beyond the Kalman Filter” 260
7.4 The Ensemble Kalman Filter 262
7.5 The Unscented Kalman Filter 265
7.6 The Particle Filter 269
8 The “Go-Free” Concept, Complementary Filter, and Aided Inertial Examples 284
8.1 Introduction: Why Go Free of Anything? 284
8.2 Simple GPS Clock Bias Model 285
8.3 Euler/Goad Experiment 287
8.4 Reprise: GPS Clock-Bias Model Revisited 289
8.5 The Complementary Filter 290
8.6 Simple Complementary Filter: Intuitive Method 292
8.7 Kalman Filter Approach—Error Model 294
8.8 Kalman Filter Approach—Total Model 296
8.9 Go-Free Monte Carlo Simulation 298
8.10 INS Error Models 303
8.11 Aiding with Positioning Measurements—INS/DME Measurement Model 307
8.12 Other Integration Considerations and Concluding Remarks 309
9 Kalman Filter Applications to the GPS and Other Navigation Systems 318
9.1 Position Determination with GPS 318
9.2 The Observables 321
9.3 Basic Position and Time Process Models 324
9.4 Modeling of Different Carrier Phase Measurements and Ranging Errors 330
9.5 GPS-Aided Inertial Error Models 339
9.6 Communication Link Ranging and Timing 345
9.7 Simultaneous Localization and Mapping (SLAM) 348
9.8 Closing Remarks 352
APPENDIX A Laplace and Fourier Transforms 365

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