Adaptive Filtering and Change Detection

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Adaptive Filtering and Change Detection
Fredrik Gustafsson
JOHN WILEY & SONS, 2000
ISBN 0 471 49287 6

Preface ix
Part I: Introduction 1
1 . Extended summary 3
1.1. About the book .......................... 3
1.2. Adaptive linear filtering ..................... 8
1.3. Change detection ......................... 17
1.4. Evaluation and formal design .................. 26
2 . Applications 31
2.1. Change in the mean model ................... 32
2.2. Change in the variance model .................. 35
2.3. FIR model ............................. 37
2.4. AR model ............................. 39
2.5. ARX model ............................ 42
2.6. Regression model ......................... 46
2.7. State space model ........................ 49
2.8. Multiple models .......................... 49
2.9. Parameterized non-linear models ................ 51
Part II: Signal estimation 55
3 . On-line approaches 57
3.1. Introduction ............................ 57
3.2. Filtering approaches ....................... 59
3.3. Summary of least squares approaches .............. 59
3.4. Stopping rules and the CUSUM test .............. 63

3.5. Likelihood based change detection ............... 70
3.6. Applications ............................ 81
3.A. Derivations ............................ 84
4 . Off-line approaches 89
4.1. Basics ............................... 89
4.2. Segmentation criteria ....................... 91
4.3. On-line local search for optimum ................ 94
4.4. Off-line global search for optimum ............... 98
4.5. Change point estimation ..................... 102
4.6. Applications ............................ 106
Part 111: Parameter estimation 111
5 . Adaptive filtering 113
5.1. Basics ............................... 114
5.2. Signal models ........................... 115
5.3. System identification ....................... 121
5.4. Adaptive algorithms ....................... 133
5.5. Performance analysis ....................... 144
5.6. Whiteness based change detection ............... 148
5.7. A simulation example ...................... 149
5.8. Adaptive filters in communication ............... 153
5.9. Noise cancelation ......................... 167
5.10. Applications ............................ 173
5.11. Speech coding in GSM ...................... 185
5.A. Square root implementation ................... 189
5.B. Derivations ............................ 190
6 . Change detection based on sliding windows 205
6.1. Basics ............................... 205
6.2. Distance measures ........................ 211
6.3. Likelihood based detection and isolation ............ 218
6.4. Design optimization ....................... 225
6.5. Applications ............................ 227
7 . Change detection based on filter banks 231
7.1. Basics ............................... 231
7.2. Problem setup .......................... 233

7.3. Statistical criteria ........................ 234
7.4. Information based criteria .................... 240
7.5. On-line local search for optimum ................ 242
7.6. Off-line global search for optimum ............... 245
7.7. Applications ............................ 246
7.A. Two inequalities for likelihoods ................. 252
7.B. The posterior probabilities of a jump sequence ........ 256
Part W: State estimation 261
8 . Kalman filtering 263
8.1. Basics ............................... 264
8.2. State space modeling ....................... 267
8.3. The Kalman filter ........................ 278
8.4. Time-invariant signal model ................... 286
8.5. Smoothing ............................. 290
8.6. Computational aspects ...................... 295
8.7. Square root implementation ................... 300
8.8. Sensor fusion ........................... 306
8.9. The extended Kalman filter ................... 313
8.10. Whiteness based change detection using the Kalman filter . . 324
8.11. Estimation of covariances in state space models ........ 326
8.12. Applications ............................ 327
9 . Change detection based on likelihood ratios 343
9.1. Basics ............................... 343
9.2. The likelihood approach ..................... 346
9.3. The GLR test ........................... 349
9.4. The MLR test ........................... 353
9.5. Simulation study ......................... 365
9.A. Derivation of the GLR test ................... 370
9.B. LS-based derivation of the MLR test .............. 372
I0 . Change detection based on multiple models 377
10.1. Basics ............................... 377
10.2. Examples of applications ..................... 378
10.3. On-line algorithms ........................ 385
10.4. Off-line algorithms ........................ 391
10.5. Local pruning in blind equalization ............... 395

10.A.Posterior distribution ....................... 397
11 . Change detection based on algebraical consistency tests 403
11.1. Basics ............................... 403
11.2. Parity space change detection .................. 407
11.3. An observer approach ...................... 413
11.4. An input-output approach .................... 414
11.5. Applications ............................ 415
Part V: Theory 425
12 . Evaluation theory 427
12.1. Filter evaluation ......................... 427
12.2. Evaluation of change detectors ................. 439
12.3. Performance optimization .................... 444
13 . linear estimation 451
13.1. Projections ............................ 451
13.2. Conditional expectations ..................... 456
13.3. Wiener filters ........................... 460
A . Signal models and notation 471
B . Fault detection terminology 475
Bibliography 477
Index 493

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