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Adaptive lọc và phát hiện thay đổi P5

The noise is here assumed white with variance X, and will sometimes be restricted to be Gaussian. The last expression is in a polynomial form, whereas G, H are filters. Time-variability is modeled by time-varying parameters Bt. The adaptive filtering problem is to estimate these parametersb y an adaptive filter, | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic Part III Parameter estimation Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic 5 Adaptive filtering 5.1. Basics.114 5.2. Signal models.115 5.2.1. Linear regression models. 115 5.2.2. Pseudo-linear regression models. 119 5.3. System identification.121 5.3.1. Stochastic and deterministic least squares. 121 5.3.2. Model structure selection. 124 5.3.3. Steepest descent minimization . 126 5.3.4. Newton-Raphson minimization. 127 5.3.5. Gauss-Newton minimization. 128 5.4. Adaptive algorithms .133 5.4.1. LMS. 134 5.4.2. RLS. 138 5.4.3. Kalman filter. 142 5.4.4. Connections and optimal simulation. 143 5.5. Performance analysis.144 5.5.1. LMS. 145 5.5.2. RLS. 147 5.5.3. Algorithm optimization. 147 5.6. Whiteness based change detection.148 5.7. A simulation example.149 5.7.1. Time-invariant AR model. 150 5.7.2. Abruptly changing AR model. 150 5.7.3. Time-varying AR model. 151 5.8. Adaptive filters in communication.153 5.8.1. Linear equalization. 155 5.8.2. Decision feedback equalization . 158 5.8.3. Equalization using the Viterbi algorithm. 160 5.8.4. Channel estimation in equalization. 163 5.8.5. Blind equalization. 165 5.9. Noise cancelation.167 5.9.1. Feed-forward dynamics. 167 5.9.2. Feedback dynamics. 171 114 Adaptive filtering 5.10. Applications .173 5.10.1. Human EEG. 173 5.10.2. DC motor. 173 5.10.3. Friction estimation. 175 5.11. Speech coding in GSM.185 5.A. Square root implementation.189 5.B. Derivations.190 5.B.I. Derivation of LS algorithms. 191 5.B.2. Comparing on-line and off-line expressions. 193 5.B.3. Asymptotic expressions. 199 5.B.4. Derivation of marginalization.200 5.1. Basics The signal model in this chapter is in its most general form yt G q 0 ut H q 0 et 5.1 A q 0 yt B g- 0 C q- 0 D q-0 Ut F q-0 et- 5-2 The .