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 . . Signal . Linear regression models. 115 . Pseudo-linear regression models. 119 . System . Stochastic and deterministic least squares. 121 . Model structure selection. 124 . Steepest descent minimization . 126 . Newton-Raphson minimization. 127 . Gauss-Newton minimization. 128 . Adaptive algorithms .133 . LMS. 134 . RLS. 138 . Kalman filter. 142 . Connections and optimal simulation. 143 . Performance . LMS. 145 . RLS. 147 . Algorithm optimization. 147 . Whiteness based change . A simulation . Time-invariant AR model. 150 . Abruptly changing AR model. 150 . Time-varying AR model. 151 . Adaptive filters in . Linear equalization. 155 . Decision feedback equalization . 158 . Equalization using the Viterbi algorithm. 160 . Channel estimation in equalization. 163 . Blind equalization. 165 . Noise . Feed-forward dynamics. 167 . Feedback dynamics. 171 114 Adaptive filtering . Applications .173 . Human EEG. 173 . DC motor. 173 . Friction estimation. 175 . Speech coding in . Square root . . Derivation of LS algorithms. 191 . Comparing on-line and off-line expressions. 193 . Asymptotic expressions. 199 . Derivation of . Basics The signal model in this chapter is in its most general form yt G q 0 ut H q 0 et A q 0 yt B g- 0 C q- 0 D q-0 Ut F q-0 et- 5-2 The .
