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State-Space Kalman Filters 7.2 Sample-Adaptive Filters y(m) e(m) µ α w(m) α z –1 wk(m+1) ADAPTIVE FILTERS 7.3 Recursive Least Square (RLS) Adaptive Filters 7.4 The Steepest-Descent Method 7.5 The LMS Filter 7.6 Summary A daptive filters are used for non-stationary signals and environments, or in applications where a sample-by-sample adaptation of a process or a low processing delay is required. Applications of adaptive filters include multichannel noise reduction, radar/sonar signal processing, channel equalization for cellular mobile phones, echo cancellation, and low delay speech coding. This chapter begins with a study of the state-space Kalman filter. In Kalman theory a state equation models the dynamics of the. | Advanced Digital Signal Processing and Noise Reduction Second Edition. Saeed V. Vaseghi Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-62692-9 Hardback 0-470-84162-1 Electronic 7 y m e m O a w m w4 m 1 ADAPTIVE FILTERS 7.1 State-Space Kalman Filters 7.2 Sample-Adaptive Filters 7.3 Recursive Least Square RLS Adaptive Filters 7.4 The Steepest-Descent Method 7.5 The LMS Filter 7.6 Summary Adaptive filters are used for non-stationary signals and environments or in applications where a sample-by-sample adaptation of a process or a low processing delay is required. Applications of adaptive filters include multichannel noise reduction radar sonar signal processing channel equalization for cellular mobile phones echo cancellation and low delay speech coding. This chapter begins with a study of the state-space Kalman filter. In Kalman theory a state equation models the dynamics of the signal generation process and an observation equation models the channel distortion and additive noise. Then we consider recursive least square RLS error adaptive filters. The RLS filter is a sample-adaptive formulation of the Wiener filter and for stationary signals should converge to the same solution as the Wiener filter. In least square error filtering an alternative to using a Wiener-type closedform solution is an iterative gradient-based search for the optimal filter coefficients. The steepest-descent search is a gradient-based method for searching the least square error performance curve for the minimum error filter coefficients. We study the steepest-descent method and then consider the computationally inexpensive LMS gradient search method. 206 Adaptive Filters 7.1 State-Space Kalman Filters The Kalman filter is a recursive least square error method for estimation of a signal distorted in transmission through a channel and observed in noise. Kalman filters can be used with time-varying as well as time-invariant processes. Kalman filter theory is based on a state-space approach in .
