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adaptive FIR filtering - recursive least squares algorithm - bias compensation - forward prediction - backward prediction |
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Forward/backward prediction solution for adaptive noisy FIR filtering
JIA LiJuan(1), TAO Ran(1), WANG Yue(1), WADA Kiyoshi(2)
(1) Department of Electronic Engineering, Beijing Institute of Technology, Beijing, 100081, China (2) Department of Electrical and Electronic System Engineering, Kyushu University, Fukuoka 819-0359, Japan
An important and hard problem in signal processing is the estimation of parameters in the presence of observation noise. In this paper, adaptive finite impulse response (FIR) filtering with noisy input-output data is considered and two developed bias compensation least squares (BCLS) methods are proposed. By introducing two auxiliary estimators, the forward output predictor and the backward output predictor are constructed respectively. By exploiting the statistical properties of the cross-correlation function between the least squares (LS) error and the forward/backward prediction error, the estimate of the input noise variance is obtained; the effect of the bias can thereafter be removed. Simulation results are presented to illustrate the good performances of the proposed algorithms.
Supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104), the Ministerial Foundation of China (Grant No. A2220060039) and the Fundamental Research Foundation of BIT (Grant No. 1010050320810)