- July 2010
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It is a well-known result of estimation theory that biased estimators can outperform unbiased ones in terms of expected quadratic error. In steady state, many adaptive filtering algorithms offer an unbiased
estimation of both the reference signal and the unknown true parameter
vector. In this correspondence, we propose a simple yet effective scheme
for adaptively biasing the weights of adaptive filters using an output
multiplicative factor. We give theoretical results that show that the
proposed configuration is able to provide a convenient bias versus
variance tradeoff, leading to reductions in the filter mean-square
error, especially in situations with a low signal-to-noise ratio (SNR).
After reinterpreting the biased estimator as the combination of the
original filter and a filter with constant output equal to 0, we propose
practical schemes to adaptively adjust the multiplicative factor.
Experiments are carried out for the normalized least-mean-squares (NLMS)
adaptive filter, improving its mean-square performance in stationary
situations and during the convergence phase.