On the bias of adaptive first-order recursive smoothing

In signal processing, first-order recursive smoothing is often used to determine the mean of a nonstationary random variable. In order to find a better compromise between the tracking speed and the variance of the estimate, adaptive smoothing factors have been proposed, e.g., for single-channel background noise power spectral density estimators. In this paper, the bias of recursive smoothing using adaptive smoothing functions is investigated. For adaptive functions that do not depend on the estimated mean an analytical derivation of the bias is given. For adaptive functions having a dependence on the recursively estimated mean, an iterative procedure is proposed which allows to approximately determine the bias with a sufficiently high precision.