Application of regularized Savitzky–Golay filters to identification of time-varying systems

Abstract

Savitzky–Golay (SG) filtering is a classical signal smoothing technique based on the local least squares approximation of the analyzed signal by a linear combination of known functions of time (originally — powers of time, which corresponds to polynomial approximation). It is shown that the regularized version of the SG algorithm can be successfully applied to identification of time-varying finite impulse response (FIR) systems. Such a solution is possible owing to the recently proposed preestimation technique, which converts the problem of identification of a time-varying FIR system into the problem of smoothing of the appropriately generated preestimates of system parameters. The resulting fast regularized local basis function estimators, optimized using the empirical Bayes approach, have very good parameter tracking capabilities, favorably comparing with the state-of-the-art in terms of accuracy, computational complexity and numerical robustness.