Adaptive recovery of a noisy chirp: performance of the SSLMS algorithm

This paper investigates the ability of state space least mean square (SSLMS) algorithm to track a chirped signal buried in additive white Gaussian noise. The signal is a sinusoid whose frequency is drifting at a constant rate. After incorporating second order linear time varying state space model of the chirped sinusoid, SSLMS exhibits superior tracking performance over standard LMS & RLS and their known variants. The step size parameter plays an important role in this context. For various values of step size parameter, time average auto-correlation function (ACF) of prediction error is evaluated when responding to chirped signal. Whiteness of prediction error verifies excellent tracking by SSLMS.