Fast converging and low complexity adaptive filtering using an averaged Kalman filter

Kalman filtering is applied to obtain a fast converging, low complexity adaptive filter that is of the matrix stepsize normalized least mean square (NLMS) type. By replacing certain variables with averages, the solution of an averaged diagonal Riccati equation allows optimal time varying adaptation gains to be precomputed or computed online with a small number of scalar Riccati equations. The adaptation gains are computed from prior assumptions on impulse response power and shape. This fact results in a systematic procedure for adaptation gain tuning in the time-varying matrix stepsize case. Simulations using music as input, show significant performance improvements as compared with the NLMS algorithm.