Use of the fast Kalman estimation algorithm for adaptive system identification

The fast Kalman estimation (FKE) algorithm for recursive least squares described by Falconer and Ljung has convergence properties superior to those of least mean square (LMS) gradient algorithms. It is used here in a time domain system identification application in which both the system input and output are known. The input is a chirp, linearly swept in frequency. With an unwindowed chirp as input, the FKE algorithm identifies the impulses in the unknown system accurately. Windowing the chirp to smooth its ends results in a loss of resolution. This same effect is observed in the nonadaptive solution found with the Levinson recursion method. Adaptive and nonadaptive solutions exhibit signs of instability, which are eliminated by prewhitening.