Adaptive deconvolution and identification of nonminimum phase FIR systems using Kalman filter

It is shown how a Kalman filter can be applied to the problem of adaptive deconvolution and system identification for a non-Gaussian white noise driven linear, nonminimum phase finite impulse response (FIR) system. The adaptive scheme is, in fact, a blind equalization (deconvolution) scheme, based on approximating the FIR system by noncausal autoregressive (AR) models and using higher-order cumulants of the system output. Without prior knowledge about the channel, the filter algorithm leads to faster convergence than other methods, its speed of convergence depending only on the number of data. Theoretical results are given and computer simulations are used to corroborate the theory and to compare the algorithm with the classical steepest descent method