State-space adaptive recursive filters

The authors propose an LMS (least-mean-squares) algorithm for adapting the poles and zeros of state-space IIR (infinite-impulse-response) filters. Recently presented state-space sensitivity formulae are used to obtain gradients which are required to adapt the filter coefficients. The number of computations for a general state-space adaptive filter is seen to be large, but a modified companion-form filter is shown to require much less computation. Also, it is shown that, in general, it is possible to efficiently adapt any state-space system by modifying any one column of its A matrix. This could prove useful where only small changes in coefficients are expected. Finally, simulation results are presented