Adaptive recursive state-space filters using a gradient-based algorithm

To aid in the search for better adaptive filter structures, a method is presented to obtain the gradients required to adapt general state-space filters. Unfortunately, the number of computations for this general case is quite high. To reduce the number of computations, two new state-space adaptive filters are introduced. One application where these new structures are shown to be useful is in oversampled filtering where an estimate of the final pole locations is known and the adaptive filter is required only to fine-tune the transfer function. It is shown that for this type of application, the new adaptive structures can have much improved adaptation rates and roundoff noise performance as compared to the corresponding direct-form realizations