Adaptive recursive state-space filtering

The least-mean-square adaptation algorithm is extended to state-space recursive filtering in order to obtain improved adaptive filter structures and take advantage of the better numerical performance of state-space filtering. The gradients for the parameters are derived directly from the state equations and formulated by matrix derivative linear operations. Simulation results showing that the adaptive state-space filters provide better performance in terms of stability control, convergence rate, and roundoff noise are reported, and the initialization of system matrices is considered. To speed up the adaptive process, a VLSI implementation is given