Realization and implementation of adaptive state-space recursive filters

The authors extend the LMS (least mean squares) adaptation algorithm to state-space recursive filtering. Based on the state equations in the time domain, gradients for all parameters are formulated by matrix derivative linear operations and are calculated recursively. The stability of the filter during the adaptive process is guaranteed by adding the constraints of a specified system matrix A. Simulation results show that any desired state-space system can be achieved by initializing the system properly. Since the adaptive state-space filtering requires intensive computations and all computations involved are matrix operations, a high-speed VLSI architecture is presented for real-time or near real-time applications