Adaptive state space filtering with FIR convergence behaviour

An adaptive filter that addresses the problems of convergence to a stable filter, the optimization of multimodal performance surface, and the computational complexity of implementing an infinite impulse response (IIR) filter is described. The adaptive filter is based on describing the adaptive IIR filter in its state space form. The adaptive state space filter algorithm can best be described as a recursive form of the matrix minimum principle. The adaptive state space is a two-part algorithm. The first part is a recursive algorithm for optimizing a predictor matrix which describes the transformation from past data to future data. The second part determines the system parameters from the optimized predictor matrix by the decomposition of the predictor matrix and the use of projection techniques. Assurance of convergence to a stable filter is also proven