Analysis of the error surface of the adaptive stochastic filter

A filter structure, called a stochastic filter, that consists of a parallel bank of three fixed second-order filters each multiplied by a probability is developed. The fixed filters are chosen such that the stochastic filter will always have roots inside the unit circle. By varying the probabilities with time, an adaptive stochastic filter (ASF) is implemented. While the single stage ASF has a quadratic error surface, the error surface of cascaded stages of this structure is not quadratic. A theoretical analysis of the cascaded structure´s error surface in the constrained region of operation is presented