LOCAL STABILITY OF THE MEDIAN LMS FILTER

Local stability properties of the recently proposed median LMS adaptiv e filter are investigated by relating the behavior of the algorithm to the behavior of an associated ordinary differential equation. With in dependent inputs, the differential equation and the algorithm are show n to be locally stable. On the other hand, several classes of (periodi c, nonindependent) inputs are described which cause the differential e quation and the algorithm to be unstable about its equilibrium, even i n the no disturbance case. This will help delineate those applications for which the median LMS is an appropriate adaptive algorithm.