Local Stability of the Median LMS Filter

by William A. Sethares

Local stability properties of the recently proposed median LMS adaptive filter are investigated by relating the behavior of the algorithm to the behavior of an associated ordinary differential equation.With independent inputs, the differential equation and the algorithm are shown to be locally stable. On the other hand, several classes of (periodic, nonindependent) inputs are described which cause the differential equation and the algorithm to be unstable about its equilibrium, even in the no disturbance case. This helps to delineate those applications for which the median LMS is an

This analysis first appeared in the IEEE Transactions on Signal Processing, in November 1994.

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