Kalman filter with hypothesis testing: A tool for estimating uncertain parameters

In this paper we present a simple and practical algorithm for the estimation of uncertain parameters of linear systems. The uncertainty is twofold, involving random observation noise, and possible jumps in the parameter values. The jumps may occur at unknown points in time, and are of unknown magnitudes and directions. The algorithm is based on the Kalman filter, with a single-sample hypothesis test, which is used to employ a three-state decision rule (yes, no, maybe). The maybe choice invokes a fading memory Kalman filter. The overall algorithm contains the constant parameter filter, fading memory filter, and the set of tests and rules that enable it to switch back and forth between the two filters. Application examples are presented.