A New Generalized Likelihood Ratio Test for Sequential Jumps Detection

Abstract

For sequential jumps detection, isolation and estimation in discrete-time stochastic linear systems, Willsky and Jones (1976) have developed the Generalized Likelihood Ratio (GLR) test. For the treatment of sequential jumps, the jump-free Kalman filter is updated on-line after each detection of one jump by a direct state estimate and covariance incrementation using the informations produced by the GLR detector. This paper proposes another updating strategy based on a reference model updated on-line by the states of jumps declared to be occurred during the sequential processing. The augmented state Kalman filter designed on this updated reference model will be optimaly initialized at each detection time from information given by the GLR detector.