Tracking Algorithm Designed by the Local Asymptotic Approach

The problem of sequential detection of parameter jumps in linear systems with constant noise level is discussed. The detection problem is analyzed by the asymptotic local approach using the normalized output error sequence as the detection signal. For linear regression, ARMAX, and state-space models, a central limit theorem is proved, transforming the original problem into the problem of detecting an increase in the mean of an asymptotically Gaussian distributed scalar process. The performance of the tracking algorithm which consists of a parameter estimator with decreasing gain and a single Hinkley's detector have been studied by simulations and compared to constant and adaptive gain parameter estimators. The proposed algorithm seems to be superior in performance while a little, and generally negligible, additional computational effort is required.