The modified CUSUM algorithm for slow and drastic change detection in general HMMs with unknown change parameters

We study the change detection problem in a general HMM when the change parameters are unknown and the change can be slow or drastic. Drastic changes can be detected easily using the increase in tracking error or the negative log of observation likelihood (OL). But slow changes usually get missed. We have proposed in past work a statistic called ELL which works for slow change detection. Now single time estimates of any statistic can be noisy. Hence we propose a modification of the cumulative sum (CUSUM) algorithm which can be applied to ELL and OL and thus improves both slow and drastic change detection performance.

[1]  B. Azimi-Sadjadi,et al.  Change detection for nonlinear systems; a particle filtering approach , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  R. Kulhavý.  A geometric approach to statistical estimation , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[3]  Visakan Kadirkamanathan,et al.  Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems , 2001, IEEE Trans. Syst. Man Cybern. Part C.

[4]  Namrata Vaswani,et al.  Change Detection in Stochastic Shape Dynamical Models with Applications in Activity Modeling and Abnormality Detection , 2004 .

[5]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[6]  Christophe Andrieu,et al.  Particle methods for change detection, system identification, and control , 2004, Proceedings of the IEEE.

[7]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[8]  F. Gland,et al.  STABILITY AND UNIFORM APPROXIMATION OF NONLINEAR FILTERS USING THE HILBERT METRIC AND APPLICATION TO PARTICLE FILTERS1 , 2004 .

[9]  Y. Bar-Shalom.  Tracking and data association , 1988 .

[10]  D. Kerridge.  Inaccuracy and Inference , 1961 .

[11]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[12]  N. Vaswani,et al.  Change detection in partially observed nonlinear dynamic systems with unknown change parameters , 2004, Proceedings of the 2004 American Control Conference.