Additive Change Detection in Nonlinear Systems With Unknown Change Parameters

We study the change detection problem in partially observed, nonlinear systems [which satisfy the hidden Markov model (HMM) property]. The change parameters are assumed unknown, and the changes can be slow or sudden. A partially observed system needs to be tracked first before changes can be detected. Sudden changes result in significant loss of track. These can be detected easily using the increase in tracking error (TE) or observation likelihood (OL) or using a CUSUM-type method applied to either of these. However, slow changes (which result in small loss of track) often get missed. We propose here a statistic that uses the tracked component of the change to detect it and, hence, detects slow changes faster than TE or OL. We show, both analytically and through simulations, that this statistic complements OL and TE for change detection

[1]  Fredrik Gustafsson,et al.  Adaptive filtering and change detection , 2000 .

[2]  Christophe Andrieu,et al.  Online expectation-maximization type algorithms for parameter estimation in general state space models , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[3]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

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

[5]  Hassan Hammouri,et al.  Observer-based approach to fault detection and isolation for nonlinear systems , 1999, IEEE Trans. Autom. Control..

[6]  Michèle Basseville,et al.  Model-based statistical signal processing and decision theoretic approaches to monitoring , 2003 .

[7]  Amit K. Roy-Chowdhury,et al.  Summarization and Indexing of Human Activity Sequences , 2006, 2006 International Conference on Image Processing.

[8]  A. Doucet,et al.  Parameter estimation in general state-space models using particle methods , 2003 .

[9]  Arnaud Doucet,et al.  A survey of convergence results on particle filtering methods for practitioners , 2002, IEEE Trans. Signal Process..

[10]  Tze-Yun Sung.  Memory-efficient and high-speed split-radix FFT/IFFT processor based on pipelined CORDIC rotations , 2006 .

[11]  Qinghua Zhang,et al.  Nonlinear system fault detection and isolation based on bootstrap particle filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[13]  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.

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

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

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

[17]  Fredrik Gustafsson,et al.  Recursive Bayesian estimation: bearings-only applications , 2005 .

[18]  Namrata Vaswani.  Bound on errors in particle filtering with incorrect model assumptions and its implication for change detection , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  F. Cerou,et al.  Efficient particle methods for residual generation in partially observed SDEs , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[20]  James M. Rehg,et al.  A multiple hypothesis approach to figure tracking , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[21]  Visakan Kadirkamanathan,et al.  Fault detection and isolation in non-linear stochastic systems—A combined adaptive Monte Carlo filtering and likelihood ratio approach , 2004 .

[22]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[23]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

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

[25]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[26]  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).

[27]  Visakan Kadirkamanathan,et al.  Particle filtering-based fault detection in non-linear stochastic systems , 2002, Int. J. Syst. Sci..

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

[29]  Namrata Vaswani,et al.  The modified CUSUM algorithm for slow and drastic change detection in general HMMs with unknown change parameters , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[30]  A. Doucet,et al.  A survey of convergence results on particle ltering for practitioners , 2002 .

[31]  Simon J. Godsill,et al.  Particle methods for Bayesian modeling and enhancement of speech signals , 2002, IEEE Trans. Speech Audio Process..

[32]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[33]  R. Chellappa,et al.  Non-Stationary "Shape Activities" , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[34]  Fredrik Gustafsson,et al.  Adaptive Filtering and Change Detection: Gustafsson: Adaptive , 2001 .

[35]  Alberto Isidori,et al.  A geometric approach to nonlinear fault detection and isolation , 2000, IEEE Trans. Autom. Control..

[36]  R. Chellappa,et al.  NonStationary “ Shape Activities ” , 2005 .

[37]  J. Fritz,et al.  Rapid task-related plasticity of spectrotemporal receptive fields in primary auditory cortex , 2003, Nature Neuroscience.

[38]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[39]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[40]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[41]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

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

[43]  Rama Chellappa,et al.  "Shape Activity": a continuous-state HMM for moving/deforming shapes with application to abnormal activity detection , 2005, IEEE Transactions on Image Processing.

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

[45]  Qinghua Zhang,et al.  Nonlinear system fault diagnosis based on adaptive estimation , 2004, Autom..