The detection and estimation of the change point in a disccrete-time stochastic system |
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Authors: | Zachary G Stoumbos |
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Institution: | Department of Management Science and Information Systems and Rutgers Center for Operations Research (RUTCOR) Rutge , The State University of New Jersey , Newark, NJ, 07102-1895 |
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Abstract: | A piecewise-constant process containing a single jump is observed under noise in the context of discrete time. The conditional density and maximum a posteriori (MAP) estimator of the jump time as well as the Bayes detector of the jump itself are determined using the powerful measure transformation approach. The Bayes detector provides a convenient sequential detection rule for practical on-line implementation. An asymptotic result for the distribution of the MAP estimator's estimation error and the corresponding convergence rate are derived. This result provides a reference measure of optimal performance for jump-time estimators in discrete-time stochastic systems that does not depend on the jump time's prior distribution |
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Keywords: | Bayes Detector Large Deviations Likelihood Ratio Maximum-a-Posteriori Estimator Measure Transformation Quality Control Sequential Detection |
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