TAILIEUCHUNG - Adaptive lọc và phát hiện thay đổi P9

This chapter is devoted to the problem of detecting additive abrupt changes in linear state space models . Sensor and actuator faults as a sudden offset or drift can all be modeled as additive changes . In addition. disturbances are traditionally modeled as additive state changes . The likelihood ratio formulation provides a general framework for detecting such changes. and to isolate the fault/disturbance . | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic __9 Change detection based on likelihood ratios . . The likelihood . . . Likelihood . The GLR test .349 . The MLR . Relation between GLR and . A two-filter . Marginalization of the noise . State and variance . . Simulation . A Monte Carlo . . Derivation of the GLR test .370 . Regression model for the . The GLR . LS-based derivation of the MLR test .372 . Basics This chapter is devoted to the problem of detecting additive abrupt changes in linear state space models. Sensor and actuator faults as a sudden offset or drift can all be modeled as additive changes. In addition disturbances are traditionally modeled as additive state changes. The likelihood ratio formulation provides a general framework for detecting such changes and to isolate the fault disturbance. 344 Change detection based on likelihood ratios The state space model studied in this chapter is t i .t t T Bv iVt Ti iqBo yt Ctxt et Du tut at_kD6fiv. 9-1 9-2 The additive change fault v enters at time k as a step Jt denotes the step function . Here vt et and xq are assumed to be independent Gaussian variables vt et GN 0 J t x0 GN O no . Furthermore they are assumed to be mutually independent. The state change v occurs at the unknown time instant k and 5 j is the pulse function that is one if j 0 and zero otherwise. The set of measurements yi y2 . yjv each of dimension p will be denoted yN and y denotes the set yt yt i . yx- This formulation of the change detection problem can be interpreted as an input observer or input estimator approach. A similar model is used in Chapter

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