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A Two-Filter Off-Line Solution to Optimal Detection
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1991 (English)Report (Other academic)
Abstract [en]

The problem of detecting abrupt changes of the dynamics in linear systems is addressed. First the generalized likelihood ratio test for detection in a state space model is examined. This test can be interpreted as a simultaneous maximum likelihood (ML) estimator of the jump time and jump magnitude. The problem is that this test requires a large number of matched filters which increases linearly with time. This is shown by simulations to be very time consuming. Therefore, a two-filter implementation of the ML estimator of the jump time is derived, which is very efficient in off-line detection. It consists of two Kalman filters, one running forwards and one backwards in time. The algorithm gives a considerable improvement on-line as well, if a batchwise data processing is allowed. A major problem in detection is the sensivity to incorrect values of the noise variance. This is solved by treating the noise variance as a stochastic variable, possibly changing at the jump time. A modified algorithm is given, which is still optimal for this case.

Place, publisher, year, edition, pages
Linköping: Linköping University , 1991.
LiTH-ISY-I, ISSN 8765-4321 ; 1267
Keyword [en]
Dynamics, Linear system, Maximum likelihood estimator, Simulations, Kalman filters, Algorithms
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-55473OAI: diva2:316131
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2013-07-29

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Gustafsson, Fredrik
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Automatic ControlThe Institute of Technology
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