A Two-Filter Off-Line Solution to Optimal Detection
1991 (English)Report (Other academic)
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
Dynamics, Linear system, Maximum likelihood estimator, Simulations, Kalman filters, Algorithms
IdentifiersURN: urn:nbn:se:liu:diva-55473OAI: oai:DiVA.org:liu-55473DiVA: diva2:316131