Bounds on the Optimal Performance for Jump Markov Linear Gaussian Systems
2013 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 1, 92-98 p.Article in journal (Refereed) Published
The performance of an optimal filter is lower bounded by the Bayesian Cramer-Rao Bound (BCRB). In some cases, this bound is tight (achieved by the optimal filter) asymptotically in information, i.e., high signal-to-noise ratio (SNR). However, for jump Markov linear Gaussian systems (JMLGS) the BCRB is not necessarily achieved for any SNR. In this paper, we derive a new bound which is tight for all SNRs. The bound evaluates the expected covariance of the optimal filter which is represented by one deterministic term and one stochastic term that is computed with Monte Carlo methods. The bound relates to and improves on a recently presented BCRB and an enumeration BCRB for JMLGS. We analyze their relations theoretically and illustrate them on a couple of examples.
Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2013. Vol. 61, no 1, 92-98 p.
Jump Markov linear Gaussian systems, Performance bounds, Statistical signal processing
IdentifiersURN: urn:nbn:se:liu:diva-89524DOI: 10.1109/TSP.2012.2223690ISI: 000313896100011OAI: oai:DiVA.org:liu-89524DiVA: diva2:608232
FunderSwedish Research Council
Funding Agencies|Linneaus Center for Control, Autonomy, and Decision-making in Complex Systems (CADICS)||Swedish Research Council (VR)||2013-02-262013-02-262015-09-14