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Reduced Complexity HMM Filtering With Stochastic Dominance Bounds: A Convex Optimization Approach
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-0355-2663
2014 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 23, 6309-6322 p.Article in journal (Refereed) Published
Abstract [en]

This paper uses stochastic dominance principles to construct upper and lower sample path bounds for Hidden Markov Model (HMM) filters. We consider an HMM consisting of an X-state Markov chain with transition matrix P. By using convex optimization methods for nuclear norm minimization with copositive constraints, we construct low rank stochastic matrices (P) under bar and (P) over bar so that the optimal filters using (P) under bar, (P) over bar provably lower and upper bound (with respect to a partially ordered set) the true filtered distribution at each time instant. Since (P) under bar and (P) over bar are low rank (say R), the computational cost of evaluating the filtering bounds is O(XR) instead of O(X-2). A Monte-Carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior. Finally, explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds in terms of the Dobrushin coefficient.

Place, publisher, year, edition, pages
2014. Vol. 62, no 23, 6309-6322 p.
Keyword [en]
Hidden Markov model filter, stochastic dominance, copositive matrix, nuclear norm minimization, importance sampling filter, Dobrushin coefficient
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-158814DOI: 10.1109/TSP.2014.2362886ISI: 000344988500019Scopus ID: 2-s2.0-84910120533OAI: oai:DiVA.org:kth-158814DiVA: diva2:784134
Note

QC 20150128

Available from: 2015-01-28 Created: 2015-01-12 Last updated: 2017-12-05Bibliographically approved

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Rojas, Cristian R.

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