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Bayesian and geometric subspace tracking

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic systems and control Communication, information

Published online by Cambridge University Press:  01 July 2016

Anuj Srivastava  and
Eric Klassen
Anuj Srivastava*
Affiliation:
Florida State University
Eric Klassen*
Affiliation:
Florida State University
*
∗ Postal address: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA. Email address: anuj@stat.fsu.edu
∗∗ Postal address: Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA.
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Abstract

We address the problem of tracking the time-varying linear subspaces (of a larger system) under a Bayesian framework. Variations in subspaces are treated as a piecewise-geodesic process on a complex Grassmann manifold and a Markov prior is imposed on it. This prior model, together with an observation model, gives rise to a hidden Markov model on a Grassmann manifold, and admits Bayesian inferences. A sequential Monte Carlo method is used for sampling from the time-varying posterior and the samples are used to estimate the underlying process. Simulation results are presented for principal subspace tracking in array signal processing.

Keywords

Subspace trackingGrassmann manifoldBayesian trackingnon-Euclidean filteringsequential Monte Carlo

MSC classification

Primary: 93E11: Filtering
Secondary: 94A11: Application of orthogonal and other special functions 65C35: Stochastic particle methods
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 36 , Issue 1 , March 2004 , pp. 43 - 56
Copyright
Copyright © Applied Probability Trust 2004 

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