Closed-Form Solutions to Forward-Backward Smoothing

We propose a closed-form Gaussian sum smoother and, more importantly, closed-form smoothing solutions for increasingly complex problems arising from practice, including tracking in clutter, joint detection and tracking (in clutter), and multiple target tracking (in clutter) via the probability hypot...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2012-01, Vol.60 (1), p.2-17
Main Authors: Ba-Ngu Vo, Ba-Tuong Vo, Mahler, R. P. S.
Format: Article
Language:English
Subjects:
Analytical models
Applied sciences
Bernoulli model
Closed-form solution
Clutter
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
filtering
Gaussian sum smoother
Information, signal and communications theory
Mathematical model
Numerical models
PHD
Signal and communications theory
Signal, noise
smoothing
Smoothing methods
Target tracking
Telecommunications and information theory
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Summary:We propose a closed-form Gaussian sum smoother and, more importantly, closed-form smoothing solutions for increasingly complex problems arising from practice, including tracking in clutter, joint detection and tracking (in clutter), and multiple target tracking (in clutter) via the probability hypothesis density. The solutions are based on the corresponding forward-backward smoothing recursions that involve forward propagation of the filtering densities, followed by backward propagation of the smoothed densities. The key to the exact solutions is the use of alternative forms of the backward propagations, together with standard Gaussian identities. Simulations are also presented to verify the proposed solutions.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2168519