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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Veröffentlicht in:IEEE transactions on signal processing 2012-01, Vol.60 (1), p.2-17
Hauptverfasser: Ba-Ngu Vo, Ba-Tuong Vo, Mahler, R. P. S.
Format: Artikel
Sprache:eng
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Zusammenfassung: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