TY - GEN
T1 - Poisson's equation in nonlinear filtering
AU - Laugesen, Richard
AU - Mehta, Prashant G.
AU - Meyn, Sean P.
AU - Raginsky, Maxim
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014
Y1 - 2014
N2 - The goal of this paper is to gain insight into the equations arising in nonlinear filtering, as well as into the feedback particle filter introduced in recent research. The analysis is inspired by the optimal transportation literature and by prior work on variational formulation of nonlinear filtering. The construction involves a discrete-time recursion based on the successive solution of minimization problems involving the so-called forward variational representation of the elementary Bayes' formula. The construction shows that the dynamics of the nonlinear filter may be regarded as a gradient flow, or a steepest descent, for a certain energy functional with respect to the Kullback-Leibler divergence pseudo-metric. The feedback particle filter algorithm is obtained using similar analysis. This filter is a controlled system, where the control is obtained via consideration of the first order optimality conditions for the variational problem. The filter is shown to be exact, i.e., the posterior distribution of the particle matches exactly the true posterior, provided the filter is initialized with the true prior.
AB - The goal of this paper is to gain insight into the equations arising in nonlinear filtering, as well as into the feedback particle filter introduced in recent research. The analysis is inspired by the optimal transportation literature and by prior work on variational formulation of nonlinear filtering. The construction involves a discrete-time recursion based on the successive solution of minimization problems involving the so-called forward variational representation of the elementary Bayes' formula. The construction shows that the dynamics of the nonlinear filter may be regarded as a gradient flow, or a steepest descent, for a certain energy functional with respect to the Kullback-Leibler divergence pseudo-metric. The feedback particle filter algorithm is obtained using similar analysis. This filter is a controlled system, where the control is obtained via consideration of the first order optimality conditions for the variational problem. The filter is shown to be exact, i.e., the posterior distribution of the particle matches exactly the true posterior, provided the filter is initialized with the true prior.
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U2 - 10.1109/CDC.2014.7040041
DO - 10.1109/CDC.2014.7040041
M3 - Conference contribution
AN - SCOPUS:84988286468
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4185
EP - 4190
BT - 53rd IEEE Conference on Decision and Control,CDC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Y2 - 15 December 2014 through 17 December 2014
ER -