TY - GEN

T1 - A mean-field control-oriented approach to particle filtering

AU - Yang, Tao

AU - Mehta, Prashant G.

AU - Meyn, Sean P.

PY - 2011/9/29

Y1 - 2011/9/29

N2 - A new formulation of the particle filter for nonlinear filtering is presented, based on concepts from optimal control, and from the mean-field game theory framework of Huang et. al. [8]. The optimal control is chosen so that the posterior distribution of a particle matches as closely as possible the posterior distribution of the true state, given the observations. In the infinite-N limit, the empirical distribution of ensemble particles converges to the posterior distribution of an individual particle. The cost function in this control problem is the Kullback-Leibler (K-L) divergence between the actual posterior, and the posterior of any particle. The optimal control input is characterized by a certain Euler-Lagrange (E-L) equation. A numerical algorithm is introduced and implemented in two general examples: A linear SDE with partial linear observations, and a nonlinear oscillator perturbed by white noise, with partial nonlinear observations.

AB - A new formulation of the particle filter for nonlinear filtering is presented, based on concepts from optimal control, and from the mean-field game theory framework of Huang et. al. [8]. The optimal control is chosen so that the posterior distribution of a particle matches as closely as possible the posterior distribution of the true state, given the observations. In the infinite-N limit, the empirical distribution of ensemble particles converges to the posterior distribution of an individual particle. The cost function in this control problem is the Kullback-Leibler (K-L) divergence between the actual posterior, and the posterior of any particle. The optimal control input is characterized by a certain Euler-Lagrange (E-L) equation. A numerical algorithm is introduced and implemented in two general examples: A linear SDE with partial linear observations, and a nonlinear oscillator perturbed by white noise, with partial nonlinear observations.

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M3 - Conference contribution

AN - SCOPUS:80053144595

SN - 9781457700804

T3 - Proceedings of the American Control Conference

SP - 2037

EP - 2043

BT - Proceedings of the 2011 American Control Conference, ACC 2011

T2 - 2011 American Control Conference, ACC 2011

Y2 - 29 June 2011 through 1 July 2011

ER -