2018/04/11 by Jin W. Kim, Kim, Jin W., Amirhossein Taghvaei +3
Computer Science · #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.1804.04199
This paper is concerned with a duality-based approach to derive the linear\nfeedback particle filter (FPF). The FPF is a controlled interacting particle\nsystem where the control law is designed to provide an exact solution for the\nnonlinear filtering problem. For the linear Gaussian special case, certain\nsimplifications arise whereby the linear FPF is identical to the square-root\nform of the ensemble Kalman filter. For this and for the more general nonlinear\nnon-Gaussian case, it has been an open problem to derive/interpret the FPF\ncontrol law as a solution of an optimal control problem. In this paper, certain\nduality-based arguments are employed to transform the filtering problem into an\noptimal control problem. Its solution is shown to yield the deterministic form\nof the linear FPF. An extension is described to incorporate stochastic effects\ndue to noise leading to a novel homotopy of exact ensemble Kalman filters. All\nthe derivations are based on duality formalisms.\n