Sampling-based algorithm for filtering using Markov chain approximations
Author(s)Karaman, Sertac; Frazzoli, Emilio; Chaudhari, Pratik Anil
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In this paper, the filtering problem for a large class of continuous-time, continuous-state stochastic dynamical systems is considered. Inspired by recent advances in asymptotically-optimal sampling-based motion planning algorithms, such as the PRM* and the RRT*, an incremental sampling-based algorithm is proposed. Using incremental sampling, this approach constructs a sequence of Markov chain approximations, and solves the filtering problem, in an incremental manner, on these discrete approximations. It is shown that the trajectories of the Markov chain approximations converge in distribution to the trajectories of the original stochastic system; moreover, the optimal filter calculated on these Markov chains converges to the optimal continuous-time nonlinear filter. The convergence results are verified in a number of simulation examples.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Proceedings of the 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Institute of Electrical and Electronics Engineers (IEEE)
Chaudhari, Pratik, Sertac Karaman, and Emilio Frazzoli. “Sampling-based algorithm for filtering using Markov chain approximations.” In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 5972-5978. Institute of Electrical and Electronics Engineers, 2012.
Author's final manuscript