TY - GEN
T1 - Gain function approximation in the feedback particle filter
AU - Taghvaei, Amirhossein
AU - Mehta, Prashant G.
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/12/27
Y1 - 2016/12/27
N2 - This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to approximate this solution using only particles sampled from the probability distribution. Two algorithms are presented: a Galerkin algorithm and a kernel-based algorithm. Both the algorithms are adapted to the samples and do not require approximation of the probability distribution as an intermediate step. The paper contains a preliminary error analysis for the algorithms as well as some comparative numerical results for a non-Gaussian distribution. These algorithms are also applied and illustrated for a simple nonlinear filtering example.
AB - This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to approximate this solution using only particles sampled from the probability distribution. Two algorithms are presented: a Galerkin algorithm and a kernel-based algorithm. Both the algorithms are adapted to the samples and do not require approximation of the probability distribution as an intermediate step. The paper contains a preliminary error analysis for the algorithms as well as some comparative numerical results for a non-Gaussian distribution. These algorithms are also applied and illustrated for a simple nonlinear filtering example.
UR - http://www.scopus.com/inward/record.url?scp=85010825384&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2016.7799105
DO - 10.1109/CDC.2016.7799105
M3 - Conference contribution
AN - SCOPUS:85010825384
T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
SP - 5446
EP - 5452
BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 55th IEEE Conference on Decision and Control, CDC 2016
Y2 - 12 December 2016 through 14 December 2016
ER -