Gain function approximation in the Feedback Particle Filter
Taghvaei, Amirhossein ; Mehta, Prashant G. ; Meyn, Sean P.
arXiv, Tome 2019 (2019) no. 0, / Harvested from
This paper is concerned with numerical algorithms for the problem of 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 numerical problem is to approximate this solution using only particles sampled from the probability distribution. A diffusion-map based algorithm is presented for this problem. The algorithm does not require approximation of the probability distribution as an intermediate step. A procedure for carrying out error analysis of the approximation is introduced and certain asymptotic estimates for bias and variance are derived. The paper contains some comparative numerical results for a problem with non-Gaussian distribution. The algorithm is also applied and illustrated for a numerical filtering example.
Publié le : 2019-02-19
Classification:  Mathematics - Optimization and Control,  Mathematics - Numerical Analysis,  Mathematics - Probability 
@article{1902.07263,
     author = {Taghvaei, Amirhossein and Mehta, Prashant G. and Meyn, Sean P.},
     title = {Gain function approximation in the Feedback Particle Filter},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1902.07263}
}

Taghvaei, Amirhossein; Mehta, Prashant G.; Meyn, Sean P. Gain function approximation in the Feedback Particle Filter. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1902.07263/