2016/12/16 by Amirhossein Taghvaei, Taghvaei, Amirhossein, Prashant G. Mehta +3 · 1 citation
Computer Science · Earth and Planetary Sciences · Environmental Science · #FOS: Mathematics #Hydrological Forecasting Using AI #Numerical Analysis (math.NA) #Target Tracking and Data Fusion in Sensor Networks #Underwater Acoustics Research
paper · pdf · doi:10.48550/arxiv.1612.05606
openalex publication_date 2016/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the analysis of the kernel-based algorithm for\ngain function approximation in the feedback particle filter. The exact gain\nfunction is the solution of a Poisson equation involving a probability-weighted\nLaplacian. The kernel-based method -- introduced in our prior work -- allows\none to approximate this solution using em only particles sampled from the\nprobability distribution. This paper describes new representations and\nalgorithms based on the kernel-based method. Theory surrounding the\napproximation is improved and a novel formula for the gain function\napproximation is derived. A procedure for carrying out error analysis of the\napproximation is introduced. Certain asymptotic estimates for bias and variance\nare derived for the general nonlinear non-Gaussian case. Comparison with the\nconstant gain function approximation is provided. The results are illustrated\nwith the aid of some numerical experiments.\n