2022/03/09 by Zezhong Zhang, Zhang, Zezhong, Richard Archibald +3 · 1 citation
Computer Science · Earth and Planetary Sciences · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Numerical Analysis (math.NA) #Target Tracking and Data Fusion in Sensor Networks #Underwater Acoustics Research
paper · pdf · doi:10.48550/arxiv.2203.05031
openalex publication_date 2022/03/09 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a target stochastic dynamical system based on partial noisy observational data. The mathematical model that we use to formulate the propagation of the state dynamics is the Fokker-Planck equation, and we introduce an operator decomposition method to efficiently solve the Fokker-Planck equation. An adaptive kernel method is introduced to adaptively construct Gaussian kernels to approximate the probability distribution of the target state. Bayesian inference is applied to incorporate the observational data into the state model simulation. Numerical experiments have been carried out to validate the performance of our kernel method.