2019/07/15 by Ajay Jasra, Jasra, Ajay, Fangyuan Yu +3 · 1 citation
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · #Algorithm #Applied mathematics #Combinatorics #Computer science #Discretization #FOS: Mathematics #Filter (signal processing) #Geometry #Kalman filter #Mathematical analysis #Mathematics #Mean squared error #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA) #Order (exchange) #Particle (ecology) #Particle filter #Probability (math.PR) #SIGNAL (programming language) #Seismic Imaging and Inversion Techniques #Square (algebra) #Statistics #Traffic Prediction and Management Techniques #cs.NA #math.NA #math.PR
paper · pdf · doi:10.48550/arxiv.1907.06328
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/07/15 · openalex created_date 2019/07/23 · arxiv created 2020/06/09 · arxiv updated 2020/06/11 · openalex updated_date 2026/08/05
In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we resort to a first order time discretization of the non-linear filter, followed by an Euler discretization of the signal dynamics. In order to approximate the associated discretized non-linear filter, one can use a particle filter (PF). Under assumptions, this can achieve a mean square error of O(ε2), for ε>0 arbitrary, such that the associated cost is O(ε-4). We prove, under assumptions, that the multilevel particle filter (MLPF) of Jasra et al (2017) can achieve a mean square error of O(ε2), for cost O(ε-3). This is supported by numerical simulations in several examples.