Multilevel particle filters for the non-linear filtering problem in continuous time
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Embargo End Date2021-06-15
Permanent link to this recordhttp://hdl.handle.net/10754/660815
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AbstractIn 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. 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 of Jasra et al. (SIAM J Numer Anal 55:3068–3096, 2017) can achieve a mean square error of O(ϵ2) , for cost O(ϵ- 3). This is supported by numerical simulations in several examples.
CitationJasra, A., Yu, F., & Heng, J. (2020). Multilevel particle filters for the non-linear filtering problem in continuous time. Statistics and Computing, 30(5), 1381–1402. doi:10.1007/s11222-020-09951-9
SponsorsAJ was supported by KAUST baseline funding. We thank two referees for comments that have greatly improved the article.
JournalStatistics and Computing