- 控制理论和非线性滤波讨论班

Error Estimate for Nonlinear Filtering Problems with Stochastically Diffusive and Point Processes

组织者

丘成栋

演讲者

董文慧

时间

2023年11月03日 20:00 至 20:30

地点

Online

摘要

In this paper, we consider a nonlinear filtering (NLF) problem modelled by a diffusive signal process with two independent observation processes. One of the observation processes is driven by a Gaussian diffusive noise correlated with the signal process, and the other one is an independent Poisson point process. It is well-known that the signal's unnormalized density conditioned on the continuous observation history satisfies the Zakai equation. In practice, the observation is discrete or discretized. The unnormalized density conditioned on the sub-filtration generated by the discretized observations is the approximate solution to the Zakai equation. The main contribution of this paper is that we show under certain conditions the mean square error of this approximate solution is no more than the order O(√h), where h is the time step in the regular time discretization, by the technique of Brownian and Poisson bridges. To verify this convergence rate, we propose the Zakai filter with Brownian-Poisson-bridge and numerically experiment it on the benchmark cubic sensor problem, which confirms the theoretic convergence rate. Moreover, we compare this algorithm with the particle filter to illustrate its accuracy and efficiency.