In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in [20], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameter of that algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples.

翻译：本文研究了一类部分观测的逐段确定性马尔可夫过程（PDMPs）的滤波问题。特别地，我们假设常微分方程（ODE）驱动确定性元素，且只能通过时间离散化进行数值求解。基于文献[20]的方法，我们提出了一种新的粒子滤波器和多层粒子滤波器（MLPF），以逼近与离散化ODE关联的滤波器。我们给出了MLPF均方误差的界，该界为算法模拟参数的设置提供了指导，并表明与使用粒子滤波器相比，可获得显著的计算收益。我们的理论结果在多个数值实例中得到了验证。