A stochastic approximation based state estimation algorithm for Stochastic Hybrid Systems

This paper is focused on the state estimation for the Stochastic Hybrid System (SHS) which is a class of continuous-time stochastic processes with the interacting continuous and discrete dynamics. The state estimation problem considered in this paper involves computing the probability distributions of both the continuous and the discrete state of a SHS with the information given by a series of noisy discrete-time observations from sensors at each sampling time. The numerical state estimation algorithm proposed in this paper is based on a stochastic approximation approach by using a Markov Chain (MC) to approximate the dynamics of the SHS and thus estimates the state of the MC instead of the SHS. The proposed algorithm is validated through a scenario of aircraft tracking for air traffic control.