A stochastic grid filter for multi-target tracking

In this paper, we discuss multi-target tracking for a submarine model based on incomplete observations. The submarine model is a weakly interacting stochastic dynamic system with several submarines in the underlying region. Observations are obtained at discrete times from a number of sonobuoys equipped with hydrophones and consist of a nonlinear function of the current locations of submarines corrupted by additive noise. We use filtering methods to find the best estimation for the locations of the submarines. Our signal is a measure-valued process, resulting in filtering equations that can not be readily implemented. We develop Markov chain approximation approach to solve the filtering equation for our model. Our Markov chains are constructed by dividing the multi-multi-targettarget state space into cells, evolving particles in these cells, and employing a random time change approach. These approximations converge to the unnormalized conditional distribution of the signal process based on the back observaions. Finally we present some simulation results by using the refining stochastic grid (REST) filter (developed from our Markov chain approximation method).