Reduced complexity spatio-temporal image-based tracking for maneuvering targets

There is significant motivation to develop reduced complexity filtering algorithms (with explicit performance bounds) for tracking maneuvering targets. Maneuvering target estimation is an important problem in target tracking due to the uncertainty in maneuvers of the target. In a hostile environment a target will try to avoid being tracked by maneuvering in such a way so that its motion is difficult to follow. The idea behind image-based and image enhanced tracking is to use two-dimensional imagery to obtain information about the mode of the target (e.g. orientation information) apart from conventional measurements. Simulation studies demonstrate that this modal information can lead to marked improvements in the target tracking performance. As is widely done we assume the mode of the target with time is modelled as a finite state Markov chain and the target's trajectory is modelled as a jump Markov linear system. The image sensor processor response to the modal information is blurred to due the range of the target, weather conditions, etc. Finally, the blurred images are processed by an imager which generates a marked Poisson process according to the noisy state of the Markov chain. In summary the image-based target tracking model is a multivariate Poisson process modulated by a single finite state Markov chain, i.e., a Markov Modulated Poisson Process (MMPP). Estimating the target's mode and coordinates then involves two filtering algorithms: (i) The optimal (MMSE) estimate of the orientation is computed by a MMPP filter (which is essentially a continuous-time Hidden Markov Model filter). (ii) The trajectory of the target (modelled as a jump Markov linear system) given the noisy modal measurements is estimated using an image-based filter. This is a finite dimensional filter (i.e. given by an ordinary differential equation driven by a Poisson observation process) which requires estimates from the MMPP filter The main contributions of this paper are to present robust reduced complexity temporal and spatial approximations to the above MMPP and image-based filters.