Mixture reduction algorithms for target tracking in clutter

The Bayesian solution of the problem of tracking a target in random clutter gives rise to Gaussian mixture distributions, which are composed of an ever increasing number of components. To implement such a tracking filter, the growth of components must be controlled by approximating the mixture distribution. A popular and economical scheme is the Probabilistic Data Association Filter (PDAF), which reduces the mixture to a single Gaussian component at each time step. However this approximation may destroy valuable information, especially if several significant, well spaced components are present. In this paper, two new algorithms for reducing Gaussian mixture distributions are presented. These techniques preserve the mean and covariance of the mixture, and the fmal approximation is itself a Gaussian mixture. The reduction is achieved by successively merging pairs of components or groups of components until their number is reduced to some specified limit. Further reduction will then proceed while the approximation to the main features of the original distribution is still good. The performance of the most economical of these algorithms has been compared with that of the PDAF for the problem of tracking a single target which moves in a plane according to a second order model. A linear sensor which measures target position is corrupted by uniformly distributed clutter. Given a detection probability of unity and perfect knowledge of initial target position and velocity, this problem depends on only tw‡ non-dimensional parameters. Monte Carlo simulation has been employed to identify the region of this parameter space where significant performance improvement is obtained over the PDAF.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.