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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 twç 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. |
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