Mixture reduction algorithms for target tracking

The paper is concerned with the development of practical filters for tracking a target when the origin of sensor measurements is uncertain. The full Bayesian solution to this problem gives rise to mixture distributions. From knowledge of the mixture distribution, in principle, an optimal estimate of the state vector for any criteria may be obtained. Also, if the problem is linear and Gaussian, the distribution becomes a Gaussian mixture in which each component probability density function is given by a Kalman filter. The author only considers this case. The methods presented are based on the premise that the number of mixture components should be minimized without modifying the `structure´ of the distribution beyond a specified limit. The techniques operate by merging similar components in such a way that the approximation preserves the mean and covariance of the original mixture. Also to allow the tracking filter to be implemented as a bank of Kalman filters, it is required that the approximated distribution is itself a Gaussian mixture