Cost-function-based gaussian mixture reduction for target tracking

The problem of tracking targets in clutter nat- urally leads to a Gaussian mixture representation of the probability density function of the target state vector. St ate- of-the-art Multiple Hypothesis Tracking (MHT) techniques maintain the mean, covariance and probability weight cor- responding to each hypothesis, yet they rely on ad hoc merging and pruning rules to control the growth of hy- potheses. This paper proposes a structured cost-function- based approach to the hypothesis control problem, utiliz- ing the newly defined Integral Square Difference (ISD) cost measure. The performance of the ISD-based algorithm for tracking a single target in heavy clutter is compared to that of Salmond's joining filter, which previously had provided the highest performance in the scenario examined. For a larger number of mixture components, it is shown that the ISD algorithm outperforms the joining filter remark- ably, yielding an average track life more than double that achievable using the joining filter. Furthermore, it appear s that the performance of the algorithm will continue to grow exponentially as the number of mixture components is in- creased, hence the performance achievable is limited only by the computational resources available.