Cost-Function-Based Gaussian Mixture Reduction for Target Tracking

The problem of tracking targets in clutter naturally leads to a Gaussian mixture representation of the probability density function of the target state vector. Stateof-the-art Multiple Hypothesis Tracking (MHT) techniques maintain the mean, covariance and probability weight corresponding to each hypothesis, yet they rely on ad hoc merging and pruning rules to control the growth of hypotheses. This paper proposes a structured cost-functionbased approach to the hypothesis control problem, utilizing 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 remarkably, yielding an average track life more than double that achievable using the joining filter. Furthermore, it appears that the performance of the algorithm will continue to grow exponentially as the number of mixture components is increased, hence the performance achievable is limited only by the computational resources available.