MAP track fusion performance evaluation

The purpose of this paper is to develop a quantifiable performance evaluation method for MAP (Maximum A Posterior) track fusion algorithm. The goal is to provide analytical fusion performance without extensive Monte Carlo simulations. The idea is to develop methodologies for steady state fusion performance. Several fusion algorithms such as simple convex combination, cross-covariance combination (CC), information matrix (IM), and MAP fusion have been studied and several performance evaluation methods have been proposed. But most of them are not based on the steady state of an actual dynamic system. This paper conducts similar analysis for MAP fusion algorithm. It has been shown that the MAP or Best-Linear Unbiased Estimate (BLUE) fusion formula provides the best linear minimum mean squared estimates (LMMSE) given local estimates under the linear Gaussian assumption in a static situation (i.e., single iteration). However, in a dynamic situation, recursive fusion iterations are needed and the impact on the performance is not obvious. This paper proposes a systematic analytical procedure to evaluate the performance of such algorithm under two different communication strategies. Specifically, hierarchical fusion with and without feedback is considered. Theoretical curves for the steady state performance of the fusion algorithm with various communication patterns are given. They provide performance bounds for different operating conditions.