On nonlinear track-to-track fusion with Gaussian mixtures

The problem of fusing state estimates is encountered in many network-based multi-sensor applications. The majority of distributed state estimation algorithms are designed to provide multiple estimates on the same state, and track-to-track fusion then refers to the task of combining these estimates. While linear fusion only requires the joint cross-covariance matrix to be known, dependencies between estimates in nonlinear estimation problems have to be represented by high-dimensional probability density functions. In general, storing and keeping track of nonlinear dependencies is too cumbersome. However, this paper demonstrates that estimates represented by Gaussian mixtures prove to be an important exception to this rule. The dependency structure can as well be characterized in terms of a higher-dimensional Gaussian mixture. The different processing steps of distributed nonlinear state estimation, i.e., prediction, filtering, and fusion, are studied in light of the joint density representation. The presented concept is complemented with different simpler suboptimal representations of the dependency structure between Gaussian mixture densities.