Accumulated state densities and their use in decorrelated track-to-track fusion

In tracking and sensor data fusion applications, the full information on kinematic object properties accumulated over a certain discrete time window up to the present time is contained in the conditional joint probability density function of the kinematic state vectors referring to each time step in this window. This density is conditioned by the time series of all sensor data collected the present time and has accordingly been called an accumulated state density (ASD). ASDs provide a unified treatment of filtering and retrodiction insofar as by marginalizing them appropriately, the standard filtering and retrodiction densities are obtained. In addition, ASDs fully describe the posterior correlations between the states at different instants of time. We here provide an introduction into the notion of ASDs, derive closed formulae for calculating them, and discuss their relevance for problem solving in exact track-to-track fusion in distributed sensor networks.