On Accumulated State Densities with Applications to Out-of-Sequence Measurement Processing

In target tracking applications, the full information on the kinematic target states accumulated over a certain time window up to the present time is contained in the joint probability density function of these state vectors, given the time series of all sensor data. This joint density may also be called an accumulated state density (ASD) and provides a unified treatment of filtering and retrodiction insofar as by marginalizing the ASD, the standard filtering and retrodiction densities are obtained. In addition, ASDs fully describe the posterior correlations between the states at different instants of time. The notion of ASDs and closed formulae for calculating them are discussed. The practical usefulness of considering ASDs is illustrated by applications, where out-of-sequence (OoS) measurements are to be processed within the framework of a centralized measurement fusion architecture, i.e., when the sensor data do not arrive in the temporal order, in which they were produced. The approach can be applied to Kalman, multiple hypothesis tracking (MHT), and interacting multiple model (IMM) filtering.