Multitarget Moments and their Application to Multitarget Tracking

摘要

The concept of a 'statistical moment' has played a fundamental role in practical single-target tracking. The optimal tracking approach, the recursive Bayes filter, propagates the entire posterior density through time. Because this filter is computationally daunting, most practical single-target tracking approaches assume that signal-to-noise ratio is large enough that the posterior is approximately characterized by its low-order moments. For example, the alpha-beta-gamma filter propagates the first-order moment (the posterior expectation) whereas the extended Kalman filter (EKF) additionally propagates a second-order moment (the posterior covariance). Until recently, the possibility of an analogous multitarget approach seems to have been ignored---apparently for lack of a systematic statistical foundation for multitarget problems. In two recent papers, I introduced multitarget moment statistics of arbitrary order and developed a Bayes filtering theory for the first-order multitarget moment, the 'probability hypothesis density (PHD).' In this paper I continue this line of investigation. I will describe a preliminary implementation of the first-order filter. I will introduce the concept of multitarget posterior covariances of arbitrary order. Using them, I will show how a suitable extension of the finite- set statistics (FISST) multisensor-multitarget differential calculus can be used to construct multitarget statistical analogs of the EKF.