The collapse of sequential Bayesian estimator in two-target tracking problem

Abstract

Track coalescence is a phenomenon that occurs in multi-target tracking applications where certain types of manoeuvres performed simultaneously by several targets can utterly confuse algorithms that track their positions. In its simplest form, the phenomenon occurs when two similar objects, initially well separated, get close to each other and follow similar manoeuvres for a period of time sufficient to confound the tracking algorithm so that when the objects finally depart from each other the tracking algorithm is prone to provide erroneous estimates. This two-target track coalescence is discussed in this paper with the focus on the compound coalescence, when two identical tracks follow the midpoint of two well separated targets. First, the problem is illustrated on a classic problem of tracking two targets manoeuvring in a clutter, which is modeled as a nonlinear stochastic system. It is shown how, otherwise accurate and precise, estimates obtained by a standard particle filter eventually collapse leading to the coalescence of tracks. The phenomenon is given theoretical explanation by the analysis of Bayesian update operator acting on L2-space of probability densities that reveals that the coalescence is an unavoidable consequence of the probabilistic mixing between distributions describing positions of two targets. Finally, the practical consequences of these theoretical results are discussed together with potential approaches to deal with track coalescence in real applications.