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

pp. 31-46

**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.

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