On Indistinguishability and Antisymmetry Properties in Multiple Target Tracking

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1 December 2019

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The notion of indistinguishable targets is well established in advanced target tracking. If no specific target attributes are sensed, indistinguishability is often unavoidable and sometimes even desirable, for example, to enable “privacy by design” in public surveillance. Conceptually, this notion is rooted in quantum physics where functions of joint quantum particle states are considered that are either symmetric or antisymmetric under permutation of the particle labels. This symmetry dichotomy explains why quite fundamentally two disjunct classes of particles exist in nature: bosons and fermions. Besides symmetry, also antisymmetry has a place in multiple target tracking as we will show, leading to well-defined probability density functions describing the joint target states. Inbuilt antisymmetry implies a target tracking version of Pauli’s exclusion principle: Real-world targets are “fermions” in the sense that cannot exist at the same time in the same state. This is of interest in dense tracking scenarios with resolution conflicts and split-off and may mitigate track coalescence phenomena, for example. We discuss the framework that is illustrated by an example.