Single-target density for tracking indistinguishable objects

Abstract

The concept of indistinguishability in multi-target tracking leads to correlations in their statistical description even without explicit interactions between the objects. These correlations can be described in terms of a wave function – the square-root of the multi-target probability density function (pdf) – which is necessarily either symmetric or anti-symmetric under the exchange of two target indices. [1] This symmetry dichotomy, well-known in quantum many particle physics as bosonic and fermionic behavior, leads to specific properties of the multi-target pdf. While anti-symmetry results in a repulsive behavior in terms of the single object states, symmetry leads to clustering of single objects into the same state. This different behavior can be exploited to describe macroscopic objects which either tend to avoid each other or to form groups.In this paper, we develop an approach for tracking multiple non-interacting indistinguishable targets in the presence of false alarms. The goal is to avoid the treatment of the high-dimensional multi-target pdf by approximating it in terms of the square of so-called Slater determinants and permanents build from single target pdfs. From the intensity (first order statistical moment) of the multi-target pdf, we derive approximations for single target pdfs which show the specific fermionic and bosonic behavior. These "corrected" single target pdfs can serve as input into standard data association and filtering algorithms. Exemplary implementations in a JPDAF framework demonstrate the mitigation of track coalescence.