Sequential Quantum Monte-Carlo for Tracking of Indistinguishable Targets

For indistinguishable targets, the probability density function is symmetric under exchange of the target labels and can be formulated as the square of a symmetric or antisymmetric real-valued wave function. [1] Anti-symmetry implicitly describes objects that cannot share the same physical state at the same time-a property macroscopic real world objects possess. Based on the approach in [1], we develop a sequential Monte Carlo method that propagates and updates the anti-symmetric wave function. Anti-symmetry is maintained using an approximation in the time update step. The algorithm is closely related to Quantum Monte Carlo methods applied in nuclear and condensed matter physics. Preliminary results for a simple two-target scenarios are presented and limitations and possible further developments are discussed.