Two linear complexity particle filters capable of maintaining target label probabilities for targets in close proximity

In this work, we introduce two particle filters of linear complexity in the number of particles that take distinct approaches to solving the problem of tracking two targets in close proximity. We operate in the regime in which measurements do not discriminate between targets and hence uncertainties in the labeling of the tracks arise. For simplicity, we limit our study to the two target case for which there are only two possible associations between targets and tracks. The proposed Approximate Set Particle Filter (ASPF) introduces some approximations but has similar complexity and still provides much more accurate descriptions of the posterior uncertainties compared to standard particle filters. The fast Forward Filter Unlabeled Backward Simulator (fast FFUBSi) employs a smoothing technique based on rejection sampling for the calculation of target label probabilities. Simulations show that neither particle filter suffers from track coalescence (when outputting MMOSPA estimates) and both calculate correct target label probabilities.