Labeled Random Finite Sets and Multi-Object Conjugate Priors

TLDR

Multi‑object estimation seeks to simultaneously estimate the number and states of objects from noisy observations with data association uncertainty, and it can be formulated in a Bayesian framework using random finite sets, where a prior on the hidden RFS and the observation likelihood yield the posterior via Bayes’ rule. The authors propose a new class of RFS distributions that is conjugate with respect to the multi‑object observation likelihood. This class is closed under the Chapman‑Kolmogorov equation, enabling analytic propagation of the posterior. The proposed conjugate RFS class was evaluated within a Bayesian multi‑target tracking algorithm, demonstrating its applicability.

Abstract

The objective of multi-object estimation is to simultaneously estimate the number of objects and their states from a set of observations in the presence of data association uncertainty, detection uncertainty, false observations, and noise. This estimation problem can be formulated in a Bayesian framework by modeling the (hidden) set of states and set of observations as random finite sets (RFSs) that covers thinning, Markov shifts, and superposition. A prior for the hidden RFS together with the likelihood of the realization of the observed RFS gives the posterior distribution via the application of Bayes rule. We propose a new class of RFS distributions that is conjugate with respect to the multiobject observation likelihood and closed under the Chapman-Kolmogorov equation. This result is tested on a Bayesian multi-target tracking algorithm.