A random finite set conjugate prior and application to multi-target tracking

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) where the model for the observation covers thinning, Markov shifts and superposition of false observations. A prior for the hidden RFS together with the likelihood of the realisation of the observed RFS gives the posterior distribution via the application of Bayes rule. We propose a new class of prior distribution and show that it is a conjugate prior with respect to the multi-target observation likelihood. This result is then applied to develop an analytic implementation of the Bayes multi-target filter for the class of linear Gaussian multi-target models.