A random finite set formalism for multiple hypothesis tracking

This paper is generally concerned with mathematical formalisms to support theory and algorithm developments of multiple hypothesis tracking (MHT), as a class of solutions to multiple target tracking (MTT) problems based on targetwise detections. In particular, this paper presents a new perspective on random set (RFSet) formalism to support a form of MHT, in which an unknown number of targets is modeled by a RFSet of continuous-time stochastic processes, rather than a single stochastic process defined on the space of finite sets in a given target state space, while generally multiple sensors provide noisy and cluttered target detections without any explicit indications of origins. The focus is on a clearcut approach to avoid any complication resulting from diagonal sets in direct-product spaces when a space of finite subsets of a state space is defined as its quotient space, instead of a subspace of the space of closed subsets in the state space with Fell-Matheron topology.

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