A Technical Note on (Labeled) RFS-AA Fusion: Derivation from PHD Consistency

21 Sep 2022  ·  Tiancheng Li ·

The arithmetic average (AA) fusion is a fundamental information fusion methodology which has recently demonstrated great performance for multi-sensor tracking of a random number of objects based on the random finite set (RFS) theory. Since there are additional multi-object set cardinality (namely the number of objects) and even identities need to be estimated jointly with the multi-object states, the AA fusion has to be tailored in various specific means to accommodate different point processes. All can be strictly derived from the same unlabeled/labeled probability hypothesis density (PHD)-AA fusion formulation which seeks (labeled) PHD-consistency. In this paper, we first explain how the (labeled) PHD-consistency/AA fusion can lead to more accurate and robust detection and localization of the present objects which therefore forms a both theoretically solid and physically meaningful reason for fusion. Then, we derive and analyze the formulas of RFS-AA fusion for different (labeled) RFS filters on the same base of the (labeled) PHD-AA/consistency. These derivations are exact and need no approximation or mystifying reasoning. Finally, a technically unified approach is proposed for joint label matching and labeled multi-Bernoulli fusion.

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