The labeled random finite set (LRFS) theory of B.-T. Vo and B.-N. Vo is the first systematic, theoretically rigorous formulation of true multitarget tracking, and is the basis for the generalized labeled multi-Bernoulli (GLMB) filter (the first implementable and provably Bayes-optimal multitarget tracking algorithm). An earlier paper showed that labeled multi-Bernoulli (LMB) RFS's are the labeled analogs of Poisson RFS's (which are not LRFS's); and, consequently, that the LMB filter of Reuter et al. can be interpreted as a labeled PHD (LPHD) filter for the "standard" multi-target measurementmodel. In like manner, this paper derives an LPHD/LMB filter for superpositional sensors. Whereas the LPHD/LMB filter for the "standard" model is combinatoric, the superpositional LPHD/LMB filter has computational order O(n) where n is the current number of tracks.
Ronald Mahler, "A fast labeled multi-Bernoulli filter for superpositional sensors," Proc. SPIE 10646, Signal Processing, Sensor/Information Fusion, and Target Recognition XXVII, 106460E (Presented at SPIE Defense + Security: April 17, 2018; Published: 27 April 2018); https://doi.org/10.1117/12.2305465.
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