Abstract
The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion was introduced in the mid-1990s and extended in 2001. FISST was devised to be as “engineering-friendly” as possible by avoiding avoidable mathematical abstraction and complexity—and, especially, by avoiding measure theory and measure-theoretic point process (p.p.) theory. Recently, however, an allegedly more general theoretical foundation for multitarget tracking has been proposed. In it, the constituent components of FISST have been systematically replaced by mathematically more complicated concepts—and, especially, by the very measure theory and measure-theoretic p.p.’s that FISST eschews. It is shown that this proposed alternative is actually a mathematical paraphrase of part of FISST that does not correctly address the technical idiosyncrasies of the multitarget tracking application.
Highlights
The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion—stochastic geometry, random finite sets (RFS’s), belief-mass functions, and set derivatives and integrals—was introduced in the mid-1990s [1]
This is because FISST (a) has an integro-differential calculus of possibly nonadditive set functions and their density functions (Section 3.1); and (b) it Bayes-optimally addresses multitarget-multisource information fusion using “hard + soft” data in a unified manner [2] (Chapters 3–7); [3] (Chapter 22)
The latter is attributable to the fact that FISST is based on stochastic geometry, which in turn is based on the theory of random closed subsets (RCS’s) [19], which in turn is the basis of FISST’s unification of
Summary
The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion—stochastic geometry, random finite sets (RFS’s), belief-mass functions, and set derivatives and integrals—was introduced in the mid-1990s [1]. Still fewer have studied point process (p.p.) theory (which typically requires proficiency in measure theory), and few are proficient For this reason, FISST does not employ measure theory or measure-theoretic p.p.’s, because simpler and more practical concepts, such as multitarget density functions, RFS’s, and Volterra functional derivatives, suffice. [4,11], is intended to answer this question It will address the alternative multitarget statistical theory described in Refs. (Section 2.1); RFS’s are simpler than simple p.p.’s (Section 2.2); non-RFS p.p.’s are inappropriate for multitarget tracking (Section 2.3); vectors are poor multitarget state representations (Section 2.4); simple p.p.’s produce a flawed mathematical paraphrase of RFS’s (Section 2.5); and FISST is more general than MPMT (Section 2.6)
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