Abstract
Conventional single-point-target tracking algorithms are recursive point estimators with point-measurement input data. In less well-known approaches, the tracking algorithm is a recursive set estimator with point-measurement or set-measurement input data. This paper provides a very general, systematic, and theoretically rigorous foundation for Bayes-optimal single-target trackers of the latter kind; as well as specific trackers arising from that foundation. This foundation is intuitive and conceptually simple and, in particular, requires no measure-theoretic complexities.
Highlights
Conventional single-point-target tracking algorithms are recursive point estimators with point-measurement input data
Conventional likelihood functions can be interpreted as limiting cases of GENERALIZED LIKELIHOOD FUNCTIONS (GLF’s). It follows that the conventional recursive Bayes filter, (1,2), can be rigorously generalized to GENERALIZED MEASUREMENTS (GM’s) and generalized measurement function (GLF)’s:
The KEF is an exactclosed-form implementation of the “fuzzy Dempster-Shafer (FDS) filter,” which is an exact-closed-form special case of the generalized recursive Bayes filter (GRBF) that accepts Fuzzy Dempster-Shafer measurement (FDSM)’s as inputs and outputs FDS states (FDSS’s)
Summary
Conventional single-point-target tracking algorithms are recursive point estimators with point-measurement input data. The estimate γk|k is constructed either from z1:k or, more generally, from a time-sequence θ1:k of closed-set measurements θ1,...,θk ⊆ R (e.g., ellipsoids) which are believed to constrain the values of the point measurements. In this paper it will be shown that this theory can be considerably extended, thereby providing a very general, systematic, and theoretically rigorous foundation for Bayesoptimal single-point-target set-valued trackers; as well as specific trackers arising from that foundation. This foundation is intuitive and conceptually simple and, in particular, requires no measure-theoretic complexities.
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