Second order multi-object filtering with target interaction using determinantal point processes

Abstract

The n th order conditional factorial moment density of the point process Φ|Ξ = z 1:m at the point configurations x 1:n. 2.1.3 Branching Processes Definition 2.1.10. Ancestor-Descendant Random Variables. Suppose the r.v X and Y have dependency of an ancestor-descendant relationship, where X yields Y. Then, X is known as the ascestor r.v and Y is the descendant r.v. The branching process of X is described as, for any realization X = m, the conditional r.v Y |X = m is a superposition of m independent and identical r.v Z that collectively yield Y , that is, Y = m i=1 Z i. The conditional PGF is given by G Y |X (v|m) = (G Z (v)) m (2.6) where G Z is the PGF of r.v Z.