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Void Probabilities and Cauchy-Schwarz Divergence for Generalized Labeled Multi-Bernoulli Models

The generalized labeled multi-Bernoulli (GLMB) is a family of tractable models that alleviates the limitations of the Poisson family in dynamic Bayesian inference of point processes. In this paper, we derive closed form expressions for the void probability functional and the Cauchy-Schwarz divergence for GLMBs. The proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a GLMB, while the proposed analytic Cauchy-Schwarz divergence provides a tractable measure of similarity between GLMBs. We demonstrate the use of both results on a partially observed Markov decision process for GLMBs, with Cauchy-Schwarz divergence based reward, and void probability constraint.