The Cauchy-Schwarz divergence for Poisson point processes

Abstract

In this paper, we extend the notion of Cauchy-Schwarz divergence to point processes and establish that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared ${\mathbf{L}}^2$-distance between their intensity functions. Extension of this result to mixtures of Poisson point processes and, in the case where the intensity functions are Gaussian mixtures, closed form expressions for the Cauchy-Schwarz divergence are presented. Our result also implies that the Bhattachryaa distance between the probability distributions of two Poisson point processes is equal to the square of the Hellinger distance between their intensity measures. We illustrate the result via a sensor management application where the system states are modeled as point processes.

Two colunms, 11 pages, 5 figures. This paper has been published in the IEEE Transaction on Information Theory. Part of the paper was presented at the 2014 IEEE Workshop on Statistical Signal Processing, Gold Coast, Australia

References in corpus (1)

• Sensor management for multi-target tracking via Multi-Bernoulli filtering

Cited by in corpus (11)

• Online UAV Path Planning for Joint Detection and Tracking of Multiple Radio-tagged Objects
• Fusion of labeled RFS densities with minimum information loss
• Multi-Sensor Control for Multi-Object Bayes Filters
• Heterogeneous Multi-sensor Fusion with Random Finite Set Multi-object Densities
• An Overview of Multi-Object Estimation via Labeled Random Finite Set
• Cell Multi-Bernoulli (Cell-MB) Sensor Control for Multi-object Search-While-Tracking (SWT)
• Control of Large Swarms via Random Finite Set Theory
• A New Probabilistic Distance Metric With Application In Gaussian Mixture Reduction
• Phase space distributions in information theory
• Generalized Fisher-Darmois-Koopman-Pitman Theorem and Rao-Blackwell Type Estimators for Power-Law Distributions
• Probing information theoretic measures of nonlinear ultracold quantum gases using phase-space distributions