The Cauchy-Schwarz divergence for assessing situational information gain

In this paper, we consider the evaluation of information divergence and information gain as they apply to a hybrid random variable (i.e. a random variable which has both discrete and continuous elements) for multi-target tracking problems. In particular, we develop a closed-form solution for the Cauchy-Schwarz information divergence under the assumption that the continuous element of the random variable may be represented by a Gaussian mixture distribution and present the associated relationships for evaluating the Cauchy-Schwarz information gain. The developed information gain relationships are applied to a 0-1 target tracking problem common to space object tracking to determine the sensitivities to the information gain due to probability of detection, prior probability of object existence, and measurement noise.