A theoretical look at information-driven sensor management criteria

In sensor management, the usefulness of information theoretic measures seems to be validated by a large number of empirical studies, but theoretical justification presented until so far, both for selection of the measure and for the use of information-driven sensor management itself, still seems inconclusive, conflicting, or debatable. In this paper, we suggest that information-driven sensor management may be justified on the basis of uncertainty reduction rather than information gain. We subsequently identify that, due to well-known relationships between Shannon entropy, mutual information and Kullback-Leibler (KL) divergence, for sensor management purposes using the Kullback-Leibler (KL) divergence (a measure of information gain; thus a relative measure) is exactly the same as using the the Shannon entropy (a measure of uncertainty; an absolute measure). This is also used to demonstrate that, if uncertainty reduction is desirable, the asymmetry of the KL divergence is not relevant to the sensor management problem. Finally, we show some counterpoints to some arguments for replacing the KL divergence with the more general Rényi divergences.