Utilizing Csiszar Divergences to Analyze Deployments of Binary Sensors with Modulators

Divergences or their counterpart (dis)similarity measures of two probability distributions play an important role in information theory. Especially, Csiszar divergences have many forms. Among so many forms of Csiszar divergences, we plan to find which divergence is the best suit of the analysis of binary sensor deployments. A binary sensor outputs a binary digit 1 or 0 when detecting an object or not, respectively. Recently, modulators made of opaque materials are utilized to modulate the sensing view of binary sensors to enhance their spatial awareness. In this paper, we construct two probability models of binary sensors modulated by modulators, i.e., an ideal model and an actual deployment model. Moreover, we utilize 13 forms of Csiszar divergences to analyze the distribution of those probability models. Based on the divergence calculation results, we classify the 13 divergences into five classifications. Furthermore, we propose a smoothing method to deal with the events which are absent in the experiments, i.e., occurring with zero probability. Our experiment results show that the smoothing method eliminates the zero probabilities and has little influence on the nonzero probabilities. Finally, we select the best divergence among the 13 divergences to analyze binary sensors modulated with modulators.