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.

The increasingly wide utilization of Wireless Sensor Networks (WSNs) in industrial applications outstands the significance of the Delay Constrained Relay Node Placement (DCRNP) problem. Existing algorithms to the DCRNP problem are designed based on the ideal geometric disk wireless channel model, and no real-world deployments are performed to verify the effectiveness of these algorithms. However, the unreliable and unpredictable wireless links in WSNs may lead these algorithms to fail in practice. Therefore, we first conduct extensive real-world deployments under the guidance of existing algorithms to evaluate their performance and to gain some insights for designing practical deployment algorithms. The results exhibit that the WSNs built by existing algorithms have a favorable performance in end-to-end delay but a poor performance in reliability, which is mainly due to the lack of methods ensuring high-quality links. To this end, we first devise a Set-Covering-based Algorithm (SCA) which figures out the DCRNP problem while ensuring the quality of each link better than a given threshold. As our experiments also show that the fault-tolerant topology can significantly improve network reliability, we then design a k-Set-Covering-based Algorithm (kSCA) to build fault-tolerant WSNs based on the methodology of SCA. Furthermore, the elaborate analysis proves that both SCA and kSCA are polynomial-time algorithms, and their approximation ratios are both O(ln n), where n is the number of sensor nodes. Finally, extensive experiments are performed under the guidance of SCA and kSCA to demonstrate the effectiveness of these two algorithms.

Recently, many researchers multiplex binary infrared sensors in object tracking, habitat monitoring, and atypical behavior detection. Due to the binary digit output of binary sensors, multiplex binary sensors may lead to count the wrong number of targets when three or more targets present in the field of interest (FOI). We call this as the invisible targets' problem. To enhance the sensing results of sensors, a reference structure tomography technique is used to segment and code the FOI by modulating the sensing view of sensors. In this paper, we propose a subregion coding method to count targets moving in the FOI. Hexagon modulators are designed to make their projections segment the FOI into hexagon cells. We also propose a signature construct scheme to code cells and a encoder to count the number of targets in the FOI. Experiment results show that the accuracy to correctly count targets of our method is around 90% which is much better than 45% of a conventional method.