Optimal Design for Modulated Binary Sensors

A paramount factor limiting the applications of binary sensors is these senors’ on-off property outputting binary digits of “0” or “1”. To overcome this limitation, modulators or obscurants are added to enhance the sensing ability of binary sensors and render them usable in applications such as multi-target tracking and human activity recognition. Obscurants segment the field of interest into subregions and distinguish each subregion by a list of sensor states called signatures. This paper studies two placement scenarios in a two-dimensional planar graph. In the first scenario, we prove upper and lower bounds on the maximum number of achievable signatures. In the second scenario, starting from the placement of sensors and obscurants in which the maximum number of signatures is achievable, we propose a novel mathematical model based on four main metrics: the object space size, the sensor space size, the obscurant space size, and the sizes of individual obscurants. We find the minimum and maximum radiuses that bound the object detection area given the number and sizes of sensors and obscurants. We derive the obscurant space size as a function of the object space size and the size of individual obscurants. We also provide a linear relationship formula between the obscurant space radius, the sensor space radius, and the obscurants’ radiuses and conduct modeling experiments to study the relationship between these metrics. Finally, we deduct an explicit formula for the maximum obscurant space size for the sensor space and the individual obscurant sizes.