Optimal Geometry Analysis for TDOA-Based Localization Under Communication Constraints

The sensor-source geometry has a significant effect on accuracy of source localization problems. In a sensor placement problem, one attempts to optimally place the sensors in the surveillance area so as to optimize a performance criterion. Sensor placement methods mainly solve the associated problems without taking any specific constraint on permissible location of sensors into account. In practical applications, however, possible location for deployment of the sensors are subject to such limitations as environmental, industrial, and communication constraints, which affects the optimal sensor-source geometry. In this article, we consider the problem of optimal sensor placement, based on time difference of arrival measurement, under some communication constraints. It is assumed that the sensors can communicate with the reference sensor only when the associated sensor-reference interdistance is lower than a given constant value (due to a limited communication budget). The analysis conducted in this article is based on the D-optimality criterion, i.e., maximizing the determinant of associated Fisher information matrix. We theoretically analyze the optimal sensor-source geometry with an arbitrary number of sensors in two cases of the source being inside and outside of the permissible sensor placement area. Numerical simulations are included to verify the theoretical results.