A study of two-dimensional sensor placement using time-difference-of-arrival measurements

Finding the position of a radiative source based on time-difference-of-arrival (TDOA) measurements from spatially separated receivers has important applications in sonar, radar, mobile communications and sensor networks. Each TDOA defines a hyperbolic locus on which the source must lie and the position estimate can then be determined with the knowledge of the sensor array geometry. While extensive research works have been performed on algorithm development for TDOA estimation and TDOA-based localization, limited attention has been paid in sensor array geometry design. In this paper, an optimum two-dimensional sensor placement strategy is derived with the use of optimum TDOA measurements, assuming that each sensor receives a white signal source in the presence of additive white noise. The minimum achievable Cramér–Rao lower bound is also produced.