Sensor Allocation for Source Localization With Decoupled Range and Bearing Estimation

The source localization accuracy is known to be affected by the placement of sensors. This paper addresses the problem of optimum sensor allocation for decoupled range and bearing estimation, as well as position estimation of an emitting source, under the constraint that all sensors must be confined within a certain area. The source is assumed to be distant and has a curved wavefront when arriving at the sensors. The optimization criterion is the minimum estimation variance defined by the Cramer–Rao lower bound that is derived under Gaussian noise model. A geometric approach is employed to arrive at the optimum geometries and no complicated optimization technique is required. The optimum sensor allocations for time difference of arrival (TDOA), angle of arrival (AOA), and time of arrival (TOA) positionings are derived and their estimation accuracies are contrasted. The optimum geometries belong to the generic structure of a ring array plus some sensors at the center. TDOA and TOA are found to have identical optimum geometries for bearing estimation and yield the same accuracy, although the position localization accuracy of TDOA is known to be worse than that of TOA. Simulations are included to confirm the theoretical development and illustrate the improvement of using an optimum array compared to a random sensor placement array.