Optimal Sensor Placement for Multiple Target Positioning with Range-Only Measurements in Two-Dimensional Scenarios

The problem of determining the optimal geometric configuration of a sensor network that will maximize the range-related information available for multiple target positioning is of key importance in a multitude of application scenarios. In this paper, a set of sensors that measures the distances between the targets and each of the receivers is considered, assuming that the range measurements are corrupted by white Gaussian noise, in order to search for the formation that maximizes the accuracy of the target estimates. Using tools from estimation theory and convex optimization, the problem is converted into that of maximizing, by proper choice of the sensor positions, a convex combination of the logarithms of the determinants of the Fisher Information Matrices corresponding to each of the targets in order to determine the sensor configuration that yields the minimum possible covariance of any unbiased target estimator. Analytical and numerical solutions are well defined and it is shown that the optimal configuration of the sensors depends explicitly on the constraints imposed on the sensor configuration, the target positions, and the probabilistic distributions that define the prior uncertainty in each of the target positions. Simulation examples illustrate the key results derived.