Optimal Geometry Analysis for Target Localization With Bayesian Priors

Relative sensor-target geometry is well known to significantly affect the performance of target localization using a sensor network. This article analyzes the optimal sensor-target geometries for the problem of target localization with Bayesian priors. We present a unified geometry optimization framework for different types of sensor networks including bearing-only sensor network, range-only sensor network, received signal strength-only sensor network and mixed network of these sensor types. For geometry optimization of Bayesian target localization with these sensor networks, we establish the equivalence between the A-optimality criterion (i.e., minimizing the estimation mean squared error) and the D-optimality criterion (i.e., minimizing the area of the estimation uncertainty ellipse). Under these optimality criteria, the geometry optimization problem is shown to be mathematically equivalent to the problem of minimizing the modulus of a vector sum. This thus makes the optimal geometry conditions algebraically simple and easy to be computed. We conclude the article with extensive simulation studies to verify the accuracy of the analytical findings.