Optimal configuration analysis for range-only target localization with uncertain sensor positions

Abstract

The relative sensor-target geometries are of significance in the context of cooperative localization involving multiple sensors working together to localize a target. The optimality analysis of sensor-target geometries is commonly conducted assuming precise knowledge of the sensors’ positions. However, this is not the case in practice due to various uncertainties such as sensor drift, environmental factors, and measurement errors. In this paper, we address the issue of uncertain positions of range-only sensors. Specifically, we consider randomized positions for the sensors, modeled by a Gaussian probability density function. Consequently, the parameters to be estimated become hybrid, comprising both randomized (the sensors’ positions) and non-randomized (the target’s position) elements. A hybrid CRLB is proposed as a measure to characterize the estimation performance of the localization problem under consideration. To efficiently calculate the hybrid CRLB, we derive an approximation and quantify the corresponding error. Furthermore, we determine the optimality condition of sensor-target geometries for range-only localization. A gradient-based algorithm is designed to facilitate the optimization process. The analytical findings are verified through simulations.