A GDOP-Based Performance Description of TOA Localization with Uncertain Measurements

In this paper, we study a geometric dilution of a precision (GDOP)-based localization performance metric for multisite radar adopting a time-of-arrival (TOA)-based localization scheme. In contrast to the existing literature, we consider an actual uncertain measurement situation where the detection probabilities of radar nodes are assumed to be less than unity. The aim is to formulate a general signal-decoupled metric to describe the system localization performance while fully considering detection and estimation operations. Specifically, to match the uncertain measurements, we first establish effectively detected time delay measurements (TDMs) for localization and modify the traditional performance bounds for TDM estimation. Then, by combining the localization performance with the effective detection (ED) via probability, we propose a novel geometric dilution of precision with uncertain measurements (GDOP-UM) metric. The proposed metric can truly characterize the localization performance under the uncertain measurement situation. Finally, the simulation results show that the proposed GDOP-UM can describe the actual localization performance regardless of how the detection performance changes.