Spatial Distribution Characteristics of Positioning Accuracy in 3D-TDOA Localization: Analysis and Applications

Based on existing research, we hypothesize that the positioning performance of Time Difference of Arrival (TDOA) systems may exhibit specific spatial distribution characteristics. Through two approaches—performance metric function construction and derivation and geometric intersection analysis—this study reveals the spatial distribution characteristics of positioning performance in minimal 3D-TDOA systems. We systematically establish and refine the theoretical framework for this research. The study confirms the hypothesis, demonstrating that positioning accuracy (PA) is a function of input parameter precision, target location, and sensor placement. Furthermore, we propose and develop core concepts, fundamental theorems, and key properties, including PA boundary (PAB), algorithm shadow zones (regions with poor localization performance), and tangential conditions. This theoretical framework exhibits strong generalizability and applicability. Simulations and experiments validate the theoretical findings. Additionally, we explore the practical applications of this research in target location optimization and sensor deployment optimization. This study provides new theoretical insights for system optimization and performance evaluation, advancing the field of positioning theory.