Spatial Distribution Characteristics of Positioning Accuracy for TOA Localization

This article focuses on the positioning performance of 3-D time of arrival (TOA) localization. The performance of TOA localization varies with the target’s position, yet the analytical laws and macro characteristics of this phenomenon remain unclear. Through analytical derivation and geometric intersection analysis, we reveal the spatial distribution characteristics of the positioning accuracy (PA) in a minimum number of parameters (MNOP) system. Our study indicates that PA is a function of the target’s position, sensor positions, and the precision of input parameters. When the sensor array is fixed, PA is proportional to the standard deviation of the input parameters, with its relative distribution characteristics depending on the variance ratios of the input parameters. PA exhibits progressive spatial variations and features an extreme zone, which can be described by tangency conditions. Our research confirms that these tangency conditions are inherent to the system, describing a spatial set of positions that lie on a plane defined by three sensors. The area near this plane exhibits poorer localization performance, forming the algorithm shadow zone. Simulations and experimental validations corroborate the theoretical analysis results. The spatial distribution characteristics of PA provide new insights and theoretical support for enhancing localization performance and applications, such as anti-detection.