Performance Analysis and Sensor-Target Geometry Optimization for TOA and TDOA-Based Hybrid Source Localization Method

Abstract

Currently, the performance analysis of positioning algorithms and optimization of ground station deployment schemes are predominantly based on pure TOA or TDOA measurement information, and the relevant theoretical analysis is primarily the geometric analysis of optimal station deployment for fixed point targets, with few placement ranges and amount of station constraints. In practice, however, there are typically several measurements from TOA and TDOA stations, with a focus on positioning precision within a certain region or line trajectory, as well as the necessity for constraints on the ground station placement range. This paper proposes an efficient method for hybrid source localization using TOA and TDOA measurement information, establishes a mathematical model for hybrid source localization based on TOA and TDOA measurement information, derives and simulates the Gauss–Newton iterative localization algorithm with the least squares criterion, and performs a theoretical analysis of the least squares error and CRLB boundary to improve the accuracy of target localization in the aforementioned scenarios. Taking the average CRLB value of target line trajectory positioning error as the objective function, the ground station placement scheme of TOA- and TDOA-receiving sensors is optimized by utilizing a Genetic Algorithm with strong global optimization capability under the constraints of station placement range and station quantities, and a station placement geometry with better performance than typical station placement is obtained. Meanwhile, we summarize the general placement principles for TOA and TDOA hybrid source localization of target line trajectories.

Keywords

• TOA
• TDOA
• hybrid source localization
• least-square algorithm
• Cramer Rao Low Bound (CRLB)
• Genetic Algorithm (GA)