A Novel Closed-Form Algorithm for TDOA-Based Localization with a Linear Base Stations Array

In this paper, we investigate the challenge of 2D target localization using Time Difference of Arrival (TDOA) measurements with a linear array of base stations (BSs) in cellular networks. Target localization is often modeled as a least squares problem. However, in this modeling approach, the linear arrangement of BSs can result in singular matrices, negatively impacting localization accuracy. To address this issue, a novel closed-form algorithm, termed Cosine Geometries (cosGEO), is proposed. This algorithm innovatively utilizes the relationship between measured distance differences and geometric structure to correct ranging errors. Specifically, by employing trigonometric cosine and inequality theorems, cosGEO generates multiple preliminary localization results from different three-BS combinations. To obtain a more accurate ultimate estimation, these preliminary results are integrated through a weighted average method based on the Cramér–Rao Lower Bound (CRLB). Simulation results demonstrate that cosGEO is more robust and accurate than the three conventional least squares-based approaches. The method holds significant potential for practical implementation in TDOA-based target positioning with linear array settings.