Lost at the Center of a Circle: A Failure Mode and Its Remedy in the Two-Step Weighted Least Squares Method

Two-Step Weighted Least Squares (TSWLS) method (or the Chan method) is a classical TDOA-Based localization algorithm. We find that the Chan method will yield exceptionally large localization error if the target node is near the center of a circle formed by the anchor nodes. We name such a phenomenon Lost at the Center of a Circle (LCC). It is shown that LCC has no connection with the Geometric Dilution of Precision (GDOP). We explore when and why LCC develops utilizing the singular value decomposition (SVD) method. Based on the insight from SVD analysis, we propose a robust positioning algorithm to solve the LCC problem. Computer simulations and field experiments show that the new algorithm has better localization performance than the Chan method.