A New Parametric Three Stage Weighted Least Squares Algorithm for TDoA-Based Localization

The time-difference-of-arrival method is popular for indoor tracking systems due to its simple usage, efficiency, performance, and power economy. To solve the non-linear optimization problem of tag coordinates calculation from number of measurements on synchronized anchors, often a low complexity linear least square technique or one of its more advanced variants are used: e.g. two-step weighted least squares or constrained weighted least squares methods. However, these techniques suffer from an ill-conditioned problem for a specific anchors and tags locations, so a new Parametric Three-stage Weighted Least Squares algorithm is proposed. New algorithm identifies a family of solutions and works even in rank deficient conditions, ensuring accurate and reliable estimates for core areas of the anchor nodes mesh cells. To achieve the best performance outside the core area, the hybrid algorithms are also introduced utilizing the eigenvalue ratio and independent parameter correlation criteria to switch between algorithms. The performance of the proposed algorithms was analyzed for Gaussian noise, reference and non-reference anchors desynchronization errors, and multipath shadowing environment for square, hexagon, and triangular anchor node mesh patterns.