A Robust Bias Reduction Method with Geometric Constraint for TDOA-Based Localization

In this paper, a robust algorithm for enhancing indoor positioning accuracy utilizing time difference of arrivals is proposed. Addressing limitations of maximum likelihood estimation and traditional weighted least squares methods, which often suffer from matrix ill-conditioned problem and numerical instability, leading to significant biases and reduced accuracy, we propose a novel bias reduction technique based on \({{\varvec{QR}}}\) $\mathit{QR}$ factorization. Incorporating geometric relationship information, our method improves precision. Through rigorous analysis and simulation under zero-mean white Gaussian noise, the algorithm demonstrates superior performance, overcoming matrix ill-conditioned problem, surpassing traditional methods, and closely aligning with the Cramér-Rao lower bound.