TDOA Localization via Fixed-Point Iteration

Abstract

Using time-difference-of-arrival (TDOA) measurements from several sensors to locate a target is one of the most widely used wireless localization methods. A challenge for TDOA localization is that the measurement equations are highly nonlinear. The weighted least-squares (WLS) based method tends to incur the threshold effect, and the convex relaxation based method has a high computational complexity. This paper presents a new iterative method derived directly from maximum likelihood estimation (MLE), and it does not require any matrix operations in its iterations. In order to reduce the likelihood of reaching a local minimum or a saddle point, multiple initial values are randomly selected from the region of interest, and the one that results in the lowest cost function is chosen as the output. Besides, the theoretical bias and covariance matrix of the proposed estimator are derived. The proposed algorithm outperforms state-of-the-art methods and achieves the Cramer-Rao lower bounds (CRLB).