Regularized Constrained Total Least Squares Source Localization Using TDOA and FDOA Measurements

This letter investigates source localization using time difference of arrival (TDOA) and frequency difference of arrival (FDOA). The improper distribution of the sensors can lead to a numerical ill-conditioning of the coefficient matrix, adversely affecting the accuracy of source localization. A two-stage method based on regularized constrained total least squares (RCTLSs) is proposed to solve this problem. First, the RCTLS theory is utilized to solve the ill-conditioned problem and the regularization parameter is obtained via minimizing the mean square error (MSE), thereby allowing for a more robust estimation. Second, the error of the RCTLS solution caused by ignoring the constraints in the first step is identified via the Taylor expansion of the intermediate variables. Simulation results reveal that the proposed method attains superior localization accuracy compared to other implemented methods by selecting the regularization parameter properly in diverse scenes.