Multidimensional Scaling-Based TDOA Localization Scheme Using an Auxiliary Line

This work deals with source localization with time-difference-of-arrival (TDOA) measurements in two-dimensional (2-D) scenarios. Although the celebrated two-step weighted least squares (2WLS) method is quite successful, its drawback lies in an ill-conditioning problem when the sensor array is quasi-linear. This work presents a multidimensional scaling (MDS)-based localization scheme. Based on the subspace analysis of the scalar product matrix, an auxiliary line is defined in the plane, close to the global minimizer of the cost function. Then, the minimizer on the auxiliary line is found as the estimation of the source position. Simulations show that the proposed scheme achieves high localization accuracy for all kinds of sensor arrays including quasi-linear arrays.