Computational-Efficient Iterative TDOA Localization Scheme Using a Simplified Multidimensional Scaling-Based Cost Function

This work deals with source localization with time-difference-of-arrival (TDOA) measurements. Recently, a multidimensional scaling (MDS)-based iterative localization scheme is introduced in the literature, where an MDS-based cost function is defined as the norm of the difference matrix between two scalar product matrices. The minimizer of the MDS-based cost function which is computed by Newton's iteration is considered as the estimate of the source position. However, the scalar product matrices of the MDS-based cost function are of high order, which need a lot of computations in each step of the Newton's iteration. In this paper, a computational-efficient iterative localization scheme is proposed. In the proposed scheme, a simplified MDS-based cost function is constructed from two low-order matrices that are converted from the high-order scalar product matrices by a few steps of Lanczos iteration, and then the Newton's iteration is applied to find the minimizer of the simplified MDS-based cost function. Simulation results show that the localization accuracy of the proposed scheme is nearly the same as that of the original scheme, whereas the computational complexity of the proposed scheme is about 20% as much as that of the original scheme.