Fast and efficient multidimensional scaling algorithm for mobile positioning

Mobile station (MS) localisation that plays an important role in the process of target continuous localisation has received considerable attention. In this study, a new framework based on subspace approach for positioning an MS at minimum localisation system with the use of time-of-arrival measurements is introduced. Unlike ordinary multidimensional scaling algorithm using eigendcomposition or inverse computation to estimate the MS position, a computationally simple weighting estimator is proposed by introducing Lagrange multiplier and mean-square error weighting matrix. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with several conventional algorithms as well as the Cramer–Rao lower bound (CRLB). It is shown that the new method with low computational complexity attains the CRLB for zero-mean white Gaussian range error at moderate noise level.