Biased time-of-arrival-based location dominating linear-least-squares estimation

Determining the location of a mobile station (MS) is a fundamental problem in many applications. In this paper, three algorithms are discussed for accurate mobile location using the time-of-arrival (TOA) measurements. First, we describe the general linear least squares (LLS) approach which is unbiased. Then based on biased estimation theory we propose two bias methods - the minimax trace MSE (MXTM) and minimax matrix MSE (MXMM). By comparing the mean-squared error (MSE), we analyze the localization accuracy of the three algorithms. Theoretical analysis and simulation reveal that in the prior range of the MS, at the expense of bias error the MXTM approach dominates LLS in trace MSE and the MXMM method can dominate LLS in terms of both trace and component wise MSE.