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We propose a line-of-sight (LOS)/non-line-of-sight (NLOS) mixture source localization algorithm that utilizes the weighted least squares (WLS) method in LOS/NLOS mixture environments, where the weight matrix is determined in the algebraic form. Unless the contamination ratio exceeds 50 %, the asymptotic variance of the sample median can be approximately related to that of the sample mean. Based on this observation, we use the error covariance matrix for the sample mean and median to minimize the weighted squared error (WSE) loss function. The WSE loss function based on the sample median is utilized when statistical testing supports the LOS/NLOS state, while the WSE function using the sample mean is employed when statistical testing indicates that the sensor is in the LOS state. To testify the superiority of the proposed methods, the mean square error (MSE) performances are compared via simulation.

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We present robust range-based localization algorithms for which range measurements are used to estimate the location parameter. Non-line-of-sight (NLOS) propagation of signal can deteriorate the estimation performance severely in the indoor and crowded urban areas. A study for localization has been intensively performed in the line-of-sight (LOS) conditions, but the work for the positioning in the mixed LOS/NLOS environments is comparatively rare. Thus, we aim at the robust localization in the LOS/NLOS mixture environments. The Hampel and skipped filters-based weighted least squares (WLS) methods are proposed for situations where the variance for inliers is unknown in LOS/NLOS mixture environments. For the unsupervised clustering algorithm, Gaussian mixture expectation maximization-based WLS algorithm is utilized. It is demonstrated that the positioning accuracy of the proposed methods is higher than that of conventional methods through extensive simulation.