Robust closed-form time-of-arrival source localization based on α-trimmed mean and Hodges–Lehmann estimator under NLOS environments

•The robust closed-form TOA source localization methods are proposed.•The proposed estimators have not been used in the TOA source localization context.•The proposed methods have an advantage that they are the closed-form.•The mixed version of the JMAP-ML estimator and proposed estimators is also proposed.

In this paper, we propose an NLOS source localization method that utilizes the robust statistics, namely, the α-trimmed mean and Hodges–Lehmann estimator. The root mean squared error average of the proposed methods is similar to that of the other estimators such as M-estimator and Taylor-series maximum likelihood estimator using the median, but the proposed robust estimators have advantages that they have the closed-form solution. The simulation results show that the root mean squared error performance of the proposed methods is similar or outperforms that of the iteration-based M-estimator. The Taylor-series maximum likelihood estimator based on the sample median is most superior among the investigated localization methods, but it has the disadvantages that the computational complexity is high and that the solution may converge to the local maxima. Also, it is shown that the performances of the closed-form proposed estimators outperform the JMAP-ML and LS estimator in the above of certain NLOS noise level.