# Comprehensive Evaluations of NLOS and Linearization Errors on UWB Positioning
## 1 Introduction
Then, it was verified by using TOA data, and the results showed that WLS was superior to LS in NLOS conditions. [PERSON] et al. [23] proposed a factor graph-based UWB positioning algorithm based on an improved Turkey robust kernel, which was verified via a set of NLOS UWB-TOA data. The experimental results proved that the UWB positioning algorithm based on the improved Turkey robust kernel outperformed the LS algorithm in NLOS environments. The corresponding positioning accuracy improvements on average were 20-30%. [PERSON] et al. [24] proposed an improved robust adaptive cubature Kalman filter (IRACKF) algorithm. The autocorrelation covariance matrix-based robust algorithm was used to alleviate the impact of these NLOS errors polluted UWB data on the UWB positioning accuracy. The results based on both simulation and field experiments showed that IARCKF can reduce positioning errors by the percentages of 52.6%, 38.0%, 45.1%, and 25.3% compared with the solutions of CKF, robust cubature Kalman filter (RCKF), adaptive cubature Kalman filter (ACKF), and robust adaptive CKF (RACKF), respectively. [PERSON] et al. [25] adopted an adaptive unscented Kalman filter (UKF) filter in the UWB system. The experiment test presented its adaptive ability, and the positioning accuracy of UWB can be upgraded to 7 cm on average. [PERSON] et al. [26] proposed the adaptive square root cubature Kalman filtering (ASRCKF) algorithm to solve the problem that the filtering accuracy decreases when the measurements are abnormal. It was verified by using TDOA/AOA combined data. The results showed that the RMSE of ASRCKF was slightly affected and the tag's position can converge to the real value rapidly. [PERSON] et al. [14] developed a positioning system based on particle filter (PF). The results proved that about 75% and 82% reduction in the median position error in simulation and experiment tests with providing sub-meter level positioning accuracy. Although the UWB positioning technique was studied, the influence of different parameter estimation methods on UWB positioning accuracy, and the impacts of linearization error and NLOS error on UWB 3D positioning accuracy were not analyzed comprehensively. Hence, we adopted a robust particle filter (RPF) to evaluate the effects of NLOS errors and linearization errors on the UWB positioning accuracy in both horizontal and vertical components based on the simulated and measured TOF UWB data. For comparison, the conventional methods including the Bancroft algorithm, LS, EKF, UKF, CKF, and PF were also analyzed. Compared to the existing works, the contributions of our work are that (1) we considered both NLOS errors and linearization errors in UWB 3D positioning, and provided the RPF to reduce their impacts on UWB positioning accuracy; and (2) we analyzed linearization errors by comparing the results based on LS and EKF with those based on UKF, CKF, and PF. The paper is arranged as: Section 2 introduces the relevant mathematical principles and the details of the proposed positioning algorithm, Section 3 introduces the experiments and results, which is followed by conclusions in Section 4.