# Comprehensive Evaluations of NLOS and Linearization Errors on UWB Positioning
## 1 Introduction  
High accuracy requirement in indoor positioning applications is growing rapidly. Although global navigation satellite systems (GNSS, i.e., BDS and GPS) satisfy users' high-accuracy location service needs in open environments [1], it is difficult for GNSS to provide location services [2] in satellite signals blocked areas, such as indoor environments [3]. To this end, researchers studied indoor positioning methods based on infrared [4], ultrasonic [5], Bluetooth [6], Wi-Fi [7, 8], and PDR [9, 10]. These techniques have obvious weaknesses of low accuracy and short distance. For example, infrared light is easily blocked by walls during transmission, which leads to a short transmission distance [11]. Ultrasound is measured by echo signal resulting high accuracy position solution, but multi-path and non-line of sight (NLOS) will degrade the accuracy. Bluetooth technology is only available in small areas. In large-range areas, the signal stability is poor, resulting in low positioning accuracy [12]. Wi-Fi, with the advantages of low cost, wide signal source, and wide range, is supported by the location information of network nodes. However, it provides a low accuracy position and is easily affected by environments [13]. In addition, these indoorpositioning techniques are mainly used in horizontal positioning, which cannot meet the urgent demand for high-precision indoor three-dimensional positioning. In order to overcome these shortcomings existing in conventional indoor positioning methods, an indoor positioning method based on ultra-wideband (UWB) was proposed. Compared with the indoor positioning technologies mentioned above, UWB has the advantages of high interference resistance, low power consumption, and high range accuracy [14; 15]. Additionally, UWB has a strong penetration ability under the situations such as in woods and stones, and these penetration errors can be corrected by modeling. However, UWB has a weak ability to penetrate water and metal [16]. Currently, UWB modes include Time of Arrival (TOA), Time of Flight (TOF), Difference of Time-Of-Arrival (TDOA), Angle of Arrival (AOA), Received Signal Strength Indication (RSSI) [17; 18]. TOF is widely used in indoor applications because the tag does not need to be synchronization with the base station precisely [19; 20]. However, while suffering complex indoor environments, indirect UWB signals will be received because of reflection, refraction, diffraction, or passing through walls [1]. Such indirect signals could increase transmission time and lead to NLOS ranging errors. NLOS errors result in a major impact on the UWB positioning accuracy. Additionally, since the relationship between the UWB range and the tag's position is nonlinear, it is necessary to linearize the observation function by Taylor expansion while using the traditional least squares (LS) and extended Kalman filter (EKF). Here, only the first-order item in Taylor expansion was adopted and the second-order and higher-order terms were abandoned. However, for the UWB ranging system, its maximum ranging distance was no more than hundreds of meters at present ([[https://www.nooploop.com/en/](https://www.nooploop.com/en/)]([https://www.nooploop.com/en/](https://www.nooploop.com/en/)), accessed on 9 May 2023). Therefore, omitting higher-order terms in LS and EKF would introduce significant linearization errors, which could result in an accuracy degradation and even lead to a divergence in parameter estimation [21]. Therefore, reducing the impacts of NLOS errors and linearization errors on UWB positioning accuracy is an important issue for UWB-based indoor positioning technologies. In recent years, many works were carried out on the effects of attenuated NLOS errors and linearization errors on the positioning accuracy of UWB. For the NLOS error, [PERSON] et al. [22] introduced a novel weighted least squares (WLS) algorithm that used the LOS likelihood values. The improvements compared to the conventional LS were demonstrated firstly via Monte Carlo simulations.