# Comprehensive Evaluations of NLOS and Linearization Errors on UWB Positioning
## 2 Methods
### Robust Particle Filter
Table 1 summarizes the advantages and disadvantages of the existing adjustments that can be used in UWB positioning. Based on the above models, the proposed UWB algorithm can be simply presented in Figure 1. Firstly, use eight LinkTrack P base stations ([[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) to collect the distance between each base station and the tag. Then, seven algorithms, namely Bancroft, LS, EKF, UKF, CKF, PF, and RPF, were used to calculate the positions of the tag. Finally, the impacts of NLOS errors and linearization errors on the UWB positioning accuracy were analyzed using indicators such as RMSE, CDF curve, and running time of different algorithms. \begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Advantages** & **Disadvantages** \\ \hline Bancroft & This algorithm does not need to iterate the direct solution method with algebraic analytic properties and the solution speed is fast [40]. & This algorithm cannot achieve the optimal solution in terms of statistical characteristics. \\ \hline LS & The optimal matching method between data is found by finding the sum of minimum error squares [41]. & It does not have error resistance, a small amount of gross error can cause unreliable parameter estimation, and the number of iterations and position accuracy are affected by the initial value. \\ \hline EKF & The EKF linearizes the nonlinear system locally and can be applied to the weak nonlinear system. & When linearizing the nonlinear equation, EKF retains only one term coefficient, and the truncation error caused by discarding the higher-order term will have a significant impact on positioning accuracy [21]. \\ \hline UKF & The UKF approximates the posterior probability density function of the nonlinear system through UT transformation, and computes the mean value and covariance of the state vector, avoiding the linearized truncation error [42]. & UKF has poor robustness in the case of system state mutation, and its accuracy is easily affected. \\ \hline CKF & CKF algorithm uses spherical radial volume criterion to approximate the state posterior distribution of optimal estimation. CKF can not only overcome the shortcomings of UKF in high and strong nonlinear state estimation. However, it also has higher filtering accuracy [25]. & The standard CKF requires Cholesky decomposition of the covariance of the posterior state when constructing volume points. This requires that the covariance of the transfer is a non-negative definite matrix, and the decomposition operation not only consumes time, but also reduces the stability of the increment algorithm [43]. \\ \hline PF & The core idea of the PF algorithm is to randomly select a group of particles to replace the posterior probability distribution of the current system state [44]. When the system is in a nonlinear environment, compared with other algorithms, this algorithm has better filtering performance and the ability to deal with the influence of non-Gaussian noise, so it is more and more widely used in the positioning system. \\ \hline RPF & The influence of anomaly observation is weakened and the accuracy of parameter estimation and the reliability of filtering are improved [45]. \\ \hline \end{tabular}
\end{table} 
Table 1: Advantages and disadvantages of algorithms.