## 2 Data Preprocessing Model Establishment and Solution  
The key chip of the UWB positioning system is the DW1000 transceiver chip (RF frequency range from 3.5 GHz to 6.5 GHz, compliant with fcc and 2.8 V to 3.6 V, low power consumption, sleep current 1 A, data rate of 110 kbps/850 kbps/6.8 mbps) developed by Decawave, which has precise position recognition and data transmission functions. It can provide a new positioning method for real-time positioning and indoor positioning systems, position services, and wireless sensor networks. Apart from the transceiver chip, the architecture of the UWB positioning system includes the perception layer, network layer, solution layer, and application layer. In particular, the perception layer includes positioning labels, positioning anchors, exciters, and base stations. The network layer includes communication base stations, switches, and firewalls. The communication base station aggregates the ranging information to the firewall and transmits it to the intranet server through the Ethernet. The solution layer installs a solution platform and database on the server, which are mainly used to store and calculate the data reported by the acquisition terminal, and obtain the physical position coordinates, and the application layer is used for the display of real-time positioning. According to the introduction, this paper mainly considers positioning technology based on the ranging principle, and the target point positioning depends on the distance from the anchor point to the target point. Every 4 lines of data in the UWB provides 4 distance parameters from anchor point to target point for a group. Therefore, the distance value is first grabbed, redundant Tag identification and other information are removed, and character matching is used to convert it into a two-dimensional distance. Each row of the matrix represents a set of data. The key to data cleaning is the identification of \"useless\" (abnormal, missing, identical, or similar) data. Among them, for sites that only contain part of the time points, if there are too many incomplete data and cannot be supplemented, the sites will be deleted; since the anchor points are essentially repeated measurements with equal precision, their abnormal data can be analyzed by 3\(\sigma\) criterion to identify [20; 21]. The methods described above were used to identify and remove missing abnormal data from all 648 samples. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Variable** & **Variable Description** \\ \hline
1 & \(\mu\) & Expectation \\
2 & \(\sigma\) & Standard deviation \\
3 & RMSE & Root mean square error \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of the symbols. The experimental data are multiple sets of information measured at the same position. Ideally, the measured data should be equal each time. If there are points far from the mean, it may be \"useless data\". Figure 1 shows the distance data extracted in the initial state. It can be clearly seen that there is an abnormal point that is different from other data. The 3\(\sigma\) criterion is based on the repeated measurement of equal precision with the normal distribution (as shown in Figure 2), and it is difficult for the interference or noise of the singular data to satisfy the normal distribution, which is in line with the form of the anchor point range. Therefore, we use the 3\(\sigma\) principle to identify and filter useless data. The normal distribution function formula is as follows:  
\[\mathrm{f}(x)=\frac{1}{\sqrt{2\pi\sigma}}\mathrm{e}^{-\frac{(x-\mu)^{2}}{2 \sigma^{2}}} \tag{1}\]  
Figure 1: Data in the initial state. Figure 2: Normal distribution curve. If the absolute value of the residual error of a certain measurement value in a set of measurement data is >3\(\sigma\), the measurement value will be a bad value and will be rejected. Usually, an error equal to \(\pm\)3\(\sigma\) is regarded as the limit error. For the random error of normal distribution, the probability of falling outside \(\pm\)3\(\sigma\) is only 0.27%.