## 2 GNSS/IMU Sensors Data Characteristics Analysis
### IMU Data  
The Huawei Mate 30 integrates an internal IMU chip ICM-20690 developed by Invensense corporation; it is a six-axis motion tracking device which combines a three-axis gyroscope and a three-axis accelerometer in a small \(2.5\times 3\times 0.91\) mm package. The low-cost device provides high robustness by supporting 20,000 g shock reliability, while it was also widely used in other smartphones such as Xiaomi Mi 8 and Huawei P40 [29; 30]. The initial zero-rate output (ZRO) tolerance of the three-axis gyroscope is \(\pm 1^{\circ}/\mathrm{s}\) and the rate noise spectral density is \(0.004^{\circ}/\mathrm{s}/\mathrm{v}\mathrm{Hz}\). The initial tolerance of the three-axis accelerometer is \(\pm 40\) mg, and the power spectral density is \(0.1\) mg/\(\surd\mathrm{Hz}\). The specifications of Analog Devices ADIS16405 are shown in Table 1. As shown in Figure 1 for device placement, it should be noted that the \(x\)-axis and \(z\)-axis of ADIS16405 point to the opposite direction to the \(y\)-axis and \(z\)-axis of Mate 30, respectively. The ADIS16405 default sample rate setting of 819.2 samples per second (SPS) and the IMU raw data of Mate 30 were recorded with sample rate of 100 SPS. The comparisons of the IMU data from Mate 30 and ADIS16405 on the playground are shown in Figure 7.  
Although the IMU data of three-axis gyroscope and three-axis accelerometer recorded by the Mate 30 agree well with the data of ADIS16405, the IMU data of ADIS16405 are smoother than those of Mate 30, which is in line with the comparisons of IMU data recorded by the smartphone Honor Play and the commercial IMU STIM 300 [29]. The mean absolute deviation (MAD) can describe the measuring spread of data, which can be written as:  
\[MAD=\frac{1}{n}\sum_{i=1}^{n}|x_{i}-\overline{x}| \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Gyroscope** & **Parameter** & **Accelerometer** \\ \hline Initial Bias Error (\({}^{\circ}/\mathrm{s}\)) & \(\pm 3\) (1 \(\mathrm{\SIUnitSymbolMicro}\)) & Initial Bias Error (mg) & \(\pm 50\) (1 \(\mathrm{\SIUnitSymbolMicro}\)) \\ In-Run Bias Stability (\({}^{\circ}/\mathrm{s}\)) & 0.007 (1 \(\mathrm{\SIUnitSymbolMicro}\)) & In-Run Bias Stability (mg) & 0.2 (1 \(\mathrm{\SIUnitSymbolMicro}\)) \\ Angular Random Walk (\({}^{\circ}/\mathrm{sqrt}\)(h)) & 2.0 (1 \(\mathrm{\SIUnitSymbolMicro}\)) & Velocity Random Walk (m/s/sqrt(h)) & 0.2 (1 \(\mathrm{\SIUnitSymbolMicro}\)) \\ Rate Noise Density (\({}^{\circ}/\mathrm{s}\)/sqrt(Hz)) & 0.05 & Noise Density (mg/sqrt(Hz)) & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of Analog Devices ADIS16405. The \(\mathrm{\SIUnitSymbolMicro}\) is one sigma (confidence level). Figure 7: Comparisons of the IMU data from Mate 30 and ADIS16405. (a) Three-axis gyroscope; (b) three-axis accelerometer. where \(\overline{x}\) is the average value of data. In Figure 7a, The MAD of pitch and roll recorded by Mate 30 are 0.265 rad/s and 0.071 rad/s, which are 18.9% and 4.6% higher than those of ADIS16405, respectively. The MAD of yaw from Mate 30 is 0.078 rad/s, which is almost the same as that of ADIS16405. In Figure 7b, the MAD of \(x\)-, \(y\)-, and \(z\)-axis of the accelerometer recorded by the Mate 30 were 21.1%, 1.2%, and 53.0% higher than those of ADIS16405, respectively. Moreover, the IMU data from Mate 10 were used for comparison, as shown in Figure 8.  
The Euclidean metric measure is a widely used distance measure for determining the distance between any two vectors, and the Euclidean distance \(\eta\) between two \(n\)-dimensional vectors is given by:  
\[\eta=\sqrt{\sum_{i=1}^{n}(x_{i}-y_{i})^{2}} \tag{5}\]  
The Euclidean distances of pitch, roll, and yaw between Mate 30 and ADIS16405 are 83.30, 20.66, and 20.40, respectively. However, in Figure 8a, the Euclidean distances between Mate 30 and Mate 10 are 86.86, 25.69, and 24.16, respectively. Meanwhile, in Figure 8b, the average Euclidean distance of the accelerometer between Mate 30 and Mate 10 is 632.05, which is also higher than that between Mate 30 and ADIS16405.