## 2 GNSS/IMU Sensors Data Characteristics Analysis
### GNSS Measurements  
The position estimation accuracy of GNSS measurements depends on the geometry of available GNSS satellite [32]. The PDOP is a factor which indicates the factor of precision of the position with least square estimation (LSE). The [PERSON]'s series expansion method is used to linearize the pseudorange equation at the approximate receiver position to obtain the difference between the estimated and true receiver positions [33], and the dilution of precision (DOP) measurement matrix can be written as:  
\[Q_{Z}=\left(H^{T}H\right)^{-1} \tag{1}\]  
where \(Q_{Z}\) is a \(4\times 4\) matrix; \(H\) is the Jacobian matrix formed with direction cosines from receiver to the satellites. Without the time dilution of precision (TDOP), the PDOP factor is defined as the square root of the trace of the measurement matrix [32]:  
\[\mathrm{PDOP}=\sqrt{trace(Q_{X})} \tag{2}\]  
where \(Q_{X}\) can be expressed as:  
\[Q_{X}= \begin{bmatrix}q_{11}&q_{12}&q_{13}\\ q_{21}&q_{22}&q_{23}\\ q_{31}&q_{32}&q_{33}\end{bmatrix}  \tag{3}\]  
The number of GPS and BDS satellites observed by [PERSON] and PDOP values calculated by the formula around the playground twice are shown in Figure 3a. The average number of visible GPS satellites is about 8.1 while that of BDS satellites is about 16.6, and the average PDOP values of GPS and BDS are 1.96 and 1.31, respectively. Although the GNSS signals are slightly degraded due to the trees, the number of visible GPS satellites observed by [PERSON] still fluctuate within a narrow range. For the geodetic receiver, as shown in Figure 3b, it is easy to determine whether the GNSS signals are blocked with the number of visible satellites observed by the geodetic receiver. Meanwhile, although the average number of visible GPS satellites observed by [PERSON] is higher than that of [PERSON], it can be found that the carrier phase measurements of more than half of the visible satellites cannot be logged by [PERSON]. Figure 3: Number of GNSS satellites and PDOP values on the playground in area 1. (**a**) GPS and BDS measurements observed by Mate 30; (**b**) GPS measurements observed by the geodetic receiver and Mate 10. With the GNSS signals slightly degraded due to the trees, as shown in Figure 4b, there are still more than four GPS satellites that can be observed by the Mate 30, as shown in Figure 3a. However, the C/N\({}_{0}\) values of some visible GNSS satellites decrease significantly, as shown in Figure 4a, marked by the red boxes. The C/N\({}_{0}\) is usually used to describe signal noise level in a GNSS receiver, and the value is signal-to-noise ratio (SNR) in 1 Hz width with the unit of dB-Hz. In Figure 4a, there are 9, 56, and 19 epochs for which the satellite signals of GPS pseudorandom noise (PRN) 17, PRN 19, and PRN 21 cannot be detected in 300 epochs, where the unlock rates are 3.00%, 18.67%, and 6.33%, respectively. The unlock rates of BDS PRN 05, PRN 09, and PRN 21 are 28.00%, 13.33%, and 5.00%, respectively. Both the C/N\({}_{0}\) values of GPS and BDS decrease significantly around 50 epochs and 180 epochs. The average C/N\({}_{0}\) value of GPS in the first 50 epochs is 33.01 dB-Hz, and the average C/N\({}_{0}\) value in the second 50 epochs is 27.20 dB-Hz, which decreases by 17.60%. The average C/N\({}_{0}\) value of BDS in the first 50 epochs is 32.25 dB-Hz, and the average C/N\({}_{0}\) value in the second 50 epochs is 24.67 dB-Hz, which decreases by 23.50%. The maximum C/N\({}_{0}\) values of GPS and BDS are 44 dB-Hz and 39 dB-Hz, while the minimum values are 11 dB-Hz and 9 dB-Hz, respectively. The second experiment was conducted on the sidewalk where the GNSS signals are significantly degraded due to the buildings and trees on both sides, as shown in Figure 5. The standard deviation (STD) of PDOP values observed by Mate 30 on the sidewalk was 1.17, as shown in Figure 5a, which is 137.96% higher than that of Mate 30 observed on the playground.