*3.2. DBA Altitude Accuracy Evaluation at Different Baseline Lengths*

The altitude accuracy and practical range obtained by the BMP280 barometer DBA model were evaluated through different baseline lengths outdoors. The experimental data were collected on 18 September 2020, and Figure 2 shows the hardware equipment of the reference station and mobile stations. The reference station was arranged on the observation pier on the roof of the Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences (APM, CAS). Figure 3 shows five different mobile station locations at baseline lengths of 0 m, 65 m, 2.6 km (shopping mall plaza), 6.0 km (Wufu Plaza on the Yangtze River), and 10.0 km (the roof of the PET center of Tongji

Medical College), with a data acquisition time of about 30 min for each static point. Figure 4 and Table 1 show the time series and RMSE accuracy statistics of the altitude results of the DBA system under five groups of different baseline lengths.

**Figure 3.** Five mobile station locations at different baseline lengths for altitude accuracy evaluation of the outdoor DBA systems.

**Figure 4.** Time series of the DBA altitude results for five mobile station locations at different baseline lengths: (**a**) 0 m; (**b**) 65 m; (**c**) 2.6 km; (**d**) 6.0 km; (**e**) 10.0 km.


**Table 1.** The DBA altitude statistical results of the five different baseline lengths (Unit: m).

In Table 1, DBA\_min and DBA\_max denote the minimum and maximum altitude results obtained by the DBA model. Mean and STD denotes the average value of DBA altitude and standard deviation. As can be seen from Figure 4 and Table 1, the outdoor DBA altitude RMSE increased gradually with an increase of baseline length, and the DBA altitude RMSE was submeter level within the 2 km baseline length and did not exceed 2 m within the 10 km baseline length. This result can provide a priori information to determine the weight matrix *PDBA* in Equation (11) for the DGNSS/DBA combined positioning.

#### *3.3. DGNSS/DBA Combined Static Positioning Results*

This section mainly evaluates the static positioning performance of the single-frequency low-cost NEO-M8T receiver and BMP280 barometer DGNSS/DBA combined positioning algorithm. The experimental data were consistent with Section 3.2, and the 65 m and 6.0 km baseline length data were selected for processing and analysis. Two data processing modes, DGNSS and DGNSS/DBA, were set, and each mode was divided into single GPS, single BDS, and GPS+BDS dual systems by the satellite system.

### 3.3.1. Baseline Length 65 m

This experiment used 65 m short baseline static data and performed statistical analysis by setting the elevation mask angle from 10 to 40 degrees, and the prior error of the DBA system was *σDBA* = 1.0 m. Table 2 shows the average number of visible satellites at different elevation mask angles, and Table 3 lists the average PDOP values for DGNSS and DGNSS/DBA modes at different elevation mask angles.


**Table 2.** The average number of GNSS visible satellites at different elevation mask angles.

As can be seen from Table 2, the average number of visible satellites was seven to eight for GPS and 12 to 14 for BDS at a low elevation mask angle of 10 or 20 degrees. With the increase of the elevation mask angle, the number of available satellites of both GPS and BDS systems decreased significantly, the satellite space geometry distribution became worse, and the PDOP value gradually increased. The number of GPS satellites was only three at the elevation mask angles of 40 degrees, and the user receiver could not be positioned at this time, while the number of visible satellites of BDS in the China region was larger with eight to 10 visible satellites at the elevation mask angles of 30 or 40 degrees. The GPS+BDS

dual system significantly increased the number of visible satellites compared to the single system, which significantly improved the satellite geometry and reduced the PDOP value. As shown in Table 3, increasing a DBA observation was equivalent to adding a virtual satellite, which improved the satellite geometry distribution and reduced the PDOP value; and the reduction of PDOP value was more significant in the environment with a higher elevation mask angle. When the elevation mask angle was 40 degrees, three GPS satellites could not complete the positioning, and adding a DBA observation ensured the availability of user receiver positioning. Figures 5–8 show the north (N)/east (E)/up (U) direction deviation sequence of the two data processing modes at the elevation mask angle 10 to 40 degrees. Each mode included single GPS, single BDS, and a GPS+BDS dual system. Table 4 shows the RMSE values in the N/E/U directions for the two data processing modes at different elevation mask angles.


**Table 3.** The average PDOP values for DGNSS and DGNSS/DBA modes at different elevation mask angles.

**Figure 5.** The deviation sequence diagram in the N/E/U directions at 10−degree elevation mask angles: (**a**) DGNSS positioning mode; (**b**) DGNSS/DBA positioning mode.

**Figure 6.** The deviation sequence diagram in the N/E/U directions at 20−degree elevation mask angles: (**a**) DGNSS positioning mode; (**b**) DGNSS/DBA positioning modes.

**Figure 7.** The deviation sequence diagram in the N/E/U directions at 30−degree elevation mask angles: (**a**) DGNSS positioning mode; (**b**) DGNSS/DBA positioning mode.

**Figure 8.** The deviation sequence diagram in the N/E/U directions at 40−degree elevation mask angles: (**a**) DGNSS positioning mode; (**b**) DGNSS/DBA positioning mode.


**Table 4.** The RMSE values of the two data processing modes in the N/E/U directions at different elevation mask angles.

Tables 2–4 and Figure 5 show that due to sufficient number of visible satellites and low PDOP values at the elevation mask angle of 10 degrees, the positioning accuracy of the DGNSS mode in the N/E/U directions could reach the decimeter to submeter level, and the RMSE of single GPS and single BDS in the N/E/U directions were 0.82/0.53/1.32 m and 0.72/0.96/1.08 m, respectively. In DGNSS/DBA mode, the RMSE of GPS/DBA and BDS/DBA in the N/E/U directions were 0.76/0.52/0.89 m and 0.69/0.96/0.63 m, respectively, which were 30% to 40% better than DGNSS in the U direction and slightly better in N and E directions. Due to the increase of available observations and better satellite geometry of the GPS+BDS dual system, the RMSE of DGNSS and DGNSS/DBA mode in the N/E/U directions were 0.58/0.61/0.94 m and 0.57/0.60/0.57 m, respectively. Both had some improvements over the single system. The results at the elevation mask angle of 20 degrees were similar to that of 10 degrees.

Tables 2–4 and Figure 7 show that the PDOP value became larger due to the fewer available observation satellites and worse satellite geometry at the elevation mask angle of 30 degrees, and the RMSE in the N/E/U directions became significantly larger than that of 10 and 20 degrees. The RMSE in the N/E/U directions were 1.24/0.99/4.81 m and 1.33/0.93/2.85 m for single GPS and single BDS, and 0.71/0.56/1.47 m for GPS+BDS dual system in DGNSS mode, respectively. Compared with the DGNSS mode, the accuracy of the N/E/U directions was significantly improved by the DGNSS/DBA combination, and the RMSE of GPS/DBA and BDS/DBA in the N/E/U directions were improved by 6.4%/40%/77.3% and 29.3%/20.4%/66.6%, and the RMSE of GPS+BDS/DBA combination in the N/E/U directions were improved by 8.5%/25%/45.6%.

When the elevation mask angle was 40 degrees, the number of available satellites for single GPS was three and they could not be located. The RMSE of single BDS was 2.21/1.23/5.81 m in the N/E/U directions, and 0.89/0.85/3.07 m for the GPS+BDS dual system (Tables 2–4 and Figure 8). In DGNSS/DBA mode, GPS/DBA met the most basic positioning requirements for four satellites and the RMSE in the N/E/U directions was 1.23/1.08/1.02 m; the RMSE of BDS/DBA in the N/E/U directions was improved by 44.3%/12.2%/82.4%, and the RMSE of the GPS+BDS/DBA combination in the N/E/U directions was improved by 33.7%/0%/60.9%, respectively.

#### 3.3.2. Baseline Length 6.0 km

In this experiment, static data with 6.0 km baseline length were processed and analyzed, the elevation mask angle was 10 degrees, and the priori error of the DBA system was *σDBA* = 1.5 m. Figure 9 shows the number of GNSS visible satellites and the PDOP value sequence for both DGNSS and DGNSS/DBA modes at the baseline length of 6.0 km. The RMSE accuracy statistics and corresponding deviation sequence in the N/E/U directions for the DGNSS and DGNSS/DBA mode are shown in Table 5 and Figure 10, respectively.

**Figure 9.** Observation values of static experiment at the baseline length of 6.0 km: (**a**) the number of GNSS visible satellites; (**b**) the sequence of PDOP values.

**Table 5.** The RMSE of bias in the N/E/U directions for the DGNSS and DGNSS/DBA mode at 6.0 km baseline length.


Table 5 and Figures 9 and 10 show that the PDOP value of BDS was smaller than GPS in the China region due to a large number of observable satellites. The RMSE of single BDS in the N/E/U directions was 0.61/2.27/2.64 m, which was better than that of single GPS in DGNSS mode (2.23/1.12/4.41 m). The RMSE of the GPS+BDS dual system in the N/E/U directions was 0.60/1.01/2.22 m with higher positioning accuracy than single system. Compared to DGNSS mode, the RMSE in the U direction of DGNSS/DBA mode reduced by 0.5 m and 0.1 m for single GPS and single BDS, and there was also some improvement in the N and E directions. However, the GPS+BDS dual system did not improve significantly, due to the higher DGNSS accuracy and the lower DBA height accuracy at 6.0 km baseline length did not prove to be an obvious constraint.

**Figure 10.** The deviation sequence diagram in the N/E/U directions at 6.0 km baseline length: (**a**) DGNSS positioning mode; (**b**) DGNSS/DBA positioning mode.
