## 4 Experiments and Results
### Experiment Results
And we must adaptively select the existing trustworthy information in the sliding window. Near the end of the experiment, some 3 DMA GNSS solutions wrongly estimated the position of the next block, as shown in Figure 8a. The reason is that the receiver was located in a relatively open area. The PCA result of the average skymask indicates that the two eigenvalues are similar, and there are no clear major or minor axes. Results in the candidate distribute as a full circle, and the solution estimates at the local minima, as shown in Figure 8b. The candidate might have to distribute based on the user's average historical motion to resolve this issue. However, a pedestrian's motion is not as consistent as a vehicle's, therefore distributing candidates based on average motion cannot capture a rapid motion change. Another consideration is the detection of an instant motion change with an inertial measurement unit (IMU) that could be integrated into the camera or platform, more broadly. Lastly, we also demonstrate a vehicle case in Hong Kong using the same receiver. The experiment covers different scenarios of an urban city, from open-sky areas to deep urban canyons. The data can be found in [50]. The data is collected using the same receiver model, u-blox ZED-F9P, with a patch antenna. The reference trajectory is provided by NovAtel SPAN-CPT [54], a GNSS RTK/INS (fiber-optic gyroscopes, FOG) integrated navigation system. Positioning statistics are shown in Table 2, and the map plot and error plot are shown in Figure 9. The vehicle case covers more scenarios across different environmental complexities and velocities, as shown in Figure 9c,d, respectively. Urban scenarios covering  
Figure 8: (a) zoom\(-\)in map plot near the end of Trip 2. (b) one of the epochs with large position error due to local minima problem. an average skymask elevation angle of around 20 degrees up to nearly 80 degrees are covered. And velocities from 0 m/s up to about 12 m/s are presented in this case. Both 3 DMA GNSS and FGO outperformed WLS in this case. RMSE of WLS, 3 DMA GNSS, LC-FGO, and LC-FGO-PP are 14.92 m, 7.94 m, 8.09 m, and 5.80 m, respectively. Overall, the positioning outperformed what was noted for New York. There are two main reasons for the excellent positioning performance. Firstly, the local environments in NY and HK were different; the testing areas in NY were more urbanized, i.e., the average skymasks' elevation angle at ground truths in all navigation trips was \(58.6^{\circ}\) and \(46.9^{\circ}\) for New York and Hong Kong, respectively. Secondly, measurement noise was notably higher in NY, likely secondary to motion variation [55]. The vehicle (HK) had higher dynamic motion, and measurements suffered less from the multipath effects, therefore better positioning performance could be obtained. We labelled the pseudorange error using the double differencing technique [56] for a good case in the New York dataset (Trip 6) and Hong Kong, as shown in Figure 10. The double difference [56] requires measurements from the reference station. The pseudorange of the commonly received satellites is differenced. The common clock and atmospheric errors are eliminated. Geometric distance, \(D\), is given by the calculated satellite position from the ephemeris, surveyed location of the reference \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **RMSE (m)** & **STD (m)** \\ \hline
1. WLS & 14.92 & 9.20 \\
2. 3 DMA GNSS & 7.94 & 4.85 \\
3. LC-FGO & 8.09 & 4.55 \\
4. LC-FGO-PP & 5.80 & 2.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics of vehicle-mounted trip results. Figure 9: (**a**) map plot, (**b**) positioning errors, (**c**) number of received satellites and average skymask elevation angle, and (**d**) velocities under the ECEF coordinate system provided by NovAtel SPAN\(-\)CPT of the vehicle-mounted experiment. station, and our labelled ground truth. The reference station was set up in an open-sky area where measurement can be assumed to be healthy.