## 4 Test and Result
### Position Accuracy Test  
Figure 3 depicts the available satellites and the relative dilution of the precision (RDOP) on BONE. The other stations will obtain similar indicators for the short baseline. The average available satellites for filtering in the whole day are 6 for GPS, 6 for Galileo, and 10 for GPS+Galileo. The RDOP for GPS+Galileo is 0.7228 and indicates an ideal environment for relative positioning [1]. If the available satellite number of Gallileo is less than four, the position result is obtained only by GPS.  
The root mean square (RMS) and standard deviation (STD) of positioning errors on the East (E), North (N), and Up (U) components are shown in Table 2, where the positive and negative values represent improvement and degradation.  
For AMC-KF, the RMS on BONE-QCLF, QCLF-ANGS and ANGS-BONE is (0.13417 m, 0.20254 m, 0.30294 m), (0.09421 m, 0.17402 m, 0.27439 m), (0.16395 m, 0.18714 m, 0.26284 m), respectively. While the RMS for DD-KF is (0.28258 m, 0.43671 m, 0.80099 m), (0.23641 m, 0.23035 m, 0.96756 m), (0.53574 m, 0.15190 m, 0.65454 m). The accuracy improvement by (+52.52%, +53.62%, +62.18%), (+60.15%, +24.45%, +71.64%), (+69.40%, -23.20%, +59.84%) is achieved for AMC-KF. Similarly, the STD on each baseline for AMC-KF is (0.10886 m, 0.18606 m, 0.30278 m), (0.08226 m, 0.16659 m, 0.26107 m) and (0.16027 m, 0.16694 m, 0.24867 m) while for DD-KF is (0.10066 m, 0.33062 m, 0.40077 m), (0.11478 m, 0.17340 m, 0.52163 m), (0.23124 m, 0.10958 m, 0.53847 m). AMC-KF ameliorates the performance by (\(-8.15\%\), +43.72%, +24.45%), (+28.33%, +3.93%, +49.95%), (+30.69%, \(-52.35\%\), +53.82%).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Baseline** & **Distance** & **Sample** & **Cut-Off** & **Processing** \\  & & **(km)** & **Interval** & **Elevation** & **Model** \\ \hline
1 & STNY-NEWH & 19.562 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\
2 & BONE-QCLF & 26.363 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\
3 & BONE-STNY & 29.231 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\
4 & QCLF-ANGS & 41.335 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\
5 & NEWH-BONE & 42.606 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\
6 & ANGS-BONE & 60.213 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\
7 & BONE-WBEE & 58.942 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\
8 & BONE-GSBN & 106.877 & 30 s & \(10^{\circ}\) & AMC-KF, DD-KF \\ \hline \hline \end{tabular}
\end{table}
Table 1: Information for different baselines.  
Figure 2: Distribution of CORS station BONE, QCLF, ANGS, STNY, NEWH, GSBN, WBEE. ([[https://gnss.ga.gov.au/network](https://gnss.ga.gov.au/network)]([https://gnss.ga.gov.au/network](https://gnss.ga.gov.au/network)) (accessed on 1 January 2021)).  
For BONE-STNY, STNY-NEWH, NEWH-BONE, the AMC-KF possesses an RMS improvement by (+55.90%, +64.82%, +85.24%), (\(-\)22.94%, +60.42%, +83.79%), (+53.43%, +82.67%, +67.43%), and an STD improvement by (+31.55%, +46.827%, +78.57%), (\(-\)11.22%, +35.33%, +53.71%) and (+47.26%, +73.50%, +66.16%), respectively.  
Compared to DD-KF in each direction, the proposed AMC-KF obtains an improvement by (32.24%, 34.48%, 63.07%) on average, despite negative values existing. Thus, AMC-KF is a beneficial scheme for short baseline RTK as it retains a low-level positioning error. Particularly, the positioning errors on U are reduced by more than 60%. One possible reason for the negative values is that AMC-KF also redistributes the positioning residual since errors in different directions are coupled [57].