## 3 Experimental Results and Analysis
### Real Signal Experiments
The results show that ADBO achieves slightly better positioning accuracy than 2 SP, with MRG performing the worst. This indicates that the search capability of the MRG is insufficient under the current configuration, while ADBO remains effective. Figure (b)b shows the total positioning error (\(\Delta R\)) and the positioning errors of the three methods in the East (\(\Delta E\)), North (\(\Delta N\)), and up (\(\Delta U\)) directions. The blue, red, and green lines represent the positioning error curves for 2 SP, ADBO, and MRG, respectively. The corresponding numerical results are summarized in Table 12.  
Figure 11: Performance comparison of 2 SP, ADBO, and MRG in the static receiver scenario. (**a**) Positioning platform map. (**b**) Comparison of positioning error. Figure 10: Dataset Characteristics in the static receiver scenario. (**a**) Sky plot. (**b**) \(C/N_{0}\) for each satellite. \begin{table}
\begin{tabular}{l r r r} \hline \hline
**Item** & **2 SP** & **MRG** & **ADBO** \\ \hline Sum position error (m) & 10.41 & 17.3 & 9.41 \\ Position error in East (m) & 2.16 & 3.48 & 1.88 \\ Position error in North (m) & 2.37 & 3.65 & 2.04 \\ Position error in Up (m) & 9.30 & 15.60 & 8.43 \\ Execution time (s) & – & 19.15 & 3.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Performance comparison in the static receiver scenario. ADBO demonstrates significantly better search accuracy than MRG, with smaller positioning errors in all ENU directions. Specifically, ADBO reduces the total positioning error from 17.3 m in MRG to 9.41 m, achieving an improvement of approximately 45.6%. The positioning errors in the ENU directions are reduced by 46.0%, 44.1%, and 46.0%, respectively. Additionally, ADBO requires significantly less execution time than the MRG method, with a reduction from 19.15 s to 3.42 s, achieving an 82.1% decrease in computational time. This is because ADBO evaluates far fewer candidate points than MRG. If higher accuracy is desired, the computational cost for MRG increases exponentially, making it impractical. In the dynamic receiver scenario, the initial search space is configured identically to that in the static scenario. For each subsequent epoch, the algorithm centers the search space around the previous solution, with a search space size reduced to half of that in the static scenario. The sky plot and energy levels are shown in Figure 12a,b. While PRN 4 exhibits relatively lower \(C/N_{0}\) and PRN 23 shows a noticeable signal attenuation between 25 s and 28 s, such variations are representative of realistic conditions in dynamic environments. The goal is to evaluate the algorithm's robustness under challenges like signal fading and multipath. The positioning results span from 5978 ms to 38,988 ms, resulting in a total of 3302 positioning outcomes. Figure 13a displays the road map of the positioning results, with the black line representing the true track and the blue, green, and red stars indicating the positioning results of the 2 SP, MRG, and ADBO algorithms, respectively. Compared with 2 SP and MRG, the positioning traces of ADBO exhibit higher accuracy and smaller fluctuations, demonstrating the ability of the proposed method to handle dynamic scenarios effectively. Figure 13b further illustrates the total positioning error and the positioning errors in the ENU directions for the three methods. It is evident that the MRG method performs relatively poorly, particularly around the middle of the experiment, where signal quality deteriorates. The corresponding numerical results are summarized in Table 13. Compared to the static reception scenario, 2 SP experiences a greater degradation in positioning performance in the dynamic scenario than both MRG and ADBO, with reductions of 40.5%, 16.3%, and 14.2%, respectively. ADBO still outperforms the MRG method with better positioning performance and lower computational cost. Specifically, ADBO reduces the total position error from 20.12 m in MRG to 10.75 m, achieving an improvement of approximately 46.6%.