## 3 Experimental Results and Analysis
### Simulated Signal Experiments
#### 3.1.1 Fine Satellite Geometry
The DBO algorithm demonstrates advantages over other swarm intelligence algorithms, showing fast convergence and being less likely to fall into local optima. Building on this foundation, ADBO significantly enhances performance compared with DBO, outperforming other algorithms in terms of search capability and achieving the lowest fitness value. It is worth noting that at the beginning of the search, ADBO's fitness values do not decrease as quickly as those of other algorithms. This is because, for a complex search problem like DPE, FLA guides ADBO to prioritize a more global search initially, coupled with Gaussian mutation, rather than focusing on rapidly achieving lower fitness values locally. In the later stages of the search, ADBO shifts to favoring local search, incorporating Cauchy mutation to maintain continuous search capability. Consequently, ADBO tends to outperform other algorithms in obtaining the lowest fitness function value by the end of the iteration. As shown in Figure 6a, the convergence trends of the position error curve and the cost function curve are similar. However, due to the multi-peaked nature of the cost function in DPE, the position error curves do not continuously decrease like the convergence curves but instead fluctuate. This fluctuation occurs because the optimization problem in DPE essentially involves the correlation value between the signal corresponding to a candidate point and the true received signal. A candidate point achieves a smaller fitness value when some code phases are aligned and the global optimum when it aligns with all satellite code phases. This can result in situations where candidate points with smaller fitness values are actually further from the true position. By considering the fitness landscape of the cost function, the ADBO algorithm exhibits minimal fluctuation and the fastest convergence, demonstrating its superiority. Due to the inherent randomness in population distribution during each independent experiment, the mean value of FDC and ruggedness appears as a gently declining curve, which does not clearly illustrate the relationship with the convergence curve of the fitness \begin{table}
\begin{tabular}{l r r r r r r r r r r r} \hline
**Algs.** & **2 SP** & **MRG** & **ARS** & **PSO** & **SSA** & **GWO** & **HHO** & **PIO** & **PO** & **DBO** & **ADBO** \\ \hline PE (m) & 32.7 & 58.3 & 103.5 & 1206.7 & 1283.9 & 99.3 & 1218.7 & 1289.8 & 407.1 & 61.1 & 36.5 \\ CBE (m) & 4.6 & 7.3 & 13.0 & 41.4 & 67.4 & 10.3 & 70.7 & 71.8 & 31.8 & 9.2 & 5.1 \\ PN (\(10^{3}\)) & – & 400 & 400 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 \\ ET (s) & – & 103.7 & 109.8 & 15.0 & 15.1 & 15.7 & 29.3 & 15.6 & 15.5 & 15.6 & 16.0 \\ \hline \end{tabular}
\end{table} 
Table 7: Performance comparison of different optimization algorithms with fine geometry. value. To better demonstrate this relationship, the convergence curve from a single experiment, along with the corresponding FDC and ruggedness curves, is shown in Figure 7. As shown in Figure 7b, at the beginning of the search, the initial population is randomly distributed, presenting lower values of \(C_{f}\) and \(R_{f}\) across a large search space. ADBO maintains a broad search range, promoting extensive exploration and foraging behavior. Around the 17 th iteration, \(R_{f}\) reaches its peak value, corresponding to a larger Cauchy mutation, which favors a more exhaustive search of the entire space. By the 61 th iteration, \(R_{f}\) rapidly decreases, and Gaussian mutation becomes more dominant. Despite the already low fitness value, FDC remains within the range of 0.6 to 0.8 until approximately the 265 th iteration, enabling ADBO to retain its global search capability. This persistence is crucial in the DPE positioning problem, where even with individuals showing low fitness values, the FDC between individual populations remains high across the entire search space, indicating the problem's deceptive nature. ADBO can adopt a suitable search strategy guided by FLA, which is unmatched by other algorithms.