## 2 Methods
### Procedure of the NSWOA-Based Satellite Selection Algorithm  
As indicated by Equation (6), the decision space for the satellite selection strategy within the observational field for positioning is denoted as \(\mathbb{R}=\left\{\mathbb{R}_{n_{4}},\mathbb{R}_{n_{5}},\ldots,\mathbb{R}_{n_{ \max}}\right\}\). In this context, the NSWOA, which incorporates both archiving and guiding selection mechanisms, selects a set of Pareto non-dominated satellite combinations from the decision space \(\mathbb{R}\). The resulting set of Pareto non-dominated satellite combination agents is denoted as \(x^{*}=\left\{x_{n_{4}}^{*},x_{n_{5}}^{*},\cdots,x_{n_{\max}}^{*}\right\}\), where \(n=\left\{n_{4},n_{5},\cdots,n_{\max}\right\}\) and \(n_{i}\) represents the selection of \(i\) LEO satellites. The steps of the NSWOA rapid satellite selection algorithm are shown in Table 1. The flow of the NSWOA rapid satellite selection algorithm is illustrated in Figure 1. The pseudocode for the satellite selection algorithm is presented in Table 2. The initial phase involves data preprocessing, during which \(M\) visible satellites are identified and a viable satellite selection strategy space \(\mathbb{R}\) is generated. This process utilizes satellite IDs, downlink signal power, and orbital information derived from Two-Line Element (TLE) data. Satellites are considered visible if they meet two criteria: a remaining observable time greater than zero and a signal power exceeding the receiver's sensitivity threshold. **NSWOA Process**  
**Step 1. ** Initialization  
Initialize the satellite combination subset and parameters. Randomly initialize parameters \(a\), \(A\), and \(C\), and generate \(N\) initial satellite combination agent subsets \(\left\{\overset{\rightarrow}{x}_{1}^{(1)},\overset{\rightarrow}{x}_{2}^{(1)}, \ldots,\overset{\rightarrow}{x}_{N}^{(1)}\right\}\in\overset{\rightarrow}{x} ^{(1)}\), where \(\overset{\rightarrow}{x}^{(t)}\) represents the subset of satellite combination agents in the \(t\)-th iteration, with \(\overset{\rightarrow}{x}^{(t)}\in\mathbb{R}\), \(\left|\overset{\rightarrow}{x}^{(t)}\right|=N\)  
**Step 2. ** Calculate Fitness Function Values  
Compute the objective vector fitness function values \(J(x)=[f_{1}(x),f_{2}(x)]\), where \(f_{1}(x)=DGDOP\) represents the DGDOP of the observed non-cooperative LEO satellite combinations, reflecting positioning accuracy, and \(f_{2}(x)=n\) represents the number of selected satellites, reflecting the computational burden. Update and determine the fitness values \(f_{1}(x)\) for the \(t\)-th satellite combination. **Step 3. ** Archiving Control  
Based on Step 2, calculate the objective vector fitness function values \(J(x)\) for each satellite combination in the subset \(\overset{\rightarrow}{x}^{(t)}\). Determine the dominance of each satellite combination and assess the non-dominated satellite combinations in \(\overset{\rightarrow}{x}^{(t)}\) for archiving. If the archiving criteria are met, store the qualifying non-dominated combinations in the archive and make necessary adjustments. **Step 4. ** Select Guiding Combination agent and Update Satellite Combination Subset  
After obtaining the current archive, divide the archive space into grids and calculate crowd density. Based on the crowd density results, assign different selection probabilities to each grid. Use the guiding selection mechanism to choose a guiding satellite combination agent \(\overset{\rightarrow}{x}_{n}^{(t)}\) from the non-dominated satellite combination archive. Update the satellite combination subset \(\overset{\rightarrow}{x}^{(t)}\) based on the guiding satellite combination agent using Equations (7) and (8). **Step 5. ** Define the Mapping Function for Search Boundaries  
A mapping function is established to define the search boundaries, ensuring that all selected satellite combination elements remain within the observational field of the satellite selection strategy decision space, denoted as \(\mathbb{R}=\left\{\mathbb{R}_{n_{a}},\mathbb{R}_{n_{s}},\ldots,\mathbb{R}_{n_{ max}}\right\}\).