## 2 Materials and Methods
### Improving the Partial Ambiguity Fixed Solution  
Considering the increase in Global Navigation Satellite System (GNSS) and the exponential increase in the number of satellites, researchers at home and abroad have shown that fixing all ambiguity parameters is unnecessary, and the risk of ambiguity fixation failure can be reduced by selecting a partial subset of ambiguities for fixation under the condition that the number of participating satellites is sufficient. [PERSON] [21] first proposed a partial ambiguity fixation strategy for the selection of the optimal subset and a fixation strategy for the selection of the optimal subset based on the bootstrapping success rate. Some scholars also proposed partial ambiguity resolution (PAR) algorithms based on satellite elevation angle, signal-to-noise ratio, continuous tracking ephemeris number, ambiguity dilution of precision (ADOP) value, ambiguity variance, etc., in the following. Now, based on the PAR idea, a new partial ambiguity fixation method is proposed for the network RTK reference station ambiguity solution, which improves the ambiguity fixation rate by selecting the optimal subset at the satellite level and ambiguity level, i.e., taking full advantage of the data from satellites with high elevation angles to participate in the floating-point solution, and shortening the convergence time compared with the search of all the observed data. The basic idea of partial fuzzy degree fixation is to divide the fuzzy degree into two subsets based on some criterion, giving priority to fixing the more easily fixed subset [24]. Specifically, the ambiguity vector \(\vec{a}\) is divided into two subsets \(\left[\vec{a}_{1}\;\vec{a}_{2}\right]^{T}\), then its variance-covariance matrix can be expressed accordingly as:  
\[Q_{\vec{a}\vec{a}}=\left[ \begin{array}{cc}Q_{\vec{a}_{1}\vec{a}_{1}}&Q_{ \vec{a}_{1}\vec{a}_{2}}\\ Q_{\vec{a}_{2}\vec{a}_{1}}&Q_{\vec{a}_{2}\vec{a}_{2}}\end{array} \right] \tag{19}\]  
where \(\vec{a}_{1}\) represents the selected ambiguity subset that is easier to fix, and \(\vec{a}_{2}\) represents the remaining ambiguity subset. When the subset \(\vec{a}_{1}\) is fixed by the LAMBDA method, the integer solution of \(\vec{a}_{1}\) can be utilized to modify \(\vec{a}_{2}\) and its variance-covariance matrix \(Q_{\vec{a}_{2}\vec{a}_{2}}\) to obtain the integer solution of \(\vec{a}_{2}\) and its fixed variance-covariance matrix:  
\[\left\{ \begin{array}{cc}\widehat{\mathbf{a}}_{2}=\widetilde{a}_{2}-Q_{\vec{ a}_{2}\vec{a}_{1}}Q_{\vec{a}_{1}\vec{a}_{1}}^{-1}(\widetilde{a}_{1}-\widehat{ \mathbf{a}}_{1})\\ Q_{\widehat{\mathbf{a}}_{2}\widehat{\mathbf{a}}_{2}}=Q_{\vec{a}_{2}\vec{a}_{2}} -Q_{\vec{a}_{2}\vec{a}_{1}}Q_{\vec{a}_{1}\vec{a}_{1}}^{-1}Q_{\vec{a}_{1}\vec{ a}_{2}}\end{array} \right. \tag{20}\]  
The specific steps of this method are as follows:  
1. Firstly, we try to fix all ambiguities, i.e., without rejection filtering of the ambiguity set, the search of the floating-point ambiguity parameters obtained by Kalman filtering using LAMBDA algorithm directly, and the search results are tested jointly by R-ratio and bootstrapping success rate indicators, and if they pass the test, the fixation is considered successful; otherwise, we proceed to the next step. 2. The ambiguity subsets are divided at the satellite level, and the total set of satellite azimuths (0\({}^{\circ}\)\(\sim\)360\({}^{\circ}\)) is divided into one subset as long as it is over 90\({}^{\circ}\), and subsets are denoted as \(Q_{1}\), \(Q_{2}\), \(Q_{3}\), and \(Q_{4}\) separately, and one satellite is removed from the divided subset to ensure that the GDOP value of the set is the smallest after removing a satellite. Then, the ambiguity of all remaining satellite sets \(H_{1}\) is fixed. 3. If the second step fails to be fixed, the set \(H_{1}\) is then optimally filtered at the fuzzy degree level, and the three fuzzy degrees with larger ADOP values \(\alpha_{max1}\), \(\alpha_{max2}\), \(\alpha_{max3}\) are selected from the subset.