## 5 Conclusions  
We present a giant LEO constellation dual-satellite alternate switching ranging integrated navigation algorithm combined with an altimeter; based on the inherent characteristics of LEO satellites and the advantages of the ELO constellation, the use of LEO constellation for navigation and positioning can eliminate the need to consider clock bias (this is also considerable for reducing the cost of receivers and on-board equipment). In addition, by constructing the position of the moving carrier as a large ellipsoid similar to the earth, the navigation and positioning model can be described more accurately, and then the dynamic navigation and positioning solution can be realized, which has the advantage of accurate positioning. Our experimental results show that only by combining the altimeter, our algorithm can significantly improve the large navigation and positioning error caused by the INS + LEO2 switching without altimeter when the switching time is large. In addition, it is compared with the traditional dual-satellite navigation and \begin{table}
\begin{tabular}{l l l l} \hline
**Error Index** & **Algorithm** & **Mean** & **Standard Deviation** \\ \hline \multirow{4}{*}{Longitude (\({}^{\circ}\))} & this paper & \(0.1371\times 10^{-4}\) & \(0.4628\times 10^{-4}\) \\  & Reference [15] & \(2.4564\times 10^{-4}\) & \(157.0000\times 10^{-4}\) \\  & Reference [17] & / & / \\  & Reference [20] & \(-0.06539\times 10^{-4}\) & \(0.56238\times 10^{-4}\) \\  & Reference [21] & \(1.6753\times 10^{-4}\) & \(0.1320\times 10^{-4}\) \\ \hline \multirow{4}{*}{Latitude (\({}^{\circ}\))} & this paper & \(0.0063\times 10^{-4}\) & \(0.3289\times 10^{-4}\) \\  & Reference [15] & \(1.7986\times 10^{-4}\) & \(134.0000\times 10^{-4}\) \\ \cline{1-1}  & Reference [17] & / & / \\ \cline{1-1}  & Reference [20] & \(-0.0539\times 10^{-4}\) & \(0.4452\times 10^{-4}\) \\ \cline{1-1}  & Reference [21] & \(16.0000\times 10^{-4}\) & \(3.5382\times 10^{-4}\) \\ \hline \multirow{4}{*}{Altitude (m)} & this paper & \(0.0479\) & \(0.1132\) \\  & Reference [15] & \(35.9300\) & \(14.1989\) \\ \cline{1-1}  & Reference [17] & \(2.0434\) & \(0.6221\) \\ \cline{1-1}  & Reference [20] & \(-0.0543\) & \(0.5229\) \\ \cline{1-1}  & Reference [21] & \(34.6000\) & \(6.0518\) \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of different algorithms. positioning algorithm, dual-mode system navigation and positioning algorithms and some advanced navigation and positioning algorithms in difficult environments and in those cases it can significantly improve the position error. In practical applications, we can choose an altimeter with different accuracy according to our needs, even if the altimeter has a large deviation, but when we deduct the fixed error of the altimeter, the effect is still obvious. Since the LEO constellation is closer to earth, navigation and positioning based on the LEO constellation will gain many advantages over the MEO and HEO constellations. For example, the propagation delay is relatively low, so compared with the MEO and HEO constellations, the real-time performance is stronger; in addition, due to the light weight, small size and low cost of LEO satellites, the constellation can be supplemented by rapid deployment. In general, our algorithm is a high-precision, low-cost, and real-time location service solution, and it is suitable for navigation and positioning in difficult environments such as occlusion, urban blocks, and mountains. [PERSON] and [PERSON] conceived the conceptualization and algorithm. [PERSON] completed the implementation of the algorithm and the writing of the paper, and supported the writing--review and editing. [PERSON] completed some preliminary simulations, and performed preliminary research and summary of the work. [PERSON] provided theoretical guidance and suggestions for revision of the paper. [PERSON] and [PERSON] provided funding support and provided necessary assistance for thesis writing. All authors have read and agreed to the published version of the manuscript.