###### Abstract  
Low Earth orbit (LEO) satellites have unique advantages in navigation because of their high signal intensity and rapid geometric changes in a short period. In order to solve the problem of constellation performance degradation after a potential failure pertaining one or more medium Earth orbit (MEO) navigation satellites, this paper designs the LEO navigation constellation and considers the task requirements of different stages of constellation deployment. Firstly, the LEO navigation constellation is designed by a non-dominated sorting genetic algorithm II (NSGA-II). The average position dilution of precision (PDOP) is 1.6%, which is an improvement compared to the average PDOP offered by the four traditional GNSS. Secondly, the staged deployment of constellation takes into account the degradation of constellation performance caused by the failure of MEO navigation satellites, and the Monte Carlo method is used to analyze the case of three simultaneous satellite failures. The results show that a single satellite failure within each orbital plane and adjacent satellites with close phase separation has a great impact on the performance of the MEO navigation constellation. On this basis, a staged deployment strategy was adopted in order to balance cost, risk, and performance. The three phases deploy 66, 156, and 288 satellites, respectively; as a make-up constellation under contingencies, a navigation enhancement constellation, and an independent navigation constellation, the deployment of the staged sub-constellations meets the mission requirements. The constellation design and staged deployment method proposed in this paper can provide reference for the future study of LEO navigation constellations. LEO constellation design; satellite failure analysis; staged deployment; NSGA-II 2024 16 3667 10.390/rs16193667 10.  
the mathematical model is complex, the calculation workload is large, and it is difficult to find the global optimal point when the objective function has multiple extreme value points. The simulation comparison method reflects the condition of the real system through the simulation program to obtain a more accurate assessment result. It is more flexible in constellation design and is no longer limited to a single configuration. The advantage is that it can reflect the condition of the real system to obtain more accurate evaluation results. However, it requires a larger cost of time and storage space and is suitable for schemes with fewer parameters and smaller solution space. The intelligent optimization method searches for the optimal solution by simulating the group behavior of natural organisms or introducing random variables. With the increase in constellation design parameters and the complexity of performance index requirements, the intelligent optimization method can be applied to various types of problems. The intelligent optimization method focuses on the diversity of the solution and the convergence speed of the balance. It can experimentally produce relatively good solutions, although it is not possible to verify whether the results obtained are optimal or not, and it is important to note that it may fall into a local optimal solution in the process of solving. Numerous scholars have used different types of intelligent optimization algorithms for constellation design, such as the genetic algorithm (GA) [1], multi-objective genetic algorithm (MOGA) [2], improved particle swarm optimization algorithm (HRPSO) [3], ant colony optimization method [4], elite-guided dynamic multi-objective differential evolutionary algorithm (DMODE-EG) [5], Bayesian optimization algorithm [6], and so on. [PERSON] et al. identified seven key attributes for the design of a constellation, including coverage, robustness, autonomous collision avoidance, configuration preservation, launch, deployment, and off-orbit disposal. These were simplified into multi-objective optimization problems to determine the optimal constellation on a global scale [7]. [PERSON] et al.