In a scenario where GNSS signal is blocked due to interference or occlusion, it is of considerable value to establish a regional navigation system providing emergency services for ground users by using long-endurance and long-range fixed-wing Unmanned Aerial Vehicles (UAVs). The main work of this paper consists of two parts. First, we designed a set of UAV-based pseudolite navigation system (UAV-PNS) architecture based on fixed-wing UAVs. Then, considering the flight cost of the UAV swarm, the optimization of the UAV swarm's flight path aimed at improving regional navigation performance was studied. In this paper, the fitness functions for UAVs' flight path optimization are proposed, taking into account the navigation and positioning performance, the aircraft utilization rate of UAVs under flight constraints, and the response speed of the system to the emergency mission. Based on this, an acceptance-rejection mutated non-dominated sorting genetic algorithm III (ARMNSGA-III) is proposed for the UAVs' flight path optimization. The research results show that the flight path strongly guarantees navigation service performance with constraints on the operating cost. The ARMNSGA-III proposed in this paper can provide a 44.01% algorithm timeliness improvement compared to the NSGA-III in the flight path optimization, supporting rapid establishment and continuous service of the UAV-PNS in emergency scenarios.