Layout Optimization of Hybrid Pseudolite Systems Based on an Incremental GDOP Model

Global Navigation Satellite Systems (GNSSs) are widely used in many applications but can be out of use in some critical conditions. Hybrid pseudolite systems utilize ground and aero stations as pseudolites to provide positioning signals for users within the covered area. The positioning accuracy is an important performance parameter for the pseudolite system and is decided by the layout of the pseudolites. This paper proposes a layout optimization method based on an Incremental Geometric Dilution of Precision (IGDOP) model. The IGDOP considers the GDOP value into two parts. One is the fixed part corresponding to the ground stations, and the other is the varying part related to the movable aero pseudolite stations. Thus, when the aero pseudolites’ position changes, the new GDOP value could be obtained only by calculating the varying part. Then, a Monte-Carlo Genetic Algorithm (MC-GA) is proposed for the IGDOP calculation for a minimum value. This algorithm comprises two main components: first, it leverages the random sampling capability of the Monte-Carlo Algorithm to provide sample points that satisfy the sample space for the subsequent Genetic Algorithm, which serve as individuals of the initial population; subsequently, it searches for the minimum value of IGDOP via the Genetic Algorithm and determines the optimized layout of the hybrid pseudolite system. Simulations are carried out using a hybrid pseudolite system with four fixed stations and n movable stations. The results validate the developed IGDOP model and show that the approach enables scalable optimization of n − 1 movable stations via four fixed stations, providing an efficient, low-complexity solution to the system layout optimization.