Second-order design of GNSS networks with different constraints using particle swarm optimization and genetic algorithms

Abstract The optimal design of geodetic networks is essential across various fields. For global navigation satellite system (GNSS) networks, the most critical design phase is the second-order design (SOD) problem, which focuses on selecting the optimal GNSS observational plan to achieve the highest possible precision and reliability in measurements. Eliminating unnecessary baseline observations reduces the time, effort, and cost, particularly in networks with long distance baselines. In this research, we employed both genetic algorithms (GAs) and particle swarm optimization (PSO) to determine the optimal baselines for an observed real GNSS network with long distance baselines. The analysis was conducted for two types of networks: minimally constrained and over-constrained solutions. Unlike most previous studies, which primarily focused on either simulated datasets or small-scale geodetic networks with a limited number of points and short baselines, this study addresses a large-scale geodetic network including a significant number of points and long distance baselines. The network consisted of 30 points and 435 baselines, with the longest baseline reaching 301.7 km and a total baseline length of 95168.2 km. This extensive network was designed and observed to provide a fair and comprehensive evaluation of the results achieved by both methods and solution types. The network under study was established in the Sinai region, situated in the northeastern part of Egypt. The results demonstrate the effectiveness of GAs and PSO in optimizing GNSS network baselines. Both methods reduced the total number and length of observed baselines by approximately 42.4 and 41.4%, respectively. This optimization translates to a reduction of around 42% in fieldwork time and associated costs by roughly the same amount. Additionally, the findings indicate that over-constrained optimization using GAs and PSO yields more accurate results, with consistent coordinate differences. These results are particularly advantageous for networks with long baselines, making them a better alternative to minimally constrained solutions.