A Parallel Particle Swarm Optimization Algorithm for Reference Stations Distribution

Abstract

Parallel Particle Swarm Optimization (PPSO) algorithm is proposed to optimize the reference stations distribution and this algorithm will increase the User Differential Range Error (UDRE) accuracy and enhance the flight safety. Due to the reference stations distribution largely influence the accuracy of UDRE, a concept of Satellite Surveillance Dilution of Precision (SSDOP) is used to reflect the effect of changing the reference stations distribution on UDRE. After analyzing the expressions of SSDOP and UDRE, UDRE is influenced by restriction factor and SSDOP when measurement noise is a certain value, and the restriction factor is independent on SSDOP. Then, a mathematical equation between SSDOP and UDRE is deduced from the SSDOP and UDRE expressions, and a linear trend is showed. A Particle Swarm Optimization (PSO) algorithm is proposed, and it first randomly generates a group of particles and each particle represents a reference stations distribution. The average SSDOP is used as the fitness function to evaluate each particle. Both the local best and global best are used to guide the search direction. However, the proposed PSO algorithm may converge too fast which makes the optimizing result to become the local optimization. Thus, the PPSO algorithm with parallel computing is proposed to overcome this problem. Experiments are made to compare the performance of the proposed PPSO algorithm, the proposed PSO algorithm, “N-Angled” method and Exhaustive Grid Search method. The proposed PPSO algorithm can find the best solution without falling in local optimization, and isn’t restricted by the state and amount of the satellites and the outline of the searching area.