Design Of LEO Navigation Augmentation Constellation Using Multi-Objective Evolutionary Algorithm

As an important space-time infrastructure,the Global Navigation Satellite System(GNSS)has been widely used in the fields of navigation,positioning and timing.However,GNSS signals are not only weakened or lost due to occlusion in areas such as cities and woods,but the weaker signals are more susceptible to interference and spoofing.Meanwhile,autonomous driving has placed higher demands on the navigation and positioning performance of GNSS.In recent years,Low Earth Orbit(LEO)constellations,represented by StarLink,have gained increasing attention.The miniaturization of satellites and the maturation of rocket launch technologies have contributed significantly to the construction of the LEO constellation.LEO satellites not only have the advantage of low signal attenuation,but can also improve the navigation performance of GNSS through information enhancement and signal enhancement.The design of Low Earth Orbit Navigation Augmentation(LEO-NA)constellations is the primary issue to address,as it directly affects the system performance and cost.Additionally,some evolutionary algorithms for solving the corresponding multi-objective optimization problem in constellation design often obtain unsatisfactory results.To address these challenges,this paper conducts research on both multi-objective evolutionary algorithm improvement and LEO-NA constellation design.The specific work is as follows:1.In this paper,the dynamic multi-objective differential evolution algorithm based on elite guidance(DMODE-EG)is proposed to address the shortcomings of differential evolution algorithms,such as low iteration efficiency,tendency to converge on locally optimal solutions and sensitivity to evolutionary parameter settings.First,the DMODE-EG algorithm is able to determine whether the current evolution of a population is in the exploration or exploitation stage based on the evolutionary binary of individuals.The goal of the exploration phase is to maintain population diversity,and the DMODE-EG algorithm uses the rand/bin/1 difference operator to perform the mutation operation.The goal of the exploitation phase is to accelerate evolution and convergence,and the DMODE-EG algorithm proposes a DE/current-to-pbest/1 difference operator for multi-objective optimization to guide the evolutionary direction of the population.In addition,the DMODE-EG algorithm is able to dynamically adjust evolutionary parameters such as the mutation factor during the evolution of the population based on the inverse parameter control method.2.In this paper,to overcome the limitations of fixed constellation configurations and limited decision variables in the constellation design based on evolutionary algorithms,a design scheme of the LEO-NA constellation based on the two-layer Walker constellation is proposed.First,neither the polar nor the inclined circular orbit constellation alone can achieve ideal global coverage,thus this paper chooses the two-layer Walker constellation as the basic structure.In order to expand the feasible solution space for the constellation design,the number of satellites,Keplerian orbit parameters and other constellation configuration parameters of each layer are all used as decision variables,with the total number of satellites fixed at 150.Meanwhile,the PDOP,the number of visible satellites and the mean orbital altitude are taken as objective functions,thus transforming the LEO-NA constellation design problem into a multi-objective optimization problem.3.In this paper,the performance of multi-objective evolutionary algorithms is compared and analyzed on some standard test function sets.The simulation results show that the proposed DMODE-EG algorithm not only has excellent convergence and parameter dynamic adjustment capability,but also can maintain the distributivity of the solution set well during the evolutionary process.In addition,different constellations are cosimulated with BeiDou Navigation Satellite-3(BDS-3)to analyze the improvement in navigation performance.The simulation results verify the validity of the LEO-NA constellation design proposed in this paper.Compared to other designed LEO-NA constellations and three realistic LEO constellations,the C1 constellation obtained by the DMODE-EG algorithm not only solves the problem of high PDOP values in some areas,but also improves the distribution of PDOP and increases the number of visible satellites.