Evolutionary Algorithms For Initial Orbit Determination With Too Short Arc

The sky surveys of space objects have obtained a huge quantity of too short arc(TSA)observation data,and the length of many observed arcs are even about 10 s.However,the classical method of initial orbit determination(IOD)is not applicable for TSAs.Then a new approach is necessary to effectively utilize these data.In this paper,TSA is studied from an evolutionary point of view.Based on three evolutionary algorithms(EAs)with different evolutionary mechanisms—genetic algorithm(GA),particle swarm optimization(PSO)and differential evolution algorithm(DE),a unified computational framework is constructed for the optimization method,and the optimal variables are determined.Programmed with MATLAB,numerical experiments based on the real measurements show that for near circular orbit the method can provide valid initial values,and the error of 10 s arc is only about 10 km.The results show that EA is an effective way to TSAs.Bootstrap estimation is used to evaluate the accuracy of results of TSAs.At the same time,by adopting least median square in the fitness function,the robust estimation method is put to use for a robust estimation in EAs.Since the 3? method for outliers editing cannot be applicable for EAs.The selection of parameters and operators in EAs has a great influence on the solution.For parameters and operators of DE are more convenient than other algorithms,design of experiment(DOE)is used to optimize the parameters of DE.The optimization has strong theoretical basis.While the three kinds of EAs studied previously focus on the individual with best fitness value,estimation of distribution algorithm(EDA)based on kernel density estimation is applied to TSAs by building the probabilistic model in the solution space.Different from other algorithms,EDA characterizes the distribution of dominant population,and the results are valid as well.On account of advantages and disadvantages of the previous EAs,a combination method of EDA and DE is established for TSAs.Then both the global information and local information are well fused in the search of optimum.This combination improves the accuracy and confidence level of the results,and the distribution of the results is more concentrated than the one with EDA only.Moreover,the accuracy of 3s arc still keeps high with the combination method.Through modifying the geometric model,EAs are applied to the TSAs with space-based observation and large eccentricity orbit.Numerical simulations show EAs are applicable to space-based TSAs with small eccentricity orbit for 10 s arc.But for large eccentricity orbit,due to complexity of itself,EAs can only achieve a " V "type distribution of the results rather than getting the results directly.By adopting area searching of eccentricity,it is found that the fitness of the region around true solution is better while the density is sparse,and the true solution will be covered up easily because of the insufficient number during the evolution process.Evolving with the constraints of "V" type distribution,the dominant solutions are found to be clustered in a few areas,and the region of the true solution is included in these areas,which reduces the search region of IOD and facilitates the follow-up work.