The accuracy of angles-only initial orbit determination(IOD)is significantly compromised when only a short-arc orbit is observed.The ill-conditioned problem in matrices due to weak geometric constraints caused by shor...The accuracy of angles-only initial orbit determination(IOD)is significantly compromised when only a short-arc orbit is observed.The ill-conditioned problem in matrices due to weak geometric constraints caused by short arcs and observation errors typically causes significant errors in the estimated ranges and thus unsatisfactory IOD.This paper presents a critical analysis of the ill-conditioned problem using the Gooding algorithm and proposes several techniques to improve it.On the basis of multiple observations,a least-squares method is proposed to solve the ranges at the first and last epochs.For the short-arc case,the ridge estimation technique is applied to mitigate the ill-conditioned problem.To determine whether an orbit is eccentric,a procedure to assess orbit eccentricity is developed via the range-search method,which aims to provide reasonably accurate initial ranges to the Gooding algorithm.Finally,an eccentricity-constraint technique for the Gooding algorithm is proposed for cases where the orbit is determined to be nearly circular.The performances of these techniques on space-based simulation data are assessed,and an improved Gooding algorithm(I-Gooding)suitable for various observation conditions is proposed.The I-Gooding algorithm is subsequently applied to process actual ground-based observations.The results show that its accuracy in estimating the semimajor axis is 47%higher than that afforded by the standard Gooding algorithm.展开更多
An initial orbit determination (IOD) solution from angles-only observations of a single short orbit arc is often required for applications such as tracklet association and fast reacquisition of a newly detected space ...An initial orbit determination (IOD) solution from angles-only observations of a single short orbit arc is often required for applications such as tracklet association and fast reacquisition of a newly detected space object. Modern optical observations can collect tens or even hundreds of data points over a short arc, thus enabling a large number of IOD solutions to be determined when using an IOD algorithm of 3 lines of sight (3-LOSs), such as the Gooding algorithm. It is necessary but difficult to find an optimal solution from a solution pool, particularly in the case of too short arc (TSA). Another issue in using 3-LOSs IOD methods is the neglect of perturbation effects on the observations. That is, 3-LOSs IOD methods are developed in the 2-body frame, but the observations are perturbed. Thus, the IOD solutions may have additional errors if the observations are not corrected for perturbation effects. In this study, we investigate the distribution of the semi-major axis and eccentricity of IOD solutions in a pool and find that choosing the solution with the maximum kernel density in the distribution is a much better way to determine the final solution from the pool. We also propose a technique to correct J2 secular effects on observed angle data. We use the Gooding algorithm as the basic 3-LOSs IOD algorithm to demonstrate the effectiveness of the proposed techniques in improving the IOD accuracy in the cases of short-arc ground-based observations and space-based simulation data.展开更多
基金supported by the Special Fund of the Hubei Luojia Laboratory(Grant No.230100003)the Chongqing Municipal Natural Science Foundation of the General Program(Grant No.CSTB2022NSCQ-MSX1093)the Science and Technology Research Program of the Chongqing Municipal Education Commission(Grant No.KJQN202200701)。
文摘The accuracy of angles-only initial orbit determination(IOD)is significantly compromised when only a short-arc orbit is observed.The ill-conditioned problem in matrices due to weak geometric constraints caused by short arcs and observation errors typically causes significant errors in the estimated ranges and thus unsatisfactory IOD.This paper presents a critical analysis of the ill-conditioned problem using the Gooding algorithm and proposes several techniques to improve it.On the basis of multiple observations,a least-squares method is proposed to solve the ranges at the first and last epochs.For the short-arc case,the ridge estimation technique is applied to mitigate the ill-conditioned problem.To determine whether an orbit is eccentric,a procedure to assess orbit eccentricity is developed via the range-search method,which aims to provide reasonably accurate initial ranges to the Gooding algorithm.Finally,an eccentricity-constraint technique for the Gooding algorithm is proposed for cases where the orbit is determined to be nearly circular.The performances of these techniques on space-based simulation data are assessed,and an improved Gooding algorithm(I-Gooding)suitable for various observation conditions is proposed.The I-Gooding algorithm is subsequently applied to process actual ground-based observations.The results show that its accuracy in estimating the semimajor axis is 47%higher than that afforded by the standard Gooding algorithm.
基金supported by the National Natural Science Foundation of China(grant nos.12103035 and 12373083)the Fundamental Research Funds for the Central Universities(grant no.2042023gf0007).
文摘An initial orbit determination (IOD) solution from angles-only observations of a single short orbit arc is often required for applications such as tracklet association and fast reacquisition of a newly detected space object. Modern optical observations can collect tens or even hundreds of data points over a short arc, thus enabling a large number of IOD solutions to be determined when using an IOD algorithm of 3 lines of sight (3-LOSs), such as the Gooding algorithm. It is necessary but difficult to find an optimal solution from a solution pool, particularly in the case of too short arc (TSA). Another issue in using 3-LOSs IOD methods is the neglect of perturbation effects on the observations. That is, 3-LOSs IOD methods are developed in the 2-body frame, but the observations are perturbed. Thus, the IOD solutions may have additional errors if the observations are not corrected for perturbation effects. In this study, we investigate the distribution of the semi-major axis and eccentricity of IOD solutions in a pool and find that choosing the solution with the maximum kernel density in the distribution is a much better way to determine the final solution from the pool. We also propose a technique to correct J2 secular effects on observed angle data. We use the Gooding algorithm as the basic 3-LOSs IOD algorithm to demonstrate the effectiveness of the proposed techniques in improving the IOD accuracy in the cases of short-arc ground-based observations and space-based simulation data.
