For the two newly launched satellites(PRN number 27 and 28) of the future global BeiDou navigation satellite system(BDS-3), there is no available broadcast ephemeris data and other initial orbit information, but the i...For the two newly launched satellites(PRN number 27 and 28) of the future global BeiDou navigation satellite system(BDS-3), there is no available broadcast ephemeris data and other initial orbit information, but the initial orbit is the fundamental of the comprehensive analysis of the satellites and their signals. Precise orbit determination(POD) also requires determination of a priori initial value with a certain precision in order to avoid problems such as filter divergence during POD. Compared with the Newton iteration method, which relies on the initial value, this study utilizes the Bancroft algorithm to directly solve the nonlinear equations with the advantage of numerical stability. The initial orbits of these two satellites are calculated based on new code signals, and their results are analyzed and discussed. The experimental results show that, with the exception of very few epochs, when the new code signal is utilized, the median and robust variance factor of the observed residuals computed using pseudo-range observations and the solved initial orbits are less than 4 and 2 m, respectively. It also shows that this solution can be used for rapid initial orbit recovery after maneuvers of the new BeiDou satellites.展开更多
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 algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly ...An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit.展开更多
This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the...This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability.In previous work,the solution to this problem had been shown to be non-global optimal in the sense of least square and had only been discussed in the context of Clohessy–Wiltshire.In this paper,the emphasis is placed on developing a more compact and improved solution to the problem by using state augmentation least square method in the context of the Clohessy–Wiltshire and Tschauner–Hempel dynamics,derivation of corresponding error covariance,and performance analysis for typical rendezvous missions.A two-body Monte Carlo simulation system is used to evaluate the performance of the solution.The sensitivity of the solution accuracy to camera offset,observation period,and the number of observations are presented and discussed.展开更多
基金supported by the Collaborative Precision Positioning Project funded by the Ministry of Science and Technology of China (No.2016YFB0501900)China Natural Science Funds (No.41231064,41674022,41574015)
文摘For the two newly launched satellites(PRN number 27 and 28) of the future global BeiDou navigation satellite system(BDS-3), there is no available broadcast ephemeris data and other initial orbit information, but the initial orbit is the fundamental of the comprehensive analysis of the satellites and their signals. Precise orbit determination(POD) also requires determination of a priori initial value with a certain precision in order to avoid problems such as filter divergence during POD. Compared with the Newton iteration method, which relies on the initial value, this study utilizes the Bancroft algorithm to directly solve the nonlinear equations with the advantage of numerical stability. The initial orbits of these two satellites are calculated based on new code signals, and their results are analyzed and discussed. The experimental results show that, with the exception of very few epochs, when the new code signal is utilized, the median and robust variance factor of the observed residuals computed using pseudo-range observations and the solved initial orbits are less than 4 and 2 m, respectively. It also shows that this solution can be used for rapid initial orbit recovery after maneuvers of the new BeiDou satellites.
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co-funded by the Centre National d’Études Spatiales(CNES)through A.FossàPh.D.program and made use of the CNES orbital propagation tools,including the PACE library.
文摘An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit.
基金this work is supported in part by the National Postdoctoral Program for Innovative Talents(No.BX201700304)the Foundation of Science and Technology on Aerospace Flight Dynamics Laboratory(No.61422100306707).
文摘This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability.In previous work,the solution to this problem had been shown to be non-global optimal in the sense of least square and had only been discussed in the context of Clohessy–Wiltshire.In this paper,the emphasis is placed on developing a more compact and improved solution to the problem by using state augmentation least square method in the context of the Clohessy–Wiltshire and Tschauner–Hempel dynamics,derivation of corresponding error covariance,and performance analysis for typical rendezvous missions.A two-body Monte Carlo simulation system is used to evaluate the performance of the solution.The sensitivity of the solution accuracy to camera offset,observation period,and the number of observations are presented and discussed.
