Comparison of angles only initial orbit determination algorithms for space debris cataloguing

Fadrique, F. M. Martinez; Mate, Alberto Agueda; Grau, Joan J.; Sánchez, J Fernández; Garcia, Laura Aivar

doi:10.7446/jaesa.0401.04

Cited by 12 publications

(6 citation statements)

References 2 publications

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“…Two arcs association based on Lambert equation Generally, the IOD would need an arc length longer than 1% of the orbital period (that is, about 15 min for GEO objects), and then the improved-Laplace [33], Gauss [15], or Gooding [16] methods are likely used to generate stable IOD solutions. Otherwise, illconditioned equations in these methods make the IOD difficult to converge [34,35]. The use of the range-search-based IOD method [27] may have the problems of expansive search time and solution optimization.…”

Section: Angle Observationsmentioning

confidence: 99%

Short-Arc Association and Orbit Determination for New GEO Objects with Space-Based Optical Surveillance

Jian¹,

Lei

Zhao

et al. 2021

Aerospace

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For Geosynchronous Earth Orbit (GEO) objects, space-based optical surveillance has advantages over regional ground surveillance in terms of both the timeliness and space coverage. However, space-based optical surveillance may only collect sparse and short orbit arcs, and thus make the autonomous arc association and orbit determination a challenge for new GEO objects without a priori orbit information. In this paper, a three-step approach tackling these two critical problems is proposed. First, under the near-circular orbit assumption, a multi-point optimal initial orbit determination (IOD) method is developed to improve the IOD convergence rate and the accuracy of the IOD solution with angles-only observations over a short arc. Second, the Lambert equation is applied to associate two independent short arcs in an attempt to improve accuracy of the single-arc IOD semi-major axis (SMA) with the use of virtual ranges between the optical sensor and GEO object. The key idea in the second step is to generate accurate ranges at observation epochs, which, along with the real angle data, are then used to achieve much improved SMA accuracy. The third step is basically the repeated application of the second step to three or more arcs. The high success rate of arc associations and accurate orbit determination using the proposed approach are demonstrated with simulated space-based angle data over short arcs, each being only 3 min. The results show that the proposed approach is able to determine the orbit of a new GEO at a three-dimensional accuracy of about 15 km from about 10 arcs, each having a length of about 3 min, thus achieving reliable cataloguing of uncatalogued GEO objects. The IOD and two-arc association methods are also tested with the real ground-based observations for both GEO and LEO objects of near-circular orbits, further validating the effectiveness of the proposed methods.

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Section: Angle Observationsmentioning

confidence: 99%

Short-Arc Association and Orbit Determination for New GEO Objects with Space-Based Optical Surveillance

Jian¹,

Lei

Zhao

et al. 2021

Aerospace

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“…Many methods can solve the angles-only initial orbit determination problem. The Laplace method, the Gauss method, the Double-r method, and the Gooding method are most commonly used [24]- [26]. However, these methods choose only three pairs of observations, with many observations wasted.…”

Section: The Laplace-least Square Initial Orbit Determinationmentioning

confidence: 99%

Uncertainty Analysis of the Short-Arc Initial Orbit Determination

Tao

Gong

et al. 2020

IEEE Access

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The solution of the short-arc angles-only orbit determination problem has large uncertainty because the topocentric range is not observable. For a certain angular observation tracklet with measurement noise, there exist numerous potential orbits, all of which are compatible with the observations. However, the solution of a deterministic initial orbit determination algorithm is usually far different from the true orbit, especially for the semimajor axis and the eccentricity. A new sampling method is proposed to describe the probability distribution of the orbit determination solutions. Firstly, a series of orbits are sampled in the semimajor axis-eccentricity plane. A chi-square test method is proposed to select candidate orbits from the sample orbits. The weights of the candidate orbits are calculated to measure their probability being the true orbit. Finally, the kernel density estimation algorithm is used to estimate the probability density function of the true orbits. With some a priori assumptions, the candidate orbits can be further screened, and their weight can be modified. The a priori knowledge can significantly improve the accuracy of the orbit determination solution. INDEX TERMS Error analysis, initial orbit determination, Kernel density estimation, orbit sampling, short-arc optical observations.

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“…Meanwhile, short-arc and fragmentary observations make it difficult to perform POD through a Kalman filter. In [9], F. M. Fadrique compared three different IOD algorithms: Gauss, Baker-Jacoby and Gooding algorithm to illustrate their different performances on wide variety of orbital scenarios. In recent years, D. P. Lubey et al [10] proposed a new IOD method based on Polynomial Chaos algorithm without an initial guess of the object's state.…”

Section: A Orbit Determinationmentioning

confidence: 99%

A Novel Space-Based Orbit Determination Method Based on Distribution Regression and Its Sparse Solution

Feng

Zhang

et al. 2019

IEEE Access

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There is an inherent need to track and catalog space debris (objects) in geosynchronous earth orbits (GEO) based on space-based surveillance networks and a large amount of observation data. However, for objects in GEO, angle-only measurements containing noises have been regarded as difficult for shortarc orbit determination (OD) when pursuing high accuracy. In this paper, from a data-driven perspective, we propose a novel method for space-based OD based on distribution regression (DR), which is called the weighting distribution-regression OD (WDR-OD) method. The OD is treated as a regression process, which is learned from abundant observation data and the corresponding orbits of known objects. First, we propose the structure of space-based OD samples, wherein the feature variables with a weighting matrix are introduced to enhance prediction accuracy. Second, a two-stage sampled learning theory is employed to learn the mapping from measurements to objects' orbit through kernel mean embedding. The proposed method is experimentally compared with the improved Laplace method and shows greater robustness in measurements with white Gaussian noise (WGN) and colored noise. The positional RMSE reaches 0.8793 km with WGN and 1.6972 km with colored noise, which are significantly smaller than the corresponding Laplace method's 5.0804 km and 14.8132 km. Furthermore, we propose a RIP-based ROMP algorithm to provide the theoretical bound of sparsity and then to pursue a sparse solution. Although the positional RMSE increases to 1.6554 km in the sparse method, it shrinks the 90% to 93% nonzero elements of the coefficients matrix to zero, which is helpful in reducing the computing load, and it meaningfully extends the application domain of the WDR-OD method.

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Comparison of angles only initial orbit determination algorithms for space debris cataloguing

Cited by 12 publications

References 2 publications

Short-Arc Association and Orbit Determination for New GEO Objects with Space-Based Optical Surveillance

Short-Arc Association and Orbit Determination for New GEO Objects with Space-Based Optical Surveillance

Uncertainty Analysis of the Short-Arc Initial Orbit Determination

A Novel Space-Based Orbit Determination Method Based on Distribution Regression and Its Sparse Solution

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