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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.

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.