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

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 short-arc 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.