Abstract
Abstract A new method of orbit determination (OD) is proposed: distribution regression. The paper focuses on the process of using sparse observation data to determine the orbit of the spacecraft without any prior information. The standard regression process is to learn a map from real numbers to real numbers, but the approach put forward in this paper is to map from probability distributions to real-valued responses. According to the new algorithm, the number of orbital elements can be predicted by embedding the probability distribution into the reproducing kernel Hilbert space. While making full use of the edge of big data, it also avoids the problem that the algorithm cannot converge due to improper initial values in precise OD. The simulation experiment proves the effectiveness, robustness, and rapidity of the algorithm in the presence of noise in the measurement data.
Highlights
In the past decade, with the advances of micro-satellite technology and the reduced costs of entering space, the number of space missions saw a rapid growth
Based on the traditional regression problem in machine learning, this paper proposes a method for orbit determination by distribution regression
This method does not rely on the prior information of the orbit and the dynamic model of the spacecraft, but only uses the observation data
Summary
With the advances of micro-satellite technology and the reduced costs of entering space, the number of space missions saw a rapid growth. An orbit determination method of spacecraft based on distribution regression and analyzed the distribution density. Under this framework, the convergence speed was very slow for high-dimensional space scenarios (Wasserman 2006). Some studies have shown that the use of kernel embedding or its various extended forms of kernel methods to solve the distribution regression problem is an effective way (Yoshikawa et al 2014). Szabó et al (2015) reproduced this problem and significantly improved the prediction accuracy via distribution regression method in comparison to the traditional density function method. This paper, without making a priori assumption about the orbit, uses distribution regression method to determine the orbit for spacecraft with the range-only information of the ground station. A weighted Fastfood algorithm is proposed to improve efficiency of the kernel trick which is often used to solve the distribution regression problems
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