基于 Chebyshev 多项式近似的空间碎片可达域 求解算法

To address the conflict between real-time performance and accuracy in existing reachable domain algorithms for space debris collision warning，a novel algorithm based on Chebyshev polynomial approximation is proposed. This method establishes the mapping from the velocity increment sphere of space debris to the envelope surface of the reachable domain using Chebyshev polynomial fitting. A sparse sampling strategy on the velocity increment sphere is proposed to characterize the mapping relationship via orbit propagation with a small number of samples. Then，the reachable domain envelope of space debris is reconstructed with high precision through polynomial interpolation of the sample orbits，enabling efficient and high-precision computation of the reachable domain. The proposed method is applied to the calculation of reachable domains for medium and low Earth orbit space debris. Simulation results demonstrate that the proposed method achieves accuracy close to the Monte Carlo method with only about 1% of the computational cost and an average error of less than 1 meter.