M Harsha, Singh Gurpreet, Kumar Vinod, Buduru Arun Balaji, Biswas Sanat K
Indraprastha Institute of Information Technology Delhi, New Delhi, 110020, India.
U R Rao Satellite Centre, ISRO, Bengaluru, 560071, India.
Sci Rep. 2024 Feb 9;14(1):3350. doi: 10.1038/s41598-024-51897-9.
With the sustained rise in satellite deployment in Low Earth Orbits, the collision risk from untracked space debris is also increasing. Often small-sized space debris (below 10 cm) are hard to track using the existing state-of-the-art methods. However, knowing such space debris' trajectory is crucial to avoid future collisions. We present a Physics Informed Neural Network (PINN)-based approach for estimation of the trajectory of space debris after a collision event between active satellite and space debris. In this work, we have simulated 8565 inelastic collision events between active satellites and space debris. To obtain the states of the active satellite, we use the TLE data of 1647 Starlink and 66 LEMUR satellites obtained from space-track.org. The velocity of space debris is initialized using our proposed velocity sampling method, and the coefficient of restitution is sampled from our proposed Gaussian mixture-based probability density function. Using the velocities of the colliding objects before the collision, we calculate the post-collision velocities and record the observations. The state (position and velocity), coefficient of restitution, and mass estimation of un-tracked space debris after an inelastic collision event along with the tracked active satellite can be posed as an optimization problem by observing the deviation of the active satellite from the trajectory. We have applied the classical optimization method, the Lagrange multiplier approach, for solving the above optimization problem and observed that its state estimation is not satisfactory as the system is under-determined. Subsequently, we have designed Deep Neural network-based methods and Physics Informed Neural Network (PINN) based methods for solving the above optimization problem. We have compared the performance of the models using root mean square error (RMSE) and interquartile range of the predictions. It has been observed that the PINN-based methods provide a better estimation performance for position, velocity, mass and coefficient of restitution of the space debris compared to other methods.
随着低地球轨道卫星部署的持续增加，未被追踪的空间碎片造成碰撞的风险也在上升。通常，小型空间碎片（直径小于10厘米）很难用现有的先进方法进行追踪。然而，了解此类空间碎片的轨迹对于避免未来的碰撞至关重要。我们提出了一种基于物理信息神经网络（PINN）的方法，用于估计有源卫星与空间碎片碰撞事件后空间碎片的轨迹。在这项工作中，我们模拟了8565次有源卫星与空间碎片之间的非弹性碰撞事件。为了获取有源卫星的状态，我们使用了从space-track.org获得的1647颗星链卫星和66颗狐猴卫星的两行轨道数据（TLE）。空间碎片的速度使用我们提出的速度采样方法进行初始化，恢复系数从我们提出的基于高斯混合的概率密度函数中采样。利用碰撞前碰撞物体的速度，我们计算碰撞后的速度并记录观测结果。通过观察有源卫星与轨迹的偏差，可以将非弹性碰撞事件后未被追踪的空间碎片以及被追踪的有源卫星的状态（位置和速度）、恢复系数和质量估计作为一个优化问题提出。我们应用经典优化方法——拉格朗日乘数法来解决上述优化问题，发现由于系统欠定，其状态估计并不令人满意。随后，我们设计了基于深度神经网络的方法和基于物理信息神经网络（PINN）的方法来解决上述优化问题。我们使用均方根误差（RMSE）和预测的四分位间距比较了模型的性能。结果发现，与其他方法相比，基于PINN的方法在空间碎片的位置、速度、质量和恢复系数估计方面提供了更好的性能。
