Ryui Hara, Kyushu university; Yasuhiro Yoshimura, Kyushu university; Toshiya Hanada, Kyushu university
Keywords: Light Curves, Attitude, Gaussian Process Regression
Abstract:
Recent advances of large constellations drastically increase the population of resident space objects (RSOs) around the Earth. Moreover, once a collision or breakup of satellites occurs, a lot of space debris is generated. Thus, space domain awareness (SDA), aiming to detect, tracking, and understanding the motion of Earth-orbiting RSOs, is becoming more important in managing the traffic of satellites. For highly-accurate SDA, much information such as orbit, attitude, and shape of RSOs enables improving the accuracy of state propagation of RSOs. The attitude of RSOs is especially a key state for the improvement, because nongravitational forces such as solar radiation pressure and atmospheric drag depend on the object’s attitude. In this context, this study focuses on the attitude estimation of an RSO using light curves.
Light curves are a series of space objects’ brightness observed by ground-based telescopes. Light curves depend on the RSO’s orbit, attitude, shape, and surface properties. In other words, these characteristics can be inversely deduced from light curves. This is known as light curve inversion and is a promising and cost-effective method to estimate the RSO attitude. Light curve inversion has been studied for a long time in the field of astronomy to determine the axis and shape of asteroids. Although asteroids are usually assumed to have a convex shape and diffusive reflection, the RSOs have nonconvex shape and optical properties including anisotropic reflection, which significantly makes the light curve inversion of the RSOs challenging. In previous studies, various attitude estimation methods via light curves are proposed. For example, a study determines an RSO’s attitude by using the 3-D virtual reality model, and another one estimates the RSO attitude by using Bayesian filter such as particle filter and unscented Kalman filter. However, most of the proposed methods assume that the target object’s parameters such as shape and surface parameters are known, though they are usually unknown for space debris generated by a collision or breakup. When the object’s shape and surface parameters are unknown, the light curve cannot be calculated because the light curves are parametrically formulated with the object’s orbit, attitude, shape, and surface parameters.
This study tackles this problem by combining Gaussian process regression (GPR) and unscented Kalman filter (UKF), called GP-UKF. The GP-UKF is an estimation method that combines the UKF with the GPR. The GPR is one of the machine learning methods and enables a non-parametric regression. The UKF is one of the Bayesian filters and is used for filtering the noise and estimating the state of non-linear systems from observed values. A conventional UKF consists of a prediction step and an observation step in the estimation sequence, which require parametric models. On the other hand, the GP-UKF uses the GPR for representing the models non-parametrically. This study uses the GPR to describe the light curve model in the estimation sequence, which requires no information of shape and surface parameters. Thus, the non-resolved object’s attitude can be estimated from the light curves with GP-UKF even if the object shape and surface parameters are unknown. Thanks to a non-parametric model, this estimation method is robust against those parameters.
Although GPR would enable describing the system model and light model in the prediction step and observation step, respectively, this study focuses on the GPR of the light curve model. To this end, the training data of the GPR are calculated by varying the initial attitude and angular rate of the object by numerical simulations. Such sequential attitude and angular rate are used as the input of the GPR, while the light curves are used as the output to configure the GPR model. In this numerical simulation for training data, a Box-Wing object is used. To verify the GP-UKF for the attitude estimation with light curves, a different initial state from the training data is examined. The numerical simulation results evaluate the errors between the estimated attitude and the true one and verify the GP-UKF for the light curve inversion. In addition, the attitude estimation with different surface parameters from training data is examined to verify GP-UKF estimation method’s robustness.
Date of Conference: September 17-20, 2024
Track: Satellite Characterization