Andrea Scorsoglio, The University of Arizona; Andrea D’Ambrosio, The University of Arizona; Luca Ghilardi, The University of Arizona; Roberto Furfaro, The University of Arizona; Vishnu Reddy, The University of Arizona
Keywords: Orbit determination, Physics informed neural networks, Cislunar space monitoring
Abstract:
Since the beginning of space exploration, determining the orbit of a spacecraft, known as orbit determination (OD), has been a critical issue. The success of every mission hinges on accurately estimating the spacecraft’s state at any given time. This reliable and precise state estimation is crucial for planning necessary adjustments and tasks, such as station-keeping and correction maneuvers, as well as missions involving relative motion, like rendezvous and docking. In recent years, there has been a growing interest in OD in the cislunar space, as the Moon becomes a target for both human and robotic exploration. Specifically, with the Lunar Orbital Platform-Gateway’s development as a lunar outpost orbiting one of the Lagrangian points in the Earth-Moon system, there has been renewed attention on OD in the cislunar space.
When conducting missions in Low Earth Orbits (LEO), state estimation measurements can be obtained from multiple sources and are generally straightforward to acquire, such as using onboard Global Positioning System (GPS) or ground-based observations. There are two commonly used techniques for Orbit Determination (OD): Initial Orbit Determination (IOD) and statistical estimation methods. IOD methods, including Gauss Method, Double-R Iteration, or Goodings Method, only require a small set of angular measurements to estimate an orbit. In contrast, statistical orbit determination methods rely on a larger collection of measurements to refine the estimate and can be categorized into batch algorithms (commonly referred to as least squares) or sequential algorithms (such as the Kalman filter and its variants), which estimate the initial state and current state in real time, respectively. These methods are interdependent and typically require a track initialization using IOD methods, followed by batch least squares, and finally an online orbit determination method using the solution from the previous step as an initial reference trajectory. However, implementing this procedure for objects in cislunar space is challenging and requires a thorough understanding of measurement quality.
The application of standard space traffic management techniques to objects in cislunar space has been found to produce inadequate results or be unusable altogether. In the past, spacecraft traveling towards the Moon have typically used a combination of ground-based initial state updates and inertial measurements. Although these methods are effective, they are prone to error drift caused by numerical integration. For cooperative objects in cislunar space, such as the ARTEMIS spacecrafts, orbit determination is now achieved using a batch least-squares method that analyzes range and Doppler tracking measurements obtained from the NASA Deed Space Network (DSN). This method is also employed for tracking deep-space satellites, including those located further away from the Moon. Despite its ability to reduce estimation error to less than 0.1 km and 0.1 cm/s for position and velocity, respectively, this method cannot be utilized for non-cooperative objects. In such cases, orbit determination can only be accomplished through optical observations. However, for cislunar objects whose dynamics is chaotic, most orbit determination techniques can only provide state estimates for short periods close to the observation time. Additionally, if the non-cooperative object is an artificial satellite, orbit determination is nearly impossible due to the need for frequent station-keeping maneuvers that cannot be accounted for in the OD process unless they are known, further degrading its capabilities.
The objective of this paper is to perform orbit determination in cislunar space using angle only observations in a restricted perturbed two body problem framework. Our approach utilizes Physics Informed Neural Networks (PINN), a unique type of neural network designed for solving forward and inverse problems governed by parametric differential equations. To address the OD problem, we treat it as a dynamical problem and aim to estimate the solution of the governing differential equations based on observation data. To achieve this, we use a neural network to approximate the solution of the system of differential equations, which is trained by incorporating the dynamical model into the neural network’s loss function as a regularizer. This ensures that the network’s training is penalized when the physics of the problem is violated. By including the maneuvers as unknown dynamical components in the equations of motion, the system is capable of estimating both the state of a maneuvering target and the maneuvers themselves at any time within the observation span using passive angle-only observations, without requiring any initial guess or integration. The method will be tested on synthetically generated data at first to prove its capabilities in a controlled environment. Then the method will be tested on real angle-only observation data of cislunar objects acquired by the telescopes of the Space4 Center at the University of Arizona located in Tucson, Arizona.
Date of Conference: September 19-22, 2023
Track: Machine Learning for SDA Applications