An iterative scheme to learn system dynamics of space objects from partial state information

Improved computational infrastructure and abundant data have made studying physical systems comparatively easy in recent years. Data-Driven techniques based on system identification and machine learning are leading efforts in this domain. However, the ability to learn from partial measurements, owing to various reasons such as corrupted/unusable data or just the inability to capture certain types of information due to lack of sensors is emerging to be a central challenge. Restricted observational capabilities and lack of robust sensors within the aerospace domain, specifically resident space object observation, requires alternative compensation techniques. Currently, range measurements based on radar/optics are most commonly used for orbit determination as true state information from ephemeris data is almost exclusively reserved for satellite operators. This paper aims to develop a technique that can reconstruct the complete dynamics of a space object's dynamics from low-fidelity incomplete state measurements. Methods developed are applied to different types of measurements; generated from mathematical models, obtained from satellite operators, and noisy models replicating sensor observations. This work proposes an iterative learning scheme inspired by the value function iteration framework for solving Hamilton–Jacobi–Bellman (HJB) equations. % The method of time-delay embedding justified by Taken's theorem has demonstrated with reasonable success the reconstruction of low dimensional, non-linear systems purely from scalar time series. An imperfect version of full-state data is created by using suitable initial guesses for the missing states. The guesses and the estimates of the dynamics are then iteratively improved within this scheme. It can be split into a two-step process with a nested loop structure, an inner and an outer loop. The outer loop will function as a state updater and will provide new guesses as input to each iteration. The inner loop is a data-driven technique that can learn the spatio-temporal evolution of a physical system from data. This work considers i) a Hankel-based DMD (Dynamic Mode Decomposition) method, ii) a Feed-forward neural network, and iii) an LSTM(Long Short-Term Memory) network as suitable candidates for the inner loop. This paper presents initial ideas, methods, and observations.