Knowledge Bank

The modern world depends on space-based infrastructure for GPS, intelligence, telecommunications, weather, scientific research, and much more. And we are expanding our capabilities and usage each year, a process that is accelerated with the rise of satellite mega constellations. Accurate tracking and forecasting of resident space objects (RSO) is increasingly needed as a result to avoid collisions that can both damage key space assets and create potentially harmful debris fields. This task is not easy however due to a minimal number of measurement sources, a measurement's inability to capture full-state data, the nonlinear dynamics of orbital mechanics, and the often unknown parameters of those dynamics. Standard model identification methods struggle as a result, especially for use in long-duration propagation. We propose a recursive estimator as a solution to this problem. The idea is to adaptively estimate both the state variables and model parameters simultaneously, utilizing partial-state measurements to achieve convergence in both (states and model parameters) over time. This estimator starts off with an initial guess of model parameters to make predictions and compares those predictions to sensor measurements as they become available. Based on the perceived error between the forecast and measurement values, it executes a parameter update step, thus setting up the next cycle of forecasting. This solution was developed in MATLAB for identifying the eccentricity of an orbit, before being applied to estimation of the Earth's oblateness parameter $J2$. The results thus far have shown good convergence and an ability to handle the unknowns of the model while also making good predictions of the state variables. In the present version of the dual estimator, a simple feedback control type parameter correction step is implemented, proving to be effective under favorable conditions. Further analysis is required to understand its behavior, in particular, stability and convergence characteristics. The ultimate objective of this work is to integrate it within a larger uncertainty forecasting system with unknown parameters in a physics-based dynamic model, or, in a data-driven black box dynamic model. It could also be applied to a prognostics digital twin model where key model parameters are missing or unknown.