Efficient and accurate error propagation in the semi-analytic orbit dynamics system for space debris

Abstract

Orbital error provides a strict accuracy description of the space object’s state in a perturbing environment and plays a vital role in space situation awareness (SSA) related tasks like space conjunction analysis. However, challenge occurs for hundreds of thousands of space debris that how efficiently and accurately can the orbital error be propagated in a way that agrees well with the nonlinear orbit dynamics system (ODS). In this paper, the problem is addressed by propagating the orbital error in the semi-analytic ODS (SODS). By applying the multiscaling technique to separate out the effects of a perturbation acting on an orbit in short-periodic and long-term time scales, the developed SODS allows the long-term error component to be propagated by numerically integrating the mean equations with 1-day step, while the short-periodic error component is analytically recovered. Performance of the error propagation in the SODS is verified using statistical state moments of 104 samples of two low-Earth-orbit (LEO) satellites. Experimental results from the Monte Carlo simulation demonstrate that the SODS is capable of propagating orbital error that can well capture the statistical characteristics of predicted states in terms of the error magnitude. More importantly, the computational efficiency of the SODS against the high-fidelity ODS is improved by nearly 95%, making it attractive for the error propagation of numerous debris.