Observability Analysis for Orbit Determination Using Spaceborne Gradiometer

Abstract

The application of a spaceborne gradiometer to satellite orbit determination has been proposed in recent years. The advantages lie in its full autonomy and its immunity against spoofing attacks. The objective of this paper is to study the observability of the spaceborne gradiometer-based orbit determination (SGOD) system. To address the problem of unknown biases in spaceborne gradiometer measurements, the joint estimation of satellite orbital states and gradiometer biases is adopted. Then, the system observability matrices are formulated based on the theory of nonlinear observability. The local weak observability is assessed numerically by singular values and condition numbers of the observability matrices. A special unobservable case is demonstrated, which is the circular orbit in the Keplerian two-body model. Different orbital parameters, attitude control modes, and gravity models are furtherly employed to analyze their effects on system observability. The observability analysis shows that low altitudes, large eccentricities, large inclinations, attitude maneuverings, and the J2 perturbation can improve the system observability. Furthermore, a numerical simulation using the extended Kalman filter (EKF) is developed to obtain accuracies and convergence rates of the SGOD system. Effects of orbital parameters, attitude control modes, and the J2 perturbation on orbit determination results are also studied. It is shown that the simulation results agree with the observability analysis. Using a spaceborne gradiometer with 0.1 E (1 E=10−9 s−2) accuracy, position accuracy of tens of meters is achieved for a low Earth orbit.