On the Feasibility of Orbit Determination from Gravity Gradient Invariants

The capability of full-tensor gravity gradients for spacecraft orbit determination has been demonstrated in recent studies. The advantages lie in its independence from ground-based systems and its immunity against spoofing attacks. A common practice is to use Earth rotation parameters and star sensor measurements to isolate the orientation contributions to gravity gradients, which implies that the orbit determination accuracy is affected by the quality of attitude data. This article investigates the feasibility of orbit determination using gravity gradient invariants instead of full-tensor gravity gradients in order to eliminate the necessity of attitude information for frame transformation. The orbit observability is first partially explained by formulating the geometric relationship between orbital elements and geocentric distance and latitude, the latter of which can be obtained from gravity gradient invariants. Then a covariance analysis technique based on the computation of a posterior Cramér-Rao lower bound is developed to assess the orbit determination accuracy. It is assumed that the gravity gradient biases due to bandwidth limitation have been calibrated. Simulations are carried out to analyze the effects of sampling rate, orbital inclination, orbital height, and gradiometer noise level. Results show that orbit determination from gravity gradient invariants has better position accuracy in the radial direction but has degraded accuracies in the along-track and cross-track directions compared to orbit determination using full-tensor gravity gradients. The covariance analysis technique is applied to real flight data from gravity field and steady-state ocean circulation explorer. Radial, along-track, and cross-track position accuracies of 1.8, 78, and 255 m have been achieved. Future study will deal with biases in actual measurements to fulfill real orbit determination.