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.

中文翻译：

---

利用重力梯度不变量确定轨道的可行性

在最近的研究中已经证明了全张量重力梯度确定航天器轨道的能力。优点在于它独立于地面系统，并且不受欺骗攻击的影响。一种常见的做法是使用地球旋转参数和恒星传感器测量值来隔离定向对重力梯度的影响，这意味着定轨精度会受到姿态数据质量的影响。本文研究了使用重力梯度不变式代替全张量重力梯度确定轨道的可行性，从而消除了姿态信息用于帧转换的必要性。首先通过公式化轨道元素与地心距离和纬度之间的几何关系来部分解释轨道的可观测性，后者可以从重力梯度不变式获得。然后，开发了基于后克拉姆-拉奥下界的计算的协方差分析技术，以评估轨道确定精度。假定已经校准了由于带宽限制而引起的重力梯度偏差。进行仿真以分析采样率，轨道倾角，轨道高度和梯度仪噪声水平的影响。结果表明，与使用全张量重力梯度进行的轨道确定相比，根据重力梯度不变性进行的轨道确定在径向方向上具有更好的位置精度，但在沿轨道和跨轨道方向上的精度有所降低。协方差分析技术应用于重力场和稳态海洋环流探测器的真实飞行数据。径向，沿轨道和跨轨道的位置精度分别为1.8 m，78 m和255 m。未来的研究将处理实际测量中的偏差，以实现真实的轨道确定。