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On the Feasibility of Orbit Determination From Gravity Gradient Invariants

机译：论重力梯度不变的轨道测定的可行性

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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 Cramer-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.
机译：最近的研究已经证明了用于航天器轨道轨道测定的全张力重力梯度的能力。优势在于其独立性与地面系统的独立性及其免疫力避免欺骗攻击。常见做法是使用地球旋转参数和星传感器测量来将方向贡献与重力梯度隔离，这意味着轨道确定精度受到态度数据质量的影响。本文调查使用重力梯度不变的轨道测定的可行性，而不是全张力重力梯度，以消除帧变换的态度信息的必要性。首先通过制定轨道元素和地理距离和纬度之间的几何关系来局部解释轨道可观察性，其后者可以从重力梯度不变量获得。然后，开发了一种基于后克拉-RAO下限的计算的协方差分析技术以评估轨道确定精度。假设由于带宽限制而导致的重力梯度偏置已经校准。进行模拟，以分析采样率，轨道倾斜，轨道高度和成绩计噪声水平的影响。结果表明，与使用全张力重力梯度的轨道确定相比，重力梯度不变量的轨道轨道偏离不变的轨道测定具有更好的位置精度，而是在轨道和交叉轨道方向上具有劣化的精度。协方差分析技术应用于来自重力场和稳态海洋循环探险家的实线数据。已经实现了径向，沿轨道和1.8,78和255米的交叉轨道位置精度。未来的研究将在实际测量中处理偏见以实现真正的轨道决定。

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