The m-dimensional spatial Nyquist limit using the wave telescope for larger numbers of spacecraft

IF 1.7 4区 地球科学 Q3 ASTRONOMY & ASTROPHYSICS
Leonard Schulz, Karl-Heinz Glassmeier, Ferdinand Plaschke, Simon Toepfer, Uwe Motschmann
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引用次数: 0

Abstract

Abstract. Spacecraft constellations consisting of multiple satellites are becoming more and more interesting not only for commercial use but also for space science missions. The proposed and accepted scientific multi-satellite missions that will operate within Earth's magnetospheric environment, like HelioSwarm, require researchers to extend established methods for the analysis of multi-spacecraft data to more than four spacecraft. The wave telescope is one of those methods. It is used to detect waves and characterize turbulence from multi-point magnetic field data, by providing spectra in reciprocal position space. The wave telescope can be applied to an arbitrary number of spacecraft already. However, the exact limits of the detection for such cases are not known if the spacecraft, acting as sampling points, are irregularly spaced. We extend the wave telescope technique to an arbitrary number of spatial dimensions and show how the characteristic upper detection limit in k space imposed by aliasing, the spatial Nyquist limit, behaves for irregularly spaced sampling points. This is done by analyzing wave telescope k-space spectra obtained from synthetic plane wave data in 1D up to 3D. As known from discrete Fourier transform methods, the spatial Nyquist limit can be expressed as the greatest common divisor in 1D. We extend this to arbitrary numbers of spatial dimensions and spacecraft. We show that the spatial Nyquist limit can be found by determining the shortest possible basis of the spacecraft distance vectors. This may be done using linear combination in position space and transforming the obtained shortest basis to k space. Alternatively, the shortest basis can be determined mathematically by applying the modified Lenstra–Lenstra–Lovász (MLLL) algorithm combined with a lattice enumeration algorithm. Thus, we give a generalized solution to the determination of the spatial Nyquist limit for arbitrary numbers of spacecraft and dimensions without any need of a priori knowledge of the measured data. Additionally, we give first insights into the application to real-world data incorporating spacecraft position errors and minimizing k-space aliasing. As the wave telescope is an estimator for a multi-dimensional power spectrum substituting spatial Fourier transform, the results of this analysis can be applied to power spectral density estimation via Fourier transform or other methods making use of irregular sampling points. Therefore, our findings are also of interest to other fields of signal processing.
m维空间奈奎斯特极限使用波望远镜对更大数量的航天器
摘要由多颗卫星组成的航天器星座不仅在商业用途上,而且在空间科学任务上也变得越来越有趣。在地球磁层环境中运行的科学多卫星任务,如HelioSwarm,要求研究人员将现有的多航天器数据分析方法扩展到四个以上的航天器。波望远镜就是其中一种方法。它通过在互反位置空间中提供光谱,用于从多点磁场数据中检测波浪和表征湍流。波望远镜已经可以应用于任意数量的航天器。然而,如果作为采样点的航天器的间隔不规则,则不知道这种情况下检测的确切限度。我们将波望远镜技术扩展到任意数量的空间维度,并展示了k空间中由混叠施加的特征检测上限,即空间奈奎斯特极限,对不规则间隔采样点的表现。这是通过分析从一维到三维合成平面波数据获得的波望远镜k空间光谱来完成的。从离散傅里叶变换方法可知,空间奈奎斯特极限可以表示为一维中的最大公约数。我们将其扩展到任意数量的空间维度和航天器。我们证明空间奈奎斯特极限可以通过确定航天器距离向量的最短可能基来找到。这可以使用位置空间中的线性组合,并将得到的最短基变换到k空间中。或者,可以通过将改进的Lenstra-Lenstra-Lovász (MLLL)算法与点阵枚举算法相结合,在数学上确定最短的基。因此,我们给出了确定任意数量的航天器和尺寸的空间奈奎斯特极限的广义解,而不需要对测量数据的先验知识。此外,我们首次深入了解了将航天器位置误差和最小化k空间混叠应用于现实世界数据的应用。由于波望远镜是替换空间傅里叶变换的多维功率谱估计器,因此本分析结果可应用于傅里叶变换或利用不规则采样点的其他方法进行功率谱密度估计。因此,我们的发现也对信号处理的其他领域感兴趣。
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来源期刊
Annales Geophysicae
Annales Geophysicae 地学-地球科学综合
CiteScore
4.30
自引率
0.00%
发文量
42
审稿时长
2 months
期刊介绍: Annales Geophysicae (ANGEO) is a not-for-profit international multi- and inter-disciplinary scientific open-access journal in the field of solar–terrestrial and planetary sciences. ANGEO publishes original articles and short communications (letters) on research of the Sun–Earth system, including the science of space weather, solar–terrestrial plasma physics, the Earth''s ionosphere and atmosphere, the magnetosphere, and the study of planets and planetary systems, the interaction between the different spheres of a planet, and the interaction across the planetary system. Topics range from space weathering, planetary magnetic field, and planetary interior and surface dynamics to the formation and evolution of planetary systems.
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