论文标题
关于超过四个航天器星座中的混叠效应条件
On the Conditions of Aliasing Effects in Constellations with More than Four Spacecraft
论文作者
论文摘要
k过滤/波望远镜方法已成功地应用于群集II和MMS的四翼飞船测量值，揭示了四维功率频谱密度$ \ textrm {psd}（ω，\ m athbf k）$。随着星座内的航天器数量的增加，几何形状变得更加复杂，很难找到类似第一brillouin的区域，因为我们无法使用已知的公式来计算该区域的几何形状。据我们所知，尚未提出一项关于混叠效应的定量研究以及尚未提出超过4个航天器的星座的第一brillouin样区域的几何形状。因此，我们提供了一种方法来估计和比较多飞机运动物星座中类似第一木的几何形状。波形空间中相应的晶格的相应阵列形成了布里渊区。我们将符合``单板''的预设PSD和``平板 + 2D''模式作为基准，并使用4、5和9虚拟飞机将它们与重建的PSD进行比较。我们的结果验证了类似布罗林的区域的估计。该方法可能会限制混叠效应。我们提出的方法可能对使用多空间星座的未来探索会话的设计和分析很有用。
The k-filtering/wave telescope method has been successfully applied to the four-spacecraft measurements from Cluster II and MMS, revealing the four-dimensional power spectral density $\textrm{PSD}(ω, \mathbf k)$. As the number of spacecraft within a constellation increases, the geometry becomes more complicated, and it is harder to find the first-Brillouin-like zone, since we cannot use known formulas to calculate the geometry of the zone. To our knowledge, a quantitative study on the aliasing effects as well as the geometry of the first-Brillouin-like zone for the constellation with more than 4 spacecraft has not been proposed yet. Herewith we provide a method to estimate and compare the geometry of the first-Brillouin-like zone in multi-spacecraft constellations. The corresponding array of reciprocal lattice in the wavevector space forms the Brillouin zone. We set the preset PSDs conforming to the ``slab-only' and ``slab + 2D' patterns as the benchmark, and compare them with the reconstructed PSDs using 4, 5, and 9 virtual spacecraft. Our results validates the estimation of the Brillouin-like zones. The method may provide a constraint of aliasing effects. Our proposed method may be useful for the design and analysis of future exploration sessions with multi-spacecraft constellation.
