# Correction: Tanaka, T., et al. Dual-Satellite Lunar Global Navigation System Using Multi-Epoch Double-Differenced Pseudorange Observations. Aerospace 2020, 7, 122

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## Reference

- Tanaka, T.; Ebinuma, T.; Nakasuka, S. Dual-Satellite Lunar Global Navigation System Using Multi-Epoch Double-Differenced Pseudorange Observations. Aerospace
**2020**, 7, 122. [Google Scholar] [CrossRef]

Page | Part | Published Form | Corrected Form |
---|---|---|---|

6 | Sentence between Equations (16) and (17) | ${t}_{1}$− ${t}_{N}$ | ${t}_{k}$− ${t}_{k+N-1}$ |

6 | Equation (18) | $R={\left[\begin{array}{ccc}R\left({t}_{1}\right)& \cdots & R\left({t}_{N}\right)\end{array}\right]}^{T}$ | $R={\left[\begin{array}{ccc}R\left({t}_{k}\right)& \cdots & R\left({t}_{k+N-1}\right)\end{array}\right]}^{T}$ |

6 | Equation (20) | $w={\left[\begin{array}{ccc}-\u2206\nabla \mathsf{\omega}\left({t}_{1}\right)& \cdots & -\u2206\nabla \mathsf{\omega}\left({t}_{1}\right)\end{array}\right]}^{T}$ | $w={\left[\begin{array}{ccc}-\u2206\nabla \mathsf{\omega}\left({t}_{k}\right)& \cdots & -\u2206\nabla \mathsf{\omega}\left({t}_{k+N-1}\right)\end{array}\right]}^{T}$ |

6 | Equation (21) | $G=$ $\left[\begin{array}{ccc}\frac{\partial \u2206\nabla r\left({t}_{1}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{1}\right)}{\partial y}& \frac{\partial \u2206\nabla r\left({t}_{1}\right)}{\partial z}\\ \vdots & \vdots & \vdots \\ \frac{\partial \u2206\nabla r\left({t}_{N}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{N}\right)}{\partial y}& \frac{\partial \u2206\nabla r\left({t}_{N}\right)}{\partial z}\end{array}\right]$ | $G=$ $\left[\begin{array}{ccc}\frac{\partial \u2206\nabla r\left({t}_{k}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{k}\right)}{\partial y}& \frac{\partial \u2206\nabla r\left({t}_{k}\right)}{\partial z}\\ \vdots & \vdots & \vdots \\ \frac{\partial \u2206\nabla r\left({t}_{k+N-1}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{k+N-1}\right)}{\partial y}& \frac{\partial \u2206\nabla r\left({t}_{k+N-1}\right)}{\partial z}\end{array}\right]$ |

8 | Equation (34) | $R={\left[\begin{array}{ccc}R\left({t}_{1}\right)& \cdots & R\left({t}_{N}\right)\end{array}\right]}^{T}$ | $R={\left[\begin{array}{ccc}R\left({t}_{k}\right)& \cdots & R\left({t}_{k+N-1}\right)\end{array}\right]}^{T}$ |

8 | Equation (36) | $w={\left[\begin{array}{ccc}-\u2206\nabla \omega \left({t}_{1}\right)& \cdots & -\u2206\nabla \omega \left({t}_{1}\right)\end{array}\right]}^{T}$ | $w={\left[\begin{array}{ccc}-\u2206\nabla \mathsf{\omega}\left({t}_{k}\right)& \cdots & -\u2206\nabla \mathsf{\omega}\left({t}_{k+N-1}\right)\end{array}\right]}^{T}$ |

8 | Equation (37) | $G=\left[\begin{array}{cc}\frac{\partial \u2206\nabla r\left({t}_{1}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{1}\right)}{\partial y}\\ \vdots & \vdots \\ \frac{\partial \u2206\nabla r\left({t}_{N}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{N}\right)}{\partial y}\end{array}\right]$ | $G=\left[\begin{array}{cc}\frac{\partial \u2206\nabla r\left({t}_{k}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{k}\right)}{\partial y}\\ \vdots & \vdots \\ \frac{\partial \u2206\nabla r\left({t}_{k+N-1}\right)}{\partial x}& \frac{\partial \u2206\nabla r\left({t}_{k+N-1}\right)}{\partial y}\end{array}\right]$ |

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## Share and Cite

**MDPI and ACS Style**

Tanaka, T.; Ebinuma, T.; Nakasuka, S.
Correction: Tanaka, T., et al. Dual-Satellite Lunar Global Navigation System Using Multi-Epoch Double-Differenced Pseudorange Observations. *Aerospace* 2020, *7*, 122. *Aerospace* **2021**, *8*, 8.
https://doi.org/10.3390/aerospace8010008

**AMA Style**

Tanaka T, Ebinuma T, Nakasuka S.
Correction: Tanaka, T., et al. Dual-Satellite Lunar Global Navigation System Using Multi-Epoch Double-Differenced Pseudorange Observations. *Aerospace* 2020, *7*, 122. *Aerospace*. 2021; 8(1):8.
https://doi.org/10.3390/aerospace8010008

**Chicago/Turabian Style**

Tanaka, Toshiki, Takuji Ebinuma, and Shinichi Nakasuka.
2021. "Correction: Tanaka, T., et al. Dual-Satellite Lunar Global Navigation System Using Multi-Epoch Double-Differenced Pseudorange Observations. *Aerospace* 2020, *7*, 122" *Aerospace* 8, no. 1: 8.
https://doi.org/10.3390/aerospace8010008