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

The authors regret that this paper [1] contains typographical errors in the sentence between Equation (16) and Equation (17), as well as in Equations (18), (20), (21), (34), (36) and (37), with respect to the point that they use the wrong notations $t_1$ − $t_N$, while the correct notations are $t_k$ − $t_{k+N-1}$. The correct form is shown in

Table 1. Correct form of equations.

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)	$w={\left[\begin{array}{ccc}-∆\nabla \mathsf{\omega }\left(t_1\right)& \cdots & -∆\nabla \mathsf{\omega }\left(t_1\right)\end{array}\right]}^T$	$w={\left[\begin{array}{ccc}-∆\nabla \mathsf{\omega }\left(t_k\right)& \cdots & -∆\nabla \mathsf{\omega }\left(t_{k+N-1}\right)\end{array}\right]}^T$
6	Equation (21)	$G=$ $\left[\begin{array}{ccc}\frac{\partial ∆\nabla r\left(t_1\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_1\right)}{\partial y}& \frac{\partial ∆\nabla r\left(t_1\right)}{\partial z}\\ ⋮& ⋮& ⋮\\ \frac{\partial ∆\nabla r\left(t_N\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_N\right)}{\partial y}& \frac{\partial ∆\nabla r\left(t_N\right)}{\partial z}\end{array}\right]$	$G=$ $\left[\begin{array}{ccc}\frac{\partial ∆\nabla r\left(t_k\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_k\right)}{\partial y}& \frac{\partial ∆\nabla r\left(t_k\right)}{\partial z}\\ ⋮& ⋮& ⋮\\ \frac{\partial ∆\nabla r\left(t_{k+N-1}\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_{k+N-1}\right)}{\partial y}& \frac{\partial ∆\nabla r\left(t_{k+N-1}\right)}{\partial z}\end{array}\right]$
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)	$w={\left[\begin{array}{ccc}-∆\nabla \omega \left(t_1\right)& \cdots & -∆\nabla \omega \left(t_1\right)\end{array}\right]}^T$	$w={\left[\begin{array}{ccc}-∆\nabla \mathsf{\omega }\left(t_k\right)& \cdots & -∆\nabla \mathsf{\omega }\left(t_{k+N-1}\right)\end{array}\right]}^T$
8	Equation (37)	$G=\left[\begin{array}{cc}\frac{\partial ∆\nabla r\left(t_1\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_1\right)}{\partial y}\\ ⋮& ⋮\\ \frac{\partial ∆\nabla r\left(t_N\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_N\right)}{\partial y}\end{array}\right]$	$G=\left[\begin{array}{cc}\frac{\partial ∆\nabla r\left(t_k\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_k\right)}{\partial y}\\ ⋮& ⋮\\ \frac{\partial ∆\nabla r\left(t_{k+N-1}\right)}{\partial x}& \frac{\partial ∆\nabla r\left(t_{k+N-1}\right)}{\partial y}\end{array}\right]$

.

The error, not noticed during the proofreading process, was a simple mistype. The analytical developments and the results following these equations are in no way adversely affected by this typo. The authors would like to apologize for any inconvenience caused. The manuscript will be updated and the original will remain online on the article webpage.