_applied sciences_  
_Correction_  
**Correction: [PERSON] et al. Mathematical Considerations for Unmanned Aerial Vehicle Navigation in the Magnetic Field of Two Parallel Transmission Lines. _Appl. Sci._**2021**, _11_, 3323  
**[PERSON], [PERSON] \({}^{\star}\)\({}^{\copyright}\) and [PERSON] \({}^{\copyright}\)**  
\({}^{\star}\) Correspondence: [EMAIL_ADDRESS]  
The authors wish to make the following changes to their paper [1]. **1. Changes in Section 2.2: Orientation Determination**  
The results regarding the roll angle calculation in Section 2.2: Orientation Determination are wrong and should be corrected. The following original text is affected:  
\({}^{\star}\) The roll angle \(\gamma\) can also be computed by exploiting the zero field property (2). However, the rotation matrix \(R_{G}^{L_{x}}\) does not in general contain \(\gamma\) in its \(x\)-row. Thus, a different sensor \(k\) must have a different local frame \(L_{k}\) in order for the zero to appear in the \(y\)- or \(z\)-row containing all three angles. This can be achieved by, for example, placing the sensor so that it is rotated relative to the UAV body frame \(L_{u}\) by an angle \(\delta\) about the \(y\)-axis, i.e., it is:  
\[R_{L_{u}}^{L_{k}}=R_{y}(\delta) \tag{11}\]  
Then, from Equation (5), it follows that after applying the coordinate transformation \(A=R_{G}^{L_{x}}R_{y}^{T}(\delta)R_{L_{u}}^{G}\), the vector \(\overset{\rightarrow}{B}\left(\overset{\rightarrow}{p}_{k}\right)\) is expressed in \(L_{u}\):  
\[\overset{\rightarrow}{B}\left(\overset{\rightarrow}{p}_{k}\right)=A \overset{\rightarrow}{B}\left(\overset{\rightarrow}{p}_{k}\right)=R_{G}^{L_ {u}}R_{y}^{T}(\delta)R_{L_{u}}^{G}R_{y}(\delta)\overset{\rightarrow}{v}_{k}, \tag{12}\] \[\text{for }\delta=\frac{\pi}{2}\Rightarrow \begin{pmatrix} \beta_{x}\left(\overset{\rightarrow}{p}_{k}\right)\\ \beta_{y}\left(\overset{\rightarrow}{p}_{k}\right)\\ 0\end{pmatrix} =R_{G}^{L_{u}}\overset{\rightarrow}{v}_{k}.\]  
From Equation (12), it follows that the rotation of \(\overset{\rightarrow}{B}\left(\overset{\rightarrow}{p}_{k}\right)\) for a given angle \(\delta=\frac{\pi}{2}\) around the \(y\)-axis of \(L_{u}\) has forced the \(z\)-component of the resulting vector \(\overset{\rightarrow}{B}\left(\overset{\rightarrow}{p}_{k}\right)\) to zero:  
\[\beta_{z}\left(\overset{\rightarrow}{p}_{k}\right)=0=\left(R_{G}^{L_{u}} \overset{\rightarrow}{v}_{k}\right)\overset{\rightarrow}{e}_{z}, \tag{13}\]  
where \(\overset{\rightarrow}{e}_{z}\) is the Cartesian unit vector. Then, in a first step, Equation (13) can be written as:  
\[0=\left(s_{\gamma}s_{\alpha}+c_{\gamma}c_{\alpha}s_{\beta}\right)v_{kx}+ \left(c_{\gamma}s_{\beta}s_{\alpha}-c_{\alpha}s_{\gamma}\right)v_{ky}+c_{ \gamma}c_{\beta}v_{kz}.\]  
Next, the division by \(c_{\gamma}\) forms the tangent function \(t_{\gamma}\), which can be isolated and finally solved for \(\gamma\):  
\[ \begin{split} 0=\left(t_{\gamma}s_{\alpha}+c_{\alpha}s_{\beta} \right)v_{kx}+\left(s_{\beta}s_{\alpha}-c_{\alpha}t_{\gamma}\right)v_{ky}+c_{ \beta}v_{kz}\\ \Rightarrow\gamma=atan(\frac{v_{ky}s_{\alpha}+v_{\alpha}s_{ \beta}c_{\alpha}+v_{\alpha}c_{\beta}}{v_{ky}c_{\alpha}-v_{\alpha}s_{\alpha}}) \end{split}  \tag{14}\]  
The sensor can be placed anywhere on the UAV. However, the result only applies to the local frame definition in (11). Theoretically, arbitrary local frame definitions can be chosen,but in this case, there is no zero in any coordinate, and the whole system of Equation (12) must be solved since the sensor position \(\overrightarrow{p}_{k}\) is unknown. However, the equations are complicated, and it is questionable whether an analytical solution exists. The presented formulas are valid if the UAV angles are within the definition range \(D\), respectively, \(\alpha\), \(\beta\), \(\gamma\in D=[-\frac{\gamma}{2},\frac{\gamma}{2}]\).