## 2 Changes in Section 2.3: Position Determination
**_Two of the \(y\)-solutions in (18) can immediately be excluded, because they are complex._\"  
\"The square root addends in Equation (22) represented by \(S\) now can be replaced by this result, leading to:\" should be changed to \"The square root addends in Equation (18) represented by \(S\) can now be replaced by this result, leading to:\"  
\"with \(r\) and \(\varphi\) according to (24).\" should be changed to \"with \(r\) and \(\varphi\) according to (20).\"  
\"The hypothesis is true if the absolute value of the square root addends in Equation (22) is always greater than \(C|V_{z}|P^{-2}\).\" should be changed to \"The hypothesis is true if the absolute value of the square root addends in Equation (18) is always greater than \(C|V_{z}|P^{-2}\).\"  
\"Further, with \(a\), \(b\) from (23), it follows for the left and right side:\" should be changed to \"Further, with \(a\), \(b\) from (19), it follows for the left and right side:\"  
\"The two real solutions \(y_{1,2}\) can again be obtained from (25) or from the general Equation (22).\" should be changed to \"The two real solutions \(y_{1,2}\) can again be obtained from (21) or from the general Equation (18).\"  
\"Once the corresponding \(y\) is determined, in a final step, \(z\) can be calculated from Equation (20):\" should be changed to \"Once the corresponding \(y\) is determined, in a final step, \(z\) can be calculated from Equation (16):\"  
\"There are also situations where, for a given \(y\), a subset of the \(z\)-solutions in (28) can become complex.\" should be changed to \"There are also situations where, for a given \(y\), a subset of the \(z\)-solutions in (24) can become complex.\"  
\"For all solutions \(y_{1,2,3}\) obtained, \(g\geq 0\) holds, since they were obtained using the \(z^{2}\)-expression (20).\" should be changed to \"For all solutions \(y_{1,2,3}\) obtained, \(g\geq 0\) holds, since they were obtained using the \(z^{2}\)-expression (16).\"  
**3. Changes in Section 2.4: Selecting the Right Solution**  
\"Equation (28) yields four \(z\)-solutions for each \(y\)-solution of Cases (I)-(IV).\" should be changed to \"Equation (24) yields four \(z\)-solutions for each \(y\)-solution of Cases (I)-(IV).\"\"where \(y_{1,2}\) comes from Equation (27) and \(z^{2}\) comes from (20).\" should be changed to \"where \(y_{1,2}\) comes from Equation (23) and \(z^{2}\) comes from (16).\"  
\"Now, the idea is to investigate which of the eight remaining positions lead to a match with the sensor measurement \(\overrightarrow{V}\), i.e., which positions satisfy Equation (16).\" should be changed to \"Now, the idea is to investigate which of the eight remaining positions lead to a match with the sensor measurement \(\overrightarrow{V}\), i.e., which positions satisfy Equation (12).\"  
\"**Theorem 3. **_Given a sensor \(k\) that measures \(\overrightarrow{V}_{k}=\left(V_{ky},V_{bz}\right)^{T}\) and has two \(y\)-solutions according to (25) in Case (I), for each of the two values, there are four associated \(z\)-solutions according to Equation (28).\"_ should be changed to \"**Theorem 3. **_Given a sensor \(k\) that measures \(\overrightarrow{V}_{k}=\left(V_{ky},V_{bz}\right)^{T}\) and has two \(y\)-solutions according to (21) in Case (I), for each of the two values, there are four associated \(z\)-solutions according to Equation (24).\"_  
\"In summary, there are only two possible locations for a single sensor, so that Equation (16) is satisfied.\" should be changed to \"In summary, there are only two possible locations for a single sensor so that Equation (12) is satisfied.\"  
\"Since both points must be in areas with the same direction of the magnetic field lines to satisfy Equation (16), one is outside the circle and one is inside.\" should be changed to \"Since both points must be in areas with the same direction of the magnetic field lines to satisfy Equation (12), one is outside the circle and one is inside.\"