Correction: Renaudin, V. et al. Use of Earth’s Magnetic Field for Mitigating Gyroscope Errors Regardless of Magnetic Perturbation. Sensors 2011, 11, 11390-11414

Although the equations' derivation in our paper published in Sensors 2011 [1] is correct, a typo has been found in the summarizing Equations (48) and (49). The dot on the B in the skew matrix should be removed. Equations (48) and (49) should be corrected as:

$$\delta {\dot{\mathbf{\text{B}}}}_{QS{F}_{k+1}}^b=\left[\begin{array}{cc}{\mathbf{0}}_{\mathit{3}\times \mathit{3}}& -\left[{\mathbf{\text{B}}}_{QS{F}_{k+1}}^b\times \right]\end{array}\right]\left[\begin{array}{c}{\mathbf{\varepsilon }}^n\\ \delta {\mathbf{\text{b}}}_{\omega }\end{array}\right]+\left[\begin{array}{cc}{\mathbf{0}}_{\mathit{1}\times \mathit{3}}& {\mathbf{0}}_{\mathit{1}\times \mathit{3}}\\ {\mathbf{0}}_{\mathit{1}\times \mathit{3}}& \left[{\widehat{\mathbf{\omega }}}_{\mathbf{\text{B}}}^b\times \right]\end{array}\right]\left[\begin{array}{c}{\mathbf{0}}_{\mathit{3}\times \mathit{1}}\\ {\mathbf{\eta }}_{\mathbf{\text{B}}}\end{array}\right]$$

(48)

$$\underset{\delta \mathbf{\text{z}}}{\underbrace{\left[\begin{array}{c}\delta {\mathbf{\text{B}}}_{QS{F}_{k+1}}^n\\ \delta {\dot{\mathbf{\text{B}}}}_{QS{F}_{k+1}}^b\end{array}\right]}}=\underset{H_{\mathit{\text{QSF}}}}{\underbrace{\left[\begin{array}{cc}-\left[{\mathbf{\text{B}}}_{QS{F}_k}^n\times \right]& {\mathbf{0}}_{\mathit{3}\times \mathit{3}}\\ {\mathbf{0}}_{\mathit{3}\times \mathit{3}}& -\left[{\mathbf{\text{B}}}_{QS{F}_{k+1}}^b\times \right]\end{array}\right]}}\underset{\delta \mathbf{\text{x}}}{\underbrace{\left[\begin{array}{c}{\mathbf{\varepsilon }}^n\\ \delta {\mathbf{\text{b}}}_{\omega }\end{array}\right]}}+\left[\begin{array}{c}-{\mathbf{\text{C}}}_b^n\\ {\widehat{\mathbf{\omega }}}_B^b\end{array}\right]{\mathbf{\eta }}_B$$

(49)