## Appendix C  
The Lie derivative of the measurement function \(\mathbf{h}(\mathbf{x})\) with respect to the vector \(\mathbf{f}(\mathbf{x})\) is written as follows:  
\[L_{\mathbf{f}}\mathbf{h}(\mathbf{x})=\
abla_{\mathbf{f}}\mathbf{h}(\mathbf{x})=\frac{\partial\mathbf{h}(\mathbf{ x})}{\partial\mathbf{x}}\mathbf{f}(\mathbf{x}). \tag{13}\]  
The \(k\)-th order Lie derivative of \(\mathbf{h}(\mathbf{x})\) with respect to \(\mathbf{f}(\mathbf{x})\) is written as follows:  
\[L_{\mathbf{f}}^{k}\mathbf{h}(\mathbf{x})=\frac{\partial\Big{(}L_{f}^{k-1}\mathbf{h}(\mathbf{x}) \Big{)}}{\partial\mathbf{x}}\mathbf{f}(\mathbf{x}). \tag{14}\]  
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