I understand that for a linear system, the observability Gramian is given by $W_{o}=\sum_{\tau=0}^{\text{inf}}(A^{T})^{\tau}C^{T}CA^{T}$.
However, I am wondering, how would be the calculation of $W_{o}$ for a nonlinear system $\dot{x}=f(x,u)$ and $y=h(x,u)$.
Will it be the same formula, replacing the matrices A, C, by the respective Jacobians?
Also, once I have these matrices, how do I proceed with the calculation of the $W_{o}$. Since I will be having matrices in terms and not constant values, and from the literature that I have been reading, it seems that $W_{o}$ has values which reflect how observable a state is.
Thanks for the help in advance.