In the standard maximum likelihood setting (iid sample $Y_{1}, \ldots, Y_{n}$ from some distribution with density $f_{y}(y|\theta_{0}$)) and in case of a correctly specified model the Fisher information is given by
$$I(\theta) = -\mathbb{E}_{\theta_{0}}\left[\frac{\partial^{2}}{\theta^{2}}\ln f_{y}(\theta) \right]$$
where the expectation is taken with respect to the true density that generated the data. I have read that the observed Fisher information
$$\hat{J}(\theta) = -\frac{\partial^{2}}{\theta^{2}}\ln f_{y}(\theta)$$
is used primary because the integral involved in calculating the (expected) Fisher Information might not be feasible in some cases. What confuses me is that even if the integral is doable, expectation has to be taken with respect to the true model, that is involving the unknown parameter value $\theta_{0}$. If that is the case it appears that without knowing $\theta_{0}$ it is impossible to compute $I$. Is this true?