Optimal filtering is a classical method for inferring the distribution of a hidden process from data. As an input it requires a probability model, which needs to be separately estimated. In this talk, we will look at what happens when we include the uncertainty of this estimation into our filtering problem, using a nonlinear expectation approach. A key difficulty is that one obtains a pathwise optimal control problem, which requires some care in analysis. We will see how we can ensure this problem remains well posed, and demonstrate the gains in performance from using this approach.