What could be the optimal filter given this situation?

I am using a camera and a Deep Neural Network to predict one angle. This network received as input the frame, and calculates the mean and the variance associated to the prediction (which is basically its uncertainty), so that the output of the systen consists of a normal distribution.

I want to use this extra information (the uncertainty of the prediction) to better aproxmate the angle I want to predict. Since I have no experience with this, I don’t know which filters could be better:

I have implemented a Kalman Filter that works really well with linear environments, as expected. However, if the angle starts to change non-linearly, which filter could use the information I have obtained (mean and variance for each sample) to improve the accuracy of the system?