Deep Likelihood Learning for 2-D Orientation Estimation Using a Fourier Filter

Filters for circular manifolds are well suited to estimate the orientation of 2-D objects over time. However, manually deriving measurement models for camera data is generally infeasible. Therefore, we propose loss terms that help train neural networks to output Fourier coefficients for a trigonometric polynomial. The square of the trigonometric polynomial then constitutes the likelihood function used in the filter. Particular focus is put on ensuring that rotational symmetries are properly considered in the likelihood. In an evaluation, we train a network with one of the loss terms on artificial data. The filter shows good estimation quality. While the uncertainty of the filter does not perfectly align with the actual errors, the expected and actual errors are clearly correlated.