A New Perspective and Extension of the Gaussian Filter

The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. This representation can be too restrictive to accurately capture the dependencies in systems with nonlinear observation models. In this paper, we investigate how the GF can be generalized to alleviate this problem. We therefore look at the GF from a variational inference point of view, and analyze how restrictions on the form of the belief can be relaxed while maintaining its simplicity and efficiency. This provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.