PGF 42: Progressive Gaussian filtering with a twist

A new Gaussian filter for estimating the state of nonlinear systems is derived that relies on two main ingredients: i) the progressive inclusion of the measurement information and ii) a tight coupling between a Gaussian density and its deterministic Dirac mixture approximation. No second Gaussian assumption for the joint density of state and measurement is required, so that the performance is much better than that of Linear Regression Kalman Filters (LRKFs), which heavily rely on this assumption. In addition, the new filter directly works with the generative system description. No Likelihood function is required. It can be used as a plug-in replacement for standard Gaussian filters such as the UKF.