Progressive Gaussian Filtering
This work addresses a specific challenge in Bayesian estimation for nonlinear systems, but it appears incremental as it builds on existing Gaussian approximation techniques.
The paper tackles the problem of tracking non-Gaussian posteriors in Bayesian filtering by proposing a progressive Gaussian filtering method that continuously integrates measurement information via an ODE system derived from a coupled density representation, achieving performance evaluated on the cubic sensor benchmark.
In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a system of ordinary first-order differential equations (ODE) by employing a new coupled density representation comprising a Gaussian density and its Dirac Mixture approximation. The ODE is used for continuously tracking the true non-Gaussian posterior by its best matching Gaussian approximation. The performance of the new filter is evaluated in comparison with state-of-the-art filters by means of a canonical benchmark example, the discrete-time cubic sensor problem.