Progressive Gaussian filter using importance sampling and particle flow

We propose a novel progressive Gaussian filter for nonlinear stochastic systems. A Gaussian approximation of the posterior is computed without an explicit assumption of a linear relation between the system state and the measurement. This allows for better quality of the estimation compared to Kalman filters for nonlinear problems like the EKF or UKF. In this work, we use the progressive filter framework, which gradually incorporates information of a measurement into the state estimate by considering a flow of probability mass from the prior to the posterior state estimate. We propose a novel particle flow by utilizing a simple linear model. This model predicts the movement of single particles over the course of the filter progression. The predicted trajectory is corrected using importance sampling and moment matching. The proposed method is evaluated in comparison with other state-of-the-art nonlinear Bayesian filters.