Generalized Gauss–Hermite filtering

We consider a generalization of the Gauss–Hermite filter (GHF), where the filter density is represented by a Hermite expansion with leading Gaussian term (GGHF). Thus, the usual GHF is included as a special case. The moment equations for the time update are solved stepwise by Gauss–Hermite integration, and the measurement update is computed by the Bayes formula, again using numerical integration. The performance of the filter is compared numerically with the GHF, the UKF (unscented Kalman filter) and the EKF (extended Kalman filter) and leads to a lower mean squared filter error.