Enhanced Quadratic Extended Kalman Filter

In this note, we present a new solution to the filtering problem for stochastic discrete-time nonlinear systems, which we refer to as the Enhanced Quadratic Extended Kalman Filter (eQEKF). Starting from the concept underlying the existing formulation of the Quadratic Extended Kalman Filter (QEKF), based on the definition of an augmented output through Kronecker powers, we propose a different method that enables us to overcome certain inevitable standard approximation issues, reducing the computational workload. Also, we show the effectiveness of the proposed approach with respect to the QEKF and with respect to the classical Extended Kalman Filter, as highlighted by two numerical examples, in the case of Gaussian and non-Gaussian noises.