The IMRE Kalman filter — A new Kalman filter extension for nonlinear applications

Abstract

The IMRE Kalman filter is designed to compute the measurement update, when nonlinearities are weak enough to be treated as a perturbation. This paper explores four different nonlinear effects that any nonlinear filter should be able to handle. Based on simple, intuitive cases we show that other comparable known filters (the second-order filter, the UKF, the IEKF, the Gauss-Hermite quadrature filter, or the cubature filter) handle only some, but not all four nonlinear effects. In contrast, the IMRE Kalman filter addresses all four kinds of nonlinear effects, which makes it more general.