Invariant extended Kalman filter

The invariant extended Kalman filter (IEKF) (not to be confused with the iterated extended Kalman filter) is a version of the extended Kalman filter (EKF) for nonlinear systems possessing symmetries (or invariances). It combines the advantages of both the EKF and symmetry-preserving filters. Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error. The main benefit is that the gain and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points that is the case for the EKF, which results in a better convergence of the estimation. The invariant extended Kalman filter (IEKF) (not to be confused with the iterated extended Kalman filter) is a version of the extended Kalman filter (EKF) for nonlinear systems possessing symmetries (or invariances). It combines the advantages of both the EKF and symmetry-preserving filters. Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error. The main benefit is that the gain and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points that is the case for the EKF, which results in a better convergence of the estimation.