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Unlike its linear counterpart, the extended Kalman filter in general is not an optimal estimator (of course it is optimal if the measurement and the state transition model are both linear, as in that case the extended Kalman filter is identical to the regular one).

kalman filter updating numerical example-50

The main benefit is that the gain and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as it is the case for the EKF, which results in a better convergence of the estimation.

However, f and h cannot be applied to the covariance directly.

Instead a matrix of partial derivatives (the Jacobian) is computed.

The invariant extended Kalman filter (IEKF) is a modified version of the EKF for nonlinear systems possessing symmetries (or invariances).

It combines the advantages of both the EKF and the recently introduced symmetry-preserving filters.

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