# Extended Kalman Filter linearization of non-linear functions

I have more general question about the extended Kalman filter usage. What is not clear to me is why the EKF uses non-linear functions $f$ and $h$ for state prediction and estimate, while in other places the Jacobian of these functions is used.

Why the following is never used?

First calculate the linearized state and measurement models at previous estimate point using Jacobian. Use the linearized state transition and measurements matrix everywhere instead of non-linear in this specific iteration.

• what f and h values we have to take to implement EKF program??? – user7379 Dec 26 '13 at 4:26

Adding up to the excellent answers by @Siva , @kaka, since the model is non-linear, having a linear approximation of it, computeted at a certain point (e.g. $X_0$) means that you have a good approximation of the model's values around that certain linearization point. How far away from it, that linearization point can still provide good approximations depends on the "severity" of the nonlinearity.
As an example from this guide on Taylor expansions one could try and linearise the sin function around $0$. Notice that for values in $(-1,1)$ the linearised approximation provides fairly accurate results. However if we go away from this range (e.g. $x = 2$) that doesn't hold and we need to relinearize the model around a new point again (ideally around $x=2$).