SI&DA - Lecture 28 'The Extended Kalman Filter'

Summary

We want to apply the theory behind the Kalman Filter to non-linear system.

$$\begin{array}{l}x(t+1)=f\left(x(t),u(t),w(t)\right)\\ y(t)=h\left(x(t),v(t)\right)\end{array}$$

We can use the algorithm for the Extended Kalman Filter, that we can found here: EKF Algorithm (Wikipedia)

The Idea behind the EKF is to linearize the two functions $f$ and $h$ using their Jacobean Matrices (derived for $x$, $v$ and $w$).

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