# Extended Kalman Filter - how do I get transition functions

I am measuring position and velocity, both have some noise in them. Velocity is defined as derivative of position. The system is apparently non-linear so I need to use EKF.

Model:

\begin{align} X&=\begin{bmatrix}p\\v\end{bmatrix}\\ p_{k+1}&=A_0\sin\left(b_0k\right)+A_1\sin\left(b_1k\right)+A_2\sin\left(b_2k\right)\\ v_{k+1}&=A_0b_0\cos\left(b_0k\right)+A_1b_1\cos\left(b_1k\right)+A_2b_2\cos\left(b_2k\right)\\ \end{align}

Questions:

1. I suppose this is a non-linear system. Am I right?
2. If yes, I should use Extended Kalman filter. But how do I get $f$ and $h$ functions for my case (below)? The current state doesn't depend on previous state; except the $k$ (step) variable. \begin{align} x_k&=f\left(x_{k-1}\right)+w_k\\ z_k&=h\left(x_k\right)+v_k \end{align}
• Your current state should depend upon its previous state, or a Kalman filter isn't going to help you much. Try solving for $p_{k+1}$ in terms of $p_k$ and so on. This would yield the state transition equation, which is an important part of the model. – Jason R Aug 13 '12 at 17:19
• Thanks for your input. I was concerned this wouldn't be applicable for Kalman's filter. – Primož Kralj Aug 13 '12 at 19:12