I want to use the Kalman filter to have a better estimate of the state of a system which I know its equations of motion:
$\ddot{\theta}=\frac{-Mr\dot{\theta}^2sin(\theta)cos(\theta)-(m+M)gsin(\theta)}{R(M+msin(\theta)^2}$
Well as you see the system is far from linear. I could make an approximation of the trigonometric functions to a linear function when $\theta$ is close to 0 but I want to use the whole domain from $0$ to $2\pi$.
Can I use the Kalman filter in this situation? Should I use a different Kalman filter for different ranges of $\theta$ having each filter a different linear approximation of the trigonometric functions? What should be my A matrix?
$\mathbf{x}^{n|n}=\mathbf{A}\mathbf{x}^{n|n-1}+\mathbf{\epsilon_x}$
with $\mathbf{x}=\begin{bmatrix} \theta\\ \dot{\theta}\\ \ddot{\theta} \end{bmatrix}$