A State space model for discrete Sine wave Using kalma filter I'm looking to apply an optimal LQR filter to a discrete signal of the form
$$
x[n]=A\sin(\omega_0n+\phi)+v[n]
$$
The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate using the filter, and $v[n]$ is an uncorrelated noise signal of variance $\sigma_v^2$.

I don't know how to build a state model to generate this sine wave, and proceed from there.
You could use a nonlinear Kalman filter, such as the extended Kalman filter (EKF), and track the phase and frequency as your state variables. 

In this case, your Kalman filter is essentially acting like a phase-locked loop (PLL). 

Example reference