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.