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.
Thanks in advance for your help.