# Discrete Sinusoidal to State Space

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.

• Is $\omega_0$ known?
– Peter K.
Sep 2 '15 at 21:48
– Royi
Apr 30 at 20:07

Kalman filters assume that you know the model and that you want to estimate the real state of $x[n]$, and if I understand well this is not your problem.