Tracking a sine wave with noise This will probably be an extremely simple question for some one with any background in signal processing(not my background)

Let say I have signal $$x(t)=A\sin(\omega t)$$ where A is known and $\omega$ is unknown. Let say I only observe a noisy signal of $x(t)$ at discrete time periods $t=1,2,3....$. My signal $y(n)$ has the following form
$$y(n)=x(n)+\epsilon$$ where $\epsilon\sim N(0,\sigma^2)$.
My question is , what would be the best estimate of $y(n+1)$ given the observations till time time period $n$.
That's actually not a trivial problem and the best approach really depends on your specific requirements. 

My first approach would be a phase-locked loop and simply use the local oscillator as the predictor (with proper amplitude scaling). This can give you extreme accuracy if you are willing to pay with time.