I have looked everywhere on the internet for this and, surprisingly, haven't found much useful information.
Given 3 or more points closest to a peak (local maximum) what are some of the most accurate techniques I can use to obtain the value of the peak. In fact, I would like the x axis coordinate of that peak to determine the exact peak locations of the autocorrelation function of a discrete signal.
The best I have been able to do is quadratic interpolation which fits a parabola between three points and finds the maximum as follows:
\begin{equation} x = \frac{1}{2} \frac{\alpha - \gamma}{\alpha - 2\beta + \gamma} \end{equation}
I tried cubic interpolation but either I'm doing it wrong or it's just not more accurate than the quadratic interpolation.
Anyway, can I not get better accuracy than quadratic interpolation? I would appreciate even just the names of algorithms or links to resources I can look at. (PS: I have way more than just three points close to the true peak).
Edit:
I'm not sure about the exact model of the peak, but it's one obtained when you do the autocorrelation of a sinusoid. To be more specific, I would like to use autocorrelation to determine, as accurately as possible, the exact fundamental frequency of an electrical grid.