Peak location estimation for a triangle wave in AGWN? Is there a more optimal peak location estimator specifically for triangle waves in AGWN, compared with peak estimation for generic waveforms?

For a "smooth" waveform in noise, a common peak locator method might involve a linear-phase low-pass filter or an overdetermined polynomial curve fit (by regression, et.al.), followed by a maxima/minima search.  But if the signal is known to be a sharp triangle wave (which may imply that any sampling included/aliased some non-filtered frequency content above Fs/2, if that is relevant), or portion thereof, and not a low order polynomial or other smooth waveform, can this information be used to improve the triangle peak location estimation?  

If so, how?

Added: Less than 1 period of the triangle wave may be available.  But assume at least one extrema is in the data window.
You may be able to determine this in the frequency domain. The noise signal is broad band and has low spectral density at any one frequency. The triangle, however, has all energy concentrated in just a few frequencies, so these should stick out in a short term Fourier spectrum. You can match against your expected spectrum (odd harmonics, amplitude proportional to 1/n^2). 

The harmonics of a triangle are all in phase. Since your triangle wave is arbitrarily located inside your analysis window, the harmonics will appear to have a linear phase. You can probably model your measured phase (after proper unwrapping) as a linear phase using a simple least squares error approach. This should give you the exact position of the peak of the triangular wave with respect to the beginning for your analysis window.