harmonic product spectrum on guitar string signals
HPS (harmonic product spectrum), ASDF, AMDF, and autocorrelation are all similar periodicity estimation methods (they use different weightings and algorithms), which might be useful for guitar note pitch estimation.  These methods have different estimation accuracy/error statistics, which may vary depending on the types of guitars, strings, microphone setup, and etc., tested.  Experiment.

HPS has one interesting advantage.  The overtone series of the lower guitar strings can be slightly inharmonic, partially due to the physics of actual guitar strings, which have non-zero thickness and stiffness.  However, there is some experimental evidence that the stretch between the inharmonic overtone series might actually correspond more closely to the typical human psychoacoustic perception of pitch, than the actual fundamental vibration mode frequency of the guitar string.

That said, naive use of these methods may be too heavyweight for an Arduino AVR processor.  Perhaps an Arduino using an ARM M0 would be more suitable.  Also, to reduce the computational load of doing a full FFT or full autocorrelation-equivalent, you may want to use a modified zero-crossing pitch estimator.  Just make sure to use a large enough set of zero crossing span pairs (not just adjacent crossings) so that you can use something like a single AMDF to pick which set of span pairs represent overtone, harmonic or noise lags, and which span pairs might represent fundamental pitch lags.  Once you validate your set of span pairs or lags, you may want to average, or median filter.