What is the maximum Theoretical accuracy of GPS?

The United States government currently claims 4 meter RMS (7.8 meter 95% Confidence Interval) horizontal accuracy for civilian (SPS) GPS. Vertical accuracy is worse. Mind you, that's the minimum. Some devices/locations reliably (95% of the time or better) can get 3 meter accuracy. For a technical document on that specification you can go here.

For more general GPS accuracy information, head to GPS.gov's website. That website also includes data and information on WAAS-enabled systems and accuracy levels depending on location. It's a great resource.

Basically, you can't get 2 meter accuracy reliably without some form of correction.

Edit: Something else to contemplate is using a device that can communicate with both GPS and GLONASS satellites. I'm not aware of any accuracy articles or studies that combine both systems to improve accuracy, but at the very least, it increases the potential satellites that may be available at one particular location/time, especially near the poles.

Ionospheric delay effects are the largest source of error in a single-frequency GPS receiver. WAAS and CORS are able to correct for this better than a receiver's almanac, so the best you can do with uncorrected GPS is typically about 15 meters. Survey-grade GPS using RTK is able to achieve centimeter accuracy.

Image source: http://www.spatial-ed.com/gps/gps-basics/135-differential-correction-methods.html

in European countries, out in the field (not inside a city with buildings), the best accuracy without any aid is 5 meters. I have also witnessed a 2 meter accuracy but that is extremely rare and I would not take it into account. The average best would be 15 meters and the average worse close to 30-40 meters.

The results stated above are from my own field work and come from using various types of smartphones. GPS accuracy greatly varies depending on surroundings, devices used, weather and many other factors. The accuracy results are derived from compairing my actual position with the GPS position.

I hope this helps.

Cheers, A