NavList:

Geoffrey Kolbe wrote:

"What I meant was the same accuracy as the commonly available GPS
receiver, where the circle of uncertainty in position has a radius
about 5 metres."

My understanding is that even for a highly skilled surveyor using a theodolite to observe celestial bodies and, most importantly, using the full gamut of statistical and other methodologies to reduce systemic and erratic errors to their minimum, plus a particularly good grasp of time (also very important) the theoretical limit of this "circle of uncertainty" is about one second of arc, so about 30-metres at the earth's surface.

However, I also understand that this one-arc-second "circle of uncertainty" was more of an ideal to aim for in the realm of Field Astronomy for surveyors, rather than an outcome likely to be achieved in practice. 

Having said that, I have achieved zero intercepts using a hand-held sextant from a known position.  Is this 0-metre accuracy?  Well no, unfortunately, since my methodology, including altitude measurement, sight reduction and resulting intercept, had a resolution precision-limitation of one-tenth of an arc minute (about 180-metres) and also since it could have simply been a lucky fluke, ie; the felicitous result of unknown errors, whether small or not, cancelling each other out.