Other than surveying and gun sighting, it's hard to imagine anything that could be done to an accuracy of a degree or better; certainly not steering a moving object of any kind.
Which was something I used to ponder on when doing a compass swing on a raw Norfolk February morning out on the airfield. I cant remember the accuracy of the headings I passed to the nav inside the aircraft after reading them off the Watts Datum Compass, but I am sure it read to less than 0.1 of a degree. Could never see the point of that, nor the laborious Fourier's Analysis which followed the swing. But then I was only a hack squadron nav - maybe somebody more versed in the mystical art of navigation might enlighten me!
On arrival at an FTS, I was informed I was going to be the new 'Navigation Officer' - the reason being that the job was vacant and it was known that my dad was a navigator. This role involved being the consultant on all things, navigational (ha ha - I failed my first attempt at the FNT!), teaching the students their navigation ground-school - and horror of all horrors - doing compass swings!
On a cold winter's morning standing in the slipstream of an aircraft at full power, I think it unlikely if any heading we recorded was within 5 degrees. And as for a Fourier analysis, I scraped a C at O level maths, so that's all I'm going to say about that matter.
As approximately half of all RAF pilots passed through my hands between 1990 and 1993, I'm probably more responsible for the decline in RAF pilot navigation standards than anyone else!