I guess I need some clues as to what might reset the processor

I guess if you read the posting guidelines, they would indicate that you should post your code, otherwise you're just wasting everyone's time. Clues are for Sherlock Holmes.

Look at an analogue clock: the angle between twelve and one o'clock is 30 degrees. Look closer. The angle between adjacent minute (or second) markings is 6 degrees.

Take out a protractor. Look at the one degree markings. Now imagine one tenth of that. Or, imagine looking at a point object 100 metres away, then look at an object 1/10th of a degree away, or just 17.5 cm away (about seven inches for the metrically-challenged, the length of a football field away).

Now do the trig / arithmetic to figure out how many bits of precision you need.

It's better if you use the F() macro for constant strings when writing serial debug code - it will help you not introduce unexpected out of RAM errors.