So your're correct that there is a Fourier Transform analogy for the uncertainty principle, but in the context of FMCW lidars (which brought up the question of velocity vs position uncertainty), the measurement of frequency actually determines both the position and the velocity. It's actually a problem for most FMCW lidars because you just get 1-2 frequency measurements and somehow need to disentangle what the range frequency is, as well as what the doppler (velocity) frequency is. A massive amount of effort has been put into developing lidar methods and architectures that solve this problem well.
But in summary, the uncertainty principle as encountered in quantum mechanics has ~nothing to do with a trade off between range accuracy and range uncertainty. It's possible that it could come into play in a very detailed treatment of FMCW lidar SNR, in the context of counting return photons, but also not generally necessary there. The time-frequency uncertainty plays a role in that the range and velocity resolution both get better the longer you stare at a signal. So for a given amount of reflected light, at a given range/velocity, there is a fundamental lower bound to how long you must integrate to a) get a signal at all and b) achieve a desired precision.
It seems to be an extract from "Foundations of Field Computation" by Bruce MacLennan, if you want to read the whole thing: http://web.eecs.utk.edu/~bmaclenn/FFC.pdf
He and Dr. Marcolli have a bunch of interesting stuff on their websites if you like this sort of stuff.
But in summary, the uncertainty principle as encountered in quantum mechanics has ~nothing to do with a trade off between range accuracy and range uncertainty. It's possible that it could come into play in a very detailed treatment of FMCW lidar SNR, in the context of counting return photons, but also not generally necessary there. The time-frequency uncertainty plays a role in that the range and velocity resolution both get better the longer you stare at a signal. So for a given amount of reflected light, at a given range/velocity, there is a fundamental lower bound to how long you must integrate to a) get a signal at all and b) achieve a desired precision.