Signal to noise ratio for a non-physical property
When talking about abstract quantities, we generally stop talking about "noise" and instead start talking about probability distribution functions (PDFs) and confidence levels.

You might be able to say, for example, that the answer (position) is correct to within 0.1 meters 95% of the time. You need to establish what your correctness criteria are for your application, and analyze how the PDF of the raw data gets transformed into the PDF of the result.

For a more detailed description, do some research into how the results are described for GPS receivers.