low earth orbit is 2000km. gps is on mid earth orbit (meo) or ico. the only leo sats i know that are still in operational service are those of iridium and globastar. i worked on both.
cm precision with gps requires terrestrial assist. surveyors have been using dgps for a long time with cm precision. however, more new gps iii sv's are being deployed, and more sv's will improve precision. right now, you'll notice an average of 9 "birds" at any one time on a sophisticated gps receiver. it's an improvement over 4 then 6 when i first tested it. now you know how old i am.