The original paper in compares the CRT approach to a more traditional Extended Kalman Filter (EKF) approach. The EKF is very efficient but it does trade of some accuracy, because it requires a linear approximation of the system to be used. Both the CRT and EKF are used to blend or fuse inertial measurement data with GPS.
To achieve the claimed centimeter-level accuracy requires a local (within ~20 miles) base station and a data connection to the base station to achieve the levels of accuracy being discussed. Depending on the quality of the GPS receiver there will be a few seconds up to 10s of minutes convergence period for the GPS filters to initialise.
The results presented in [1] show that using a moderately expensive (dual frequency, code tracking) GPS can approach (not exceed) the accuracy of a high-end GPS (dual frequency, code and carrier phase).
In summary, this is a interesting incremental improvement, not a huge breakthrough that's going to bring centimeter accuracy to cell-phone GPS tracking.
[1] https://scholar.google.com/citations?view_op=view_citation&h...