When you need position (and/or attitude) data at a high sample rate, the usual technique is to combine inertial measurement (e.g., MEMS accelerometers and rate gyros), which give you relative movement data at high sample rates, with GPS information that comes at a relatively slow rate (e.g., 1 - 10 Hz).
This information is combined in a system model (e.g., Kalman filter) in such a way that the absolute position data from GPS corrects for the long-term drift components of the inertial measurements. The result is an output that has the accuracy of the GPS, but the high sample rate of the inertial measurements.
Note that the GPS output message includes a timestamp in addition to the position values. The position values give the absolute position of the receiver at the time given by the timestamp. Even if there is a lag in terms of computing that position or transferring that message over a serial link or whatever, the data within the message is always self-consistent, within the accuracy limits of the receiver.
A lot of projects (especially those done by hobbyists) ignore the timestamp and the transmission delay and simply take the position values directly as the "most current" position, but if you really care about high sample rates and low-latency data, this is an overly-simplistic approach. A properly-constructed hybrid GPS+inertial system can provide data that's "current" within a few milliseconds.
The common term for such a system is "AHRS", which stands for Attitude and Heading Reference System, and it's a common element in pretty much any autonomous vehicle control system.