This document summarizes an approach to perform online Gaussian process regression using random feature selection in order to address the computational challenges of traditional GPR. It proposes combining random feature mapping with online Bayesian linear regression to develop a fast approximate GPR model that can perform online learning from streaming data. The goal is to apply this method to motion planning for a 7-DOF robotic arm. The algorithm will be implemented in MATLAB/Octave and tested on inverse dynamics problems using a Barrett Technology robot arm.