A method called iTEKA, which stands for iterative time elastic kernel averaging, was successfully used for averaging time series. \mbox{In this paper}, we adapt it to GPS trajectories. The key contribution is a denoising procedure that includes an over-sampling scheme, the detection and removal of outlier trajectories, a kernelized time elastic averaging method, and a down-sampling as post-processing. The experiment carried out on benchmark datasets showed that the proposed procedure is effective and outperforms straightforward methods based on medoid or Euclidean averaging approaches.