Iterative Learning Control (ILC) is a technique used to improve the tracking performance of systems carrying out repetitive tasks, which are affected by deterministic disturbances. The achievable performance is greatly degraded, however, when non-repeating, stochastic disturbances are present. This paper aims to compare a number of different ILC algorithms, proposed to be more robust to the presence of these disturbances, firstly by a statistical analysis and then by their application to a linear motor. Expressions for the expected value and variance of the error are developed for each algorithm. The different algorithms are then applied to the linear motor system to test their performance in practice. A filtered ILC algorithm is proposed when the noise and desired output spectrums are separated. Otherwise an algorithm with a decreasing gain gives good robustness to noise and achievable precision but at a slower convergence rate.