Abstract: An Adaptive Extended Kalman Filter is used for data assimilation in two non-linear dynamical systems: the Lorenz system in chaotic state and the computational model DYNAMO for the atmosphere. This approach does not require the modelling error to be stationary and uses a linear Kalman filter to estimate this error. This method is compared to the methods using Laplace Transform, Linear and Extended Kalman Filter. The conclusion was that the choice between using Laplace Transform and Adaptative Kalman Filter assimilation methods for DYNAMO depended on whether one was willing to completely reject high-frequency information or not. When that information was considered useless the Laplace filtering eliminated it better than Kalman. Otherwise Kalman assimilated it better than Laplace.