The free energy principle is a recent theory that originates from the neuroscience. It provides a unified framework that combines action perception and learning in the human brain. This research aims to implement the perception aspect of the free energy principle into robotics. This is achieved via the dynamic expectation maximisation (DEM) algorithm. DEM is derived from the free energy principle and provides a novel solution for state and input observation for LTI systems under the influence of coloured noise. This thesis provides an overview of how the DEM observer is derived from the free energy principle. Thereafter, an experimental design is presented in which data is collected to validate the performance of DEM on experimental data. The data is collected from a quadcopter drone flying in wind conditions. A detailed overview of the DEM observer settings is presented and motivated. \\ This research shows that because of its use of generalized coordinates DEM is able to leverage the coloured nature of the noise for better state estimation. This is demonstrated by the fact that DEM obtains a higher state estimation accuracy than other coloured noise state observers, such as state augmentation and SMIKF. Moreover, in input estimation, DEM is able to obtain similar results as an unknown input observer. Finally, the accuracy vs complexity trade off of DEM is highlighted.