  The free energy principle (FEP) from neuroscience provides a framework called
active inference for the joint estimation and control of state space systems,
subjected to colored noise. However, the active inference community has been
challenged with the critical task of manually tuning the noise smoothness
parameter. To solve this problem, we introduce a novel online noise smoothness
estimator based on the idea of free energy principle. We mathematically show
that our estimator can converge to the free energy optimum during smoothness
estimation. Using this formulation, we introduce a joint state and noise
smoothness observer design called DEMs. Through rigorous simulations, we show
that DEMs outperforms state-of-the-art state observers with least state
estimation error. Finally, we provide a proof of concept for DEMs by applying
it on a real life robotics problem - state estimation of a quadrotor hovering
in wind, demonstrating its practical use.
