Robust algebraic state estimation of chaotic systems

In this article, we propose an improvement of a recently introduced algebraic approach for the non-asymptotic state and parameter estimation of nonlinear systems. In particular, we increase the robustness of the estimation method with respect to zero mean, high frequency, measurement noises by introducing a so-called invariant filtering technique. In order to reduce an already fast transient to the convergence, when subject to measurement noise, we devise an estimation policy consisting of two overlapping estimators with appropriate switchings between their results. These are two identical time-shifted estimators running in parallel with an overlapping estimation period. The benefits of our method are demonstrated on the state observation of a chaotic system of the Rössler type.