A Moving Horizon State and Parameter Estimation Scheme with Guaranteed Robust Convergence

We propose a moving horizon estimation scheme for joint state and parameter estimation for nonlinear uncertain discrete-time systems. We establish robust exponential convergence of the combined estimation error subject to process disturbances and measurement noise. We employ a joint incremental input/output-to-state stability (δ-IOSS) Lyapunov function to characterize nonlinear detectability for the states and (constant) parameters of the system. Sufficient conditions for the construction of a joint (δ-IOSS Lyapunov function are provided for a special class of nonlinear systems using a persistence of excitation condition. The theoretical results are illustrated by a numerical example.