Preprints of the NIL Workshop 2011

A constrained moving horizon observer is described and analysed for nonlinear discrete-time systems. The algorithm is proved to converge exponentially under a detectability assumption and the data being persistently exciting. However, in many practical estimation problems, such as combined state and parameter estimation, the data may not be persistently exciting. The algorithm therefore has regularization mechanisms to ensure robustness and graceful degradation of performance in time periods when the data are not exciting. This includes the use of a priori estimates in the moving horizon cost function, and the use of thresholded singular value decomposition to avoid ill-conditioned or ill-posed inversion of the associated nonlinear algebraic equations that define the moving horizon state estimate. The latter regularization relies on monitoring of the rank of an estimate of a Hessian-like matrix and conditions for exponential convergence are given. The method is in particular useful with augmented state space models corresponding to mixed state and parameter estimation problems, or dynamics that are not asymptotically stable, as illustrated with simulation examples. The main example considers wheel slip estimation for automotive applications using nonlinearly overparameterized tyre friction models where persistence of excitation does not hold.