Moving-horizon estimation for discrete-time linear and nonlinear systems using the gradient and Newton methods

Abstract

The computational effort may result in an over-whelming issue that prevents to use moving-horizon state estimation in a wide range of applications. Thus, in this paper we investigate the potential of moving-horizon estimators that provide an estimate of the state variables after performing a simple descent step based on the gradient or Newton methods. The stability analysis usually drawn in the case of exact minimization of the cost function cannot be applied. Thus, novel conditions on the stability of the estimation error for moving-horizon estimation based on single or multiple iterations of the gradient and Newton algorithms are derived for discrete-time linear and nonlinear noise-free systems. In the case of the gradient method for nonlinear systems, global exponential stability of the estimation error can be ensured. By contrast, only local stability is proved for the Newton-based approach. Under linear assumptions, also the error given by this estimator is demonstrated to be globally exponentially stable. The theoretical results are verified also by means of simulations, with a chaotic nonlinear system used as a testbed to estimate all the state variables only by means of measurements of the first one. The simulation results show that the gradient and Newton-based approaches perform quite well as compared with the extended Kalman filter.