Moving-horizon state estimation for nonlinear systems using neural networks

In recent results, a moving-horizon state estimation problem has been addressed for a class of nonlinear discrete-time systems with bounded noises acting on the system and measurement equations. For the resulting estimator, suboptimal solutions can be addressed for which a certain error is allowed in the minimization of the cost function. Building on such results, in this paper the use of nonlinear parameterized functions is studied to obtain suitable state estimators with guaranteed performance. Thanks to the off-line optimization of the parameters, the estimates can be generated on line almost instantly. A new technique based on the approximation of the cost value (and not of its argument) is proposed and the properties of such a scheme are studied. Simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended Kalman filter.