Fast moving horizon state estimation for discrete-time systems using single and multi iteration descent methods

Descent algorithms based on the gradient, conjugate gradient, and Newton methods are investigated to perform optimization in moving horizon state estimation for discrete-time linear and nonlinear systems. Conditions that ensure the stability of the estimation error are established for single and multi iteration schemes with a least-squares cost function that takes into account only a batch of most recent information. Simulation results show the effectiveness of the proposed approaches also in comparison with techniques based on the Kalman filter.