Fast moving horizon state estimation for discrete-time systems with linear constraints

Fast moving horizon state estimation for nonlinear discrete-time systems affected by disturbances is addressed by means of imperfect optimization at each time instant based on few iterations of the gradient, conjugate gradient, and Newton algorithms. Linear constraints on the state vector are taken into account through a projection on the subspace associated with such constraints. The stability of the estimation error for the resulting scheme is proved under suitable conditions. The effectiveness of the proposed approach is showcased via simulation results in comparison with moving horizon estimation based on complete optimization and extended Kalman filtering.