New convergence conditions for receding-horizon state estimation of nonlinear discrete-time systems

Receding-horizon state estimation problems are addressed for a class of nonlinear discrete-time systems. We assume the system dynamics and measurement equations to be corrupted by additive, bounded noises. The statistics of such disturbances and of the initial state are unknown. We use a generalized least-squares approach that consists in minimizing a quadratic estimation cost function defined on a sliding window composed of a finite number of time stages. New results of convergence for an upper bound on the estimation error are presented that simplify the design of the estimator. The estimator is constructed either by solving an optimization problem on line or by approximating off line the optimal estimation function that solves the problem. In this last case, the approximation can be carried out under suitable assumptions via a minimax optimization.