The problem of constructing a receding-horizon estimator for nonlinear discrete-time systems affected by disturbances has been addressed. The noises are assumed to be bounded, additive, and acting on both state and measurement equations. The estimator is designed according to a sliding-window strategy, i.e., so that it minimizes a receding-horizon estimation cost function. The stability of the resulting filter has been investigated and an upper bound on the estimation error has been found. Such a filter can be suitably approximated by parametrized nonlinear approximators as, for example, neural networks. A min-max algorithm turns out to be well-suited to selecting these parameters, as it allows one to guarantee the stability of the error dynamics of the approximate receding-horizon filter. This estimator is designed off line in such a way as to be able to process any possible information pattern. This enables it to generate state estimates almost instantly with a small on-line computational burden.