A convergent neural state estimator for nonlinear stochastic systems

A neural state estimator for nonlinear stochastic discrete-time systems is addressed. The statistics of noises are not known. The estimator is designed according to the sliding-window paradigm to minimize a quadratic estimation cost function. The noises are assumed to be additive with respect to both the state equation and the measurement channel. Sufficient conditions are devised to guarantee the convergence of the estimator and explicit asymptotic bounds on the estimation error are computed. The weights tuning technique is based on a min-max algorithm in order to guarantee the convergence of the state estimates. The estimator is designed off line in such a way as to be able to process any possible measurement pattern. This enables it to generate its estimates almost instantly