The second order stochastic filter is based on difference models with uncorrelated innovation conditions structured in state space having stationary properties through a surface with bounded drift around the mean value. This allows building recursive estimation without generallity lost and basic properties over the stochastic state space surface with unknown gains viewed as a black-box scheme. The spatial region generated gave an approximation to real parametres set with a sufficient convergence rate in a probability sense. The results were applied in adaptive identifcation states with a high convergence rate, observed in the functional error described illustratively in simulations. This technique was developed over the smooth slide surface having advantages over other traditional filters.
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