State estimation scheme for nonlinear dynamical systems based on the stochastic approximation

Abstract

An algorithm for the state estimation of multivariable nonlinear dynamic systems with noisy nonlinear observation systems is investigated on the basis of stochastic approximation procedure. Using an extended version of Dvoretzky's theorem, we derive a sufficient condition that estimation error converges to zero, both in the mean square and with probability one for noise-free multivariable dynamical systems. We then show that our estimation procedure makes the estimation error bounded in the mean square norm for noisy dynamical systems. Some numerical examples are presented for the illustration of the approach mentioned above.