Convergence conditions of dynamic stochastic approximation method for nonlinear stochastic discrete-time dynamic systems

Sufficient conditions are presented under which the dynamic stochastic approximation estimate converges with probability 1 to the true state vector of a nonlinear stochastic discrete-time dynamic system. These conditions are stated in terms of system dynamics, measurement function, and noise statistics; and are closely related to the concept of on-line stochastic observability.