This paper investigates the state estimation problem for stochastic nonlinear differential systems with multiplicative noise. Our purpose is to combine the noise filtering properties of the Extended Kalman Filter with the global convergence properties of high-gain observers. We propose an observer-based algorithm and provide conditions under which a bound on the estimation error can be guaranteed. Simulations show that this algorithm reveals to be more efficient than the Extended Kalman Bucy filter for systems with large measurement errors.