AbstractIn this paper we present a numerical method for estimating the current state of a nonlinear control system. We use finite differences to discretize a modified version of the finite‐time observer equations in James. The discretized equations are simple and easily programmed. The convergence and accuracy of the scheme is proved, and the scheme enjoys a number of important properties: availability of rate of convergence estimates, good robustness characteristics, and the ability to handle certain types of discontinuities in the observations. The major disadvantage is that the number of grid points required increases exponentially with the number of state dimensions.