Two families of observers for discrete-time nonlinear systems are presented in this paper, whose design is based on the Taylor approximation of the inverse of the observation map. Semiglobal convergence results are provided under the assumption that the system observation map is a globally analytic diffeomorphism. The performances of the observers in the two families are compared both from theoretical and practical points of view. (C) 2012 Elsevier Ltd. All rights reserved.