This paper addresses the sonar-based navigation of mobile robots. The extended Kalman filtering (EKF) technique is considered, but from a deterministic, nonstochastic, point of view. For this problem, new results are presented on the robustness of the nonlinear observation scheme. The original feature is that the region-of-convergence question is posed in its complete nonlinear framework, that is, considering the dynamics not only of the estimation error xi(t), but also of the covariance matrix P(t). In this way the approach followed makes less conservative the treatment and improves the convergence analysis. The proposed ideas were tested successfully on simulation experiments of a mobile platform. (C) 2003 Elsevier Science Ltd. All rights reserved.