The topic of this article is a nonlinear observer based on a slight modification of the extended Kalman filter. The purpose of this modification is twofold: first the degree of stability can be assigned in advance and secondly this modification allows an effective treatment of the nonlinearities. Using the second method of Lyapunov it is proved that the proposed observer is an exponential observer. To examine the practical usefulness the proposed observer is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines.