An Extended-Kalman-Filter (EKF)-like observer is derived from a former observer result for a class of nonlinear systems, which can be written as a linear part in the unmeasured states on the one hand, and some additive nonlinearity with a triangular Jacobian on the other hand. It is shown how the previously presented excitation condition for exponential stability of the observer, extends to this EKF version. The observer is illustrated in simulation with two challenging examples, the first one in leak detection, and the second one in chaos synchronization.