A model-based parameter estimation method for nonlinear systems that does not require the linearization of the system equations and that can account for uncertainties in the monitored data as well as the parameters (e.g., random variations) is described. The method is particularly suitable for fault diagnosis because of its capability to assign probabilities of occurrence to user-specified parameter magnitude intervals that may be associated with system faults. The method regards system evolution in time as transitions between these intervals as well as user-specified magnitude intervals of the dynamic variables. These transition rates are obtained on-line from the system model and the monitored dynamic variable data and constitute a Markov chain in discrete time. The method then compares predicted and observed data at a given time step to narrow the estimated parameter range in the next time step. Implementations using a second-order van der Pol oscillator and a third-order system describing temporal xenon oscillations in a hypothetical reactor indicate that the method is computationally efficient and can be used for multiparameter estimation with incomplete information on the system state.