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Kalman filtering has been traditionally applied in three application areas ofestimation, state estimation, parameter estimation (a.k.a. model updating), anddual estimation. However, Kalman filter is often not sufficient whenexperimenting with highly uncertain nonlinear dynamic systems. In this study, anonlinear estimator is developed by adopting a particle filter algorithm thattakes advantage of measured signals. This approach is shown to significantlyimprove the ability to estimate states. To illustrate this approach, a modelfor a nonlinear device coupled with a hydraulic actuator plays the role of anactual plant and a nonlinear algebraic function is considered as anapproximation of the nonlinear device, thus generating non-parametric andparametric uncertainties. Then we use displacement and force signals to improvethe distribution of the states by resampling the set of particles. Finally, allof the states are estimated from these posterior density functions. A set ofsimulations considering three different noise levels demonstrates that theperformance of the particle filter approach is superior to the Kalman filter,yielding substantially better performance when estimating nonlinear physicalsystems in the presence of modeling uncertainties.

Estimating States for Nonlinear Systems Using the Particle Filter