  Kalman filtering has been traditionally applied in three application areas of
estimation, state estimation, parameter estimation (a.k.a. model updating), and
dual estimation. However, Kalman filter is often not sufficient when
experimenting with highly uncertain nonlinear dynamic systems. In this study, a
nonlinear estimator is developed by adopting a particle filter algorithm that
takes advantage of measured signals. This approach is shown to significantly
improve the ability to estimate states. To illustrate this approach, a model
for a nonlinear device coupled with a hydraulic actuator plays the role of an
actual plant and a nonlinear algebraic function is considered as an
approximation of the nonlinear device, thus generating non-parametric and
parametric uncertainties. Then we use displacement and force signals to improve
the distribution of the states by resampling the set of particles. Finally, all
of the states are estimated from these posterior density functions. A set of
simulations considering three different noise levels demonstrates that the
performance of the particle filter approach is superior to the Kalman filter,
yielding substantially better performance when estimating nonlinear physical
systems in the presence of modeling uncertainties.
