Predictive filtering for nonlinear systems

A real-time predictive filter is derived for nonlinear systems. The major advantage of this new filter over conventional filters is that it provides a method of determining optimal state estimates in the presence of significant error in the assumed (nominal) model. The new real-time nonlinear filter determines (predicts) the optimal model error trajectory so that the measurement-minus-estimate covariance statistically matches the known measurement-minus-truth covariance. The optimal model error is found by using a one-time step ahead control approach. Also, because the continuous model is used to determine state estimates, the filter avoids discrete state jumps. The predictive filter is used to estimate the position and velocity of nonlinear mass-damper-spring system. Results using this new algorithm indicate that the real-time predictive filter provides accurate estimates in the presence of highly nonlinear dynamics and significant errors in the model parameters.