Robust PFI Kalman filters

The proportional fading-integral (PFI) Kalman filter is a generalization of the proportional-integral (PI) Kalman filter. We show that integral action allows for the accurate estimate of disturbances caused by unknown inputs and plant perturbations, dramatically improving the rejection properties of the Kalman filter. The fading integral of the PFI Kalman filter further extends the robustness of the filter by increasing the filter's stability margin, while allowing the rejection of transitory disturbances with unknown distribution matrices. Through extensive simulations, as applied to the 1992 ACC robust control benchmark, we show that the fading integral doubles the stability margin of a Kalman filter-based state feedback regulator when used to estimate the rank one perturbation caused by a mismatched spring constant.