Using the Unscented Kalman Filter in Fast Hybrid Testing

Abstract

In this document the Kalman Filter is described as an algorithm to estimate the state of an unknown system. Extensions to the standard linear Kalman Filter are also described: the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Both the EKF and UKF can be used to estimate nonlinear systems to various degrees, at the cost of more computational time. The theory and basic update computations of all three filters are shown, and the process of estimating not only state but parameters is described.

An example hybrid test using the Kalman Filter is described, and an appropriate model is devised using both state and parameter variables. The filter is used to process a noisy displacement measurement and produce estimates of displacement, velocity and amplifier gains. The resulting displacement waveforms show a reduction in noise amplitude and controller instability. In addition, the filter is shown to be capable of estimating system parameters during operation; in this case, the filter proved capable of following changes in amplifier gain as a user modified the gain manually during a hybrid test.