Novel Direct and Accurate Identification of Kalman Filter for General Systems Described by a Box-Jenkins Model

Abstract

A novel robust Kalman filter (KF)-based controller is proposed for a multivari-able system to accurately track a specified trajectory under unknown stochastic disturbance and measurement noise. The output is a sum of uncorrelated signal, disturbance and measurement noise. The system model is observable but not controllable while the signal one is controllable and observable. An emulator-based two-stage identification is employed to obtain a robust model needed to design the robust controller. The system and KF are identified and the signal and output error estimated. From the identified models, minimal realizations of the signal and KF, the disturbance model and whitening filter are obtained using balanced model reduction techniques. It is shown that the signal model is a transfer matrix relating the system output and the KF residual, and the residual is the whitened output error. The disturbance model is identified by inverse filtering. A feedback-feedforward controller is designed and implemented using an internal model of the reference driven by the error between the reference and the signal estimate, the feedforward of reference and output error. The successful evaluation of the proposed scheme on a simulated autonomously-guided drone gives ample encouragement to test it later, on a real one.