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A novel robust Kalman filter (KF)-based controller is proposed for a multivariable 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 feedbackfeedforward 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. Box-Jenkins model and its applicationsIdentification of a class of system described by MIMO BJ model, and the associated Kalman filter directly from the input-output data is proposed [1,2]. There is no need to specify the covariance of the disturbance and the measurement noise, thereby avoiding the use the Riccati equation to solve for the Kalman gain. The output is the desired waveform, termed signal, corrupted by a stochastic disturbance and zero-mean white measurement noise. The state-space BJ model is an augmented system formed of the signal and disturbance model. The signal model and the disturbance models are driven respectively by a user-defined accessible input, and an inaccessible zero-mean white noise process. The signal model is generally a cascade, parallel and feedback combinations of subsystems such as controllers, actuators, plants, and sensors [3]. Unlike the ARMA model, the Box-Jenkins model is observable but not controllable while the signal model is both controllable and observable. In other words, the transfer matrix of the system is non-minimal whereas that of the signal is minimal. This issue will need to be addressed in the identification and implementation of the Kalman filter. Kalman filter and its key propertiesThe structure of the Kalman filter is determined using the internal model principle which establishes the necessary and sufficient condition for the tracking of the output of a dynamical system [3,4]. In accordance with this principle, the Kalman filter consists of (a) a copy of the system model driven by the residuals, and (b) a gain term, termed the Kalman gain, to stabilize the filter. The Kalman gain is determined such that the residual of the Kalman filter is a zero-mean white noise pr...

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