ROBUST-ADAPTIVE ESTIMATION OF UNMEASURABLE STATES AND EXTERNAL DISTURBANCES OF A DYNAMIC OBJECT BASED ON AN AUGMENTED KALMAN FILTER

Abstract

The paper addresses the problem of joint estimation of the directly unmeasurable states of a dynamic object and of external disturbances when information is available only on the control inputs and on the measured output signals. To solve this problem, a robust-adaptive algorithm based on an augmented Kalman filter is proposed, in which the external disturbance is included in the extended state vector. Two operating modes of the algorithm are considered. For slowly varying disturbances, a random-walk model with a constant process-noise covariance is used, whereas for rapidly varying inputs a signal adaptation  driven by the normalized innovation is proposed. The conditions for correct estimation are formulated on the basis of the observability and detectability of the augmented system, as well as of the boundedness of the process- and measurement-noise covariances. To increase robustness, clipping of the standardized innovation and the Joseph form of the error covariance update are used; for the multichannel case, diagonal regularization of the innovation matrix is provided when it is ill-conditioned. For a second-order test object, complete observability of the augmented system is established. A sensitivity analysis of the algorithm with respect to the adaptation parameters and a quantitative comparison of the conventional and the adaptive-robust filters in terms of RMSE, MAE and tracking delay are carried out. In the numerical experiment, the adaptive-robust algorithm reduced the tracking delay of a rapidly varying disturbance from 0.86 to 0.20 s with a practically unchanged RMSE and a simultaneous reduction of the reconstruction errors of the hidden states.