Robust state estimator of stochastic linear systems with unknown disturbances

The design of a filtering algorithm when an unknown disturbance exists is described. An alternative method to solve the disturbance estimation problem is proposed, which is to reformulate it to a tracking problem by using the relation of filter update. The reformulation of the problem makes it possible to use an effective sliding surface and fast estimate against arbitrary disturbance. A disturbance estimator using the discrete sliding mode is designed and improved by introducing a prediction parameter. In addition, a disturbance detection algorithm having a moderate calculation cost is designed using filter update and innovations. The normalised testing parameter makes it possible to use the standard chi-square table to determine the threshold level. The stability of the suggested algorithm is given and simulation results are included to demonstrate the effectiveness of the proposed technique.