State estimation method using median of multiple candidates for observation signals including outliers

The state estimation problem for systems in which observation outputs include outliers is addressed herein. When the observation output has outliers, the accuracy of the state estimation is dramatically worse. To overcome this problem, a novel observer structure using multiple candidates of the estimated state is proposed. First, multiple candidates of the estimated state are created; each candidate uses the sensing output value of a different detection timing. If outliers occur infrequently, eliminating candidates affected by outliers can prevent deterioration in estimation accuracy. Our proposed observer select one from the obtained candidates of the estimated state using a median or a weighted median operation. Through the median operation, the estimated state that does not use the outlier value is selected from these candidates. In addition, a method is provided to design the observer gains of these estimated state candidates based on a reachable set of the estimated state error, using Lyapunov-based inequalities. The effectiveness of the proposed observer is illustrated using numerical examples.