Comparison of the Guaranteed State Estimator and the Zonotopic Kalman Filter for Linear Time-Variant Systems

Abstract

This letter compares two well-known formulations of set-membership estimators for linear time-variant plants based on zonotopes. The guaranteed state estimator is based on computing sequential intersections between the predicted set and the each of strip of states consistent with the different components of the output. The zonotopic Kalman filter proposes a formulation inspired on the Kalman filter. Both formulations seek to minimize the uncertainty of the estimation, measured through the F-radius. This letter proves that both formulations are equivalent when the noises affecting the different components of the output vector are not correlated. On the other hand, when there are some cross-relations between the noise components, the zonotopic Kalman filter is able to produce more accurate estimations. Those facts are considered together with the computational requirement of both formulations, leading to a recommendation on the observer choice. The theoretical analysis is complemented with a numerical example.