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To solve the problem of state estimation for systems with dual noise terms, a zonotope and Gaussian Kalman filters based state estimation algorithm is proposed. A state estimator is designed to obtain the estimation interval of the true state in the presence of both stochastic and unknown but bounded (UBB) uncertainties. A novel coefficient that weighs the relative influence of stochastic and UBB uncertainties is introduced, and the optimal weight solution is introduced by minimizing the polyhedron space and mean square error. Finally, two simulation examples are presented to demonstrate the accuracy and effectiveness of the proposed algorithm.

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