Robust particle filter for state estimation in presence of bounded but uncertain parameters based on ellipsoidal set membership approach

Accurate estimation of state variables plays an important role in control, monitoring and optimization. Considering that the uncertainty of parameter may back-propagate to the particle and then influence the state estimation, this paper proposes a robust particle filtering method in the presence of bounded uncertain parameters based on the ellipsoidal set membership filtering (ESMF) approach. This proposed method employs ellipsoidal sets to enclose the parameter uncertainty, and each prior particle and posterior particle are determined according to the ellipsoidal calculation based on the ESMF algorithm: The prior particle is characterized by an ellipsoid derived by the ellipsoidal summation of linear transformation ellipsoid, linearization error ellipsoid and system noise ellipsoid; Each posterior particle is obtained by updating the prior particle through the ellipsoidal intersection of the prior particle ellipsoid and the measurement ellipsoid. As a result, the uncertainty of parameter may be incorporated into the state estimation, and the advantages of both ESMF and particle filter are taken by the proposed method. The efficacy of the proposed method is shown by three simulation examples.