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Electrical capacitance tomography (ECT) is considered as a promising process tomography (PT) technique, and the speed and accuracy of the image reconstruction algorithms play an important role in successful applications of ECT. In this study, a dynamic reconstruction model, which integrates the ECT measurement information and physical evolution information of the objects of interest from the dynamics equations, is presented. The constrained ensemble Kalman filter (CEnKF) method is introduced for solving the dynamic model. In the update step within the CEnKF method, a generalised objective functional, which has been developed using the M-estimation and a generalised stabilising functional, is proposed. An efficient algorithm, which integrates the beneficial advantages of the filled function method and the homotopy method, is designed for searching a possible global optimal solution. Numerical simulations are implemented to evaluate the feasibility and effectiveness of the proposed algorithm. For the cases simulated in this study, the accuracy and spatial resolution of the reconstructed images by the proposed algorithm are improved, and the artefacts in the reconstructed images can be removed effectively, which indicate that the proposed algorithm is a promising candidate for solving the ECT inverse problem.