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The robust H∞ filtering problem for the polynomial nonlinear systems against parametric uncertainty is investigated in this paper. By introducing additional matrix variables, we succeed in eliminating the coupling terms among system dynamics, filter dynamics and the Lyapunov matrix. Sufficient conditions to guarantee the filter stability with guaranteed H∞ norm from the unknown norm-bounded disturbance signal to the estimation error are derived in terms of state dependent matrix inequalities, which provide an effective way for the application of the new sum of squares programming technique to obtain computationally tractable solutions. Robust H∞ filter is designed in an efficient computational manner. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed methodology.