This note studies the resilient filtering problem for a class of discrete-time nonlinear complex networks. A novel resilient model is proposed by representing the variations of the filter gain matrix as a multiplicative noise term. By applying the variance-constrained approach to the coupled extended Kalman filter (EKF), an upper bound is derived for the estimation error covariance and such an upper bound is subsequently minimized to design the filter gain matrix at each sampling instant. A sufficient condition is established for the boundedness of the upper bound matrix that guarantees the boundedness of the estimation errors in the mean square sense. A numerical example involving tracking four mobile robots is provided to verify the effectiveness of the proposed filter.