A distributed fault estimation observer design method is proposed for a class of interconnected nonlinear systems. Firstly, an equivalent augmented interconnected system is obtained by augmenting the state vector and fault vector. Using coupling information among interconnected subsystems, the distributed fault estimation observer is designed to online estimate faults that occur in subsystems. Then, observer gain matrices are calculated based on $H_\infty$ performance and $L_2-L_\infty$ performance. Finally, a simulation is carried out to illustrate the feasibility and effectiveness of the proposed method.