The fusion estimation issue of sensor networks is investigated for nonlinear time-varying systems with energy constraints, time-delays as well as packet loss. For the addressed problem, some local estimations are first obtained by using the designed Luenberger-type local estimator and then transmitted to a fusion center (FC) to generate a desired fusion value, where two classes of channels, whose schedules are governed by a diagonal matrix, are utilized to perform the information transmission. With the help of the Lyapunov stability theory, sufficient conditions are established to ensure the predetermined local and fused H-infinity performances over a finite horizon. Furthermore, by virtue of the well-known Schur complement lemma, the desired gains of local estimators and the suboptimal fusion weight matrices are obtained in light of the solution of linear matrix inequalities. It should be pointed out that the developed scheme is a two-step process under which the design of fusion weight matrices is based on the obtained estimator gains. Finally, a simulation example for sensor networks is performed to check the effectiveness of the proposed fusion scheme.