This article studies the problem of false data injection (FDI) attacks against remote state estimation. The scenario that malicious attackers can intercept original data packets and also eavesdrop on some side information of system states with extra sensors is considered. To clarify a counterintuitive issue in existing work, a different innovation-based linear attack policy fusing all available information is proposed. First, the evolution of a posteriori estimation error covariance with FDI attacks is derived. Then, explicit solutions of optimal stealthy attack coefficients are obtained without solving optimization problems numerically. The condition under which there exist multiple optimal attacks is analyzed. In addition, an easy-to-check criterion for comparing two information fusion methods in scalar systems is given. Simulation results show that, compared with existing work, the proposed attack strategy can completely deceive the anomaly detector and cause more severe performance degradation in remote state estimation.