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Question
In the false data injection (FDI) attack, assume that the normal measurement is z=Hx+n and the attacked measurement is z_a=z+a. Assume that the weighted least square (WLS) solution is given by x ^=(H^T R^(-1) H)^(-1) H^T R^(-1) z for the normal measurement z, and let x ^_a be the WLS solution obtained from the attacked measurement z_a. Use your linear algebra knowledge to prove that the pre-attack residual r=z-Hx ^ is the same as the post-attack residual r_a=z_a-Hx ^_a if a=Hc.
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