We consider the problem of resilient state estimation in the presence of integrity attacks. There are m sensors monitoring the state and p of them are under attack. The sensory data collected by the compromised sensors can be manipulated arbitrarily by the attacker. The classical estimators such as the least squares estimator may not provide a reliable estimate under the so-called (p;m)-sparse attack. In this work, we are not restricting our efforts in studying whether any specific estimators resilient to the attack or not, but instead we aim to present some generic sufficient and necessary conditions for re silenced by considering a general class of convex optimization based estimators. The sufficient and necessary conditions are show into be tight, with a trivial gap. We further specialize our result to scalar sensor measurements case and extend our framework to incorporate estimators with correlated cost function optimization.Experimental results tested on the IEEE 14-bus test system validate the theoretical analysis.
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