  We consider the problem of robust estimation in the presence of integrity
attacks. There are m sensors monitoring the state and p of them are under
attack. The malicious measurements 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 estimator is resilient to the attack or not, but
instead we aim to present some generic sufficient and necessary conditions for
robustness by considering a general class of convex optimization based
estimators. The sufficient and necessary conditions are shown to be tight, with
a trivial gap.
