In this paper, we propose a Virtual Distributed Observer (VDO) built by virtually excluding some redundant sensors from conventional distributed observers. By using the VDO, we can construct not only robust estimators against sensor attacks but detectors of attacks by malicious agents. We also consider the new framework of estimation problem, which is more useful to adapt under distributed conditions. This relaxed problem makes it possible to estimate the partial state under sensor attacks even if the whole observer system is not detectable. Finally, we confirm the effectiveness of our proposed method through numerical simulations in the presence of measurement attacks.