  A practical challenge which arises in the operation of sensor networks is the
presence of sensor faults, biases, or adversarial attacks, which can lead to
significant errors incurring in the localization of the agents, thereby
undermining the security and performance of the network. We consider the
problem of identifying and correcting the localization errors using inter-agent
measurements, such as the distances or bearings from one agent to another,
which can serve as a redundant source of information about the sensor network's
configuration. The problem is solved by searching for a block sparse solution
to an underdetermined system of equations, where the sparsity is introduced via
the fact that the number of localization errors is typically much lesser than
the total number of agents. Unlike the existing works, our proposed method does
not require the knowledge of the identities of the anchors, i.e., the agents
that do not have localization errors. We characterize the necessary and
sufficient conditions on the sensor network configuration under which a given
number of localization errors can be uniquely identified and corrected using
the proposed method. The applicability of our results is demonstrated
numerically by processing inter-agent distance measurements using a sequential
convex programming (SCP) algorithm to identify the localization errors in a
sensor network.
