  Distributed estimation in a blockchain-aided Internet of Things (BIoT) is
considered, where the integrated blockchain secures data exchanges across the
BIoT and the storage of data at BIoT agents. This paper focuses on developing a
performance guarantee for the distributed estimation in a BIoT in the presence
of malicious attacks which jointly exploits vulnerabilities present in both IoT
devices and the employed blockchain within the BIoT. To achieve this, we adopt
the Cramer-Rao Bound (CRB) as the performance metric, and maximize the CRB for
estimating the parameter of interest over the attack domain. However, the
maximization problem is inherently non-convex, making it infeasible to obtain
the globally optimal solution in general. To address this issue, we develop a
relaxation method capable of transforming the original non-convex optimization
problem into a convex optimization problem. Moreover, we derive the analytical
expression for the optimal solution to the relaxed optimization problem. The
optimal value of the relaxed optimization problem can be used to provide a
valid estimation performance guarantee for the BIoT in the presence of attacks.
