  In this paper, we study the relationship between resilience and accuracy in
the resilient distributed multi-dimensional consensus problem. We consider a
network of agents, each of which has a state in $\mathbb{R}^d$. Some agents in
the network are adversarial and can change their states arbitrarily. The normal
(non-adversarial) agents interact locally and update their states to achieve
consensus at some point in the convex hull $\calC$ of their initial states.
This objective is achievable if the number of adversaries in the neighborhood
of normal agents is less than a specific value, which is a function of the
local connectivity and the state dimension $d$. However, to be resilient
against adversaries, especially in the case of large $d$, the desired local
connectivity is large. We discuss that resilience against adversarial agents
can be improved if normal agents are allowed to converge in a bounded region
$\calB\supseteq\calC$, which means normal agents converge at some point close
to but not necessarily inside $\calC$ in the worst case. The accuracy of
resilient consensus can be measured by the Hausdorff distance between $\calB$
and $\calC$. As a result, resilience can be improved at the cost of accuracy.
We propose a resilient bounded consensus algorithm that exploits the trade-off
between resilience and accuracy by projecting $d$-dimensional states into lower
dimensions and then solving instances of resilient consensus in lower
dimensions. We analyze the algorithm, present various resilience and accuracy
bounds, and also numerically evaluate our results.
