  Distributed state estimation arises in many applications such as position
estimation in robot swarms, clock synchronization for processor networks, and
data fusion. One characteristic is that agents only have access to noisy
measurements of deviations between their own and neighboring states. Still,
estimations of their actual state can be obtained in a fully distributed manner
using algorithms such as affine averaging. However, running this algorithm,
requires that the agents exchange their current state estimations, which can be
a privacy issue (since they eventually reveal the actual states). To counteract
this threat, we propose an encrypted version of the affine averaging algorithm
in this paper. More precisely, we use homomorphic encryption to realize an
encrypted implementation, where only one ``leader'' agent has access to its
state estimation in plaintext. One main challenge (which often arises for
recursive encrypted computations) is to prevent overflow w.r.t.~the bounded
message space of the cryptosystem. We solve this problem by periodically
resetting the agents' states with the help of the leader. We study the
resulting system dynamics with respect to different reset strategies and
support our findings with extensive numerical simulations.
