  Consider an energy harvesting sensor continuously monitors a system and sends
time-stamped status update to a destination. The destination keeps track of the
system status through the received updates. Under the energy causality
constraint at the sensor, our objective is to design an optimal online status
updating policy to minimize the long-term average Age of Information (AoI) at
the destination. We focus on the scenario where the the channel between the
source and the destination is noisy, and each transmitted update may fail
independently with a constant probability. We assume there is no channel state
information or transmission feedback available to the sensor. We prove that
within a broadly defined class of online policies, the best-effort uniform
updating policy, which was shown to be optimal when the channel is perfect, is
still optimal in the presence of update failures. Our proof relies on tools
from Martingale processes, and the construction of a sequence of virtual
policies.
