  This paper considers a sequential estimation and sensor scheduling problem in
the presence of multiple communication channels. As opposed to the classical
remote estimation problem that involves one perfect (noiseless) channel and one
extremely noisy channel (which corresponds to not transmitting the observed
state), a more realistic additive noise channel with fixed power constraint
along with a more costly perfect channel is considered. It is shown, via a
counter-example, that the common folklore of applying symmetric threshold
policy, which is well known to be optimal (for unimodal state densities) in the
classical two-channel remote estimation problem, can be suboptimal for the
setting considered. Next, in order to make the problem tractable, a side
channel which signals the sign of the underlying state is considered. It is
shown that, under some technical assumptions, threshold-in-threshold
communication scheduling is optimal for this setting. The impact of the
presence of a noisy channel is analyzed numerically based on dynamic
programming. This numerical analysis uncovers some rather surprising results
inheriting known properties from the noisy and noiseless settings.
