  This paper considers a sequential sensor scheduling and remote estimation
problem with multiple communication channels. Departing from the classical
remote estimation paradigm, which involves one communication channel (noiseless
or noisy), we consider here the more realistic setting of two channels with
different characteristics (one is cheap but noisy, the other one is costly but
noiseless). We first show, via a counter-example, that the common folklore of
applying symmetric threshold-based policy, which is well known to be optimal
(for unimodal state densities) in the classical remote estimation problem, can
no longer be optimal in our setting. In view of that, and in order to make the
problem tractable, we introduce a side channel which signals to the receiver
the sign of the underlying state. We show, under some technical assumptions,
that a threshold-in-threshold based communication scheduling is optimal. The
impact of the results is analyzed numerically based on dynamic programming.
This numerical analysis reveals some rather surprising results inheriting known
properties from the single channel settings, such as not exhausting all the
opportunities available for the noisy channel.
