  We employ reachability analysis in designing dynamic quantization schemes for
the remote state estimation of linear systems over a finite date rate
communication channel. The quantization region is dynamically updated at each
transmission instant, with an approximated reachable set of the linear system.
We propose a set-based method using zonotopes and compare it to a norm-based
method in dynamically updating the quantization region. For both methods, we
guarantee that the quantization error is bounded and consequently, the remote
state reconstruction error is also bounded. To the best of our knowledge, the
set-based method using zonotopes has no precedent in the literature and admits
a larger class of linear systems and communication channels, where the
set-based method allows for a longer inter-transmission time and lower bit
rate. Finally, we corroborate our theoretical guarantees with a numerical
example.
