  In this paper, a robust data-driven moving horizon estimation (MHE) scheme
for linear time-invariant discrete-time systems is introduced. The scheme
solely relies on offline collected data without employing any system
identification step. We prove practical robust exponential stability for the
setting where both the online measurements and the offline collected data are
corrupted by non-vanishing and bounded noise. The behavior of the novel robust
data-driven MHE scheme is illustrated by means of simulation examples and
compared to a standard model-based MHE scheme, where the model is identified
using the same offline data as for the data-driven MHE scheme.
