  The objective of this paper is to investigate how noisy and incomplete
observations can be integrated in the process of building a reduced-order
model.
  This problematic arises in many scientific domains where there exists a need
for accurate low-order descriptions of highly-complex phenomena, which can not
be directly and/or deterministically observed. Within this context, the paper
proposes a probabilistic framework for the construction of "POD-Galerkin"
reduced-order models. Assuming a hidden Markov chain, the inference integrates
the uncertainty of the hidden states relying on their posterior distribution.
Simulations show the benefits obtained by exploiting the proposed framework.
