  The study of multiplicative noise models has a long history in control theory
but is re-emerging in the context of complex networked systems and systems with
learning-based control. We consider linear system identification with
multiplicative noise from multiple state-input trajectory data. We propose
exploratory input signals along with a least-squares algorithm to
simultaneously estimate nominal system parameters and multiplicative noise
covariance matrices. Identifiability of the covariance structure and asymptotic
consistency of the least-squares estimator are demonstrated by analyzing first
and second moment dynamics of the system. The results are illustrated by
numerical simulations.
