Identification of linear systems with multiplicative noise from multiple trajectory data

The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and data is proposed for joint estimation nominal system matrices covariance matrix noise. does not need prior knowledge or stability system, but requires only independent inputs pre-designed first second moments relatively small trajectory length. study identifiability shows that there exists an equivalent class generate same second-moment dynamic states. It demonstrated how to obtain estimates covariance. Asymptotic consistency verified under sufficiently exciting controllability conditions. Non-asymptotic performance also analyzed assumption bounded. analysis provides high-probability bounds vanishing as number trajectories grows infinity. results are illustrated by numerical simulations.