Identification of Linear Systems with Multiplicative Noise from Multiple Trajectory Data

Understand

The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data.

• An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system matrices and the covariance matrix of the multiplicative noise.
• The algorithm does not need prior knowledge of the noise or stability of the system, but requires only independent inputs with pre-designed first and second moments and relatively small trajectory length.
• The study of identifiability of the noise covariance matrix shows that there exists an equivalent class of matrices that generate the same second-moment dynamic of system states.