# Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data

arXiv: https://arxiv.org/abs/2002.06613 · HTML: https://mlsanity.com/paper/2002.06613/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories](https://mlsanity.com/paper/2203.12794/) (2022)
- [Outlier-Robust Linear System Identification Under Heavy-tailed Noise](https://mlsanity.com/paper/2501.00421/) (2024)
- [Boosting-Enabled Robust System Identification of Partially Observed LTI Systems Under Heavy-Tailed Noise](https://mlsanity.com/paper/2504.18444/) (2025)

## Abstract (arXiv)

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.