Source Localization in Linear Dynamical Systems using Subspace Model Identification

We study the problem of localizing sources of unknown forced inputs in linear dynamical systems with unknown system matrices. This problem is relevant in several real-world dynamical systems, including power networks and mechanical systems, where the unknown inputs could be forced oscillations or malicious attacks. Localizing sources is key to mitigating the impact of these unwanted inputs on the system's performance. To this aim, we develop an algorithm that finds sources based on the modal information in the inputs. We obtain this information from the eigenvalues of the (sampled) system matrices, which we estimate using a subspace identification method. Importantly, our algorithm relies on a key assumption that inputs can be appropriately modeled as outputs of some latent linear systems. This assumption allows us to go beyond periodic inputs that are a mainstay in the literature of source localization problems. We illustrate our findings via multiple numerical studies.