Distributed Data-driven Unknown-input Observers for State Estimation

TL;DR

This work tackles state estimation in wireless sensor networks subject to unknown inputs and disturbances by developing a data-driven distributed unknown-input observer (D-DUIO) for continuous-time unknown-LTI systems. It first recalls a model-based DUIO and then replaces model identification with offline input/output/state data to derive data-driven observer matrices, under mild network and detectability assumptions. The authors establish consistency between offline and online trajectories, provide data-based existence and construction theorems, and demonstrate the approach on a multi-node mass-spring example, showing consensus and asymptotic convergence even with unknown inputs. The results offer a practical framework to achieve robust distributed state estimation without explicit system identification, with potential impact on CPS monitoring and security in sensor networks.

Abstract

Unknown inputs related to, e.g., sensor aging, modeling errors, or device bias, represent a major concern in wireless sensor networks, as they degrade the state estimation performance. To improve the performance, unknown-input observers (UIOs) have been proposed. Most of the results available to design UIOs are based on explicit system models, which can be difficult or impossible to obtain in real-world applications. Data-driven techniques, on the other hand, have become a viable alternative for the design and analysis of unknown systems using only data. In this context, a novel data-driven distributed unknown-input observer (D-DUIO) for unknown continuous-time linear time-invariant (LTI) systems is developed, which requires solely some data collected offline, without any prior knowledge of the system matrices. In the paper, first, a model-based approach to the design of a DUIO is presented. A sufficient condition for the existence of such a DUIO is recalled, and a new one is proposed, that is prone to a data-driven adaption. Moving to a data-driven approach, it is shown that under suitable assumptions on the input/output/state data collected from the continuous-time system, it is possible to both claim the existence of a D-DUIO and to derive its matrices in terms of the matrices of pre-collected data. Finally, the efficacy of the D-DUIO is illustrated by means of numerical examples.

Figures (8)

• Figure 1: Scheme of the proposed distributed sensor network.
• Figure 2: The sensor network topology.
• Figure 3: The estimation performance of D-DUIO.
• Figure 4: The estimation error of D-DUIO.
• Figure 5: The estimation performance of DUIO.

Theorems & Definitions (12)

• Remark 1
• Lemma 1: Solvability of Eqns. \ref{['eq:equality']}
• Theorem 1
• Remark 2
• Remark 3
• Remark 4
• Definition 1
• Theorem 2
• Lemma 2
• Theorem 3