Optimal Sensor Placement and Movement for Effective Data Assimilation: Is there anything better than Lagrangian sensors?

Designing optimal locations and trajectories for sparse sensors under a limited budget is essential for effective Data Assimilation (DA) in reconstructing and predicting dynamical systems (DS). A commonly used sensor trajectory, such as that of Lagrangian sensors, typically fails to track important features of DS due to passively tracing the flow and potential clustering, which can oversample some areas, while others leave unobserved.



This work investigates the performance of Lagrangian sensors in two DS under a nudging algorithm: the one-dimensional Kuramoto–Sivashinsky equation (1D KSE) and the two-dimensional Navier–Stokes equations (2D NSE). Results show that Lagrangian sensors fail to achieve DA reconstruction in 1D KSE, regardless of the number of sensors. In 2D NSE, the DA reconstruction is successful only with many ideal Lagrangian sensors are available; sparse Lagrangian sensors fail to recover the dynamical system.

To improve DA reconstruction, we propose two sensor placement/movement strategies: (i) Perturbed Lagrangian sensors, adding random perturbation to avoid clustering and improve coverage, and (ii) Target Sensors, moving sensors toward the most informative regions of DS. Both strategies significantly improved the DA reconstruction across the tests (e.g.,1D diffusive and reactive system and 2D isotropic turbulence). These results challenge the traditional view of Lagrangian sensors' effectiveness and offer new strategies improving DA using very sparse sensor networks.