Sequential drone routing for data assimilation on a 2D airborne contaminant dispersion problem

TL;DR

The paper addresses real-time data assimilation for airborne contaminant dispersion in emergencies, where high-fidelity models are unavailable. It combines a two- PDE physics backbone—a steady INS wind field and a transient AD concentration model—with an ensemble transform Kalman filter (ETKF) to sequentially update the state using sparse drone observations. A novel cost-function–based routing policy, EnIE-2D, guides the drone by balancing exploration and exploitation across a 2D domain with building obstacles, updating wind and concentration beliefs over time. The approach demonstrates that even with limited measurements and starting from an erroneous model, the framework can adaptively refine the contaminant map, producing actionable concentration estimates for emergency decision making and evacuation planning.

Abstract

The combined use of data from different sources can be critical in emergencies, where accurate models are needed to make real-time decisions, but high-fidelity representations and detailed information are simply unavailable. This study presents a data assimilation framework based on an ensemble Kalman filter that sequentially exploits and improves an advection-diffusion model in a case study concerning an airborne contaminant dispersion problem over a complex two-dimensional domain. An autonomous aerial drone is used to sequentially observe the actual contaminant concentration in a small fraction of the domain, orders of magnitude smaller than the total domain area. Such observations are synchronized with the data assimilation framework, iteratively adjusting the simulation. The path of the drone is sequentially optimized by balancing exploration and exploitation according to the available knowledge at each decision time. Starting from an erroneous initial model based on approximated assumptions that represent the limited initial knowledge available during emergency scenarios, results show how the proposed framework sequentially improves its belief about the dispersion dynamics, thus providing a reliable contaminant concentration map.

Figures (5)

• Figure 1: Computational domain $\Omega$. A prescribed wind flow of constant direction and intensity is imposed on the outer boundary for Eq. \ref{['eq:INS_strong']}. An initial gas concentration is defined as a scalar field $c_0(\boldsymbol{x})$, sketched together with a possible initial position of the drone at $t=0$.
• Figure 2: Quantitative error analysis for different $\theta$ values and the initial model without assimilation.
• Figure 3: Nodes of the mesh visited for $\theta = 0.0$ (red); $\theta = 0.3$ (green) and $\theta = 0.2$ (blue). Red points often overlap with blue ones. Concentration field at $t = T$ as background. Drone initial position $(i)$, initial release location marked by a yellow circular glyph $(ii)$ and drone final position at $t=T$$(iii)$.
• Figure 4: Concentration values over the curve $\gamma(s)$. True model, model based only on the initial assumptions, and filter with $\theta = 0.2$, respectively.
• Figure 5: Four representative contour plots for the contaminant concentration: the starting condition at $t = 0.0$, the reference true model at $t = T~(100.0\,s)$, the model based only on initial conditions, at the same time step, and the model reconstructed through data assimilation with $\theta=0.2$, still at $t = T$. A curve $\gamma(s)$ is highlighted by the blue poly-line and employed as section cut for a temporal evaluation of the contaminant field in Fig. \ref{['fig:conc_plot']}.