The estimation of the gas concentration (process-state) associated with a stationary or moving source using a sensing aerial vehicle (SAV) is considered. The dispersion from such a gaseous source into the ambient atmosphere is representative of an accidental or deliberate release of chemicals, or a release of gases from biological systems. Estimation of the concentration field provides a superior ability for source localization, assessment of possible adverse impacts, and eventual containment. The abstract and finite-dimensional approximation framework presented couples theoretical estimation and control with computational fluid dynamics methods. The gas dispersion (process) model is based on the advection-diffusion equation with variable eddy diffusivities and ambient winds. Cases are considered for a 2D and 3D domain. The state estimator is a modified Luenberger observer with a €�collocated€� filter gain that is parameterized by the position of the SAV. The process-state (concentration) estimator is based on a 2D and 3D adaptive, multigrid, multi-step finite-volume method. The grid is adapted with local refinement and coarsening during the process-state estimation in order to improve accuracy and efficiency. The motion dynamics of the SAV are incorporated into the spatial process and the SAV€™s guidance is directly linked to the performance of the state estimator. The computational model and the state estimator are coupled in the sense that grid-refinement is affected by the SAV repositioning, and the guidance laws of the SAV are affected by grid-refinement. Extensive numerical experiments serve to demonstrate the effectiveness of the coupled approach.