Atmospheric sensing tasks, including measuring the thermodynamic state (pressure, temperature, and humidity) and kinematic state (wind velocity) of the atmospheric boundary layer (ABL) can aid in numerical weather prediction, help scientists assess climatological and topological features over a region, and can be incorporated into flight path planning and control of small aircraft. Small uncrewed aerial vehicles (UAVs) are becoming an attractive platform for atmospheric sensing tasks as they offer increased maneuverability and are low-cost instruments when compared to traditional atmospheric sensing methods such as ground-based weather stations and weather balloons. In situ measurements using a UAV can be obtained for the thermodynamic state of the ABL using dedicated sensors that directly measure pressure, temperature, and humidity whereas the kinematic state (wind velocity) can be measured directly, using, for example, a five-hole Pitot probe or a sonic anemometer mounted on an aircraft, or indirectly. Indirect measurement methods consider the dynamics of the aircraft and use measurements from its operational sensor suite to infer wind velocity. This work is concerned with the design of the invariant extended Kalman filter (invariant EKF) for indirect wind estimation using a small, fixed-wing uncrewed aerial vehicle. Indirect wind estimation methods are classified as model-based or model-free, where the model refers to the aerodynamic force and moment model of the considered aircraft. The invariant EKF is designed for aerodynamic model-free wind estimation using a fixed-wing UAV in horizontal-plane flight and the full six degree of freedom UAV. The design of the invariant EKF relies on leveraging the symmetries of the dynamic system in the estimation scheme to obtain more accurate estimates where convergence of the filter is guaranteed on a larger set of trajectories when compared to conventional estimation techniques, such as the conventional extended Kalman filter (EKF). The invariant EKF is applied on both simulated and experimental flight data to obtain wind velocity estimates where it is successful in providing accurate wind velocity estimates and outperforms the conventional EKF. Overall, this work demonstrates the feasibility and effectiveness of implementing an invariant EKF for aerodynamic model-free indirect wind estimation using only the available measurements from the operational sensor suite of a UAV. / Doctor of Philosophy / Atmospheric sensing tasks, such as obtaining measurements of the pressure, temperature, humidity, and wind velocity of the atmospheric boundary layer (ABL), the lowest part of the atmosphere, have historically been dominated by the use of ground-based weather stations and deployment of weather balloons. Uncrewed aerial vehicles (UAVs) are emerging as an attractive, cost-effective platform for measuring desired quantities in the ABL. A UAV provides increased maneuverability when compared to fixed ground-based sensors and weather balloons as it can fly in different patterns and over any specified region within physical limits. Measurements of the ABL can help atmospheric scientists improve numerical weather prediction by providing more temporally and spatially dense data, in addition to helping assess climatological or topological features such as how the flow of wind varies over different types of terrain. A UAV can measure wind velocity directly or indirectly. Direct wind velocity measurements require mounting a dedicated wind sensor on a UAV and indirect measurement methods require only knowledge of the UAV's motion model with measurements from sensors already onboard to support automated flight. This work is concerned with designing an estimator for indirect wind velocity estimation using a small, fixed-wing UAV and only measurements from its operational sensor suite. The estimator, the invariant extended Kalman filter, leverages the symmetries of the system to provide estimates of the state or extended state of the system which can include position, velocity, and wind velocity. A system with symmetry is one that is unchanged by actions or transformations such as translation and rotation. The knowledge that the system remains unchanged under some transformations is used in the design of the invariant EKF. This estimator is then implemented for indirect wind estimation on both simulated and experimental flight data where it, in general, outperforms a conventional estimation method–the extended Kalman filter. The work presented in this dissertation demonstrates the effectiveness of implementing an invariant EKF for indirect wind estimation using a small, fixed-wing UAV and measurements from its operational sensor suite.