Numerical weather modeling can benefit from improved wind sensing in the Earth's atmospheric boundary layer (ABL). Small, low-cost, uncrewed aircraft (drones) can be used to measure wind and a distribution of these vehicles could potentially provide measurements with much greater density and resolution, in both space and time, than current methods allow. To measure wind, a drone could be equipped with dedicated wind-measuring sensors, although these can be costly and obtrusive and must be carefully calibrated to account for interference effects. State estimation algorithms that combine a drone's operational measurements with a flight dynamic model can be used to infer wind without a dedicated wind sensor, although the sensor quality affects measurement accuracy. Previous studies have explored the effects of various sensors on wind estimate accuracy, but the effect of flight dynamic model fidelity has received less attention. This dissertation presents analysis of different aerodynamic model-free and model-based wind estimation methods, comparing six wind estimation formulations using experimental flight data from a small, fixed-wing aircraft. Each formulation is implemented using a Kalman filter, an extended Kalman filter, and an unscented Kalman filter. These filters are designed based on different assumptions related to the flight dynamic model, available sensors, and available measurements. Having identified a promising estimation approach, the dissertation next explores the value of incorporating unsteady effects into a flight dynamic model for model-based wind estimation. An unsteady aerodynamic model for a small, fixed-wing aircraft is developed, identified, and validated using experimental flight data. An extended Kalman filter is then designed and implemented for two motion models -- one that includes unsteady effects and another that does not. Analysis of the wind estimates and the estimation differences show that, while the unsteady flight dynamic model better predicts the aircraft motion, the value of incorporating this model for wind estimation is questionable. / Doctor of Philosophy / Wind velocity sensing is crucial to understanding the meteorological processes at low altitudes. The integration of low-cost drones has allowed them to be used as wind-sensing platforms. This is achieved by equipping small drones with dedicated wind-measuring sensors, often costly and infeasible, or inferring wind velocity from the drone's motion. Algorithms designed to infer wind can be used by combining onboard flight sensor measurements with a drone's flight dynamic model to infer wind. However, low-cost drones are usually equipped with low-cost flight sensors, which frequently lead to higher measurement uncertainty and degrade the accuracy of wind estimates. Previous studies have explored the effects of various sensors on wind estimates, but errors due to low-fidelity dynamic models have received less attention. This dissertation first presents a detailed analysis of different flight dynamic model-free and model-based wind estimation methods. It compares six wind estimation formulations. Each formulation is implemented in wind inferring algorithms called a Kalman filter, an extended Kalman filter, and an unscented Kalman filter. These algorithms are designed based on different assumptions related to the flight dynamic model, available flight sensors, and available measurements. Secondly, the value of incorporating a fixed-wing, unsteady flight dynamic model in a wind estimation scheme is analyzed. To this end, an unsteady flight dynamic model for a fixed-wing drone is developed, identified, and validated from data acquired from the drone's flight history. Furthermore, an extended Kalman filter is designed and implemented for two motion models -- one that includes unsteady effects and another that does not. The analysis of the time histories of the wind estimates and the wind estimate differences show that both model-based estimators perform equally well.