Indirect wind estimation onboard unmanned aerial systems (UASs) can be accomplished using existing air vehicle sensors along with a dynamic model of the UAS augmented with additional wind-related states. It is often desired to extract a mean component of the wind the from frequency fluctuations (i.e. turbulence). Commonly, a variation of the KALMAN filter is used, with explicit or implicit assumptions about the nature of the random wind velocity. This dissertation presents an H-infinity (H∞) filtering approach to wind estimation which requires no assumptions about the statistics of the process or measurement noise. To specify the wind frequency content of interest a low-pass filter is incorporated. We develop the augmented UAS model in continuous-time, derive the H∞ filter, and introduce a KALMAN-BUCY filter for comparison. The filters are applied to data gathered during UAS flight tests and validated using a vaned air data unit onboard the aircraft. The H∞ filter provides quantitatively better estimates of the wind than the KALMAN-BUCY filter, with approximately 10-40% less root-mean-square (RMS) error in the majority of cases. It is also shown that incorporating DRYDEN turbulence does not improve the KALMAN-BUCY results. Additionally, this dissertation describes the theory and process for using generalized polynomial chaos (gPC) to re-cast the dynamics of a system with non-deterministic parameters as a deterministic system. The concepts are applied to the problem of wind estimation and characterizing the precision of wind estimates over time due to known parametric uncertainties. A novel truncation method, known as Sensitivity-Informed Variable Reduction (SIVR) was developed. In the multivariate case presented here, gPC and the SIVR-derived reduced gPC (gPCr) exhibit a computational advantage over Monte Carlo sampling-based methods for uncertainty quantification (UQ) and sensitivity analysis (SA), with time reductions of 38% and 98%, respectively. Lastly, while many estimation approaches achieve desirable accuracy under the assumption of known system parameters, reducing the effect of parametric uncertainty on wind estimate precision is desirable and has not been thoroughly investigated. This dissertation describes the theory and process for combining gPC and H-infinity (H∞) filtering. In the multivariate case presented, the gPC H∞ filter shows superiority over a nominal H∞ filter in terms of variance in estimates due to model parametric uncertainty. The error due to parametric uncertainty, as characterized by the variance in estimates from the mean, is reduced by as much as 63%. / Doctor of Philosophy / On unmanned aerial systems (UASs), determining wind conditions indirectly, without direct measurements, is possible by utilizing onboard sensors and computational models. Often, the goal is to isolate the average wind speed while ignoring turbulent fluctuations. Conventionally, this is achieved using a mathematical tool called the KALMAN filter, which relies on assumptions about the wind. This dissertation introduces a novel approach called H-infinity (H∞) filtering, which does not rely on such assumptions and includes an additional mechanism to focus on specific wind frequencies of interest. The effectiveness of this method is evaluated using real-world data from UAS flights, comparing it with the traditional KALMAN-BUCY filter. Results show that the H∞ filter provides significantly improved wind estimates, with approximately 10-40% less error in most cases. Furthermore, the dissertation addresses the challenge of dealing with uncertainty in wind estimation. It introduces another mathematical technique called generalized polynomial chaos (gPC), which is used to quantify and manage uncertainties within the UAS system and their impact on the indirect wind estimates. By applying gPC, the dissertation shows that the amount and sources of uncertainty can be determined more efficiently than by traditional methods (up to 98% faster). Lastly, this dissertation shows the use of gPC to provide more precise wind estimates. In experimental scenarios, employing gPC in conjunction with H∞ filtering demonstrates superior performance compared to using a standard H∞ filter alone, reducing errors caused by uncertainty by as much as 63%.