Wind Estimate Uncertainty Quantification and Sensitivity Analysis Using Generalized Polynomial Chaos

Indirect wind estimation onboard unmanned aerial systems (UASs) can be accomplished using existing onboard sensors along with a dynamic model of the UAS augmented with additional wind-related states. Although many indirect estimation approaches achieve desirable accuracy under the assumption of known system parameters, the effect of parametric uncertainty on wind estimate precision is important and has not been thoroughly investigated. This paper describes the theory and process for using generalized polynomial chaos (gPC) to recast the dynamics of a system with nondeterministic parameters as a deterministic system. The concepts are applied to the problem of wind estimation and to characterizing the precision of wind estimates over time due to known parametric uncertainties. In the multivariate case, gPC exhibits a computational advantage over Monte Carlo sampling-based methods and produces a deterministic system upon which control and estimation methods can be applied.