An air-data estimator for generic air-breathing hypersonic vehicles (AHSVs) is developed and demonstrated with an example vehicle configuration. The AHSV air-data estimation strategy emphasized improvement of the angle of attack estimate accuracy to a degree necessitated by the stringent operational requirements of the air-breathing propulsion. the resulting estimation problem involves highly nonlinear diffusion process (propagation); consequently, significant distortion of a posteriori conditional density is suspected. A simulation based statistical analysis tool is developed to characterize the nonlinear diffusion process. The statistical analysis results indicate that the diffusion process preserves the symmetry and unimodality of initial probability density shape state variables, and provide the basis for applicability of an Extended Kalman Filter (EKF). An EKF is designed for the AHSV air-data system and the air data estimation capabilities are demonstrated.