Effects of Two Modeling Assumptions on Wind Reconstruction from Longitudinal Aircraft Motion

Abstract

Modern techniques to estimate wind from a flight vehicle often combine onboard sensor measurements with mathematical models of the aircraft’s dynamics. Whereas prior studies have investigated the impact of sensor errors on estimate accuracy, this work presents a method to study the impact of a simplified flight dynamic model. The method begins by establishing a simulated “truth”: a nonlinear fixed-wing longitudinal flight dynamic model is simulated attempting straight-and-level flight in turbulent wind. Common simplifications of the flight dynamic model are derived: linearizing about a trim condition and neglecting the angular contribution of the wind velocity. For each simplification, numerical reconstructions of the wind and unsensed states are derived. Because the wind reconstructions use perfect sensor information, the discrepancy between the reconstructed wind (computed from a simplified dynamic model) and the “true” wind (which perturbs the original nonlinear model) is error incurred solely by modeling simplification. The method is demonstrated via an example study in which both open-loop and closed-loop flight simulations are conducted in a Monte Carlo fashion for a Dryden wind field. In this demonstration, neglecting angular wind is shown to cause three times as much error in wind speed estimates as linearization during closed-loop flight. The method can be extended to other aircraft and variables of interest. It is presented as a procedure that practitioners can follow to investigate the impact of flight dynamic modeling accuracy for airborne wind measurement.