An Invariant Extended Kalman Filter for Wind Estimation Using a Small, Fixed-Wing Uncrewed Aerial Vehicle

This article presents the design and implementation of an invariant extended Kalman filter (EKF) for wind estimation using a small, fixed-wing uncrewed aerial vehicle (UAV). First, it is shown that the UAV’s dynamics, extended to include a trivial model for the wind velocity dynamics, are invariant with respect to the Lie group <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {SE}(3)$</tex-math> </inline-formula>, the special Euclidean group of rigid transformations. It is also shown that an output comprising the vehicle’s inertial state and airspeed is equivariant with respect to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {SE}(3)$</tex-math> </inline-formula>. Based on these analysis results, an invariant EKF is then designed for the extended state equations and is implemented on experimental flight data. Wind estimates from the invariant EKF are compared with estimates obtained using a conventional EKF for two nominal aircraft motions: constant altitude, wings level flight, and constant altitude turning flight. The obtained wind estimates are then compared with wind measurements reconstructed using data from the aircraft’s air data unit comprising an angle of attack (AoA) flow vane, flank angle flow vane, and Kiel probe. The experimental results corroborate the expectation that the invariant EKF outperforms a conventional EKF in wind estimation accuracy.