Estimation of aerodynamic effects in coaxial rotors for UAVs using fractional Unscented Kalman Filter and DCSV

Coaxial rotors, especially in larger Unmanned Aerial Vehicles (UAVs), introduce new challenges in aerodynamic modeling and control due to complex rotor interactions. Known for their efficiency in compact designs, coaxial rotors face issues such as rotor downwash interference, turbulence, and reduced aerodynamic efficiency, all of which can severely impact flight stability and control precision. Traditional Kalman filters (KF) are often an efficient alternative to address these problems, but they are insufficient for the nonlinear dynamics of UAVs, leading to the adoption of the Unscented Kalman Filter (UKF) for more precise state estimation. However, UKF’s performance is limited by the non-local nature of aerodynamic effects. This paper proposes a two-step method to address these challenges. First, by incorporating fractional-order derivatives, the Merwe point selection technique, and the DCSV (Dynamic Confined Spaces of Velocities) criterion for multiple time scales, the proposed FUKF enhances real-time prediction accuracy. Second, to demonstrate the efficiency of the signals observed by the FUKF, a weak sparse identification technique for nonlinear dynamics with weighted integration and the Bayesian MCMC (Monte Carlo Markov Chain) method are used offline to identify aerodynamic equations, accounting for rotor-rotor interference and complex airflows. The results show that for different time scales, classical KF models fail to accurately predict the states associated with aerodynamic effects due to the lack of inclusion of parametric interdependence, a concept introduced in a forthcoming lemma. This approach improves the modeling accuracy of aerodynamic effects for coaxial rotors and represents an advancement in the performance of estimation techniques for UAVs.