Variational Adaptive LM-IEKF for Full State Navigation System of Wind Disturbance and Observability Analysis

Robust and accurate state estimation algorithms applied to the small unmanned aerial vehicles (UAVs) are always promising depending on the multiple onboard local and global sensors. This article proposes a variational adaptive Levenberg–Marquardt iterated extended Kalman filter (VA-LM-IEKF) full state estimation algorithm to calculate the reliable UAV flight state parameters in wind disturbance. The navigation system based on the LM-IEKF can provide an accurate state by expanding the optimization range of estimated points. An adaptive filter using the variational Bayesian approach is proposed to improve the filter robustness to the observation noise covariance matrix. Moreover, a judging criterion is introduced into the filter observation correction step to eliminate the observed abnormal values. In addition, observability analysis with the Lie algebra for the navigation system is established to evaluate the system observability. Simulation and real-data experiments in the self-developed small UAVs platform demonstrate that the performance of the proposed algorithm is better than the state-of-the-art methods in solution accuracy and filter robustness.