Adaptive PID-based gain control for robust vision-inertial attitude estimation on SO(3)

Existing solutions to attitude estimation for unmanned aerial vehicles (UAVs) in GPS-denied environments face a persistent trade-off: classical filtering approaches such as the extended Kalman filter (EKF) suffer from linearization errors, while geometric nonlinear observers on the special orthogonal (SO(3)) Lie group avoid this issue but rely on a manually tuned, fixed correction gain. A fixed gain cannot simultaneously deliver fast convergence during nominal operation and robust noise rejection when inertial sensors degrade, and existing adaptive or gain-scheduled alternatives either require manual heuristics or lack a real-time responsiveness mechanism, leaving gain tuning an open and recognized limitation in this line of work. This paper proposes a robust vision-inertial fusion method for UAV attitude estimation using a nonlinear observer on the SO(3) Lie group with adaptive gain control that directly addresses this gap. We introduce a PID-based gain adaptation mechanism that dynamically modulates the observer's correction term based on real-time gyroscope variance metrics. When inertial data deteriorates due to noise or bias, the observer automatically relies more on visual corrections; during stable periods, it prioritizes inertial data for faster convergence. MATLAB/Simulink simulation results demonstrate that the adaptive observer reduces attitude estimation error by approximately 65 percent during disturbances and achieves reconvergence over 10 times faster after disturbances compared to fixed-gain baselines, while maintaining bounded errors during severe gyroscope perturbations where fixed gain observers diverge. This work provides a computationally efficient solution to the gain-tuning challenge in geometric attitude estimation for autonomous UAVs operating in GPS-denied environments. Validation is performed through comprehensive simulation studies.