  In this work, we explore the recent advances in equivariant filtering for
inertial navigation systems to improve state estimation for uncrewed aerial
vehicles (UAVs). Traditional state-of-the-art estimation methods, e.g., the
multiplicative Kalman filter (MEKF), have some limitations concerning their
consistency, errors in the initial state estimate, and convergence performance.
Symmetry-based methods, such as the equivariant filter (EqF), offer significant
advantages for these points by exploiting the mathematical properties of the
system - its symmetry. These filters yield faster convergence rates and
robustness to wrong initial state estimates through their error definition. To
demonstrate the usability of EqFs, we focus on the sensor-fusion problem with
the most common sensors in outdoor robotics: global navigation satellite system
(GNSS) sensors and an inertial measurement unit (IMU). We provide an
implementation of such an EqF leveraging the semi-direct product of the
symmetry group to derive the filter equations. To validate the practical
usability of EqFs in real-world scenarios, we evaluate our method using data
from all outdoor runs of the INSANE Dataset. Our results demonstrate the
performance improvements of the EqF in real-world environments, highlighting
its potential for enhancing state estimation for UAVs.
