  Inertial Navigation Systems (INS) are algorithms that fuse inertial
measurements of angular velocity and specific acceleration with supplementary
sensors including GNSS and magnetometers to estimate the position, velocity and
attitude, or extended pose, of a vehicle. The industry-standard extended Kalman
filter (EKF) does not come with strong stability or robustness guarantees and
can be subject to catastrophic failure. This paper exploits a Lie group
symmetry of the INS dynamics to propose the first nonlinear observer for INS
with error dynamics that are almost-globally asymptotically and locally
exponentially stable, independently of the chosen gains. The observer is aided
only by a GNSS measurement of position. As expected, the convergence guarantee
depends on persistence of excitation of the vehicle's specific acceleration in
the inertial frame. Simulation results demonstrate the observer's performance
and its ability to converge from extreme errors in the initial state estimates.
