  Inertial Navigation Systems (INS) are a key technology for autonomous
vehicles applications. Recent advances in estimation and filter design for the
INS problem have exploited geometry and symmetry to overcome limitations of the
classical Extended Kalman Filter (EKF) approach that formed the mainstay of INS
systems since the mid-twentieth century. The industry standard INS filter, the
Multiplicative Extended Kalman Filter (MEKF), uses a geometric construction for
attitude estimation coupled with classical Euclidean construction for position,
velocity and bias estimation. The recent Invariant Extended Kalman Filter
(IEKF) provides a geometric framework for the full navigation states,
integrating attitude, position and velocity, but still uses the classical
Euclidean construction to model the bias states. In this paper, we use the
recently proposed Equivariant Filter (EqF) framework to derive a novel observer
for biased inertial-based navigation in a fully geometric framework. The
introduction of virtual velocity inputs with associated virtual bias leads to a
full equivariant symmetry on the augmented system. The resulting filter
performance is evaluated with both simulated and real-world data, and
demonstrates increased robustness to a wide range of erroneous initial
conditions, and improved accuracy when compared with the industry standard
Multiplicative EKF (MEKF) approach.
