Abstract
We propose a robust Extended Kalman Filter (EKF) architecture for land navigation using an array of hundreds of low-cost micro-electromechanical systems (MEMS) inertial sensors. The main challenges in this setting are bursty sensor-specific bias errors, bias drift, and the need to aggregate many inertial measurements without increasing the computational burden of the navigation filter. To address these challenges, we introduce Robust Inertial Sensor Array Fusion (RISAF), a pre-filtering framework that combines dynamic percentile gating with real-time bias tracking before the EKF prediction step. The proposed aggregation suppresses anomalous sensor readings and compensates for individual sensor drift while preserving the vehicle-level kinematic signal. Because the resulting fused inertial measurements are passed to a standard EKF, the navigation filter retains a minimal state vector and supports real-time execution. We evaluate RISAF through extensive simulations and real-world field tests in GNSS-denied environments, with the data provided as supplementary material. Compared with a baseline that averages the sensor readings, RISAF achieves substantially improved azimuth accuracy and reduced drift accumulation. These results demonstrate that robust fusion of large MEMS inertial arrays can bridge a substantial part of the gap between cost-effective hardware and tactical-grade inertial navigation performance.
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Apr 24, 2026cs.RO
Radar-Inertial Odometry (RIO) based on the Extended Kalman Filter (EKF) relies on accurate extrinsic calibration between the radar and the Inertial Measurement Unit (IMU) and is sensitive to disturbances, as large linearization errors can degrade performance or even cause divergence. To address these limitations, this letter proposes an Equivariant Filter (EqF) for RIO based on a Lie group symmetry that geometrically couples navigation states and IMU biases, extending it to incorporate radar-IMU extrinsic calibration and multi-state constraint updates. This equivariant formulation inherently preserves consistency and enhances robustness, enabling reliable state estimation even under poor or completely wrong initialization of calibration states. Real-world experiments on two different Uncrewed Aerial Vehicles (UAVs) show that the proposed EqF-RIO achieves state-of-the-art accuracy under correct extrinsic calibration and offers improved convergence under large calibration errors, where the conventional EKF-RIO fails. Evaluation code is open-sourced.
Giulio Delama, Jan Michalczyk, Morten Nissov +4
Jun 30, 2026cs.RO
Inertial navigation systems aided by three-dimensional landmark measurements constitute a fundamental problem in robotic perception and state estimation. Classical SO(3)-based Extended Kalman Filter (SO(3)-EKF) approaches provide practical solutions, but suffer from the false observability problem, in which the filter becomes overconfident in unobservable directions, leading to degraded estimation performance. The Invariant EKF (IEKF) addresses this limitation by reformulating the system dynamics as a group-affine system on a Lie group, although its measurement update does not fully satisfy certain state compatibility properties. More recently, the Iterated Invariant EKF (IterIEKF) was proposed to further improve the IEKF by ensuring, in the low-noise regime, that the estimated state remains on the observed state manifold while the uncertainty is confined to its tangent space. In this work, we formulate and apply the IterIEKF to landmark-based inertial 3D localization for the first time. Through numerical simulations, we show that the proposed approach outperforms the classical SO(3)-EKF, the Iterated SO(3)-EKF, and the IEKF in terms of both estimation accuracy and consistency.
Hilton Marques Souza Santana, João Carlos Virgolino Soares, Marco Antonio Meggiolaro
Jul 3, 2026cs.RO
Global navigation systems require state estimation algorithms that handle Earth's curvature, Earth's rotation, and gravitational variations. These factors can typically be neglected in local navigation algorithms for robots, drones, etc. In classical error-state Kalman Filtering (ESKF) the error state dynamics are trajectory-dependent. Invariant ESKFs utilize Lie Group symmetries to represent the error, which can render error propagation trajectory-independent for group-affine systems. Choosing between a standard filter (where position and velocity errors are defined additively in the navigation frame), a left-invariant filter (where errors are represented in the body frame) and a right-invariant filter (where errors are represented in the navigation/world frame) depends on system dynamics and sensor configuration. This note presents the mathematical formulas for four classical and invariant ESKFs for globally applicable aided inertial navigation systems. It is intended to serve as a systematic reference for comparison and implementation.
Antonia Hager, Torleiv H. Bryne