Closed-loop vs. Open-loop Kalman Filter Architectures in Airborne Aided Inertial Navigation

Closed-loop (or feedback) error-state Kalman filters with their relatives and offspring are the state-of-the-art in modern aided inertial navigation research. Estimated inertial navigation system (INS) errors are continually fed back to the INS to correct the nominal system state before subsequent predictions. Conversely, in safety-critical aeronautical applications, open-loop (or feedforward) systems are an undisputed standard, where the inertial mechanization is strictly decoupled to allow for operational independence and fault isolation of computing units. We assess the performance impacts of this architectural choice beyond qualitative system-safety justifications using a standard inertial mechanization in geodetic coordinates and direct position aiding. Simulations using a variety of inertial sensor error characteristics, ranging from consumer to navigation grade systems, showcase the trade-off between smooth information fusion for high-end IMUs using an open-loop filter and the inherent long-term stability of the closed-loop architecture.

Derivations of Error-State Kalman Filter Kinematics for Globally Applicable Aided Inertial Navigation Systems

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.

Airborne Magnetic Anomaly Navigation with Neural-Network-Augmented Online Calibration

Airborne Magnetic Anomaly Navigation (MagNav) provides a jamming-resistant and robust alternative to satellite navigation but requires the real-time compensation of the aircraft platform's large and dynamic magnetic interference. State-of-the-art solutions often rely on extensive offline calibration flights or pre-training, creating a logistical barrier to operational deployment. We present a fully adaptive MagNav architecture featuring a "cold-start" capability that identifies and compensates for the aircraft's magnetic signature entirely in-flight. The proposed method utilizes an extended Kalman filter with an augmented state vector that simultaneously estimates the aircraft's kinematic states as well as the coefficients of the physics-based Tolles-Lawson calibration model and the parameters of a Neural Network to model aircraft interferences. The Kalman filter update is mathematically equivalent to an online Natural Gradient descent, integrating superior convergence and data efficiency of state-of-the-art second-order optimization directly into the navigation filter. To enhance operational robustness, the neural network is constrained to a residual learning role, modeling only the nonlinearities uncorrected by the explainable physics-based calibration baseline. Validated on the MagNav Challenge dataset, our framework effectively bounds inertial drift using a magnetometer-only feature set. The results demonstrate navigation accuracy comparable to state-of-the-art models trained offline, without requiring prior calibration flights or dedicated maneuvers.