Computationally Efficient Static North-Finding: Decoupled AHRS, RLS Bias Estimation, and Attitude Error Analysis

Abstract

Accurate autonomous north-finding in GNSS-denied environments is critical; however, conventional gyrocompassing often suffers from heavy computational complexity and high sensitivity to sensor inaccuracies. To address these challenges, this article proposes a novel, computationally efficient attitude and heading reference system (AHRS) framework. The primary contributions are twofold: first, a minimal three-state error-state extended Kalman Filter (EKF) employing a horizontal specific force constraint (HSFC); second, a decoupled, parallel recursive least squares (RLS) algorithm that estimates gyroscope biases post-EKF convergence, thereby eliminating the computational overhead of augmented-state filters. Furthermore, rigorous stationary observability analysis and closed-form analytical models are derived to quantify error propagation, demonstrating how leveling and heading errors are strictly decoupled and influenced by geographic latitude. To predict bias estimation limits analytically, a novel design chart is introduced. Comprehensive Monte Carlo simulations and experimental validations utilizing multiple grades of fiber optic gyroscopes (FOGs) corroborate the theoretical findings. Ultimately, the outcomes confirm that the proposed framework significantly reduces computational burden while maintaining robust estimation fidelity, providing a highly scalable solution for static initial alignment.