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arXiv · 2606.07719

Hessian-matching Based Weighting for Attitude Determination Using Short-Range DoA Measurements with IMU Assistance

Chenxin Tu·Hengchuan Zhang·Xiaowei Cui·Gang Liu·Mingquan Lu
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Abstract

Accurate and reliable attitude determination (AD) is essential for unmanned vehicles operating in Global Navigation Satellite System (GNSS)-denied environments. Short-range wireless arrays can provide direction-of-arrival (DoA) measurements from multiple anchors, enabling AD by aligning corresponding direction vectors (DVs) expressed in the body and navigation frames. In short-range scenarios, navigation-frame DVs inherit non-negligible uncertainty induced by anchor/vehicle position errors in addition to DoA-induced errors in body-frame DVs. Moreover, due to projection and unit-norm normalization, the DV errors are generally anisotropic, which motivates a total least squares (TLS) viewpoint. This paper identifies the key modeling distinction in short-range AD, develops a TLS-consistent formulation based on the total DV error and solves the resulting covariance-weighted orthogonal Procrustes problem via a manifold Gauss--Newton method. To retain the efficiency and numerical robustness of the closed-form weighted Wahba solution, we further propose Hessian-matching based scalar weighting strategies that approximate the Hessian of Wahba formulation to the TLS formulation, including a full-attitude strategy for overall accuracy and a direction-of-interest (DOI) strategy for prioritizing a selected attitude component. Finally, we incorporate IMU-derived gravity as an additional DV pair for static initialization, leading to extended Wahba and extended TLS formulations. Simulation results demonstrate that the proposed Hessian-matching weighting improves accuracy and robustness compared with existing baselines, and that gravity-DV augmentation further reduces attitude errors and improves solution availability under limited anchor availability.

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Chenxin Tu, Hengchuan Zhang, Xiaowei Cui, Gang Liu, Mingquan Lu. 2026-06-05. Hessian-matching Based Weighting for Attitude Determination Using Short-Range DoA Measurements with IMU Assistance. https://arxiv.org/abs/2606.07719

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