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

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.

Parameterized TDOA: Instantaneous TDOA Estimation and Localization for Mobile Targets in a Time-Division Broadcast Positioning System

Localization of mobile targets is a fundamental problem across various domains. One-way ranging-based downlink localization has gained significant attention due to its ability to support an unlimited number of targets and enable autonomous navigation by performing localization at the target side. Time-difference-of-arrival (TDOA)-based methods are particularly advantageous as they obviate the need for target-anchor synchronization, unlike time-of-arrival (TOA)-based approaches. However, existing TDOA estimation methods inherently rely on the quasi-static assumption (QSA), which assumes that targets remain stationary during the measurement period, thereby limiting their applicability in dynamic environments. In this paper, we propose a novel instantaneous TDOA estimation method for dynamic environments, termed Parameterized TDOA (P-TDOA). We first characterize the nonlinear, time-varying TDOA measurements using polynomial models and construct a system of linear equations for the model parameters through dedicated transformations, employing a novel successive time difference strategy (STDS). Subsequently, we solve the parameters with a weighted least squares (WLS) solution, thereby obtaining instantaneous TDOA estimates. Furthermore, we develop a mobile target localization approach that leverages instantaneous TDOA estimates from multiple anchor pairs at the same instant. Theoretical analysis shows that our proposed method can approach the Cramer-Rao lower bound (CRLB) of instantaneous TDOA estimation and localization in concurrent TOA scenarios, despite actual TOA measurements being obtained sequentially. Extensive numerical simulations validate our theoretical analysis and demonstrate the effectiveness of the proposed method, highlighting its superiority over state-of-the-art approaches across various scenarios.