Underwater acoustic single-beacon positioning technology achieves localization by integrating vehicle motion with range measurements acquired from acoustic ranging devices, offering advantages such as system simplicity, flexible deployment, and high cost-effectiveness. However, its accuracy is limited by weak initial observability and degraded observation geometry. To address this, a sensor data correction and collaborative optimization framework is proposed. A hybrid outlier rejection strategy first suppresses acoustic multipath and sensor noise. To compensate for systematic sensor errors ignored in conventional Virtual Long Baseline methods, an affine transformation maps the true trajectory to the sensor-indicated one, reformulating error compensation as a correction to virtual beacon coordinates. To further mitigate the accuracy degradation caused by degenerated geometric configurations, this paper proposes a collaborative algorithm that integrates Chan initialization with affine transformation optimization. This approach formulates the positioning problem as an optimization task, simultaneously estimating the position information and affine transformation parameters through iterative refinement to achieve high-precision localization. The process begins with Chan’s algorithm, which provides an initial estimate from the virtual sensor array. This estimate is then refined under affine constraints to achieve high-precision localization. Experimental results show the method improves positioning accuracy by 36.30% compared to baseline algorithms, demonstrating significant performance enhancement.
Ye et al. (2026) studied this question.