解决水下声呐2D定位的全局最优解问题
A Convex and Global Solution for the P$n$P Problem in 2D Forward-Looking Sonar
- 基于正交近似将声呐定位转为点线配准，实现全局最优
- 仿真显示精度显著优于非重投影优化的现有方法
- 适用于共面等复杂场景，适合水下机器人定位研究
视角n点（P$n$P）问题在机器人位姿估计中至关重要。尽管光学相机上的该问题已得到深入研究，但因成像原理差异，2D前视声呐（FLS）在水下场景中的研究仍不足。本文证明，尽管声呐图像形成存在非线性，仍可通过正交近似，在点到线（PtL）3D配准框架下有效求解2D FLS的P$n$P问题。注册过程采用基于对偶的最优求解器，保证全局最优性。对于共面情形，通过零空间分析从对偶形式中提取解，使方法可推广至更一般情况。大量仿真系统评估了不同条件下的性能表现。与非重投影优化的最先进方法相比，所提方法精度显著更高；当两者均进行优化时，本方法精度相当或略优。
原文摘要 · Abstract (English)
The perspective-$n$-point (P$n$P) problem is important for robotic pose estimation. It is well studied for optical cameras, but research is lacking for 2D forward-looking sonar (FLS) in underwater scenarios due to the vastly different imaging principles. In this paper, we demonstrate that, despite the nonlinearity inherent in sonar image formation, the P$n$P problem for 2D FLS can still be effectively addressed within a point-to-line (PtL) 3D registration paradigm through orthographic approximation. The registration is then resolved by a duality-based optimal solver, ensuring the global optimality. For coplanar cases, a null space analysis is conducted to retrieve the solutions from the dual formulation, enabling the methods to be applied to more general cases. Extensive simulations have been conducted to systematically evaluate the performance under different settings. Compared to non-reprojection-optimized state-of-the-art (SOTA) methods, the proposed approach achieves significantly higher precision. When both methods are optimized, ours demonstrates comparable or slightly superior precision.
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