A Convex and Global Solution for the P$n$P Problem in 2D Forward-Looking Sonar

2025-04-06

AI Summary

This work addresses the lack of pose-and-orientation (PnP) estimation methods tailored to two-dimensional forward-looking sonar (FLS) underwater imaging. We formulate FLS imaging for the first time as a 3D point-to-2D line (PtL) registration problem. To solve it, we propose the first convex and globally optimal FLS-PnP framework: (i) modeling via orthogonal projection approximation to ensure tractability; (ii) employing dual optimization for efficient global solution; and (iii) incorporating null-space analysis to handle coplanar degeneracies, thereby significantly enhancing robustness and generality. Simulation results demonstrate that our method substantially outperforms state-of-the-art (SOTA) approaches without reprojection refinement. After reprojection optimization, its accuracy matches or slightly exceeds SOTA, confirming both high precision and strong robustness under challenging underwater conditions.

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Abstract

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.

Problem

• Solving PnP problem for 2D forward-looking sonar pose estimation
• Addressing nonlinear sonar imaging via point-to-line registration
• Ensuring global optimality with duality-based solver for coplanar cases

Innovation

• Uses point-to-line 3D registration paradigm
• Employs duality-based optimal solver
• Applies orthographic approximation for sonar