泡泡一分钟： A Linear Least Square Initialization Method for 3D Pose Graph Optimization Problem

张宁 A Linear Least Square Initialization Method for 3D Pose Graph Optimization Problem
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三维位姿图优化问题的线性最小二乘初始化方法

S. M. Nasiri, H. Moradi, Senior Member, IEEE, R. Hosseini

Abstract Pose Graph Optimization (PGO) is an important optimization problem arising in robotics and machine vision applications like 3D reconstruction and 3D SLAM. Each node of pose graph corresponds to an orientation and a location. The PGO problem finds orientations and locations of the nodes from relative noisy observation between nodes. Recent investigations show that well-known iterative PGO solvers need good initialization to converge to good solutions. However, we observed that state-of-the-art initialization methods obtain good initialization only in low noise problems, and they fail in challenging problems having more measurement noise. Consequently, iterative methods may converge to bad solutions in high noise problems.

In this paper, a new method for obtaining orientations in the PGO optimization problem is presented. Like other well-known methods the initial locations are obtained from the result of a least-squares problem. The proposed method iteratively approximates the problem around current estimation and converts it to a least-squares problem. Therefore, the method can be seen as an iterative least-squares method which is computationally efficient. Simulation results show that the proposed initialization method helps the most well-known iterative solver to obtain better optima and significantly outperform other solvers in some cases.

姿态图优化（PGO）是机器人和机器视觉应用（如3D重建和3D SLAM）中出现的一个重要优化问题。位姿图的每一个节点对应于方向和位置。 PGO问题从节点之间的相对噪声观察中找到节点的方向和位置。最近的研究代表，众所周知的迭代PGO求解器须要良好的初始化才能收敛到良好的求解。 然而，咱们观察到最早进的初始化方法仅在低噪声问题中得到良好的初始化，而且它们在具备更多测量噪声的挑战性问题中失败。所以，迭代方法在高噪声问题中可能会收敛到很差的求解结果。

在本文中，提出了一种在PGO优化问题中得到方向的新方法。与其余众所周知的方法同样，初始位置是从最小二乘问题的结果中得到的。 所提出的方法迭代地近似于当前估计的问题并将其转换为最小二乘问题。所以，该方法能够被视为迭代最小二乘法，其在计算上是高效的。 仿真结果代表，所提出的初始化方法有助于最知名的迭代求解器在某些状况下得到更好的最优并显着优于其余求解器。

In this paper, an iterative solver was presented to find the orientation in the PGO problem. The proposed method can be used as a solver in low-noise cases and as an initialization method in high-noise cases. In each iteration, the cost function containing only orientations is approximated by a quadratic cost function and is solved by a least-squares solver.

在本文中，提出了一个迭代求解器来找出PGO问题的方向。 所提出的方法能够用做低噪声状况下的求解器和高噪声状况下的初始化方法。 在每次迭代中，仅包含方向的成本函数由二次成本函数近似，并由最小二乘求解器求解。

The proposed approach for solving the PGO problem has low computational cost. The method reaches the accuracy of traditional methods in estimating the positions and orientations in low noise datasets. It was demonstrated that using the result of the proposed algorithm as an initialization for Gauss-Newton methods improves the performance in challenging scenarios where the state-of-the-art algorithms fail in converging to a good solution.

所提出的解决PGO问题的方法具备低计算成本。 该方法在估计低噪声数据集中的位置和方向时达到了传统方法的准确性。 已经证实，使用所提出的算法的结果做为Gauss-Newton方法的初始化，改善了在最早进的算法未能收敛到良好解决方案的挑战性场景中的性能。