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

張寧 A Linear Least Square Initialization Method for 3D Pose Graph Optimization Problem
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三維位姿圖優化問題的線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.

姿態圖優化（PGO）是機器人和機器視覺應用（如3D重建和3D SLAM）中出現的一個重要優化問題。位姿圖的每一個節點對應於方向和位置。 PGO問題從節點之間的相對噪聲觀察中找到節點的方向和位置。最近的研究代表，衆所周知的迭代PGO求解器須要良好的初始化才能收斂到良好的求解。 然而，咱們觀察到最早進的初始化方法僅在低噪聲問題中得到良好的初始化，而且它們在具備更多測量噪聲的挑戰性問題中失敗。所以，迭代方法在高噪聲問題中可能會收斂到很差的求解結果。

在本文中，提出了一種在PGO優化問題中得到方向的新方法。與其餘衆所周知的方法同樣，初始位置是從最小二乘問題的結果中得到的。 所提出的方法迭代地近似於當前估計的問題並將其轉換爲最小二乘問題。所以，該方法能夠被視爲迭代最小二乘法，其在計算上是高效的。 仿真結果代表，所提出的初始化方法有助於最知名的迭代求解器在某些狀況下得到更好的最優並顯着優於其餘求解器。

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，提出了一個迭代求解器來找出PGO問題的方向。 所提出的方法能夠用做低噪聲狀況下的求解器和高噪聲狀況下的初始化方法。 在每次迭代中，僅包含方向的成本函數由二次成本函數近似，並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.

所提出的解決PGO問題的方法具備低計算成本。 該方法在估計低噪聲數據集中的位置和方向時達到了傳統方法的準確性。 已經證實，使用所提出的算法的結果做爲Gauss-Newton方法的初始化，改善了在最早進的算法未能收斂到良好解決方案的挑戰性場景中的性能。