基于特征分解的快速位姿图优化算法

位姿图优化（pose graph optimization，PGO）是计算机视觉领域中广泛应用的高维非凸优化算法，很难直接求解，主要依赖于迭代技术，对初始值的质量要求较高，在实践中很难得到保证。针对位姿图优化问题进行了研究，提出了基于特征分解的位姿图简单封闭解算法，该算法首先对PGO问题的最大似然估计进行半定松弛，然后将其转换为特征分解问题，并利用数据的稀疏性设计了改进的模型降阶方法进行求解，进一步提高了算法的计算速度。算法具有可伸缩性、计算成本低和精度高等优点。最后，在模拟和真实的位姿图数据集上进行实验评估，结果表明在不影响精度的情况下，该算法可以快速地进行位姿图优化。

Fast pose graph optimization algorithm based on eigen decomposition

Pose graph optimization(PGO) is a high dimensional non-convex optimization algorithm widely used in the field of computer vision. It is hard to solve directly and mainly relies on iterative techniques. It requires high quality of initial value which is difficult to be guaranteed in practice. This paper studied PGO problem and proposed a simple closed solution algorithm for pose graph based on eigen decomposition. This algorithm first developed the semidefinite relaxation of maximum-likelihood estimation(MLE) for PGO problems. Then it transformed MLE into eigen decomposition problem, and designed an improved model reduction method to solve the problem by using the sparsity of data, which further improves the computational speed of the algorithm. The algorithm had the advantages of scalability, low computational cost and high precision. Finally, experimental evaluation on simulated and real-world pose-graph datasets shows that the proposed algorithm can optimize the pose graph quickly without compromising accuracy.