滑动窗口光束法平差的平方根边缘化
Square Root Marginalization for Sliding-Window Bundle Adjustment
摘要：
在本文中，我们提出了一种新的平方根滑动窗口光束法平差适用于实时测距应用。平方根公式贯穿于我们基于优化的滑动窗口估计的三个主要方面：对于束平差，我们用零空间投影消除地标变量;为了存储边缘化先验，我们采用Hessian矩阵平方根;当边缘化旧姿势时，我们避免形成正规方程，并直接用专门的QR分解更新平方根先验。我们表明，建议的平方根边缘化是代数上等同于传统的使用舒尔补（SC）的海森。此外，它优雅地处理秩亏雅可比矩阵产生一个事先等价的SC与Moore-Penrose逆。我们对真实世界数据集的视觉和视觉惯性里程计的评估表明，所提出的估计比基线快36%。它还表明，在单精度的，传统的基于海森边缘化导致数值故障和精度降低。我们分析了边缘化的数值特性，然后解释为什么我们的平方根形式不会受到同样的影响，因此需要更好的性能。
英文摘要：
In this paper we propose a novel square root sliding-window bundle adjustment suitable for real-time odometry applications. The square root formulation pervades three major aspects of our optimization-based sliding-window estimator: for bundle adjustment we eliminate landmark variables with nullspace projection; to store the marginalization prior we employ a matrix square root of the Hessian; and when marginalizing old poses we avoid forming normal equations and update the square root prior directly with a specialized QR decomposition. We show that the proposed square root marginalization is algebraically equivalent to the conventional use of Schur complement (SC) on the Hessian. Moreover, it elegantly deals with rank-deficient Jacobians producing a prior equivalent to SC with Moore-Penrose inverse. Our evaluation of visual and visual-inertial odometry on real-world datasets demonstrates that the proposed estimator is 36% faster than the baseline. It furthermore shows that in single precision, conventional Hessian-based marginalization leads to numeric failures and reduced accuracy. We analyse numeric properties of the marginalization prior to explain why our square root form does not suffer from the same effect and therefore entails superior performance.
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