将高斯分布投影到非轴对齐流形，提升机器人定位精度
Marginalizing and Conditioning Gaussians onto Linear Approximations of Smooth Manifolds with Applications in Robotics
- 用线性化方法处理非轴对齐流形上的高斯分布边缘化与条件化
- 在真实数据上验证了Koopman SLAM的协方差一致性
- 适用于需要精确不确定性建模的机器人系统
我们推导出高斯分布在直线流形上的边缘化与条件化闭式表达，并通过线性化将该方法扩展至光滑非线性流形。尽管轴对齐流形上的边缘化与条件化已有成熟方法，但非轴对齐情况仍不明确。我们通过三个应用展示其有效性：1）投影正态分布的近似，线性化近似质量随问题非线性程度降低而提高；2）在真实数据集上验证了Koopman SLAM中的协方差一致性；3）在仿真中验证了约束型GTSAM的协方差一致性。
原文摘要 · Abstract (English)
We present closed-form expressions for marginalizing and conditioning Gaussians onto linear manifolds, and demonstrate how to apply these expressions to smooth nonlinear manifolds through linearization. Although marginalization and conditioning onto axis-aligned manifolds are well-established procedures, doing so onto non-axis-aligned manifolds is not as well understood. We demonstrate the utility of our expressions through three applications: 1) approximation of the projected normal distribution, where the quality of our linearized approximation increases as problem nonlinearity decreases; 2) covariance extraction in Koopman SLAM, where our covariances are shown to be consistent on a real-world dataset; and 3) covariance extraction in constrained GTSAM, where our covariances are shown to be consistent in simulation.
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