We introduce the first comprehensive approach to determine the uncertainty in volumetric Particle Tracking Velocimetry (PTV) measurements. Volumetric PTV is a state-of-the-art non-invasive flow measurement technique, which measures the velocity field by recording successive snapshots of the tracer particle motion using a multi-camera set-up. The measurement chain involves reconstructing the three-dimensional particle positions by a triangulation process using the calibrated camera mapping functions. The non-linear combination of the elemental error sources during the iterative self-calibration correction and particle reconstruction steps increases the complexity of the task. Here, we first estimate the uncertainty in the particle image location, which we model as a combination of the particle position estimation uncertainty and the reprojection error uncertainty. The latter is obtained by a gaussian fit to the histogram of disparity estimates within a sub-volume. Next, we determine the uncertainty in the camera calibration coefficients. As a final step the previous two uncertainties are combined using an uncertainty propagation through the volumetric reconstruction process. The uncertainty in the velocity vector is directly obtained as a function of the reconstructed particle position uncertainty. The framework is tested with synthetic vortex ring images. The results show good agreement between the predicted and the expected RMS uncertainty values. The prediction is consistent for seeding densities tested in the range of 0.01 to 0.1 particles per pixel. Finally, the methodology is also successfully validated for an experimental test case of laminar pipe flow velocity profile measurement where the predicted uncertainty is within 17% of the RMS error value.

中文翻译：

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体积粒子追踪测速 (PTV) 不确定性量化

我们介绍了第一种确定体积粒子跟踪测速 (PTV) 测量不确定度的综合方法。体积 PTV 是最先进的非侵入性流量测量技术，它通过使用多相机设置记录示踪粒子运动的连续快照来测量速度场。测量链涉及使用校准的相机映射函数通过三角测量过程重建三维粒子位置。在迭代自校准校正和粒子重建步骤期间元素误差源的非线性组合增加了任务的复杂性。在这里，我们首先估计粒子图像位置的不确定性，我们将其建模为粒子位置估计不确定性和重投影误差不确定性的组合。后者是通过对子体积内视差估计的直方图进行高斯拟合而获得的。接下来，我们确定相机校准系数的不确定性。作为最后一步，使用通过体积重建过程的不确定性传播来组合前两个不确定性。速度矢量的不确定性直接作为重构粒子位置不确定性的函数获得。该框架使用合成涡环图像进行测试。结果显示预测的和预期的 RMS 不确定性值之间具有良好的一致性。对于在每像素 0.01 到 0.1 个粒子范围内测试的播种密度，预测是一致的。最后，