论文标题
合并测量的准确度如何 - 实验，模拟和理论
How accurate can combined measurements be -- experiment, simulation, and theory
论文作者
论文摘要
在本文中，我们调查了多少组合测量可以提高添加剂量的准确性的问题。因此，我们考虑了一组测量值，从$ n $标记的质量的所有可能组合选择中，然后通过线性回归方法估算$ n $ smoses的单个权重。我们提出了实验结果，激发了全面的模拟运动。这些模拟提供了实验结果的有效统计陈述和可靠的预测。深刻的分析治疗反过来支持这些模拟结果具有良好的一致性。其中一个重要的成就是估计误差的一般分析表达，不仅限于提出的两个特定称重方案。事实证明，合并的测量值允许估算质量元素的重量，其准确性是按数量级以下的数量级分辨率的分辨率估算的。由于误差取决于测量量，因此越来越多的努力获得了更高的精度。从广义上讲，我们的工作希望促进该方法，并为超出高精度质量确定的各个计量学领域的应用提供灵感。此外，新型的模拟和分析公式可以设计最佳实验。
In this paper we investigate the question of how much combined measurements can increase the accuracy of additive quantities. Therefore, we consider a set of measurements from a selection of all possible combinations of the $n$ labeled masses and then estimate the individual weights of the $n$ masses by a linear regression approach. We present experimental results which motivate comprehensive simulation campaigns. These simulations provide valid statistical statements and reliable forecasts of the experimental results. A profound analytical treatment in turn supports these simulation outcomes with excellent consistency. One important achievement therein is a general analytical expression for the estimate's error, not only limited to the two particular weighing schemes presented. It turns out that combined measurements allow to estimate the weight of mass elements with an accuracy that under-runs by orders of magnitude the resolution of the scale used. As the error depends on the amount of measurements, one gains higher accuracy with increasing effort. In a broader sense, our work wants to promote the method and give inspirations to applications in various metrological fields beyond high-precision mass determination. Moreover, the novel simulations and analytic formulas enable the design of optimal experiments.
