Lewis Ben
IEEE Trans Ultrason Ferroelectr Freq Control. 2020 Oct;67(10):2187-2190. doi: 10.1109/TUFFC.2020.2996313. Epub 2020 May 21.
Thêo1 is a frequency stability statistic that is similar to the Allan variance but can provide stability estimates at longer averaging factors and with higher confidence. However, the calculation of Thêo1 is significantly slower than that of the Allan variance, particularly for large data sets, due to a worse computational complexity. A faster algorithm for calculating the "all- τ " version of Thêo1 is developed by identifying certain repeated sums and removing them with a recurrence relation. The new algorithm has a reduced computational complexity, which is equal to that of the Allan variance. Computation time is reduced by orders of magnitude for many data sets. The new, faster algorithm does introduce an error due to accumulated floating-point errors in very large data sets. The error can be compensated for by increasing the numerical precision used at critical steps. The new algorithm can also be used to increase the speed of ThêoBr and ThêoH that are more sophisticated statistics derived from Thêo1.
Thêo1是一种频率稳定性统计量，它类似于阿伦方差，但可以在更长的平均因子下提供稳定性估计，并且具有更高的置信度。然而，由于计算复杂度较高，Thêo1的计算速度明显慢于阿伦方差，特别是对于大数据集。通过识别某些重复的和并用递归关系消除它们，开发了一种用于计算Thêo1的“全τ”版本的更快算法。新算法的计算复杂度降低，与阿伦方差的计算复杂度相同。对于许多数据集，计算时间减少了几个数量级。由于非常大数据集中的累积浮点误差，新的更快算法确实会引入误差。可以通过提高关键步骤中使用的数值精度来补偿该误差。新算法还可用于提高ThêoBr和ThêoH的速度，它们是从Thêo1派生出来的更复杂的统计量。
