论文标题
用于计算Thêo1的快速算法
A Fast Algorithm for Calculation of Thêo1
论文作者
论文摘要
Thêo1是一种频率稳定性统计量，与Allan方差相似，但可以在更长的平均因素和更高的置信度下提供稳定性估计。但是，由于计算复杂性较差，Thêo1的计算比Allan方差明显慢得多，尤其是对于大数据集。通过识别某些重复的总和并以复发关系将其删除，可以开发出一种用于计算“ all-$τ$”版本的更快的算法。新算法的计算复杂性降低了，等于Allan方差的算法。许多数据集的数量级缩短了计算时间。新的，更快的算法确实由于非常大的数据集中的浮点错误而引起了错误。可以通过增加关键步骤中使用的数值精度来补偿误差。新算法也可以用来提高Thêobr和Thêoh的速度，这是从Thêo1得出的更复杂的统计数据。
Thêo1 is a frequency stability statistic which 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 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, equal to that of the Allan variance. Computation time is reduced by orders of magnitude for many datasets. The new, faster algorithm does introduce an error due to accumulated floating point errors in very large datasets. 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 which are more sophisticated statistics derived from Thêo1.
