如何计算一组循环数据的平均值? [英] How do you calculate the average of a set of circular data?

问题描述

我想计算一组循环数据的平均值.例如，我可能有几个指南针读数的样本.问题当然是如何处理环绕.同样的算法可能对表盘有用.

I want to calculate the average of a set of circular data. For example, I might have several samples from the reading of a compass. The problem of course is how to deal with the wraparound. The same algorithm might be useful for a clockface.

实际的问题更复杂 - 统计在球体或环绕"的代数空间中意味着什么，例如加法群 mod n.答案可能不是唯一的，例如359 度和 1 度的平均值可能是 0 度或 180 度，但统计上 0 看起来更好.

The actual question is more complicated - what do statistics mean on a sphere or in an algebraic space which "wraps around", e.g. the additive group mod n. The answer may not be unique, e.g. the average of 359 degrees and 1 degree could be 0 degrees or 180, but statistically 0 looks better.

这对我来说是一个真正的编程问题，我试图让它看起来不仅仅是一个数学问题.

This is a real programming problem for me and I'm trying to make it not look like just a Math problem.

推荐答案

这个问题在书中有详细的考查:球体统计"，Geoffrey S. Watson，阿肯色大学讲座数学科学笔记，1983 年 John Wiley &Sons, Inc. 如 http://catless.ncl.ac.uk/Risks/7.44.html#subj4 作者 Bruce Karsh.

This question is examined in detail in the book: "Statistics On Spheres", Geoffrey S. Watson, University of Arkansas Lecture Notes in the Mathematical Sciences, 1983 John Wiley & Sons, Inc. as mentioned at http://catless.ncl.ac.uk/Risks/7.44.html#subj4 by Bruce Karsh.

从一组角度测量值估计平均角度 A 的好方法a[i] 0<=i

A good way to estimate an average angle, A, from a set of angle measurements a[i] 0<=i

                   sum_i_from_1_to_N sin(a[i])
a = arctangent ---------------------------
                   sum_i_from_1_to_N cos(a[i])

starblue 给出的方法在计算上是等价的，但是他的理由更清晰，可能在编程上更高效，并且在零情况下也能很好地工作，所以对他表示敬意.

The method given by starblue is computationally equivalent, but his reasons are clearer and probably programmatically more efficient, and also work well in the zero case, so kudos to him.

现在在在维基百科上更详细地探讨了这个主题，以及其他用途，例如分数零件.

The subject is now explored in more detail on Wikipedia, and with other uses, like fractional parts.

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