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基础知识:置信椭圆confidence ellipse

(2011-07-26 08:24:16)
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杂谈

分类: 视频与图像处理/算法与基础

    按照我的简要理解,置信椭圆基本上是对置信区域的描述方式,其长轴和短轴分别为置信区域的参数,置信椭圆的长短半轴,分别表示二维位置坐标分量的标准差(如经度的σλ和纬度的σφ)。一倍标准差(1σ)的概率值是68.3%,二倍标准差(2σ)的概率值为95.5%;三倍标准差(3σ)的概率值是99.7%。

    置信区域的概念如下:

In statistics, a confidence region is a multi-dimensional generalization of a confidence interval. It is a set of points in an n-dimensional space, often represented as an ellipsoid around a point which is an estimated solution to a problem, although other shapes can occur.

The confidence region is calculated in such a way that if a set of measurements were repeated many times and a confidence region calculated in the same way on each set of measurements, then a certain percentage of the time, on average, (e.g. 95%) the confidence region would include the point representing the "true" values of the set of variables being estimated. However, it does not mean, when one confidence region has been calculated, that there is a 95% probability that the "true" values lie inside the region, since we do not assume any particular probability distribution of the "true" values and we may or may not have other information about where they are likely to lie.

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