论文标题
用累积分布计算的某些形式的重心算法的定位误差概率。第一部分
Positioning Error Probability for Some Forms of Center-of-Gravity Algorithms Calculated with the Cumulative Distributions. Part I
论文作者
论文摘要
为了完成先前的论文，用经典方法得出了重中心作为定位算法的概率密度函数。如概率教科书所建议的那样，这些方法需要对累积分布函数进行初步计算。它们比以前用于这些任务的人更复杂。无论如何，累积概率分布可能很有用。随机变量的组合是轨道拟合$ x =ξ/{（ξ+η）} $，$ x =θ（x_3-x_1）（-x_3）/（x_3+x_2）+θ（x_1-x_3）x_1/（x_1+x_2）$和（x_1+x_2）$和（x_1+x_2）$和（x_1+x_2）$和$ x =（x_1-x_3）/（x_1+x_2+x_3）$。第一种组合是两个剥夺中心的部分形式。第二个是完整的形式，第三个是三个剥夺中心的简化形式。先前出版物报告了第一个表达式的累积概率分布。标准假设是$ξ$，$η$，$ x_1 $，$ x_2 $和$ x_3 $是独立的随机变量。
To complete a previous paper, the probability density functions of the center-of-gravity as positioning algorithm are derived with classical methods. These methods, as suggested by the textbook of Probability, require the preliminary calculation of the cumulative distribution functions. They are more complicated than those previously used for these tasks. In any case, the cumulative probability distributions could be useful. The combinations of random variables are those essential for track fitting $x=ξ/{(ξ+η)}$, $x=θ(x_3-x_1) (-x_3)/(x_3+x_2) +θ(x_1-x_3)x_1/(x_1+x_2)$ and $x=(x_1-x_3)/(x_1+x_2+x_3)$. The first combination is a partial form of the two strip center-of-gravity. The second is the complete form, and the third is a simplified form of the three strip center-of-gravity. The cumulative probability distribution of the first expression was reported in the previous publications. The standard assumption is that $ξ$, $η$, $x_1$, $x_2$ and $x_3$ are independent random variables.
