论文标题
某些形式的重心算法的定位错误的概率分布。第二部分
Probability Distributions of Positioning Errors for Some Forms of Center-of-Gravity Algorithms. Part II
论文作者
论文摘要
重心是具有不同分析形式以进行噪声优化的位置重建最常用的算法之一。不同形式的误差分布是改善粒子物理中轨道拟合的必要工具。他们的Cauchy-（Agnesi）尾巴具有有益的效果，可在最大似然搜索中减轻异常值的干扰。计算了一些随机变量组合的概率分布，在文献中无法找到，但与轨道拟合有关： $ x_ {g3} =θ（x_2-x_1）[（x_1-x_3）/（x_1+x_2+x_3）]+ θ（x_1-x_2）[（x_1+2x_4）/（x_1+x_2+x_4）] $和$ x_ {g4} =θ（x_4-x_5）[（2x_4+x_1-x_1-x_3）/（x_1+x_1+x_2+x_2+x_2+x_3+x_3+x_4）+ θ（x_5-x_4）[（x_1-x_3-2x_5）/（x_1+x_2+x_2+x_3+x_5）] $和$ x_ {g5} =（2x_4+x_1-x_3-2x_5）/（x_1+x_1+x_2+x_2+x_3+x_3+x_3+x_4+x_5）$。 $ x_ {g3} $，$ x_ {g4} $的概率密度函数和$ x_ {g5} $具有复杂的结构，并具有降低的概率区域。这些区域必须谨慎处理，以避免可能性功能中的错误最大值。假设集合$ \ {x_i \} $作为具有高斯概率分布的独立随机变量，则计算一般积分方程和详细的分析表达式。 ％
The center of gravity is one of the most frequently used algorithm for position reconstruction with different analytical forms for the noise optimization. The error distributions of the different forms are essential instruments to improve the track fitting in particle physics. Their Cauchy-(Agnesi) tails have a beneficial effects to attenuate the outliers disturbance in the maximum likelihood search. The probability distributions are calculated for some combinations of random variables, impossible to find in literature, but relevant for track fitting: $x_{g3}=θ(x_2-x_1)[ (x_1-x_3)/(x_1+x_2+x_3)] + θ(x_1-x_2)[(x_1+2x_4)/(x_1+x_2+x_4)]$ and $x_{g4}=θ(x_4-x_5)[(2x_4+x_1-x_3)/(x_1+x_2+x_3+x_4)]+ θ(x_5-x_4)[(x_1-x_3-2x_5)/(x_1+x_2+x_3+x_5)]$ and $x_{g5}=(2x_4+x_1-x_3-2x_5)/(x_1+x_2+x_3+x_4+x_5)$. The probability density functions of $x_{g3}$, $x_{g4}$ and $x_{g5}$ have complex structures with regions of reduced probability. These regions must be handled with care to avoid false maximums in the likelihood function. General integral equations and detailed analytical expressions are calculated assuming the set $\{x_i\}$ as independent random variables with Gaussian probability distributions. %
