摘要
p_范分布是一个包含拉普拉斯分布、正态分布、均匀分布等常见分布的分布族。用p_范分布描述观测误差的统计特性 ,只需假定误差的分布为单峰、对称 ,因此 ,p_范极大似然平差可以避免事先假定误差的具体分布模式 ,而在平差过程中确定未知参数及误差的分布具有自适应的特点。但是 p_范分布的密度函数比较复杂 ,不利于理论分析和实际应用。本文的研究表明 ,p_范分布可以近似地表示为拉普拉斯分布与正态分布或正态分布与均匀分布的线性组合。 p_范分布与本文给出的近似分布具有相同的前四阶矩。由于拉普拉斯分布、正态分布、均匀分布的密度函数都比较简单 ,用近似分布代替 p_范分布会使相关的问题得到简化。
In surveying data processing,we generally suppose that the observational errors distribute normally.In this case the method of least squares can give the minimum variance unbiased estimation of the parameters.The method of least squares does not have the character of robustness.So the use of it will become unsuitable when a few measurements inheriting gross error mixed with others.We can use the robust estimate methods that can avoid the influence of gross errors.This kind of methods does not need to know the exact distribution of the observations.But it will also cause other difficult such as the hypothesis testing for estimated parameters when the sample size is not so big.For non_normally distributed measurements we can suppose they obey the p _norm distribution law. p _norm distribution is a distributive class which includes the most frequently used distributions such as the Laplace,normal and rectangular ones.This distribution is symmetry and has a kurtosis between 3 and -6/5 when p is greater than 1.Using p _norm distribution to describe the statistical character of the errors,the only assumption is that the error distribution is symmetry and has only one peak value.So the method of the p _norm distributive maximum likelihood adjustment can avoid determining the particular distributive model exactly before the data processing.It can fix the unknown parameters and the errors distribution simultaneously.This method possesses the property of a kind of self_adapting.But the density function of the p _norm distribution is so complex,which makes the theoretical analysis more difficult.And the troublesome calculation is also makes this method not suitable for practice.The research of this paper indicates that the p _norm distribution can be represented by the linear combination of Laplace distribution and normal distribution or by the linear combination of normal distribution and rectangular distribution approximately.Which kind of representation will be taken is according to that the paramete
出处
《武汉大学学报（信息科学版）》
EI
CSCD
北大核心
2001年第3期222-225,共4页
Geomatics and Information Science of Wuhan University
基金
教育部<高等学校骨干教师资助计划>资助!项目 (2 0 0 0 5 )
