Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in...Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.展开更多
针对船用光纤罗经误差的概率分布不完全符合高斯分布的情况,提出了一种基于高斯混合模型(Gaussian mixture model,GMM)的光纤罗经误差概率分布函数(probability distribution function,PDF)建模方法。该方法使用多个高斯分布的线性叠加...针对船用光纤罗经误差的概率分布不完全符合高斯分布的情况,提出了一种基于高斯混合模型(Gaussian mixture model,GMM)的光纤罗经误差概率分布函数(probability distribution function,PDF)建模方法。该方法使用多个高斯分布的线性叠加来拟合光纤罗经误差的概率分布,并结合一种鲁棒性的期望最大化(expectation maximization,EM)算法来估计GMM中的参数。仿真分析和实测数据验证,相比于使用单一的高斯分布,基于所提方法建立的光纤罗经误差概率分布更加符合该导航设备误差的实际概率分布。展开更多
文摘Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.
