捷联惯组历次测试数据小样本统计特性研究

Research on Small Sample Statistic Characteristics of Successive Test Data of Strapdown Inertial Measurement Unit

捷联惯组历次测试数据样本总体分布及其参数是未知的,提出了"二次统计法"研究捷联惯组历次测试数据样本总体分布形式,根据捷联惯组误差系数的稳定性要求,确定了其样本总体分布的方差。在此基础上,根据验前信息的不同来源,以及验前信息与历次测试数据之间的统计关系,分4种不同情况确定其样本总体均值的验前分布。以验前分布为基础,利用贝叶斯方法获得其验后分布。验后分布集中了3种有用信息(总体信息、验前信息和样本信息),是对总体分布参数的最终认识,因此基于验后分布的统计推断是更为有效,也是最合理的。最后通过稳健性分析检验验前、验后分布的稳健性。

The population distribution and parameters of inertial measurement units are unknown, so a method named as quadric statistic method is presented for the study of its population distribution. Depending on the stability requirement, the variance of the population is defined. Based on this, according to the different sources of prior information and the statistic relationship between the prior information and the successive test data, the proper prior distribution of the population mean of the sample is confh＇med with the four different situations. Posterior distribution of the mean can be made with successive test data in terms of the prior distribution. The mean can be estimated with posterior distribution. The illustration results show that this method can implement to the statistic analysis of different error coefficients, avoid the hypothesis to the population distribution and its parameters when the prior distributions are studied, decrease the statistic analysis error when the sample is small, and greatly enhance the quality of statistic analysis.