t型Bayes估计及其在测量平差中的应用
t-type Bayesian Estimationand Its Applications to Geodetic Ajustments
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摘要: 针对t型估计不能抵抗病态性的影响这一缺陷,从Bayes估计的观点出发,通过对t分布模型引入未知参数的先验信息,提出了一种新的抗差有偏估计——t型Bayes估计,重点讨论了正态-Gamma先验分布下的t型Bayes估计及其EM算法和超参数的选取方案。数值实验证实了正态-Gamma先验分布下的t型Bayes估计能够同时抵抗粗差和病态性的不良影响,是一种性能更好的抗差有偏估计。Abstract: We discuss t-type Bayesian estimation under normal-Gamma prior distribution and the scheme of choosing the hyper parameters.It can be seen from the solution that the t-type Bayesian estimation under normal-Gamma prior distribution can resist ill-conditioning as well as gross errors if the hyper parameters are properly chosen.A numerical example is provided.The result shows the validity of the method.
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