Gauss-markov模型的t型抗差估计

测量中对含粗差的数据的处理通常采用基于等价权法的抗差M-估计,等价权及其临界值的选取决定了参数估计的效率和抗差性.本文将近年来统计界提出并有较深入理论研究的t型估计引入测量平差中,提出Gauss-Markov模型的t型抗差估计及其算法,并进行了模拟计算.t型抗差估计具有很好的统计性质;其求解采用EM算法,计算快捷稳定,收敛性好,可同时求解出位置参数和方差因子的抗差估计;t分布的自由度可方便地调节估计的效率和抗差性.计算结果显示,t型抗差估计受粗差影响不大,具有较好的抗差能力.

Robust t-type Estimation in Gauss-Markov Model

Equivalent weight method is usually employed to deal with data with gross errors.The equivalent weight function and the criterion involved influence the robustness and efficiency of the method.As an alternative way,a t-type estimation has been proposed and theoretically researched recently.Robust t-type estimation is introduced to Gauss-Markov model in geodetic adjustments.It has good statistical properties.The estimation can be calculated by the EM algorithm,which usually converges rapidly and stably.The scale parameter can be estimated simultaneously with the location parameters.The degree of freedom in t-distribution is a convenient tuning parameter between efficiency and robustness.A numerical example demonstrates the validity of the method proposed.