双线性约束过程的鲁棒自适应数据校正方法

采用污染正态分布模型进行数据校正，相对于传统的最小二乘方法具有较好的鲁棒性，然而参数估计结果的精确度依赖于误差发生概率和方差比值两个先验模型参数的选取，这在实际生产中难以获得，采用固定的方差比也不符合实际，因而其应用受到了限制。本文针对污染正态分布模型的不足，提出了一种鲁棒自适应误差分布模型，该模型具有与标准正态分布模型相似的分布密度函数，不同之处在于采用鲁棒自适应可变权重因子调节误差方差，通过放大显著误差方差，减小其对参数估计的影响。将该模型用于双线性约束数据校正问题，并采用Lagrange乘子法得到鲁棒自适应最小二乘分析解，同时还对鲁棒自适应数据校正中的测量数据相关性问题进行了研究。仿真结果证实了该方法的有效性。

Robust adaptive data rectification method for bilinear constraint process

A contaminated Gaussian distribution based method is robust for data rectification for its ability of taking probability distributions of random errors and gross errors into account simultaneously.But its application is limited because the precision of estimation depends on the selection of priori model parameters,which is difficult to obtain in practice.To avoid providing these parameters,a robust adaptive data rectification approach is proposed in this paper.First,a robust adaptive probability distribution model of errors is constructed.Adaptive factors,obtained from observations,are added to adjust the variances of the outlying observations.Then,Lagrange method is used to obtain the iterative algebraic solution.The correlation of measurements is also considered in this paper.Application to bilinear constraints process shows that the least square estimation based on the new approach can compensate the effect of gross errors effectively and give a robust estimation.