离散 GM（1，1）模型参数估计的稳健算法

摘要

When Discrete GM(1,1)model is used to describe those data with an exponential growth trend,the model parameters usually adopt orthogonal least square method for solution.Considering the poor robustness of orthogonal least square method,the total least absolute deviation is offered to estimate the parameters of discrete GM(1,1)model.In order to solve the total least absolute deviation problem,a programming model is proposed,and then a new prediction formula with better robustness is obtained.An example indicates that whether original sequence has abnormal data or not,the discrete GM(1,1)model based on total least absolute deviation will acquire higher simulation accuracy and better robustness.%离散 GM（1，1）模型主要用来描述数据具有指数增长趋势的过程，模型中的参数一般都采用最小二乘法则求解。考虑到最小二乘法在参数估计时稳健性较差的特点，提出利用全最小一乘准则估计参数，给出了求解全最小一乘问题的规划模型，得到了一种稳健性较好的预测公式。计算实例表明，基于最小一乘准则的离散 GM （1，1）模型对于有无异常点的原始序列，具有较高的模拟精度和更好的稳健性。