基于模糊隶属函数的参数稳健估计

摘要

参数估计过程经常遇到2个主要问题:一个是最小二乘与稳健估计不能兼顾最优无偏性和稳健性；另一个是非线性模型参数估计进行线性近似处理中带来的模型误差导致对粗差的错误鉴别和定位.针对以上2个问题,提出了基于模糊隶属函数的稳健估计方法.该方法通过隶属度加权来削弱个别粗差污染数据对参数估计结果的影响,从而达到提高参数估计稳健性的目的.分别用线性回归模型和非线性回归模型对该算法进行了验证,结果表明,该算法对粗差具有较好的抵抗能力,能够对参数进行稳健估计.%There are two major issues in the process of parameter estimation. The first one is that least-squares method and robust estimation method cannot give little consideration to the optimal unbiased and stabilized result. The second one is that model error makes it difficult to identify and position the gross error, which is introduced during the process of conversion from nonlinear function to a linear one. This article put forward a robust estimation method which based on the fuzzy membership function to eliminate the influence of gross error. The fuzzy membership of the residuals were used to construct the weight matrix to assess the contribution of each observation quantity, and then the one contaminated by gross error would be given very little weight to increase the accuracy of parameter estimation. This algorithm was assessed by estimating the parameters in linear regression model and nonlinear regression model contaminated by gross error. It is found that this algorithm is robust to the influence of gross error, and outperforms the common least-square algorithm to give more accurate result.