基于M估计的三维容栅微小位移系统参数估计

Parameter estimation method for three-dimensional capacitive grate tiny displacement system based on M-estimator

为解决采用传统最小二乘法对三维容栅微小位移系统进行参数估计时产生的拟合偏离问题,提出一种基于M估计的参数估计。使用Huber robust作为损失函数,减少测量数据中少数离散点的干扰。对测量的位移数据做正态性校验,确保预测模型为线性系统。对预测值和测量值进行皮尔逊相关性分析,评估二者的相关系数和显著性。实验测试结果表明,该方法在拟合性能不变的情况下进一步提高了测试系统的稳定性,对系统的参数估计有显著意义。

To calibrate the deviation error which occurs when using ordinary least squares in parameter estimation of the three-dimensional capacitance-grating tiny displacement measurement system,a parameter estimation method was carried out based on M-estimator.Huber robust was used as the loss function,eliminating the interference of few discrete points.It was necessary to ensure the linearity of the estimated model in checking the displacement data according to normal distribution.Pearson correlation analysis was performed to evaluate the correlation coefficient and statistical significance between predicted and measured va-lues.It is verified by experiments that this method increases the stability of the measurement system model in the condition of similar fitting performance,and it has significant effects in parameter estimation of the system.