一种基于半参数回归的加速度计误差模型辨识方法

Error model identification method of accelerometer based on semi-parametric regression

为了解决加速度计离心机试验中系统误差和未建模误差对加速度计模型辨识的影响,将统计学中的半参数回归方法引入到加速度计的模型辨识中,建立了加速度计的半参数回归模型,提出了一种基于最小二乘-半参数回归模型(LS-SPRM)的估计方法,该估计方法利用最小二乘法估计加速度计的误差模型系数,利用半参数回归方法估计加速度计测试中的系统误差,并通过检验残差是否为白噪声作为判断是否有系统误差的条件。在半参数模型的估计中,采用二阶段估计方法,利用三次样条函数进行非参数部分的估计,并讨论了光滑参数的选取方法。仿真试验结果表明,采用该方法能够较好地补偿由于系统误差和未建模误差带来的影响,使加速度计模型辨识的标准差较普通最小二乘法减小45%左右,估计的残差也减小了近一倍。

For the problems of the systematic errors caused by the device errors and the unmodeled errors of accelerometers tested on centrifuge,a semi-parametric regression method in statistics is introduced into model identification of accelerometers.The semi-parametric regression model of accelerometers is established,and a least square semi-parametric regression model（LS-SPRM） method is proposed.In this method,the coefficients of error model of accelerometers are estimated by least square method,and the systematic errors are estimated by semi-parametric regression method.It takes whether the residuals are white noise as the condition to judge if there are systematic errors.In the semi-parametric estimation,a two-stage estimation method is utilized,and a cubic spline function is used to estimatte the non-parametric part.Then the method of selecting smoothing parameters is discussed.The simulation results demonstrate that the LS-SPRM method can significantly compensate the influences of the systematic errors and the unmodeled errors.Compared with those by the least square method,the standard deviations of accelerometer model identification by this algorithm are reduced by about 45% and the fit residuals are reduced by half.