一种基于抗差自校正Kalman滤波的GPS导航算法

为减弱异常观测值对自校正Kalman滤波精度的影响,引入抗差M估计的等价权函数,建立了抗差自校正Kalman滤波算法,并用实例进行了验证。计算表明,该自适应滤波算法在完全未知噪声统计的情况下,不仅能够自适应地求解状态参数,而且还能在一定程度上有效地抵制观测异常对导航解的影响。     

THE PERFORMANCE OF LEAST SQUARES AND ROBUST REGRESSION IN THE CALIBRATION OF ANALYTICAL METHODS UNDER NON-NORMAL NOISE DISTRIBUTIONS

By means of Monte Carlo simulations a comparison has been made between ordinary least squaresregression and robust regression. The robust regression procedure is based on the Huber estimate and iscomputed by means of the iteratively reweighted least squares algorithm. The performance of bothprocedures has been evaluated for estimation of the parameters of a calibration function and fordetermination of the concentration of unknown samples. The influence of the distributionalcharacteristics skewness and kurtosis has been studied, and the number of measurements used forconstructing the calibration curve has also been taken into account, Under certain conditions robustregression offers an advantage over least squares regression.     

Highly Robust Variogram Estimation

The classical variogram estimator proposed by Matheron is not robust against outliers in the data, nor is it enough to make simple modifications such as the ones proposed by Cressie and Hawkins in order to achieve robustness. This paper proposes and studies a variogram estimator based on a highly robust estimator of scale. The robustness properties of these three estimators are analyzed and compared. Simulations with various amounts of outliers in the data are carried out. The results show that the highly robust variogram estimator improves the estimation significantly.