一种Kalman滤波系统误差及其协方差矩阵的半参数估计方法

提出用半参数估计理论来解决系统误差对Kalman滤波解的影响问题。即用半参数模型中的非参数分量表达观测模型和动力学模型中未知的系统误差,在移动的窗口内,基于观测残差和状态向量预测残差拟合模型系统误差,进而修正相应的观测向量和状态预测向量的协方差矩阵,以消除系统误差对滤波的影响。同时这种方法还有明显的优点,就是在滤波过程中不需要对系统误差做任何假设。文中推导了基于正则核估计来解算导航系统半参数模型的相应公式,并根据一个模拟的算例,证明了算法的有效性。

A semi-parametric estimation method of systemic errors and covariance matrices in Kalman filter

The paper present a method solving the influence of systemic errors to kalman filter based on semi-parametric estimation theory. Namely, the systemic errors existed in the observation model and dynamics model is expressed in the nonparametric part of semi-parametric model. The systematic errors are fitted based on observation residuals and prediction residuals of state vector within chosen window, subsequently,the covariance matrices of the observations and the predicted states are modified.The method has an obvious advantage, namely, no hypothesis about systematic errors is needed. The estimation formulae and calculation strategy are given. Finally, with a simulative example, the validity of the method is verified.