导航解算中的系统误差及其协方差矩阵拟合

Fittings of Systematic Errors and Covariance Matrices in Navigation

利用Kalman滤波进行导航定位计算不得不涉及观测函数模型和动力学模型,而观测函数模型和动力学模型经常含有系统误差或区域性系统误差。本文提出了一种基于移动窗口的函数模型和随机模型系统误差自适应拟合法。基于相同的窗口给出了相应的观测向量和状态预测向量的协方差矩阵估计方法,其协方差矩阵的估计与现有的Sage滤波不同。利用经系统误差修正后的观测向量和状态预测向量及相应的协方差矩阵,再进行动态导航滤波计算,能有效提高导航解的精度。文中给出了开窗估计系统误差的公式,并利用实测数据验证了该算法的可行性和实用性。计算结果表明该算法能有效地抵制系统误差对导航滤波结果的影响。

Using Kalman filtering for kinematic positioning and navigation we have to deal with an observational model and a dynamic model. Both of the functional models may contain systematic errors or local systematic errors. Adaptive fittings for both the systematic errors and covariance matrices of the model errors by using moving windows are presented. The systematic errors are fitted by using the residuals of observations and residuals of predicted states within chosen window. The covariance matrices of the modified observations and the modified predicted states are estimated within the same window, which are different from those of Sage filtering. The observations and the predicted states are then modified. The estimation formulae and calculation strategy as well as an example are given. It is shown by the theory and calculation that Kalman filtering, based on the adaptive fittings of the systematic errors and covariance matrices, can in some degree resist the influences of the systematic errors on the estimated states of navigation.