自适应Kalman滤波的改进及其在SINS/GPS组合导航中的应用

Improvement of adaptive Kalman filtering algorithm and its application in SINS / GPS integrated navigation

为解决自适应Kalman滤波中存在的问题,综合采用对观测粗差和滤波结果粗差进行判断、对系统噪声方差阵扩零和修改自适应方程减去项等措施对算法进行了改进.观测粗差的判断可以避免观测奇异,提高滤波稳定性;对滤波结果粗差的判断可避免矩阵求逆时的奇异现象;对状态噪声方差阵扩零,可保证在不影响滤波精度的情况下解决滤波过程中矩阵维数不对应的问题;修改自适应方程减去项,虽然牺牲了一定的精度,但可保证求解状态噪声协方差阵Q和观测噪声协方差阵R的等式右边非负定,从而保证Q和R的非负定.将上述改进后的自适应Kalman滤波算法应用到SINS/GPS组合导航中,仿真结果表明上述改进有效地提高了自适应Kalman滤波的稳定性,且保证了滤波的精度.

This paper uses four measures to improve the performance of adaptive Kalman filter algorithm,including judging observation outliers and outliers of the filter algorithm,extending zero to system noise variance matrix and modifying the deduction in adaptive filtering.Judging observation outliers can eliminate singular values in observation and improve the stability of the filter algorithm.Judging outliers of the filtering algorithm can avoid the excessively small values in matrix w hich may result in the outlier during matrix inversion.Extending zero to system noise variance can settle the incoordination of matrix dimension.Modifying the deduction in adaptive filtering can guarantee the right side of the equations of solving noise covariance Q and observation of noise covariance R be nonnegative,so as to guarantee Q and R be nonnegative,although it sacrifices certain accuracy.The above improved adaptive Kalman filtering algorithm is applied to the SINS / GPS（strapdow n inertial navigation system / global positioning system） integrated navigation,simulation results demonstrate that the combined four measures effectively improve the stability of the adaptive Kalman filtering,and ensure the accuracy of the filter.