先验协方差阵误差对动态Kalman滤波解的影响

Error Influences of Prior Covariance Matrices on Dynamic Kalman Filtering

分别讨论当标准Kalman滤波动力学模型的状态参数协方差阵、状态噪声的协方差阵及观测噪声的协方差阵含有误差时,对滤波结果的影响并导出相应的解式。利用GPS/INS紧组合导航系统的实测数据对上述分析进行了实验,结果表明,动力学模型信息的协方差阵和观测信息的协方差阵在滤波中具有一个理想的平衡点,该平衡点能够合理分配动力学模型信息和观测信息对滤波解的贡献,从而可以得到可靠的滤波解。

The influence of the prior covariance errors to the standard dynamic Kalman filtering is discussed.The influence expressions of the prior covariance matrix errors including the covariance matrix of state parameters,dynamical model errors and measurement noises are deduced.A GPS/INS tight integration navigation is performed,and it shows that the unreasonable errors of the covariance matrices of the dynamic model information and measurements will result in biases of the dynamic navigation results.The minus errors of the covariance matrix of dynamical model information will increase the navigation errors.If the errors of the covariance matrix of the predicted states are positive,then the effects of the dynamical model error will be weakened.However,contrary conclusion could be got if only the errors of the covariance matrix of measurement noises are considered.