一种基于可观测度的方差预测理论方法及其应用

A Theoretical Approach to Variance Prediction Based on Observability and its Application

针对机动路径设计时传统的可观测性分析方法仅能得到估计参数的可观测度而无法得到参数估计精度的工程实际情况,提出了一种基于可观测度的方差预测理论方法。首先,阐述了基于最小二乘估计理论的可观测性分析方法;其次,对提出的方差预测理论方法进行了理论推导和证明,阐明了其物理意义,并分析了该方法的预测误差模型;最后,以惯导多位置对准为例,对该方法进行了应用验证,证明有效。该方法可以在卡尔曼滤波计算之前对状态参数实时方差进行预测,为系统机动路径的设计及估计精度预测提供了重要依据。

According to actual situation that the traditional observability analysis method in the design of maneuver path can only obtain the observability of estimated parameters,but not the accuracy of the parameter estimation,a theoretical method of variance prediction based on observability is proposed.Firstly,the observability analysis method based on the least squares estimation theory is illustrated.Secondly,the proposed variance prediction theoretical method is derived and proved,its physical meaning is elucidated,and the predictive error model is analyzed.Finally,the INS multi-position alignment is taken as an example to validate the application of the method,which is proved to be effective.The method can predict the real-time variance of state parameters before Kalman filtering,which provides an important basis for the design of the maneuver path and the prediction of estimation accuracy.