基于低维SOM的可观测度分析方法及其应用

针对卡尔曼滤波器中状态可观测度的定量分析问题,提出了基于低维条带化可观测矩阵(strippedobservable matrix,SOM)的可观测度分析方法。该方法通过建立分段式定常系统(piece-wise constant system,PWCS)模型,证明了SOM与系统总的可观测矩阵具有同等的观测效力,在此基础上将PWCS模型的分段间隔作为SOM的区间分割单位,降低了其维数,进而用低维SOM的奇异值定义系统状态的可观测度。为避免定义中可能出现的基准值不确定性问题,将基准值的可信度及其影响因子引入到系统状态可观测度的定义中,给出了一种新的定义模式。最后以无源北斗/SINS深组合导航系统为例验证了该方法的有效性。

Observable degree analysis method based on SOM and its application

An observable degree analysis method based on the low dimensional SOM is presented for quantitatively analyzing the observability of the states in Kalman filter.The SOM is proved to possess the same observation effectiveness as the total observable matrix via the modeling of the PWCS,based on which the piece interval of the model is taken as the section partition unit of the SOM to reduce its dimension,and then the observable degree of system states is defined according to the singular values of the low dimensional SOM.To avoid the potential uncertainties of the datum value in the definition,the reliability of the value and its influencing factor are introduced in the definition,subsequently a new definition mode is proposed.Finally,an example of the passive Beidou/SINS deep integrated navigation system is used to illustrate the proposed method.