GPS/SINS组合导航系统状态的可观测度分析方法

Observable degree analysis method of integrated GPS/SINS navigation system

线性时变系统状态的可观测度是检验所设计的Kalman滤波器的收敛精度和速度的重要指标。传统的可观测度分析方法存在着各种缺陷,难于满足实际工程应用需求。首先,本文论述了将线性时变系统状态转化为分段式定常系统(PWCS)的可观测性分析方法,并在对PWCS可观测性矩阵进行奇异值分解的基础上,定义系统状态的可观测度。然后,详细证明GPS/SINS组合导航系统满足PWCS分析定理要求,可以用条带化可观测性矩阵(SOM)代替总的可观测性矩阵(TOM)分析系统状态的可观测度。为了分析全弹道GPS/SINS系统状态的可观测度,进一步提出改进的可观测度分析方法。最后,从松耦合GPS/SINS系统仿真结果可以看到,可观测度指标能够很好地预见系统状态的Kalman滤波误差大小。可观测度高则滤波误差小,可观测度低则滤波误差大。这初步表明改进的可观测度分析方法是合理的和可行的。

The observable degrees of linear varying-time system states are the key indexes to check the convergence accuracy and velocity of designed Kalman filter.As there are a variety of shortcomings,however,the traditional methods of observable degree analysis are unable to meet the requirements of practical engineering application.Firstly,the observability analysis method of the linear varying-time system changed into piece-wise constant system (PWCS) were described in this paper.And then based on the singular value decomposition of PWCS observability matrix,the observable degrees of system states could be defined.Secondly,the integrated GPS/SINS navigation system was demonstrated in detail to satisfy the PWCS analysis law.Thus,the observable degrees of system states could be simply analyzed by using the striped observability matrix (SOM) instead of total observability matrix (TOM).In order to analyze the observable degrees of GPS/SINS system states along a whole trajectory,the modified analysis method was presented further.Finally,it can be clearly illustrated from the results of loosely coupled GPS/SINS system simulation that the observable degree indexes are able to better predict Kalman filtering errors of system states.The higher the observable degree,the smaller is the filtering error.And the lower the observable degree,the greater is the filtering error.Therefore,it can be shown preliminarily that the modified observable degree analysis method is rational and feasible.