The method of system observability analysis using pseudo-inverse of system observability matrix
The method of system observability analysis using pseudo-inverse of system observability matrix
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发表时间：
2013-07
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通讯作者：
Dong Jin-Long;Mo Bo
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作者：
Dong Jin-Long;Mo Bo
通过计算系统可观性矩阵的秩，可以分析系统的可观性。但该方法不能表示系统各状态的可观测度。众所周知，对系统可观测性矩阵进行奇异值分解后可以得到系统可观测性矩阵的伪逆矩阵。同时，线性相容方程的通解可用系数矩阵的伪矩阵表示，系统的可观测性可通过分析方程的通解得到，其系数矩阵即为系统的可观测性矩阵。定义了“不可观测度”。通过对解的自由部分的分析，得到了系统的不可观性，并给出了系统状态的不可观度的计算公式。在惯导系统静基座初始对准中的仿真结果证明了该方法的有效性。同时，该方法也适用于线性时变系统。
The system observability can be analyzed through calculating the rank of the system observability matrix. But the observability degree of each state of the system can't be expressed by this method. It is well known that the pseudo-inverse matrix of system observability matrix can be obtained after performing the singular value decomposition of the system observability matrix. Meanwhile, the general solutions of liner consistent equations can be expressed by pseudo-matrix of the coefficient matrix, and the system observability can be obtained by analyzing the general solutions of the equations, the coefficient matrix of which is the system observability matrix. The “degree of unobservability” has been defined. By analyzing the free part of the solutions, the system unobservability can be found. The formula of system states unobservability degree has been constructed. The simulation result in INS initial alignment system on stationary base has proved that this method is available. Meanwhile, the method can be also used in liner time-varying system.