The method of system observability analysis using pseudo-inverse of system observability matrix

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.