An improved determinant method of observability and its degree analysis

There are several methods applied in the observability analysis, such as determinant method. It is well known that linear dependence relationship between the observable and unobservable state variables can be found by traditional determinant method. But there is no single method which could resolve the usual difficulties in observability completely. An improved determinant method is introduced to solve this problem in this paper. It is shown here that observable state variables can be determined by establishing an information matrix based on the linear dependence relationship between observable and unobservable state variables. Also, the best choice of unobservable state variables could be performed easily by fast evaluation of observability degree based on the established information matrix and the initial error covariance of state variables. A step by step procedure is presented. Simulation results confirm the effectiveness and advantage of the new improved approach, which is applied to application of initial alignment of SINS.