Lu Jiazhen

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.

A simplified method of PWCS observability analysis theory by research of general expressions

A novel method is discussed to simplify the calculation and analysis procedure of PWCS (piece-wise constant system) Observability Analysis Theory. By research of simplified and general expressions of observable variables, this method can be easily used to identify the relationships between observability variations and different time segments. A new transformed stripped observability matrix (TSOM) or a simplified TSOM is introduced which simplifies the analysis. The simplified observability analysis is presented as a step-by-step procedure. The use of the new method is illustrated by considering on-line calibration of a dynamic tuned gyro (DTG) strap-down inertial navigation system (SINS) on moving base. Simulation results validate the new approach.