Observable degree analysis of DGPS/SINS calibration based on singular value decomposition

The observable degree of linear time-varying system is often analyzed after Kalman filter is designed, and it's the key parameter to examine the accuracy and rate of convergence of the Kalman filter. However, traditional approaches of observable degree analysis cannot simultaneously meet the requirements in engineering applications. This necessitates the development of observable degree analysis. This paper is on the basis that inertial components error model has been set, and an approach of multiposition for calibration is introduced, which aims at improving the accuracy of calibration of strapdown inertial navigation system (SINS) based on differential global positioning system (DGPS). During the process, first, definitions of observable degree that researchers have proposed are introduced. Then, an approach of observable analysis, which can transform linear time-varying system to piece-wise constant system (PWCS), is disserted. And next, singular value decomposition (SVD) is applied to observable matrix based on PWCS, which is used to analyze whether the observability has been improved through observing the changes of singular values. Finally, results of simulation demonstrate that observable degree has been well improved, and observable parameter can predict Kalman filtering errors of system states precisely.