Kalman Filter Aided Stochastic Observability Analysis And Its Application In SINS/GPS Integrated Navigation

Various state estimation methods,such as a Kalman filtering,have been successfully applied to navigation and other fields.Among the different navigation techniques,a strapdown inertial navigation system(SINS)and the Global Positioning System(GPS)are recognized as the most appropriate integration schedule which has been studied thoroughly and deeply.Under normal motion conditions,some state components that are difficult to estimate exist in the SINS/GPS integrated navigation system model.As a fundamental property of state-space models,observability is closely related to state estimation.Through the observability analysis,the estimated effect of the states can be pre-judged,thereby providing design guidance for the improvement of navigation performance.Most of the existing observability analysis methods are limited in the framework of a deterministic system model,which means these approaches have difficulty in describing the observability of a stochastic system such as the integration of SINS/GPS.From the viewpoint of stochastic observability analysis,this work proposes a novel method after thoroughly studying a traditional approach.Based on the Orthogonality principle,the proposed method utilizes the singular value decomposition of the Kalman gain matrix to analyze every single state’s stochastic observability,which overcomes the shortcomings of the traditional approach.In this way,every state’s stochastic observability of the SINS/GPS integrated system can be directly determined.The measure of observability is another main goal for observability analysis.The existing measures of observability are generally described by attributes such as the condition number of the observability matrix,which cannot distinguish the degree of observability between different states.After further studying the traditional stochastic observability method,an approach based on the estimation error covariance matrix is proposed to measure the states’ observability.The eigenvectors of the covariance matrix reveals the structure property of the state space.This work makes use of this property to quantify observability.Furthermore,a Consider filtering is analyzed to clarify its deficiency.The proposed measure of observability and the Consider filtering are combined to develop a new approach which is called observability-based Consider filter(OCF).This filter utilizes the strength of the Consider mechanism and can estimate those weakly observable states,which is suitable for the SINS/GPS integrated system.Simulation results demonstrate that the proposed stochastic observability analysis approach can capture the states’ stochastic observability of the SINS/GPS integrated system more accurately than the traditional one.At the same time,the misleading conclusions drawing by the traditional method are justified.Being aimed at applied research,on the other hand,the proposed OCF outperforms the conventional Kalman filter in some situations.Specifically,the gyro biases and accelerometer biases can be effectively estimated which confirms the proposed method’s validity.