The Research Of Tightly Coupled SINS/GPS/DVL Applied To AUV

For the actual operating environment of Autonomous Underwater Vehicle(AUV),this paper investigates the information fusion technology of integrated SINS/GPS/DVL navigation system theoretically.Strapdown algorithm is the foundation of a strapdown inertial navigation system,for the low-dynamic property of an AUV,the attitude algorithm and the velocity algorithm and the position algorithm,which based on Runge-Kutta rule,are presented in this paper.The SINS error model serves for the implementation of a Kalman filter in an integrated navigation system.The ψ-angle model is derived by perturbing the nominal differential equation of SINS.Compared with φ-angle model,ψ-angle model is more concise,and its coefficients are more easily accessible.And it is suitable for the information fusion with the GPS data that is projected into the erath frame.The acoustic Doppler Velocity Log(DVL)measurement errors can be modeled in a Kalman filter.Considering the precision of error modeling and system observability,it is can not be guaranteed that those DVL errors can be well estimated.Therefore it is necessary to calibrate those errors before the information fusion.And,this paper provides some methods to do this job.The DVL measurements are projected into body frame,so the model between the velocity error in body frame and computed navigation frame is derived,based on this model,the measurement update is performed.Computer simulation verifies the above conclusions.Considering that the measurement model of a tightly coupled SINS/GPS is nonlinear,two different nonlinear Kalman filters,i.e.Extended Kalman filter(EKF)and Cubature Kalman filter(CKF),are presented in this paper.At the same time,it is necessary to keep the estimated error covariance matrix positive definite,so a Square-root CKF(SCKF),based on QR decomposition,is presented in this paper.This paper analyzes the precision of EKF and CKF by using the fitting Taylor series as the criterion.This paper draws the conclusion that CKF has second order accuracy,and EKF has first order accuracy.However,numeric simulation results demonstrate that two nolinear filters have the same accuracy in tightly coupled SINS/GPS.It is because that the seconed order term of the Taylor series of the measurement model is far more less than measurement noise,in other words,this term can be omitted.Considering that an EKF is more efficient than a CKF,this paper draws the conclusion that the EKF is better for tightly coupled SINS/GPS.The observability of a system determines whether the error state can be well eastimated by a filter or not.For a tightly coupled SINS/GPS,there is no measurement model(CKF)or it is very complex(EKF),which makes it impossible to use the classical observability methods in such a system.For the above reasons,this paper proposes a new method for analyzing the instantaneous observability of a tightly coupled SINS/GPS,this method consists of the following steps: Reconstructing the ψ-angle model;Deriving the instantaneous observability matrix(IOM);Modeling the translator and angle maneuvers of an AUV;Deriving the specific form of the IOM;Analyzing the Null space of the IOM and drawing relative conclusions.The main conclusions of instantaneous observability analysises: Almost all kinds of translator and angle maneuvers can make a three-channel SINS/GPS tightly coupled system be instantaneously observable,but this conclusion is not applicable to a two-channel system.Accordingly,using a three-channel SINS can improve the precision of a tightly coupled navigation system efficiently.If the number of visable satellite is less than 4,the filter is unstable,and maneuvers will intensify this trend.