Study On Initial Alignment Method Of Sins Based On Lie Group Representstion

Initial alignment is one of the key technologies of the inertial navigation system,the pros and cons of the initial alignment will directly affect the navigation accuracy and arithmetic speed.The quaternion representation is usually used to represent the attitude solution of the traditional strapdown inertial navigation system(SINS),and this method has become the most commonly used method.Although the quaternion representation of attitude avoids the singular value representation of the Euler angle,the quaternion representation of each attitude is non-unique in the sense that each attitude corresponds to two different quaternion vectors,the closed-loop properties derived from this non-unique quaternion representation might not hold for the attitude space,which leads to the almost global asymptotic stability of an equilibrium in this quaternion space does not guarantee almost global asymptotic stability of the corresponding equilibrium in attitude space.In addition,the quaternion representation must meet the constraint of the unit,which has to be normalized in the strapdown inertial navigation process,and inevitably introduces unnecessary calculation error.In this paper,aiming at the existing problem of quaternion representation,the Lie group is utilized to replace quaternion to represent the attitude matrix directly estimating the attitude matrix.Some exploratory studies have been carried out on the SINS system and its initial alignment based on Lie group representation,the content mainly comprises the following aspects:Firstly,the solution process of SINS based on Lie group representation is established.On the basis of the basic principle of Lie group,the description of the special orthogonal group and the special European group of rigid body motion is established,and then the SINS algorithm based on Lie group is established.The Lie group differential equation describing the relative motion of coordinate system is established as the performance benchmark of navigation and spinor,and the solution process of SINS based on Lie group is deduced.Secondly,the attitude matrix represented by Lie group is applied to the initial alignment.Combined with the optimal attitude estimation method,an initial alignment method of SINS based on Lie group filter is proposed.Based on the principle of Lie group representation,the problem of solving the initial alignment attitude matrix is transformed into the estimation of Lie group in the inertial coordinate system by the attitude matrix decomposition method.On account of the properties of Lie group representation and the basic principle of inertial navigation,the initial alignment system model of Lie group structure is established by combining the optimal attitude estimation method and Lie group attitude decomposition method.The minimum variance estimation method is directly used to estimate the attitude matrix to complete the initial alignment of SINS.Finally,in view of the problem of the measurement noise related to the state,two kinds of improved Lie group filters are proposed in the initial alignment system using Lie group representation.An adaptive Lie group filter is established to realize the accurate estimation of attitude by the theory of measurement residual and measurement noise variance estimation.Based on the principle of decorrelation,the error of the inertia component is separated from the original ideal model,and a precise method of calculating the covariance matrix of state correlation noise is designed.Then a more accurate model of system error analysis on Lie group structure is reconstructed,thus a decorrelation noise Lie group filter is proposed to realize the initial alignment.