An Applicable Algorithm For Strapdown Inertial Navigation System Using Lie Group

Inertial navigation technology is an indispensable important branch in the navigation field.The strapdown inertial navigation relies on its simple structure,low cost and easy maintenance and becomes a research hotspot in inertial navigation technology.Initial alignment and strapdown solution are two important components of strapdown inertial navigation system.The performance of the strapdown solution determines the accuracy and speed of the system tracking the attitude and position of the carrier;the initial alignment provides the initial information for the strapdown solution,and its speed and accuracy directly affect the solution performance.The Strapdown Inertial Navigation System relies on mathematical models and computer techniques to solve the carrier attitude by constructing a virtual platform.Therefore,the attitude matrix needs to be mathematically modeled.Euler angle and quaternion are two common models that can describe the attitude matrix.However,Euler angle will produce singular values due to the Gimble lock problem in the attitude description process because of its characteristics of three-parameter model.Although the quaternion model solves the problem of singular value,it has double coverage for the attitude space.This nature causes non-uniqueness problems which resulting unwinding phenomenon in attitude control.In order to solve the problems existing in the existing description model,this paper introduces Lie Group to model the attitude matrix directly,and completes the solution and alignment task of the strapdown inertial navigation.As a recently emerging attitude description model,Lie Group demonstrates excellent performance in describing the rotation of rigid bodies.This paper proposes a complete set of strapdown inertial navigation system solutions including strapdown solution and initial alignment with the Lie Group model.Comparing with the traditional strap-down inertial navigation scheme based on quaternion model or Euler angle model,the proposed scheme effectively solves the singular value problem and non-uniqueness problem existing in traditional schemes,and has high application value.The main research work of this paper is as follows:Firstly,using the special European group to describe the attitude and velocity of the carrier synchronously and deriving the inertial navigation strapdown solution method based on Lie Group;the Lie group solution method and the traditional quaternion solution method are compared in detail.And the analysis proves the superiority of the Lie group solution method.Secondly,according to the different environmental characteristics of static base and sway base,the self-alignment scheme of strapdown inertial navigation based on Lie Group is designed.Using the characteristics of the Lie Group model,the attitude matrix is directly estimated as the state quantity and the traditional two-step alignment is simplified to one-step alignment.The error is mapped to the Lie algebra space,and designed the Lie Group filter with the principle of mean square error to complete the self-alignment task.Finally,the Lie group optimal estimation algorithm is proposed to complete the sway base self-alignment process.By analyzing the multiplicative rules of Lie group space and referring to the idea of optimal estimation,an optimal estimation algorithm for Lie group is derived,which avoids the problem of error mapping problem in Lie Group filter and the orthogonality problem in existing optimization algorithm.The algorithm improves the speed and accuracy of self-alignment.The stability of the algorithm is analyzed and the proposed algorithm can converge is proved.