SE_k(3)-EKF-Based GNSS/SINS Positioning And Attitude Determination Algorithm Research

GNSS/SINS integrated navigation filtering usually defines the error states in vector space,when the errors such as attitude misalignment angle are large,the state error definitions such as position and velocity in the traditional EKF framework only consider the size difference,ignoring the difference in direction,and the resulting inconsistent state error coordinate definitions are more prominent;the traditional EKF framework is linearized at the state initial value point,when the state has In addition,the traditional EKF framework also has the so-called inconsistent variance estimation problem in the combined navigation state estimation,i.e.,the state that is not considerable is also filtered and estimated,which directly causes the error transfer to appear as a large deviation.To address the theoretical deficiencies of the current EKF framework commonly used for GNSS/SINS combined navigation,this paper delves into the SE_k（3）-EKF based GNSS/SINS high-precision combined positioning attitude fixing algorithm under the Li group framework,and the main contents and contributions of the paper are as follows:（1）The attitude,velocity and position states are constructed as special SE_k（3）-EKF group elements,and the gyro and accelerometer zero bias errors are considered to form a group-vector hybrid error model,based on which a GNSS/SINS loose combined anti-difference filtering algorithm（RLIEKF）based on measurement left invariance is studied.The experimental results show that the RLIEKF is better than the traditional combined GNSS/SINS algorithm.The experimental results show that,compared with the traditional EKF method,the RLIEKF method has a faster convergence speed under different large misalignment angles because the attitude angle error is taken into account in the temporal update and GNSS measurement update,and does not require a complicated and long time attitude alignment step,which can better compensate for the short time loss of the GNSS signal.It can significantly improve the filtered new holographic accuracy,has better anti-aliasing performance,is more robust to complex observation environment,and has comparable computational efficiency.（2）A left-invariant SE₂（3）-EKF based RTK/SINS tight combination filtering algorithm is derived based on the group-vector hybrid error model.The experimental results show that compared with the traditional EKF method,the proposed method has faster heading convergence speed,higher localization accuracy and ambiguity fixation rate under different sizes of initial attitude errors;the right-invariant SE₂（3）-EKF state equation and the corresponding loose combination and tight combination measurement equations are derived,in which the specific force term in the new state transfer matrix has been eliminated,and the right-invariant SE₂（3）-EKF state equation and the corresponding loose combination and tight combination measurement equations are derived by combination and tight combination of two on-board combination navigation experiments,it is verified that the right invariantSE_k（3）-EKF can guarantee the positioning accuracy and fixation rate level under the premise of higher computing efficiency after the time update frequency is reduced from 200HZ to 1HZ.（3）Due to the arbitrary flight direction of the rotorcraft UAV,the MEMS inertial guidance initial alignment can no longer use the commonly used dynamic coarse alignment scheme,so it is difficult to obtain a reliable initial attitude quickly and in real time.Based on this,this paper investigates a GNSS-assisted dynamic attitude initial alignment algorithm based on the left-invariant velocity measurement of SINS,and the attitude matrix and velocity form a Lie group.The superiority of the proposed method is verified by simulating the attitude error angle in different cases in the combined GNSS/SINS navigation experimental data.The experimental results show that the alignment method based on SE（3）-EKF filtering has faster convergence speed,higher accuracy,and higher operational efficiency compared with the traditional EKF and nonlinear error model combined with UKF method,which proves that the method is more suitable for the initial alignment of rotorcraft UAV inertial guidance.