A Lie Group Manifold-Based Nonlinear Estimation Algorithm and Its Application to Low-Accuracy SINS/GNSS Integrated Navigation

Abstract

In this article, in order to improve the performance of the micro inertial measurement unit (MIMU) based on low-accuracy navigation system under the condition of initial large misalignment angle, a nonlinear strapdown inertial navigation system (SINS)/global navigation satellite system (GNSS) integrated navigation estimation algorithm based on the Lie group manifold space is proposed. The proposed nonlinear algorithm is based on unscented Kalman filter (UKF), and its core is to realize the propagation of Lie algebra state error variable sigma points between Lie group space and Lie algebra space through the retraction operation and inverse retraction operation. Meanwhile, the sensor bias state error variable sigma points are always propagated through linear operations in the Euclidean space. Finally, the covariance of the two forms of state error variable is calculated in the Euclidean space, from which the lie algebra state error variable and sensor bias state error variable are estimated through the measurement updating process. The simulation and experimental results show that the proposed algorithm has higher accuracy and faster convergence speed compared with the existing state-of-the-art integrated navigation algorithms, and it has good estimation consistency.