Lie Group Based Nonlinear State Error for Integrated Navigation

2021 ◽  
pp. 13-25
Author(s):  
Maosong Wang ◽  
Wenqi Wu ◽  
Xiaofeng He ◽  
Jiarui Cui
Keyword(s):  
Lie Group ◽  
Integrated Navigation ◽  
Nonlinear State ◽  
State Error

Lie group based nonlinear state errors for MEMS-IMU/GNSS/magnetometer integrated navigation

2021 ◽  
pp. 1-14
Author(s):  
Jiarui Cui ◽  
Maosong Wang ◽  
Wenqi Wu ◽  
Xiaofeng He
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Linear Approximation ◽  
Lie Group ◽  
Navigation System ◽  
Integrated Navigation ◽  
Integrated Navigation System ◽  
Autonomous Equation ◽  
Nonlinear State ◽  
State Error

Abstract In the integrated navigation system using extended Kalman filter (EKF), the state error conventionally uses linear approximation to tackle the commonly nonlinear problem. However, this error definition can diverge the filter in some adverse situations due to significant distortion of the linear approximation. By contrast, the nonlinear state error defined in the Lie group satisfies the autonomous equation, which thus has distinctively better convergence property. This work proposes a novel strapdown inertial navigation system (SINS) nonlinear state error defined in the Lie group and derives the SINS equations of the Lie group EKF (LG-EKF) for the MIMU/GNSS/magnetometer integrated navigation system. The corresponding measurement equations are also derived. A land vehicle field test has been conducted to evaluate the performance of EKF, ST-EKF (state transformation extended Kalman filter) and LG-EKF, which verifies LG-EKF's superior estimation accuracy of the heading angle as well as the other two horizontal angles (pitch and roll). The LG-EKF proposed in this paper is unlimited in the choice of sensors, which means it can be applied with both high-end and low-end inertial sensors.

scholarly journals A Novel Compound Nonlinear State Error Feedback Super-Twisting Fractional-Order Sliding Mode Control of PMSM Speed Regulation System Based on Extended State Observer

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Peng Gao ◽  
Guangming Zhang ◽  
Xiaodong Lv
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Regulation System ◽  
Control Law ◽  
Error Feedback ◽  
Mode Control ◽  
Speed Regulation ◽  
Nonlinear State ◽  
State Error

In this article, a novel compound nonlinear state error feedback super-twisting fractional-order sliding mode control (NLSEF-STFOSMC) is proposed for the control of the permanent magnet synchronous motor (PMSM) speed regulation system. Firstly, a novel fractional-order proportion integration differentiation (FOPID) switching manifold is designed. A modified sliding mode control (SMC) is constructed by a super-twisting reaching law and the novel FOPID sliding surface. Secondly, the nonlinear state error feedback control law (NLSEF) has been widely used because of high control accuracy, fast convergence, and flexible operation. Therefore, combining the modified SMC with the NLSEF, the compound NLSEF-STFOSMC is proposed, which has an excellent performance. At the same time, the external disturbance of the system is observed by a novel extended state observer. Finally, the performance of the corresponding control law to the speed operation of the PMSM is fully investigated compared with other related algorithms to demonstrate the effectiveness. The comparison results show that the proposed compound control strategy has excellent dynamic and static performance and strong robustness.

scholarly journals Equivariant filtering framework for inertial-integrated navigation

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Yarong Luo ◽  
Chi Guo ◽  
Jingnan Liu
Keyword(s):  
Lie Group ◽  
Inertial Navigation System ◽  
Integrated Navigation ◽  
Extend Kalman Filter ◽  
Extended Kalman Filtering ◽  
The Earth ◽  
Kinematic System ◽  
The Matrix ◽  
Affine System ◽  
Global Navigation Satellite

AbstractThis paper proposes an Equivariant Filtering (EqF) framework for the inertial-integrated state estimation. As the kinematic system of the inertial-integrated navigation can be naturally modeled on the matrix Lie group SE2(3), the symmetry of the Lie group can be exploited to design an equivariant filter which extends the invariant extended Kalman filtering on the group-affine system and overcomes the inconsitency issue of the traditional extend Kalman filter. We firstly formulate the inertial-integrated dynamics as the group-affine systems. Then, we prove the left equivariant properties of the inertial-integrated dynamics. Finally, we design an equivariant filtering framework on the earth-centered earth-fixed frame and the local geodetic navigation frame. The experiments show the superiority of the proposed filters when confronting large misalignment angles in Global Navigation Satellite Navigation (GNSS)/Inertial Navigation System (INS) loosely integrated navigation experiments.

Extention of Strongly Stable GPC for Improvement of Steady State Error

2018 ◽  
Vol 138 (5) ◽  
pp. 498-505 ◽  
Author(s):  
Toyoaki Tanikawa ◽  
Tomohiro Henmi ◽  
Akira Inoue ◽  
Akira Yanou ◽  
Shinich Yoshinaga
Keyword(s):  
Steady State ◽  
State Error
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