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.

中文翻译：

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基于李群的MEMS-IMU/GNSS/磁力计综合导航非线性状态误差

在使用扩展卡尔曼滤波器（EKF）的组合导航系统中，状态误差通常使用线性逼近来解决常见的非线性问题。然而，由于线性近似的显着失真，这种误差定义会在某些不利情况下使滤波器发散。相比之下，李群中定义的非线性状态误差满足自治方程，因此具有明显更好的收敛性。这项工作提出了一种新的捷联惯性导航系统（SINS）非线性状态误差定义在李群中，并推导了 MIMU/GNSS/磁力计组合导航系统的李群 EKF（LG-EKF）的 SINS 方程。相应的测量方程也被推导出来。已进行陆地车辆现场测试以评估 EKF 的性能，ST-EKF（状态变换扩展卡尔曼滤波器）和 LG-EKF，验证了 LG-EKF 对航向角以及其他两个水平角（俯仰和滚动）的卓越估计精度。本文提出的 LG-EKF 在传感器的选择上是无限的，这意味着它可以与高端和低端惯性传感器一起应用。