Rotation vector-based attitude updating algorithms have been used as the mainstream attitude computation algorithms for many years. The most popular methodology for designing the rotation vector algorithm is by leveraging multiple samples of gyro integrated angular rate measurements. However, it has been pointed out by many researchers that the attitude updating accuracy is limited when using the multiple samples rotation vector algorithms, especially when the platforms work under high rate manoeuvres. The third-, fourth-, fifth- and sixth-order Picard component solutions of the rotation vector differential equation are given in this paper. A new design methodology for rotation vector-based attitude updating algorithms is proposed. Different vibratory dynamics and high rate manoeuvre roller coaster experiments were conducted to validate the effectiveness of the new algorithm. The results demonstrate the high accuracy of the new algorithm compared with conventional coning correction methods. The proposed algorithm can also be used in high accuracy attitude computation of a post-processing system, especially when the output frequency of the gyro is limited.

Zero velocity update (ZUPT) is widely discussed for error restriction in land vehicle Inertial Navigation Systems (INSs) and wearable pedestrian INSs to overcome the problems of Global Positioning System (GPS) unavailability in urban canyons or indoor scenarios. In this paper, an online smoothing method for ZUPT-aided INSs is presented. By introducing the Rauch–Tung–Striebel (RTS) smoothing method into the ZUPT-aided INS, position errors can be effectively restrained not only at stop points but during the whole trajectory. By integrating reverse navigation with a ZUPT smoother, the method realises forward and real-time processing. Compared with existing approaches, it can improve the position accuracy in real time without any other sensors, which is well suited for applications on high-accuracy navigation in GPS-challenging environments. Accuracy test results with different Inertial Measurement Units (IMUs) show that the developed method can significantly decrease position errors from hundreds or thousands of metres to below ten metres. During the whole trajectory, the online smoothing method ensures the maximum position errors at non-stop points can reach the same level of accuracy at stop points. A delay test result proves that the delay of the reverse online smoothing method proposed in this paper is much shorter than existing online smoothing methods.