An Accurate Numerical Algorithm for Attitude Updating Based on High-Order Polynomial Iteration

Abstract

To effectively improve the accuracy of attitude reconstruction under highly dynamic environments, a new numerical attitude updating algorithm is designed in this paper based on the high-order polynomial iteration according to the differential equation for quaternion. In this algorithm, a high-order polynomial is introduced to fit the angular rate accurately without increasing the number of gyro outputs during per attitude updating interval. This algorithm can provide an exact high-order polynomial solution for quaternion and the process of attitude reconstruction can be implemented efficiently. The algorithm's performance is evaluated as compared with optimal coning algorithm, attitude quaternion updating algorithm based on Picard iteration (QPI), and higher-order rotation vector attitude updating algorithm (Fourth4Rot) under coning motion. The simulation results show that this algorithm can improve the accuracy of attitude computation and clearly outperform the optimal coning algorithm, QPI, and Fourth4Rot in high dynamic environment.

Keywords

• Attitude updating algorithm
• quaternion
• high-order polynomial
• polynomial iteration