Estimation of Quaternion Motion for GPS-Based Attitude Determination Using the Extended Kalman Filter

Abstract

In this paper, the Global Positioning System (GPS) interferometer provides the preliminarily computed quaternions, which are then employed as the measurement of the extended Kalman filter (EKF) for the attitude determination system. The estimated quaternion elements from the EKF output with noticeably improved precision can be converted to the Euler angles for navigation applications. The aim of the study is twofold. Firstly, the GPS-based computed quaternion vector is utilized to avoid the singularity problem. Secondly, the quaternion estimator based on the EKF is adopted to improve the estimation accuracy. Determination of the unknown baseline vector between the antennas sits at the heart of GPS-based attitude determination. Although utilization of the carrier phase observables enables the relative positioning to achieve centimeter level accuracy, however, the quaternion elements derived from the GPS interferometer are inherently noisy. This is due to the fact that the baseline vectors estimated by the least-squares method are based on the raw double-differenced measurements. Construction of the transformation matrix is accessible according to the estimate of baseline vectors and thereafter the computed quaternion elements can be derived. Using the Euler angle method, the process becomes meaningless when the angles are at 90 degrees where the singularity problem occurs. A good alternative is the quaternion approach, which possesses advantages over the equivalent Euler angle based transformation since they apply to all attitudes. Simulation results on the attitude estimation performance based on the proposed method will be presented and compared to the conventional method. The results presented in this paper elucidate the superiority of proposed algorithm.