Implementation of Gradient-iterative Least Squares on Estimating the Quaternion Component for GNSS-based Attitude Determination

摘要

Several Euler angles-based algorithms are proposed to solve the attitude determination problem. However, the algorithms suffer from the singularity problem and the ambiguous meaning of orientation angle determination. The quaternion is introduced due to its immunity against such problems. It efficiently reduces cost during computation compared to geometric based rotation matrix representation. Nevertheless, the quaternion constraints to N~2(q) = ||q||~2 = q*q = 1. Several methods are proposed to handle this situation. It however introduces another additional parameter into estimation process, which burdens the estimation process. This contribution aims to develop an extended iterative algorithm, namely gradient iterative algorithm, which is used to solve the quaternion components efficiently. Unlike the conventional least squares method, in which the estimate parameter convergence depends on a given set of initial values, the gradient iterative algorithm is able to give convergent estimate parameter in much faster computation time. The proposed method is tested against the conventional and the iterative least squares procedures using a set of fixed antenna arrays. In order to make a comparison from the tested methods, six important indicators are evaluated. Results show that the proposed method outperforms the other two methods. It is considered more effective and efficient by mean of the parameter convergence and the processing cost, which makes this method is adaptable for practical purposes.