Attitude Determination Algorithm Based On Quaternion Nonlinear Filter For Spacecraft

Attitude determination is one of key technologies in spacecraft attitude control system. The attitude determination accuracy directly affects the accuracy of spacecraft navigation and attitude control system. The attitude determination accuracy depends not only on the performance and accuracy of hardware configuration in attitude measurement system but also on the the attitude determination algorithms. The attitude description parameter is the premise and foundation of attitude determination model. The common attitude parameters are Euler angles, modified Rodriguez parameters, direction cosines, and quaternions and so on. Quaternions have been widely used because of its less computation burden and global non-singularity. However, the quaternions must follow the standardized requirements, so how to overcome the limitations of its standardization and combining with the advanced nonlinear filtering algorithm become the problems need to be solved. In this paper, the algorithm of spacecraft attitude determination based on the quaternion nonlinear filter is studied. The main contents of this paper are as follows:Firstly, the corresponding kinematics equations are established on the basis of several common attitude parameters and the relationships of these parameters are introduced in detail. According to the attitude measurement sensors such as gyro and star sensor, the sensor measurement models are established. On the basis of it, the state space model of spacecraft attitude determination system is given. Starting at Bayesian optimal estimation theory, two types of nonlinear filtering algorithms including extended Kalman filter (EKF), unscented Kalman filter (UKF) algorithm, particle filter (PF) and its improved algorithm based on the assumptions of Gaussian distribution and non-Gaussian distribution are studied deeply.The problems and difficulties encountered in quaternion nonlinear filter are analyzed deeply. A Lagrangian cost function method is presented to compute quaternion weighted mean based on the analysis of singular value method and the eigenvector method. Starting at the mean of weighted mean quaternion, the MMSE criterion is used to eastablish quaternion cost function, the Lagrange multiplier function is used to guarantee the quaternion normalization, so that the mean quaternion can be calculated by seeking the minimal solution to the cost function. On the basis of analysis and resolving the problems of quaternion nonlinear filtering, a quaternion UKF algorithm without switching attitude parameters is proposed, where only the quaternion vector part is selected to represent attitude variable and the scalar part is calculated through the quaternion normalization, by which not only the problems of disturbed quaternion normalization is solved, but also the state dimension and the filter complexity is reduced. Cosidering the numerical stability of Q-UKF algorithm, a quaternion square root UKF algorithm (Q-SRUKF) is propsed. The Gyro/CCD simulation results verify the effectiveness of these algorithms.Aiming at the problem that the accuracy of UKF algorithm declines when noise is involed in the nonlinear transfer, the augmented UKF (AUKF) algorithm is studied. Considering the sharply increased computation burden caused by the increasement of state dimension, a state switch UKF (SSUKF) algorithm whose process and measurement noise has no correlation is proposed. Via selecting different state variables in time update and measurement update stage, the state dimension of real-time filtering is reduced and the number of Sigma points selected decreases, so the filter speed is improved. On the basis of SSUKF, a quaternion SSUKF (Q-SSUKF) is presented to solve the spacecraft attitude determination. The simulation results based on Gyro/CCD shows that compared with quaternion AUKF (Q-AUKF), the Q-SSUKF saves filter time and improves the system’s real-time ability in a certain extent.Aiming at the nonlinear/non-Gaussian attitude determination, via introducing the common parameter switching particle filter, a quaternion particle filter (Q-PF) without attitude parameter switching is proposed, where the quaternion covariance matrix trace is considered and used to calculate perturbation quaternions. Based on the Q-PF algorithm, two improved quaternion particle filter are proposed. Cosidering the attitude determination system is a linear/nonlinear system, a quaternion Rao-Blackwellized particle filter (Q-RPF) is presented, where the system is divided into linear and nonlinear part to be dealt with, and the filter time to some extent is saved. Considering the filter accuracy decreased that the prior probability density function is selected as probability density function regardless of the current observation information, a quaternion UPF (Q-UPF) is propsed to solve the attitude determination. In this method, UKF is selected to calculate the importance probability density function, which takes full advantage of the current observational information. The Gyro/CCD simulation results prove the effectiveness of these algorithms.