Cubature Kalman Filter And Robust Filter Research On Spacecraft Attitude Estimation

One of the key technologies in the field of aerospace is spacecraft attitude estimation.The attitude estimation system consisting of the gyroscopes and the star sensors has been widely used due to the high measurement precision,reliability and autonomy.For this attitude estimation system,the quaternion is regarded as the attitude description parameter because of the simple calculation,avoiding trigonometric operations and global non-singularity.In order to improve the accuracy,adaptability and robustness of the attitude estimation system,the nonlinear filtering algorithm plays a vital role in enhance those performances.As a superior nonlinear filtering algorithm,cubature Kalman filter has many advantages of easy implementaion,good numerical stability and convergence,and high precision even in the case of high dimension.Meanwhile the original attitude estimation model is too restrictive to account for different complex environment such as model uncertainties,measurement missing and measurement delay.The robust filter design has been investigated to be a valid way.Therefore,this paper has deeply researched on the applications of the cubature Kalman filter and robust filter for spacecraft attitude estimation.The main research works are as follows:Firstly,the basic theory of spacecraft attitude estimation and nonlinear filtering is described.According to the introduction about the attitude description parameter of the attitude estimation system and the measurement model of attitude sensors,the quaternion attitude estimation model based on the gyroscopes and the star sensors is established.Then,in the theoretical framework of Bayesian optimal filter,three suboptimal nonlinear filters,i.e.,extended Kalman filter,unscented Kalman filter and cubature Kalman filter are theoretically compared.The estimation performance and numerical stability is analyzed in the case of high dimension.This provides a theoretical basis for the application of cubature Kalman filter in the spacecraft attitude estimation.Aiming at the case that the quaternion must obey a normalization constraint in the attitude estimation model,an additive quaternion constrained cubature Kalman filter algorithm is presented.From the essence of the optimal filter,combining the quaternion constraint with the minimum mean square error estimation criteria,a minimum constrained cost function is constructed to modify the filtering gain so that the quaternion normalization problem can be solved.Then,three degree spherical radial cubature rule is employed to computer the posterior mean and covariance of the system state,which makes that thequaternion constrained cubature Kalman filter formula can be derived.Meanwhile,considering that the quaternion,in essence,is a rotation vector but not a normal vector,there is a multiplicative property by using the quaternion in the filter so that the quaternion weighted mean calculation remains to be addressed.So,a quaternion square-root cubature Kalman filter algorithm is proposed.This algorithm uses the simple Lagrange loss function method to compute the average quaternion,employs the cubature numerical integration theory to improve the estimation accuracy and convergence rate,and introduces the square root form to improve the stability of the filtering algorithm.The limitation of the current iterated cubature Kalman filter is that it has the assumption that the measurement noise is uncorrelated with the state and state estimation in each iteration,and the state estimation accuracy is affected on a certain extent.Thus,an improved iterated cubature Kalman filter is proposed and used for the attitude estimation system,which makes that a cubature point iterated cubature Kalman filter attitude estimation algorithm with quaternion constraint is given.This algorithm uses the three degree spherical radial cubature rule to calculate the mean and variance of the nonlinear function,utilizing the state augmented method to solve the issue that the state is correlated with the measurement noise in the iterated process.A new cubature points iterated strategy is developed,which can directly iterate the cubature points,and thus avoids generating cubature points by calculating the mean-squared root in each iteration.It overcomes the limitation that sampling points are produced by the Gauss approximation in the traditional iterative strategy,which can reduce computational complexity.The quaternion constraint is taken into account for attitude estimation,and the gain correction method is utilized in each iteration to guarantee the quaternion normalization constraint.Aiming at the shortcoming that the attitude estimation filtering algorithm has low accuracy and poor robustness in the presence of model mismatch,unknown external disturbance and state mutation,a quaternion constrained strong tracking cubature Kalman filter attitude estimation algorithm based on multiple fading factors is presented.This algorithm,to overcome the limitation of single fading factor for multi-variable system,introduces two multiple fading factors to adjust the prediction error covariance.It can make different filter channels have different adjustment ability to ensure the prediction error covariance matrix is symmetrical.Thus,the strong tracking of the filtering algorithm can be realized.At the same time,considering the quaternion normalization constraint,the filter gain is adjusted in order to satisfy the constraints for the estimated quaternion.For the attitude estimation problem under the complex environment,the robust filterdesign in three different situations is considered.First,considering the misalignment errors of gyros and star sensors and star sensor measurement delays,that uncertain attitude estimation model is established by describing the misalignment errors of gyros and star sensors as model uncertainties.Then,a new finite-horizon robust Kalman filter is proposed to deal with model uncertainties and star sensor delays.Second,considering that there are multiplicative noises and unknown external disturbances in the nonlinear attitude estimation system,a robust extended Kalman filter attitude estimation algorithm is proposed.Based on the structure of the extended Kalman filter,the proposed algorithm designs an optimal upper bound of the prediction error and the filtering error covariance matrices.In addition,the estimation error of the extended Kalman filter is bounded in mean square under certain conditions.Third,considering that there are correlated additive noises,multiplicative noises and packet losses in the nonlinear attitude estimation system,a robust recursive filter is proposed.Based on the state prediction and state correction structure of the extended Kalman filter with correlated noises,the proposed filter designs an optimal upper bound of the prediction error and the filtering error covariance matrices,respectively.Simulation results illustrate the effectiveness of these three robust filtering algorithms.