Research On Nonlinear Filtering For Relative Navigation Of Spacecraft

Spacecraft’s relative navigation involves estimation of the relative position andattitude vectors among two or more spacecraft. For both on-orbit servicing andformation flying, the principle of spacecraft’s relative navigation remains unchangeddue to the employment of the same kinematic model and sensors. To guarantee thesuccess of this type of task, relative navigation with high precision is crucial.Working on spacecraft’s relative navigation, this thesis studies several keytechnologies, including estimation of the relative attitude/position among spacecraftas well as the non-cooperative target. Main contributions of this thesis are asfollows:This thesis analyzes the performance of several nonlinear filters. It is know nthat the particle filter, extended Kalman filter (EKF), unscented Kalman filter (UKF)and cubature Kalman filter (CKF) are all based on Bayesian filtering paradigm inessence. Specifically, particle filter is a nonlinear and non-Gaussian filter capable ofapproximating the optimal value along with increasing number of particles. Theother three methods are suboptimal Gaussian filters. In this thesis, performance ofthese Gaussian filters are examined via nonlinear transformations, Gaussianweighted integral and numerical stability. Firstly, the accuracy levels of theseGaussian filters in approximating the1stand2ndorder moments of random variables’nonlinear transformations are compared. Secondly, Gaussian weighted integral’sapproximation is used to compare the accuracy of filters. The analysis shows thatUKF and CKF have better estimation accuracy than EKF. It is also proved that CKFis a special case of UKF and they have equivalent accuracy levels. Numericalanalysis indicates that CKF clearly outperforms UKF as the dimension of statesincreases. Simulation shows that CKF has slightly better estimation accuracy thanUKF and CKF is free of non-stability.By combining quaternion and CKF, an attitude estimation method forspacecraft navigation is formulated. It uses generalized Rodrigues parameters tosubstitute quaternion errors to guarantee the unit norm property of the quaternions inattitude estimation, which ensures the accuracy and stability benefits within thismethod. It also bypasses the singularity problem effectively in attitude predictionwhile maintaining fast convergence as well as good approximation accuracy, even ifthe initial error is large. Furthermore, to reduce the computational costs inmulti-sensor measurement, an information cubature quaternion estimator isproposed which eliminates the inversion of the measurement covariance matrix. Therefore, the computational cost depends on the dimension of state variables ratherthan the dimension of the measurement variables. Also its initialization is relativelystraightforward. Simulation results demonstrate the validity of this quaternionestimator.To improve the efficiency of attitude estimator, a modified Rodriguesparameter estimator is proposed based on CKF. Although modified Rodriguesparameters have better computational efficiency as compared with quaternion, thereare attitudes that can’t be described. By introducing shadow parameters into theswitching scheme, the singularity problem in large angle maneuvers can be avoided.In addition, an LM algorithm is combined with the CKF to further improve theestimation accuracy of the modified Rodrigues parameters. This method is appliedin spacecraft’s relative attitude estimation by using measurement of mutual sightline and observation vectors to calculate the relative attitude parameters.Comparisons with other methods in simulations illustrate that the proposedalgorithm achieves non-singularity estimation while maintaining high accuracy.A modified Gaussian particle filter is formulated to overcome the accuracydeterioration caused by modelling errors in spacecraft’s relative navigation. Byusing Gaussian regression model to predict the system output and the modellinguncertainties while combining Gaussian particle filter, a new algorithm is developedwhich doesn’t need an accurate system model. This modified Gaussian particle filterbased algorithm effectively overcomes the modelling uncertainties in spacecraft’srelative navigation due to the nonspherical perturbation of the earth gravity. It alsosolves the deterioration of filtering performance in the traditional approaches.Simulation confirms the effectiveness of modified Gaussian particle filter inspacecraft’s relative navigation.For non-cooperative target spacecraft, there is no communcation link betweenthe chaser and the target while the target’s geometrical characteristics are unknown.A bionocular-vision based relative navigation method is proposed to solve therelative navigation problem in this scenario. By viewing the coordinates of target’sfeature points as state variables, a coupled kinematic model is introduced toovercome the errors of CW equation when the camera is not mounted exactly on thespacecraft’s center of mass. This model also describes the rotational motion’scorrelation with the spacecraft’s translational motion. In addition, to overcome thenonlinearity and the non-stationary noise in modelling, an adaptive CKF based onSage-Husa noise estimator is proposed. Simulation results demonstrate that this newCKF, while achieving a plausible estimator accuracy in the relative navigation, canadapt to the changes of noise statistics as well.