Study On Relative Navigation Algorithm For Spacecraft Based On Dual Quaternion

Spacecraft relative navigation is the process of determining the relative motion parameters between two or more spacecraft by various means.For spacecraft rendezvous and docking,satellite formation flying and in orbit satellite capture and other tasks,the high precision of the relative navigation technology is the prerequisite for ensuring the successful completion of the task.The determination of the relative position and attitude of the spacecraft is mathematically equivalent to the conversion of two not concurrent three-dimensional coordinate systems.This paper to the spacecraft rendezvous and docking approach phase as the research object,combined with the advantage of dual quaternion which could unifiedly describe the rigid body's attitude and position,and establish spacecraft's relative position and attitude integration description form based on dual quaternion.Then the relative pose determination algorithm for spacecraft based on binocular vision and the combined relative navigation method based on Vision / Inertial / Radar is designed.The work of this paper mainly includes the following three aspects:Firstly,the unified expression of the target space position and the attitude of the spacecraft based on the dual quaternion is established and a method for determining the relative position and attitude of Spacecraft Based on binocular vision is designed.The method is based on the principle of parallel binocular vision measurement,Combining the geometric constraints of the dual quaternion to set up the target error function by means of the coordinate transformation method of dual quaternion.So that the determination of the relative position and attitude of the spacecraft is transformed into s the solution of conditional extreme value and then we can find out the position and attitude parameters which minimize the target error function by Lagrange extreme value method.The simulation results show that the algorithm has good effect in the range of 100 m,which can meet the requirements of the measurement accuracy of the spacecraft rendezvous and docking.Secondly,the cause of the error in the process of measuring the relative position and attitude of the spacecraft by binocular CCD is analyzed,and points out that it is reasonable and necessary to describe the error as the multiplicative noise.Considering extended Kalman filter is still the most widely used and mature nonlinear filtering algorithm in engineering,so next the mathematical principle of Kalman filter is analyzed and finally the method of processing the multiplicative noise in the framework of Kalman filter,in other word,the Kalman filtering with multiplicative measurement noise is given.By means of mathematical simulation,the method was proven to possess the ability of filtering out the multiplicative noise and additive noise at the same time,so that the application scope of Kalman filter is extended.Finally,using dual quaternion to describe the relative motion of spacecraft possessed the unified form,moreover,the motion's nature was also reflected better.There are 6 degrees of freedom in the space rigid body motion,while the dual quaternion has 8 components.When dual quaternion was employed to describe the spacecraft's relative motion,there will be redundancy of 2 degrees of freedom,so if dual quaternion was taken directly as state variable to estimate the motion of the spacecraft,then the amount of computation will increase.Considering that the error of the quaternion has been applied to the attitude determination algorithm of spacecraft,this paper proposes the concept of error dual quaternion and establish the relative motion model of spacecraft by it.Combined with the relative attitude determination algorithm and the Kalman filter with multiplicative measurement noise which given previously,a new algorithm for the relative navigation of spacecraft close range rendezvous is proposed.Compared to previous methods,this method has the advantages of simple form,good linearity and small calculation amount.