The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involut...The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.展开更多
This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncerta...This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncertainty of structural and aerodynamic parameters,the six-degree-of-freedom(6Do F) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established,respectively,in the inertial and body-fixed reference frames.Next,a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6Do F dynamics.Then,a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix.As long as the finitely excited condition is satisfied,the precise identification of unknown parameters can be achieved.Finally,the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.展开更多
The laser gyro is most su it able for building the strap down inertial navigation system (SINS), and its acc uracy of attitude algorithm can enormously affect that of the laser SINS. This p aper develops three improv...The laser gyro is most su it able for building the strap down inertial navigation system (SINS), and its acc uracy of attitude algorithm can enormously affect that of the laser SINS. This p aper develops three improved algorithmal expressions for strap down attitude ut ilizing the angular increment output by the laser gyro from the last two and cur rent updating periods according to the number of gyro samples, and analyses the algorithm error in the classical coning motion. Compared with the conventional algorithms, simulational results show that this improved algorithm has higher precision. A new way to improve the rotation vector algorithms is provided.展开更多
The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite traj...The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.展开更多
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence o...Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.展开更多
In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained ...In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.展开更多
The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism...The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.展开更多
Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. ...Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.展开更多
The forward kinematics of the general Stewart mechanism is studied and a fast numerical method is presented.Quaternion is utilized to model the forward kinematics and the equations are merely a system of quadratic one...The forward kinematics of the general Stewart mechanism is studied and a fast numerical method is presented.Quaternion is utilized to model the forward kinematics and the equations are merely a system of quadratic ones.The numerical method is a nice simplification of the Newton-Raphson method when applied to this system.A simulation of the movement control of the Stewart mechanism is accomplished,confirming the effectiveness of the proposed algorithm in real-time conditions.展开更多
An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the pola...An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.展开更多
A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two ...An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.展开更多
A novel on-line north-seeking method based on a three-axis micro-electro-mechanical system(MEMS)gyroscope is designed.This system processes data by using a Kalman filter to calibrate the installation error of the thre...A novel on-line north-seeking method based on a three-axis micro-electro-mechanical system(MEMS)gyroscope is designed.This system processes data by using a Kalman filter to calibrate the installation error of the three-axis MEMS gyroscope in complex environment.The attitude angle updating for quaternion,based on which the attitude instrument will be rotated in real-time and the true north will be found.Our experimental platform constitutes the dual-axis electric rotary table and the attitude instrument,which is developed independently by our scientific research team.The experimental results show that the accuracy of north-seeking is higher than 1°,while the maximum root mean square error and the maximum mean absolute error are 0.906 7 and 0.910 0,respectively.The accuracy of north-seeking is much higher than the traditional method.展开更多
In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary c...In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.展开更多
A bundle adjustment method of remote sensing images based on dual quaternion is presented,which conducted the uniform disposal corresponding location and attitude of sequence images by the dual quaternion.The constrai...A bundle adjustment method of remote sensing images based on dual quaternion is presented,which conducted the uniform disposal corresponding location and attitude of sequence images by the dual quaternion.The constraint relationship of image itself and sequence images is constructed to compensate the systematic errors.The feasibility of this method used in bundle adjustment is theoretically tested by the analysis of the structural characteristics of error equation and normal equation based on dual quaternion.Different distributions of control points and stepwise regression analysis are introduced into the experiment for RC30 image.The results show that the adjustment accuracy can achieve 0.2min plane and 1min elevation.As a result,this method provides a new technique for geometric location problem of remote sensing images.展开更多
This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selec...This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.展开更多
Euler angles and Euler kinematics equation of terminal sensing ammunition are expressed and rewritten by using quaternion to solve the singular problem in using Euler angles to describe the motion.The contrastive simu...Euler angles and Euler kinematics equation of terminal sensing ammunition are expressed and rewritten by using quaternion to solve the singular problem in using Euler angles to describe the motion.The contrastive simulations are performed in order to validate the correctness and advantage of the quaternion description.The simulation results show that the dynamic model with quaternion have stable solution,there is not singular point in the calculation,and the ballistic model rewritten by using the quaternion is suitable for describing the terminal sensing ammunition's scanning motion than the common Euler equation.展开更多
Euler angle error model, rotation vector error model （RVE） and quaternion error model （QE） were qualitatively and quantitatively compared and an in-flight alignment filter algorithm was designed. This algorithm us...Euler angle error model, rotation vector error model （RVE） and quaternion error model （QE） were qualitatively and quantitatively compared and an in-flight alignment filter algorithm was designed. This algorithm used extended Kalman filter （EKF） based on RVE and QE separately avoi- ding the accuracy problem of the Euler angle model and used Rauch-Tung-Striebel（RTS） smoothing method to refine the accuracy recuperating the coning error for simplified RVE. Simulation results show that RVE and QE are more adapt for nonlinear filter estimation than the Euler angle model. The filter algorithm designed has more advantages in convergence speed, accuracy and stability comparing with the algorithm based on the three models separately.展开更多
基金supported by NSFC(12071422)Zhejiang Province Science Foundation of China(LY14A010018)。
文摘The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.
基金partially supported by the Natural Science Foundation of China (Grant Nos.62103052,52272358)partially supported by the Beijing Institute of Technology Research Fund Program for Young Scholars。
文摘This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncertainty of structural and aerodynamic parameters,the six-degree-of-freedom(6Do F) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established,respectively,in the inertial and body-fixed reference frames.Next,a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6Do F dynamics.Then,a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix.As long as the finitely excited condition is satisfied,the precise identification of unknown parameters can be achieved.Finally,the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.
文摘The laser gyro is most su it able for building the strap down inertial navigation system (SINS), and its acc uracy of attitude algorithm can enormously affect that of the laser SINS. This p aper develops three improved algorithmal expressions for strap down attitude ut ilizing the angular increment output by the laser gyro from the last two and cur rent updating periods according to the number of gyro samples, and analyses the algorithm error in the classical coning motion. Compared with the conventional algorithms, simulational results show that this improved algorithm has higher precision. A new way to improve the rotation vector algorithms is provided.
基金Supported by the National Natural Science Foundation of China(60974107)the Research Foundation of Nanjing University of Aeronautics and Astronautics(2010219)~~
文摘The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
文摘Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.
文摘In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.
文摘The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.
文摘Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.
基金Supported by the National Natural Science Foundation of China(51375230)the Jiangsu Provincial Science and Technology Support Program(BE2012052)
文摘The forward kinematics of the general Stewart mechanism is studied and a fast numerical method is presented.Quaternion is utilized to model the forward kinematics and the equations are merely a system of quadratic ones.The numerical method is a nice simplification of the Newton-Raphson method when applied to this system.A simulation of the movement control of the Stewart mechanism is accomplished,confirming the effectiveness of the proposed algorithm in real-time conditions.
基金supported by Startup Foundation for Phd Research of Henan Normal University(No.5101119170155).
文摘An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.
文摘A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
基金supported in part by NCET (NCET06-9-23)NUDT (JC08-02-03)
文摘An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.
基金Supported by the Chongqing International Science and Technology Cooperation Base Project(cstc2014gjhz40001)the University Achievement Transformation Project of Chongqing Science and Technology Commission(KJZH17115)+3 种基金the Basic Research Project of Chongqing Science and Technology Commission(cstc2015jcyjBX0068,cstc2014jcyjA1350,cstc2015jcyjB0360)the Dr.Start-up Fund of Chongqing University of Posts and Telecommunications(A2015-40,A2016-76)the National Natural Science Foundation of Chongqing University of Posts and Telecommunications(A2015-49)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1704104,KJ1704091)
文摘A novel on-line north-seeking method based on a three-axis micro-electro-mechanical system(MEMS)gyroscope is designed.This system processes data by using a Kalman filter to calibrate the installation error of the three-axis MEMS gyroscope in complex environment.The attitude angle updating for quaternion,based on which the attitude instrument will be rotated in real-time and the true north will be found.Our experimental platform constitutes the dual-axis electric rotary table and the attitude instrument,which is developed independently by our scientific research team.The experimental results show that the accuracy of north-seeking is higher than 1°,while the maximum root mean square error and the maximum mean absolute error are 0.906 7 and 0.910 0,respectively.The accuracy of north-seeking is much higher than the traditional method.
文摘In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.
基金supported by the National Natural Science Foundations of China (Nos.41101441,60974107, 41471381)the Foundation of Graduate Innovation Center in NUAA(No.kfjj130133)
文摘A bundle adjustment method of remote sensing images based on dual quaternion is presented,which conducted the uniform disposal corresponding location and attitude of sequence images by the dual quaternion.The constraint relationship of image itself and sequence images is constructed to compensate the systematic errors.The feasibility of this method used in bundle adjustment is theoretically tested by the analysis of the structural characteristics of error equation and normal equation based on dual quaternion.Different distributions of control points and stepwise regression analysis are introduced into the experiment for RC30 image.The results show that the adjustment accuracy can achieve 0.2min plane and 1min elevation.As a result,this method provides a new technique for geometric location problem of remote sensing images.
基金supported in part by the Science and Technology Development Fund,Macao SAR FDCT/085/2018/A2the Guangdong Basic and Applied Basic Research Foundation(2019A1515111185)。
文摘This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.
文摘Euler angles and Euler kinematics equation of terminal sensing ammunition are expressed and rewritten by using quaternion to solve the singular problem in using Euler angles to describe the motion.The contrastive simulations are performed in order to validate the correctness and advantage of the quaternion description.The simulation results show that the dynamic model with quaternion have stable solution,there is not singular point in the calculation,and the ballistic model rewritten by using the quaternion is suitable for describing the terminal sensing ammunition's scanning motion than the common Euler equation.
文摘Euler angle error model, rotation vector error model （RVE） and quaternion error model （QE） were qualitatively and quantitatively compared and an in-flight alignment filter algorithm was designed. This algorithm used extended Kalman filter （EKF） based on RVE and QE separately avoi- ding the accuracy problem of the Euler angle model and used Rauch-Tung-Striebel（RTS） smoothing method to refine the accuracy recuperating the coning error for simplified RVE. Simulation results show that RVE and QE are more adapt for nonlinear filter estimation than the Euler angle model. The filter algorithm designed has more advantages in convergence speed, accuracy and stability comparing with the algorithm based on the three models separately.
