Involutions in split semi‐quaternions

A map is an involution (resp, anti‐involution) if it is a self‐inverse homomorphism (resp, antihomomorphism) of a field algebra. The main purpose of this paper is to show how split semi‐quaternions can be used to express half‐turn planar rotations in 3‐dimensional Euclidean space and how they can be used to express hyperbolic‐isoclinic rotations in 4‐dimensional semi‐Euclidean space . We present an involution and an anti‐involution map using split semi‐quaternions and give their geometric interpretations as half‐turn planar rotations in . Also, we give the geometric interpretation of nonpure unit split semi‐quaternions, which are in the form p = coshθ + sinhθ i + 0 j + 0 k = coshθ + sinhθ i , as hyperbolic‐isoclinic rotations in .     

Uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform

ABSTRACT

In this paper, we present some new elements of harmonic analysis related to the right-sided multivariate continuous quaternion wavelet transform. The main objective of this article is to introduce the concept of the right-sided multivariate continuous quaternion wavelet transform and investigate its different properties using the machinery of multivariate quaternion Fourier transform. Last, we have proven a number of uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform.     

基于四元数卡尔曼滤波的捷联惯导初始对准算法

针对晃动基座捷联惯导初始对准问题,研究了一种具有干扰抑制能力的初始对准算法。根据重力矢量在惯性空间投影构成一包含地球北向信息的旋转锥面的现象,利用坐标系惯性凝固假设将重力量测矢量和参考矢量分别投影到载体惯性坐标系和导航惯性坐标系,将晃动基座条件下的初始对准转化为基于重力量测矢量确定对准起始时刻的姿态问题。借鉴四元数线性伪量测方程的概念,利用重力投影矢量与初始姿态四元数的线性量测关系实现初始姿态四元数的直接滤波估计。初始姿态四元数在对准过程中为常值,以其作为待估计的状态可避免系统模型误差和初始误差的影响。利用转台模拟不同的摇摆对准环境,导航级惯导系统可在10 min内完成初始对准且方位误差小于3’。     

Moduli of Quaternionic Superminimal Immersions of 2-Spheres into Quaternionic Projective Spaces

The aim of this paper is to describe the moduli spaces of degree d quaternionic superminimal maps from 2-spheres to quaternionic projective spaces HPn. We show that such moduli spaces have the structure of projectivized fibre products and are connected quasi-projective varieties of dimension 2nd + 2n + 2. This generalizes known results for spaces of harmonic 2-spheres in S⁴.     

The double determinant of Vandermonde's type over quaternion field

１　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＴｈｅｒｅａｌＶａｎｄｅｒｍｏｎｄｅｍａｔｒｉｘｉｓａｕｓｅｆｕｌｔｏｏｌｉｎｔｈｅｖｉｂｒａｔｉｏｎａｎａｌｙｓｉｓｏｆｓｔｒｕｃｔｕｒｅａｎｄｔｈｅｃｏｍｐｕｔｉｎｇｏｆｄｉｓｃｒｅｔｅＦｏｕｒｉｅｒｔｒａｎｓｆｏｒｍａｎｄｔｈｅｔｈｅｏｒｙｏｆｃｏｎｔｒｏｌａｎｄｔｈｅｄｅｃｅｎｔｒａｌｉｚｅｄｓｔａｂｉｌｉｚａｔｉｏｎｆｏｒｌａｒｇｅｓｃａｌｅｓｙｓｔｅｍｓａｎｄｍａｎｙｏｔｈｅｒｐｒａｃｔｉｃａｌｆｉｅｌｄｓ［１～３］,ｉｔｉ…     

关于“四元数分析中的Neumann边值问题”的注记

本文指出了文［１］中的几个错误,并利用?－方程解的积分表示,获得了其所讨论的超球上的四元数方程的Ｎｅｕｍａｎｎ问题解的积分表示     

Multi-Focus Image Fusion Method Based on Multi-Scale Decomposition of Information Complementary

Multi-focus image fusion is an important method used to combine the focused parts from source multi-focus images into a single full-focus image. Currently, to address the problem of multi-focus image fusion, the key is on how to accurately detect the focus regions, especially when the source images captured by cameras produce anisotropic blur and unregistration. This paper proposes a new multi-focus image fusion method based on the multi-scale decomposition of complementary information. Firstly, this method uses two groups of large-scale and small-scale decomposition schemes that are structurally complementary, to perform two-scale double-layer singular value decomposition of the image separately and obtain low-frequency and high-frequency components. Then, the low-frequency components are fused by a rule that integrates image local energy with edge energy. The high-frequency components are fused by the parameter-adaptive pulse-coupled neural network model (PA-PCNN), and according to the feature information contained in each decomposition layer of the high-frequency components, different detailed features are selected as the external stimulus input of the PA-PCNN. Finally, according to the two-scale decomposition of the source image that is structure complementary, and the fusion of high and low frequency components, two initial decision maps with complementary information are obtained. By refining the initial decision graph, the final fusion decision map is obtained to complete the image fusion. In addition, the proposed method is compared with 10 state-of-the-art approaches to verify its effectiveness. The experimental results show that the proposed method can more accurately distinguish the focused and non-focused areas in the case of image pre-registration and unregistration, and the subjective and objective evaluation indicators are slightly better than those of the existing methods.     

一种改进的轨道动力学模型

航天器的矢径可以分解为矢径模和单位矢量的乘积,利用该性质将传统轨道动力学方程分解为矢径模和矢径方向的动力学方程组,实现了航天器位置信息的分离;针对两个方程分别采用常数变易法和四元数描述方法,将轨道动力学模型转化为线性无奇异的方程组,同时得到了7 个新轨道变量,且建立了新轨道变量与惯性系下航天器位置速度信息以及轨道六要素之间的相互转换关系. 该轨道模型适用于任意形式的推力和摄动,避免了奇异性,且在虚拟时间的意义下,航天器的旋转角速度只取决于法向力;在常值推力和变推力的情况下,对该模型进行了数值验证,验证了新模型的可适用性、数值稳定性以及计算精度高的优势.      

MC-ROV导航系统研究

针对研制的新型模态切换水下机器人(Mode-Converted ROV, MC-ROV),设计了一套以MEMS器件为主的微惯性组合导航系统,包括陀螺仪、加速度计、磁力计、深度传感器及微处理器等。系统采用互补滤波方法抑制陀螺漂移,设计卡尔曼滤波器计算姿态角。本文采用了改进的自适用卡尔曼滤波器,增大新近数据的作用,减小陈旧数据的作用,避免滤波发散,提高导航精度。水池实验表明结合互补滤波、自适应卡尔曼滤波能够获得比较精确、稳定的水下机器人导航信息。同时,基于实测数据进行的算法仿真表明改进后的渐消记忆指数加权自适应卡尔曼滤波可以在一定程度上改善导航效果。     

On higher order integration of angular velocities using quaternions

In the present paper the integration of angular velocities is studied. Both exact and approximate results are expressed in terms of rotational quaternions. Analytical solution is found using the theory of analytic differential systems. This exact solution serves as a suitable basis for derivation of various numerical methods. Approximative approaches based on Taylor series and several maps from pure to unit quaternions are presented. A special care is taken in describing the higher order approximations. The computational performance and comparison of numerical methods is demonstrated by examples.