加速度计/磁强计无陀螺捷联惯导姿态解算研究

针对无陀螺捷联惯导系统姿态解算随时间不断积累的问题,提出一种磁强计辅助无陀螺捷联惯导的组合方案,利用磁强计测量的地磁信息来修正无陀螺惯导系统的姿态角误差,提高了姿态角的解算精度。推导了磁强计输出和姿态角之间的关系,在此基础上提出了一种姿态优化算法,介绍了算法的基本原理;建立了误差四元数的姿态组合模型,并采用反馈校正完成动态条件下姿态的确定;最后对姿态误差角进行了仿真研究,仿真结果表明该方法有效地抑制了误差的发散。     

QuatJND: A Robust Quaternion JND Model for Color Image Watermarking

Robust quantization watermarking with perceptual JND model has made a great success for image copyright protection. Generally, either restores each color channel separately or processes the vector representation from three color channels with the traditional monochromatic model. And it cannot make full use of the high correlation among RGB channels. In this paper, we proposed a robust quaternion JND Model for color image watermarking (QuatJND). In contrast to the existing perceptual JND models, the advantage of QuatJND is that it can integrate quaternion representation domain and colorfulness simultaneously, and QuatJND incorporates the pattern guided contrast masking effect in quaternion domain. On the other hand, in order to efficiently utilize the color information, we further develop a robust quantization watermarking framework using the color properties of the quaternion DCT coefficients in QuatJND. And the quantization steps of each quaternion DCT block in the scheme are optimal. Experimental results show that our method has a good performance in term of robustness with better visual quality.     

基于张量四元数极化平滑的极化-DOA估计

为了解决相干信号的极化平滑算法在小快拍数和低信噪比条件下估计性能较差的问题,结合四元数的正交特性和协方差张量方法,提出了一种基于张量四元数的极化平滑多重信号分类（Multiple Signal Classification,MUSIC）解相干算法。首先,为了充分利用接收数据样本中的多维结构信息,建立了由张量四元数表示的柱面共形阵列极化平滑信号模型;其次,将平滑后的张量协方差矩阵通过高阶奇异值分解得到信号子空间;最后,通过极化秩亏MUSIC算法对入射相干信号分别进行二维波达方向（Direction of Arrival,DOA）估计和极化参数估计。仿真结果表明,该算法在小快拍数和低信噪比条件下具有更高的估计精度和分辨能力。     

基于四元数的直接判决并行恒模均衡算法

近年来4元数理论成为各界学者研究的热点并被应用到许多领域。该文基于4元数自适应滤波算法对正交极化信道均衡问题进行研究。为了解决4元数恒模(QCMA)算法的相位模糊问题,该文将QCMA算法与4元数最小均方算法(QLMS)相结合提出一种4元数直接判决并行恒模(QCMA+DD-QLMS) 算法。基于广义哈密顿实演算(GHR)的梯度运算规则对新的算法做了理论推导并进行MATLAB实验仿真,仿真结果表明该文所提算法不但能够解决QCMA算法相位模糊问题,还具有更小的稳态均方误差(MSE)。     

基于离散四元数余弦变换的彩色图像数字水印技术

将离散四元数余弦变换(DQCT)应用于彩色图像的数字水印技术中,提出了一种在彩色图像中嵌入水印的新技术。应用四元数理论把彩色图像作为一整体进行余弦变换,在彩色宿主图像的DQCT域中实现彩色水印图像的嵌入。实验表明,该方法具有较好的抗压缩能力,对高斯噪声、椒盐噪声和缩放攻击具有较好的鲁棒性。     

On metallic ratio in

Metallic ratio is a root of the simple quadratic equation x² = kx + 1 for k is any positive integer which is the characteristic equation of the recurrence relation of k‐Fibonacci (k‐Lucas) numbers. This paper is about the metallic ratio in . We define k‐Fibonacci and k‐Lucas numbers in , and we show that metallic ratio can be calculated in if and only if p≡ ± 1 mod (k² + 4), which is the generalization of the Gauss reciprocity theorem for any integer k. Also, we obtain that the golden ratio, the silver ratio, and the bronze ratio, the three together, can be calculated in for the first time. Moreover, we introduce k‐Fibonacci and k‐Lucas quaternions with some algebraic properties and some identities for them.     

Real structure-preserving algorithm for quaternion equality constrained least squares problem

Quaternion equality constrained least squares problem is an extremely effective tool in studying quantum mechanics and quantum field theory. However, the computation of the quaternion equality constrained least squares problem is extremely complex. In this paper, we first prove that quaternion equality constrained least squares problem is equivalent to weighted quaternion least squares problem when the parameter $\tau \to +\infty$. Then, for weighted quaternion least squares problem, applying the special structure of real representation of quaternion, we propose real structure–preserving algorithm to obtain the solution of quaternion equality contained least squares problem. At last, we give numerical examples to illustrate the effectiveness of our method.     

Controllability and Observability of Linear Quaternion-valued Systems

The aim of this paper is to define an extension of the controllability and observability for linear quaternion-valued systems (QVS). Some criteria for controllability and observability are derived, and the minimum norm control and duality theorem are also investigated. Compared with real-valued or complex-valued linear systems, it is shown that the classical Caylay-Hamilton Theorem as well as Popov-Belevitch-Hautus (PBH) type controllability and observability test do not hold for linear QVS. Hence, a modified PBH type necessary condition is studied for the controllability and observability, respectively. Finally, some examples are given to illustrate the effectiveness of the obtained results.     

基于MARG传感器的自主姿态测量新算法

针对基于三轴陀螺、三轴加速度计以及三轴磁强计组成的传感器组合(MARG传感器)的姿态测量算法存在的不足和限制,以自主姿态测量为前提,提出了一种新的基于四元数的优化递推估计算法。这一算法能够在线估计补偿陀螺漂移误差,不再需要对系统方程进行线性化处理。与基于EKF的方法相比,在同等计算复杂度下,该算法具有更高的精度和更好的稳定性。算法本身内蕴了对四元数单位长度的限制,不再需要任何归一化处理。仿真结果显示出了该算法具有令人满意的效果,利用水上漂浮试验初步验证了该算法的稳定性。