Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms for channel equalization and beamforming. With most recent developments in quaternion-valued signal processing, in this work, we fill the gap to solve the p...

The recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. In this paper, we will develop efficient algorithms for QFT, QCV, and quater...

In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express ...

Initial alignment of the strapdown inertial navigation system (SINS) is intended to determine the initial attitude matrix in a short time with certain accuracy. The alignment accuracy of the quaternion filter algorithm is remarkable, but the convergence rate is slow. To solve this problem, this paper proposes an improved quaternion filter algorithm for faster initial alignment based on the erro...

Recently, quaternion collaborative representationbased classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among different color channels. However, their performance is unstable in different conditions. For example, QSRC performs better than than QCRC on some situations but ...

In this paper, we first discuss the singular value decomposition (SVD) of a quaternion matrix and propose an algorithm to calculate the SVD of a quaternion matrix using its equivalent complex matrix. The singular values of a quaternion matrix are still real and positive, but the two unitary matrices are quaternion matrices with quaternion entries. Then, applications for color image processing b...

Based on crossed-dipole antenna arrays, quaternion-valued data models have been developed for both direction of arrival estimation and beamforming in the past. However, for almost all the models, and especially for adaptive beamforming, the desired signal is still complex-valued as in the quaternion-valued Capon beamformer. Since the complex-valued desired signal only has two components, while ...

For spacecraft attitude representation, the quaternion is preferred over other representations due to its bilinear nature of the kinematics and the singularity-free property. However, when applied in the attitude estimation filters, its unity norm constraint can be easily destroyed by the quaternions averaging operation. Although the brute-force quaternion normalization can be implemented, this...

This paper provides a general construction technique for rectangular matrices whose elements are quaternion variables and whose column vectors are formally orthogonal. These matrices are named quaternion orthogonal designs, in parallel with the well-known constructs of real and complex orthogonal designs. The proposed construction technique provides the first infinite family of this type of qua...

In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B∗-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C∗-algebras respectively. We will also give a Riesz representation theorem for quaternion...