We introduce a novel framework of continuous-time ultra-wideband-inertial sensor fusion for online motion estimation. Quaternion-based cubic cumulative B-splines are exploited parameterizing states continuously over time. Systematic derivations analytic kinematic interpolations and spatial differentiations further provided. Based thereon, new sliding-window spline fitting scheme is established ...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...

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...

This paper presents an extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (Magnetic, Angular Rate, and Gravity) sensors. Each MARG sensor contains a three-axis magnetometer, a three-axis angular rate sensor, and a three-axis accelerometer. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-s...

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...

Most of the existing color image watermarking schemes were designed to mark the image luminance component only, which have some disadvantages: (i) they are sensitive to color attacks because of ignoring the correlation between different color channels, (ii) they are always not robust to geometric distortions for neglecting the watermark desynchronization. It is a challenging work to design a ro...

This paper presents a new parameterisation approach for the graph-based SLAM problem utilising unit dual-quaternion. The rigid-body transformation typically consists of the robot position and rotation, and due to the Lie-group nature of the rotation, a homogeneous transformation matrix (HTM) has been widely used in pose-graph optimizations. In this paper, we investigate the use of unit dual-qua...

Solving quaternion kinematical differential equations is one of the most significant problems in the automation, navigation, aerospace and aeronautics literatures. Most existing approaches for this problem neither preserve the norm of quaternions nor avoid errors accumulated in the sense of long term time. We present symplectic geometric algorithms to deal with the quaternion kinematical differ...

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from ...

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 ...