This work deals with error models for trident quaternion framework proposed in the companion paper (Part I) and further uses them to investigate odometer-aided static/in-motion inertial navigation attitude alignment land vehicles. By linearizing kinematic equation, left right are obtained, which found be equivalent those derived from profound group affine. The two used design their correspondin...

In this paper, a color image inpainting problem is modeled as low rank quaternion matrix optimization problem. A has smooth property inherently and all imaginary parts of the corresponding pure are nonnegative. Based on these characteristics, we introduce novel regularized model then propose factorization algorithm with convergence analysis. Numerical experiments demonstrate efficiency our prop...

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...

A method is developed to compute the zeros of a quaternion polynomial with all terms of the form ok Xk. This method is based essentially in Niven’s algorithm (11, which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to ...

Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established based on unit dual quaternion. This paper presents a rigid iterative algorithm of the Helmert transformation using dual quaternion. One small rotation angle Helme...

Color image compression is a commonly used process to represent image data as few bits as possible, which removes redundancy in the data while maintaining an appropriate level of quality for the user. Color image compression algorithms based on quaternion are very common in recent years. In this paper, we propose a color image compression scheme, based on the real SVD, named real compression sc...

the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under functional composition. Furthermore, the composition operation is symbolically identical to quaternion multiplication, making manipulation and reduction of sy...