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...

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 ...

This paper discusses the development of a particle filter for attitude and angular rate estimation of a space object using light curve observations. The particle filter approach used is based on the generalized Rodrigues parameters (GRPs) local error representation. The global state used is the quaternion to avoid singularity in the attitude states. Uniform quaternions are generated to approxim...

In this chapter, we focused on the posture estimation problem of a body moving in 3D space. This study is devoted to the reconstruction of the body attitude and Dynamic Body Acceleration (DBA) in free ranging animal (application in Bio-logging) where the access to GPS locations is limited or impossible. A quaternion-based complementary filter is designed to provide a viable attitude estimation ...

This article compares three different algorithms used to compute Euler angles from data obtained by the angular rate sensor (e.g., MEMS gyroscope)-the algorithms based on a rotational matrix, on transforming angular velocity to time derivations of the Euler angles and on unit quaternion expressing rotation. Algorithms are compared by their computational efficiency and accuracy of Euler angles e...

The vectorized algorithms for GPS based attitude determination can be equivalent to a two-level optimal estimation problem. In the first level estimation the GPS carrier phase measurements can be converted to the vector observations in a sense of least squares. The second level estimation is the Wahba’s problem which describes how the attitude matrix can be derived from the vector observations....

In this paper, a quaternion-based finite-time sliding mode attitude controller is designed for a spacecraft performing high-thrust orbital maneuvers, with cold gas thrusters as its actuators. The proposed controller results are compared with those of a quaternion feedback controller developed for the linearized spacecraft dynamics, in terms of settling time, steady-state error, number of thrust...

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...

This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the rotation group and its Lie structure, with formulations using both quaternions and rotation matrices. It makes special attention in the definition of rotatio...