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 paper a quaternion-based Variable-State-Dimension Extended Kalman Filter (VSD-EKF) is developed for estimating the three-dimensional orientation of a rigid body using the measurements from an Inertial Measurement Unit (IMU) integrated with a triaxial magnetic sensor. Gyro bias and magnetic disturbances are modeled and compensated by including them in the filter state vector. The VSD-EKF...

In this paper, we propose a fully automatic, effective and efficient framework for 3D face reconstruction based on a single face image in arbitrary view. First, a multi-view face alignment algorithm localizes the face feature points, and then EM algorithm is applied to derive the optimal 3D shape and position parameters. Moreover, the unit quaternion based pose representation is proposed for ef...

We describe a fast algorithm for the 2-D left-side QDFT which is based on the concept of the tensor representation when the color or four-componnrnt quaternion image is described by a set of 1-D quaternion signals and the 1-D left-side QDFTs over these signals determine values of the 2-D left-side QDFT at corresponding subset of frequency-points. The efficiency of the tensor algorithm for calcu...

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...

An extension of the FastICA algorithm is proposed for the blind separation of both Q-proper and Q-improper quaternionvalued signals. This is achieved by maximising a negentropy-based cost function, and is implemented using the Newton method in the augmented quaternion statistics framework. It is shown that the use of augmented statistics and the associated widely linear modeling provide theoret...

In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter d...

A numerical solution algorithm has been developed to solve a generalization of Wahba's attitude determination problem to the case of unknown attitude and attitude rate. It provides a robust global solution to nonlinear batch attitude and rate estimation problems for spinning spacecraft. The original Wahba problem seeks the attitude that fits a set of unit-normalized direction vector measurement...

This work investigates the performances of several State-Dependent Riccati Equation algorithms for the estimation and control of attitude and attitude rates of a rigid-body spacecraft. The estimators are designed to process line-of-sight and gyros measurements corrupted by white noises and potentially drifting biases. The case of gyroless estimation is also addressed. The vector measurements ar...