In this paper, we consider a form of the generalized logistic distribution named symmetric extended generalized logistic distribution or extended type III generalized logistic distribution. The distribution is derived by compounding a two-parameter generalized Gumbel distribution with a two-parameter generalized gamma distribution. The cumulative distribution and some properties of this distrib...

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...

The natural mapping of the right quaternion vector space H onto the quaternion projective line (identified with the four-sphere) can be defined for complex quaternions H ⊗R C as well. We discuss its exceptional set, the fiber subspaces, and how the linear automorphism groups of two-dimensional quaternion vector spaces and modules induce groups of projective automorphisms of the image quadrics.

We define zonal polynomials of quaternion matrix argument and deduce some important formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and smallest eigenvalues of a quaternion central Wishart matrix W ∼ QW (n,Σ), respectively.

We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR-submanifold. 2000 Mathematics Subject Classification. 53C20, 53C21, 53C25.

We present a novel solution to the camera pose estimation problem, where rotation and translation of a camera between two views are estimated from matched feature points in the images. The camera pose estimation problem is traditionally solved via algorithms that are based on the essential matrix or the Euclidean homography. With six or more feature points in general positions in the space, ess...

In this paper, we consider some practical issues when using the quaternion to represent rotation in conjunction with gradientor Jacobian-based search algorithms. Iterative estimation techniques often incorporate gradient or Jacobian information to simultaneously solve for the parameters with respect to many non-linear constraints. We derive a simple form for the Jacobian of the rotation matrix ...

This paper addresses pose estimation problem for augmented reality applications in an urban environment. The pose is estimated based on the known wire-frame models of buildings and line segments detected on the images. One of key problems for model-based pose estimation is to establish the correspondence between the model and detected features. The main contribution of this paper is a robust ma...

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R.

The development of Kalman filters designed for state estimation of the position and velocity of a spacecraft is attempted and their performance evaluated. Three Kalman Filters are developed, each with its unique characteristics: the Extended Kalman Filter (EKF), the Robust Extended Kalman Filter (REKF) and the Adaptive Robust Extended Kalman Filter (AREKF). The three filters are implemented ass...