Orientation estimation using low cost sensors is an important task for Micro Aerial Vehicles (MAVs) in order to obtain a good feedback for the attitude controller. The challenges come from the low accuracy and noisy data of the MicroElectroMechanical System (MEMS) technology, which is the basis of modern, miniaturized inertial sensors. In this article, we describe a novel approach to obtain an ...

The definition of morphological operators for colour images needs a total ordering between the colour points. A colour can be represented according to different algebraic structures, in particular in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied different alternatives to introduce the scalar part to obtain full colour quater...

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...

Let S be a ring with identity in which 2 is invertible. In this paper we describe the structure of quaternion R = H(S) generalization Hamilton?s division real quaternions H H(R).

We present a Jacobi-like algorithm for simultaneous diagonalization of commuting pairs of complex normal matrices by unitary similarity transformations. The algorithm uses a sequence of similarity transformations by elementary complex rotations to drive the oo-diagonal entries to zero. We show that its asymptotic convergence rate is quadratic and that it is numerically stable. It preserves the ...

Recently, quaternion collaborative representationbased classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among different color channels. However, their performance is unstable in different conditions. For example, QSRC performs better than than QCRC on some situations but ...

Let G be a finite, quaternion-free group with exponent e, let F be a field of characteristic zero and let x be an absolutely irreducible character of G. Suppose that a Sylow 2-subgroup of the Galois group of F(J\) over F is cyclic. It is shown that if x is not real valued, then the Schur index of x over F is odd. Let G be a finite group with exponent e and let F be a field of characteristic zer...

We determine the Shimura modular curve X0(3) and the Jacobian of the Shimura modular curve X1(3) associated with the congruence subgroups Γ0(3), Γ1(3) of the (2, 3, 7) triangle group. This group is known to be arithmetic and associated with a quaternion algebra A/K ramified at two of the three real places of K = Q(cos 2π/7) and at no finite primes of K. Since the rational prime 3 is inert in K,...