An efficient widely linear prediction algorithm is introduced for the class of wide-sense stationary quaternion signals. Specifically, using second order statistics information in the quaternion domain, a multivariate Durbin–Levison-like algorithm is derived. The proposed solution can be applied under a very general formulation of the problem, allowing for the estimation of a function of the qu...

In this paper, we first discuss the singular value decomposition (SVD) of a quaternion matrix and propose an algorithm to calculate the SVD of a quaternion matrix using its equivalent complex matrix. The singular values of a quaternion matrix are still real and positive, but the two unitary matrices are quaternion matrices with quaternion entries. Then, applications for color image processing b...

This paper describes a Kalman filter for the real-time estimation of a rigid body orientation from measurements of acceleration, angular velocity and magnetic field strength. A quaternion representation of the orientation is computationally effective and avoids problems with singularities. The nonlinear relationship between estimated orientation and expected measurement prevent the usage of a c...

In this paper, an algorithm for autonomous stair climbing with a tracked vehicle is presented. The proposed method achieves robust performance under real-world conditions, without assuming prior knowledge of the stair geometry, the dynamics of the vehicle’s interaction with the stair surface, or lighting conditions. The approach relies on fast and accurate estimation of the robot’s heading and ...

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 ...

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...

The quaternion representation of color is shown here to be effective in the context of segmenting color images into regions of similar color texture. The advantage of using quaternion arithmetic is that a color can be represented and analyzed as a single entity. A lowdimensional basis for the color textures found in a given image is derived via quaternion principal component analysis (QPCA) of ...

Using direction vectors of unit length as measurements for attitude estimation in an extended Kalman filter inevitably results in a singular measurement covariance matrix. Singularity of the measurement covariance means no noise is present in one component of the measurement. Unit vector measurements have no noise in the radial component. Singular measurement covariances can be dealt with by th...

In this paper, we present an algorithm for autonomous stair climbing with a tracked vehicle. The proposed method achieves robust performance under real-world conditions, without assuming prior knowledge of the stair geometry, the dynamics of the vehicle’s interaction with the stair surface, or lighting conditions. Our approach relies on fast and accurate estimation of the robot’s heading and it...

Exergames have been proposed as a potential tool to improve the current practice of musculoskeletal rehabilitation. Inertial or optical motion capture sensors are commonly used to track the subject's movements. However, the use of these motion capture tools suffers from the lack of accuracy in estimating joint angles, which could lead to wrong data interpretation. In this study, we proposed a r...