A comparison between HMLP and HRBF for attitude control

Quaternion-based Parallel Feature Extraction: Extending the Horizon of Quantitative Analysis using TLC-SERS Sensing

Quantitative analysis using thin-layer chromatography coupled in tandem with surface-enhanced Raman scattering (TLC-SERS) still remains a grand challenge due to many uncontrollable variations during the TLC developing process and the random nature of the SERS substrates. Traditional chemometric methods solve this problem by sampling multiple SERS spectra in the sensing spot and then conducting statistical analysis of the SERS signals to mitigate the variation of quantitative analysis, while still ignoring the spatial distribution of the target species and the correlation among the multiple sampling points. In this paper, we proposed for the first time a parallel feature extraction and fusion method based on quaternion signal processing techniques, which can enable quantitative analysis using recently established TLC-SERS techniques. By marking three deterministic sampling points, we recorded spatially correlated SERS spectra to constitute an integral representation model of triple-spectra by a pure quaternion matrix. Quaternion principal component analysis (QPCA) was utilized for features extraction and followed by feature crossing among the quaternion principal components to obtain final fusion spectral feature vectors. Support vector regression (SVR) was then used to establish the quantitative model of melamine-contaminated milk samples with seven concentrations (1ppm to 250ppm). Compared with traditional TLC-SERS analysis methods, QPCA method significantly improved the accuracy of quantification by reaching only 7% and 2% quantization errors at 20 and 105 ppm concentration. Validation testing based on reasonable amount of statistic measurement results showed consistently smaller measurement errors and variance, which proved the effectiveness of QPCA method for TLC-SERS based quantitative sensing applications.

Robust Feedback Control Design of Underactuated Robotic Hands with Selectively Lockable Switches for Amputees

In recent years, reproduction of human mechanical hand with upgraded abilities is one of the major concerns. This paper addresses the problems of underactuated robotic hand with low cost design as it avoids electromyogram (EMG) sensors. The main goal is to balance the hand in the way, like grabbing, speed, and power, and provide a more robust and cost effective solution. All fingers have some mechanical consistency for picking up objects in a better way. A Flex sensor is attached to all fingers and it is interfaced with a computer using Arduino UNO microcontroller. The sensor aids the arm in three different directions: at first it senses whether an object is grasped or not. In the second step, it determines the coefficient of friction between the objects. Finally it grasps the object and stops. One of the primary issues of prosthetic hand is to have the capacity to satisfy every detail of torque, speed, and latency. In this research, we have developed a model of robotic hand with some modifications. The adaptability of grasping is compared with the degree of freedom (DOF) along with the quantity of fingers. We are controlling our hands via sensors based signal controlling system. The idea is to design a robotic hand, which has low cost, is easy to use, and is light in weight, which helps the amputees to use it with ease in their daily lives. The efficacy of the proposed control is verified and validated using simulations.

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized Hamilton-real (GHR) calculus, thus making a possible efficient derivation of general optimization algorithms directly in the quaternion field, rather than using the isomorphism with the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the novel quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are also introduced, opening a new avenue of research in quaternion optimization and greatly simplified the derivations of learning algorithms. The proposed GHR calculus is shown to yield the same generic algorithm forms as the corresponding real- and complex-valued algorithms. Advantages of the proposed framework are illuminated over illustrative simulations in quaternion signal processing and neural networks.

Enabling quaternion derivatives: the generalized HR calculus

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

A class of quaternion Kalman filters

The existing Kalman filters for quaternion-valued signals do not operate fully in the quaternion domain, and are combined with the real Kalman filter to enable the tracking in 3-D spaces. Using the recently introduced HR-calculus, we develop the fully quaternion-valued Kalman filter (QKF) and quaternion-extended Kalman filter (QEKF), allowing for the tracking of 3-D and 4-D signals directly in the quaternion domain. To consider the second-order noncircularity of signals, we employ the recently developed augmented quaternion statistics to derive the widely linear QKF (WL-QKF) and widely linear QEKF (WL-QEKF). To reduce computational requirements of the widely linear algorithms, their efficient implementation are proposed and it is shown that the quaternion widely linear model can be simplified when processing 3-D data, further reducing the computational requirements. Simulations using both synthetic and real-world circular and noncircular signals illustrate the advantages offered by widely linear over strictly linear quaternion Kalman filters.