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Chirality plays a pivotal role in the interaction between light and matter, yet detecting chiral signals from natural materials remains a challenge, necessitating the enhancement of their intensity. In this study, we present an approach to investigate substrate chirality through exploiting light scattering from Mie particles. To comprehensively analyze the scattering phenomenon, we theoretically derive the T-matrix for a nonchiral Mie sphere positioned on a chiral substrate. Unlike the Mie sphere in free space, our derivation accounts for the intricate coupling between the scattered light by the sphere and the reflected light by the substrate. Employing the T-matrix framework, we calculate the scattering power and circular dichroism spectra. Our findings reveal a remarkable augmentation of chiral signals originating from the substrate, thanks to the Mie resonance within high-index spheres. This research underscores the feasibility of probing local chiral properties in the vicinity of a sample surface, promising new insights into chiral interactions at the nanoscale.

Multiple scattering of parallel cylinders with arbitrary cross section is computed using the T-matrix of each single scatterer and the general translational matrix for cylindrical waves. Usually, the recommended golden rule to compute the translational matrix is Graf’s addition theorem. However, this approach cannot be properly implemented for some geometries, such as in a two-cylinder case when the center of one of them falls within the minimum circular cylinder that circumscribes the other one. In order to overcome this limitation, a transformation between cylindrical waves and plane waves, followed by propagation of the latter, is proposed. The new approach succeeds due to an adequate truncation of the evanescent plane wave spectrum. This strategy is demonstrated by studying the scattering of three infinite elliptic metallic cylinders for different electrical sizes and observing the convergence of the results as a function of the truncated spectrum. Finally, to conclusively show the interest and applicability of the approach, two more complex problems are treated: a group of infinite elliptic metallic cylinders where two different sizes are combined and a practical real-life filter in substrate integrated waveguide (SIW) technology, including several groups of rectangular dielectric cylinders. [ABSTRACT FROM AUTHOR]

In this article, a unified learning-based approach is introduced to solve inverse scattering problems (ISPs) with mixed boundary conditions (BCs). The scattering behavior of hybrid dielectric and perfect electric conductors (PEC) scatterers is modeled by the T-matrix method. A rough image of the zero-order T-matrix coefficients for unknown scatterers is first reconstructed by the backpropagation (BP) method, which is then refined by an attention-assisted pix2pix generative adversarial network (GAN). The spatial attention mechanism is utilized to enforce the generator network to learn salient features of the unknown scatterers instead of the background. The adversarial training of the generator and the discriminator further enables the reconstructed image to be constrained by high-level features of reference scatterers. Numerical tests on both synthetic and experimental data verify the superior performance of the proposed method for ISP reconstructions with hybrid scatterers. It effectively expands the application scope of learning-based ISP methods to reconstruct scatterers without knowing the BCs of scatterers in advance. [ABSTRACT FROM AUTHOR]

Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this article. The hybrid methods are particularly efficient when describing the interaction of electrically small complex objects and electrically large objects of canonical shapes such as spherical multilayered bodies where the T-matrix method is reduced to the Mie series making the method an interesting alternative in the design of implantable antennas or exposure evaluations. Method performance is tested on a spherical multilayer model of the human head. Along with the hybrid method, an evaluation of the transition matrix of an arbitrarily shaped object is presented and the characteristic mode decomposition is performed, exhibiting fourfold numerical precision compared to conventional approaches. [ABSTRACT FROM AUTHOR]

In the mixed boundary inverse scattering problem (ISP), conducting and dielectric scatterers coexist in the same region, which challenges the present quantitative inverse scattering methods. Moreover, to ensure the incident waves penetrating the lossy or high-contrast objects, lower wavelength is applied in most inverse scattering applications. Therefore, methods with wavelength or subwavelength resolution are required for the mixed boundary ISP. In this article, we devise a quantitative inversion scheme alternately updating the contrast of dielectric scatterers and the T-matrix of conducting scatterers. The proposed alternate parameter updating method (APUM) avoids the reconstruction deterioration from both the large imaginary parts of conducting contrasts and the limited expansion order of the T-matrix. Then, we further improve the resolution of the APUM by optimizing the incident fields, which is also a regularization strategy. In particular, we design superoscillatory incident fields to quantitatively converse the high spatial spectrum of objects into low spectrum contrast sources, which can retain the high-frequency information of objects in the low-passband of the Green function. The results with synthetic data and single-frequency Fresnel experimental data verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

According to the actual operation conditions, a kind of high-frequency losses testing system of magnetostrictive materials under dc bias is built. The dynamic hysteresis loops for Terfenol-D samples at different ac driving frequencies and magnetic densities are studied experimentally under variable dc bias excitation. The magnetic energy losses are obtained from these dynamic hysteresis loops. The three-variable magnetic energy loss matrix is established by these measured data. On the basis of Bertotti loss separation theory, the high-frequency losses calculating model of magnetostrictive materials considering variable dc bias excitation is proposed by using the algorithm of Levenberg–Marquardt and the method of matrix transformation. In this model, according to the multivariate parametric regression, the loss coefficients are modified by introducing dc bias-related terms. The loss comparison at different operating conditions shows that the computed results in this proposed model are in good agreement with the experimental ones. [ABSTRACT FROM AUTHOR]

Scattering and attenuation properties of rain using various drop models are calculated using Mie theory, the T-matrix method and numerical technique respectively. Ellipsoidal and oblate drops use the axis ratio of raindrops reported in literature. Scattering are presented both for small volumes containing a single drop and for large volumes with multiple drops in which the statistics of drop size distribution need to be taken into account. The angular dependence of scattering, absorption and scattering cross sections and polarization ratios are investigated. For single scattering the angular dependence and cross sections of nonspherical drops differed from those of a spherical drop. Differences between ellipsoid and oblate drops were minimal. Drop shape affected the polarization mostly at 40–140 degree detection angles. The averaged linear attenuation and rain induced cross channel signal were studied. Attenuation was close to the ITU-R.838 model and in the same order of magnitude as the attenuation due to atmospheric moisture. The cross channel signal was calculated as a function of rain rate and transmitter/receiver angle. Vertical polarization was observed to produce a higher cross channel signal than horizontal polarization. It was concluded that drop shape is not an important factor at 300 GHz due to small drops dominating the scattering signal. Overall, the results showed that in single scattering, the ellipsoid is a good approximation for raindrops and that for large volumes, a spherical drop approximation and a Mie solution may be sufficient at frequencies of 300 GHz and higher.

This article investigates the nonfragile $\mathcal {H}_{\infty }$ synchronization issue for a class of discrete-time Takagi–Sugeno (T–S) fuzzy Markov jump systems. With regard to the T–S fuzzy model, a novel processing method based on the matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of the actuator, a nonfragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this article lies in that the transition probabilities of the Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on the Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed $\mathcal {H}_{\infty }$ performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results. [ABSTRACT FROM AUTHOR]

Based on the power-law relation between rain intensity and corresponding specific attenuation, precipitation inversion by oblique earth–space link (OEL) has become a supplement to conventional method. However, the attenuation caused by melting layer has a significant effect on its performance. According to the microphysics, thermodynamics, and scattering properties of melting hydrometeors, a melting layer model is introduced to improve OEL inversion approach. Meanwhile, the observations by a microrain radar (MRR) located at Nanjing Reference Climatological Station (NRCS) are used and plenty of numerical simulations are also performed, which aim to validate the melting layer model. The choice of raindrop size distribution (DSD) determines the simulated values of radar reflectivity factor (RRF) and path-integrated attenuation (PIA). The gamma distribution gives the results of simulated RRF that are consistent with MRR observations. Considering the nonspherical shape of melting hydrometeors, its effects on attenuation calculation are discussed based on $T$ -matrix, which indicates the error due to hydrometeor shape is negligible below Ka-band. The values of PIA derived from our melting layer model show good agreements with MRR observations. In the simulation experiment, we found the average multiplier of melting layer attenuation is a function of rain intensity and frequency. The relation is established by using the nonlinear least-squares method. According to the multiplier, a novel model is proposed to estimate the melting layer attenuation. Compared with other existing attenuation models, it shows a similar performance in different frequency bands. Moreover, we introduce an equivalent multiplier into OEL rainfall inversion model, which demonstrates the obvious enhancement of effectiveness and robustness of improved model in the validation experiment. [ABSTRACT FROM AUTHOR]

As a non-iterative linear inverse scattering imaging method, the linear sampling method (LSM) has the merits of easy implementation and high computational efficiency. In this article, based on the LSM and T-matrix method, we propose a fast method to reconstruct the target medium parameters. First, we use the LSM qualitative imaging method to estimate the contour of the target. Then, the preprocessing information of the LSM is applied to the virtual experiment circles in the framework of T-matrix method. In this way, we avoid the inversion of the matrix and only need to solve a series of univariate equations. Numerical simulation results show that the reconstruction accuracy of the proposed method is similar to that of LSM quantitative imaging method, but it has higher calculation accuracy and wider application range. Although the calculation accuracy is not as good as the contrast source inversion (CSI) method, the proposed method has huge advantages in terms of calculation efficiency.

In this article, an improved T-matrix method is proposed to improve the accuracy for simultaneous reconstruction of dielectric scatterers and perfectly electric conductors (PEC). First, we modify the original T-matrix inversion method and obtain a preliminary reconstruction result. Then treat this result as a priori information, and a new initial iteration value is generated by truncating and assigning values to it. At the same time, genetic algorithm (GA) is used to optimize these truncation and assignment parameters. Finally, the optimization result is used as the initial value of the modified T-matrix method to obtain better reconstruction accuracy. The numerical simulation results under noisy conditions show that the proposed method can more clearly reconstruct the edges of the objects and have higher reconstruction accuracy.

This article concentrates on the output feedback controller design problem for discrete-time nonlinear switched systems with actuator faults. The Takagi–Sugeno fuzzy model is adopted to approximate the nonlinearity of the plant with a set of local linear models. The persistent dwell-time (DT) switching law, which is more general than DT or average DT switching, is introduced to govern the switching among subsystems. In order to alleviate the effects of actuator failures on system stability and performance, a synthesized fault-tolerant output feedback controller ensuring various performance requirements is designed. Intensive attention is focused on establishing sufficient conditions, which can guarantee the exponential mean-square stability as well as the prescribed extended dissipativity property of the closed-loop system. By virtue of the Lyapunov stability theory and appropriate matrix transformation methods, the desired controller gains can be obtained by solving a convex optimization problem. The developed method is finally applied to address the control issue of a tunnel diode circuit system model to illustrate its efficiency and applicability. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of a flocking control algorithm for a group of autonomous underwater vehicles (AUVs). A leader–follower control strategy is employed to flock a group of AUVs along a predefined desired path. In this approach, leader AUVs are assumed to have global knowledge of the desired trajectory and the follower AUVs are not provided with this information. For keeping all the AUVs connected in a group, a flocking center is estimated. This flocking center is a virtual point whose position at any instant of time can be predicted by using a consensus algorithm. The controllers for the leader and follower AUVs are developed by implementing mathematical and fuzzy artificial potential functions. A group of four AUVs is considered for analyzing the efficacy of the developed control algorithm. Simulations are carried out both in obstacle-free and obstacle-rich environments. From the obtained results, it is observed that the proposed fuzzy flocking control algorithm provides effective cooperative motion control of multiple AUVs along the desired paths and avoid obstacles successively. It is also observed that the flocking controller developed based on fuzzy artificial potential function outperforms the controller with mathematical potential functions despite uncertainties owing to external disturbances. [ABSTRACT FROM AUTHOR]

This paper proposes a generalized approach to decompose mixed-mode (MM) conducted emissions in power electronic systems into their differential and common-mode components and modal couplings. Specifically, a pair of transformation matrices are defined that map a system of MM line-to-ground voltage equations to an equivalent decomposed differential-common-mode set. The result provides exact mathematical relationships for the modal couplings induced by asymmetries between the lines described by the voltage equations. As an example, the proposed transformation is applied to generate two different, but equally valid models for studying the effect of unbalanced parasitic capacitances in a multichip power module on the common-mode (CM) behavior of a half-bridge converter. The two models provide different perspectives on the mechanisms driving CM current through the system. It is found that one model is best suited to study leakage current through the module while the other provides greater insight into currents circulating internally and its impact on the larger system. [ABSTRACT FROM AUTHOR]

This research proposes a novel low-voltage inverter-fed motor drive with variable parameters achieved through the independent armature winding for the automobile traction motor. The independent armature winding with low-voltage inverters can improve the total efficiency by reducing the converter losses. The inverters are able to change their connections to different coils groups of the armature winding in order to achieve the wide operating range. The voltage equation of each mode can be shown by using the transformation matrix when the winding connection is changed. Thus, the proposed motor is called the MATRIX motor. In this paper, the downsized model was designed to verify the principle. The principle model is able to achieve four motor parameters. It was confirmed that the principle model could extend the operating range and could achieve the high-efficiency driving in wide speed range. Furthermore, the novel winding reconfiguration method is proposed that not only avoids the surge voltage, but also compensates the torque reduction during the winding reconfigurations. [ABSTRACT FROM AUTHOR]

Reliable and efficient analysis of electromagnetic scattering by cylindrical components of vegetation is important for microwave remote sensing of vegetated terrain. It allows for the characterization of anistropicity of the effective permittivity for vegetation or tree canopy, where averaging operation over distribution of cylinder orientation is needed in general. In this paper, we propose a T-matrix formulation based on our virtual partition method (VPM) for the whole cylindric component of either homogeneous or inhomogeneous nature. Numerical simulations demonstrate that the proposed T-matrix preserves all the desirable features of the VPM method, including high fidelity prediction of the scattering amplitude function and fulfillment of energy conservation as well as the reciprocity theorem. More importantly, in the evaluation of averaging over orientation distribution, the proposed method is usually faster than the VPM by two orders of magnitude. The predicted effective permittivity for an exemplary orientation distribution shows appreciable difference from that of the infinite cylinder approximation. With its qualitatively characterized region of validity, the proposed method is expected to be helpful in multiband coherent scattering models of vegetated terrain. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel fractional transform, denoted as the fractional Krawtchouk transform (FrKT), a generalization of the Krawtchouk transform. The derivation of the FrKT uses the eigenvalue decomposition method. We determine the eigenvalues and the corresponding multiplicity of the Krawtchouk transform matrix. Moreover, the orthonormal eigenvectors of the transform matrix are derived. For validation purpose only and as a first illustration of the interest of FrKT, a watermarking example was chosen. Experimental results show that better watermark robustness and imperceptibility are achieved by adjusting the fractional orders in the FrKT. [ABSTRACT FROM PUBLISHER]

Subradiant modes can exhibit sharper spectral response, and lower radiative loss compared to the super-radiant modes of plasmonic nanostructures. Selective excitation of these modes is challenging, and has practical importance. In this paper, a systematic procedure for determining, and individually exciting the subradiant modes of a plasmonic nanostructure is presented by utilizing our previously reported T-matrix formulation. As an example, we calculate various modes of a gold nanodimer, and determine the incident field required for exciting a subradiant mode of this nanostructure. This field is then generated by a modified zone plate lens. The expansion of scattered field, as well as the scattering power spectrum confirms the excitation of the subradiant mode. The total field is compared with those obtained using the finite-difference time domain method and method of moments. [ABSTRACT FROM AUTHOR]

A five-phase fault-tolerant permanent-magnet (FTPM) motor can offer high torque density, low torque ripple, and good fault-tolerant capability. In order to improve operation performance under an open-circuit fault condition, this paper proposes a new remedial field-oriented control (RFOC) strategy for a five-phase FTPM motor. The novelty of the proposed RFOC strategy lies in the orthogonal reduced-order transformation matrix, which is derived from the fault-tolerant current references, and a new zero-sequence current related to torque ripple. The pulsation of the neutral voltage can be neglected in the RFOC strategy, having no effect on the control action. Also, the effect of the open-circuit fault on the motor drive model under the transformation matrix is discussed. A five-phase FTPM motor drive is prototyped and the proposed RFOC strategy is evaluated in terms of the steady-state and dynamic performances. The simulated and experimental results are given to verify the proposed strategy. [ABSTRACT FROM PUBLISHER]

An analytic formulation revealing exact contribution of different factors affecting the interference interaction between eigenmodes of a scatterer is presented by utilizing our previously reported modal scattering power formula. For special case of arbitrary multilayer concentric and nonconcentric nanoshells, a recursive method for analytically calculating the T-matrix, and each of these factors is derived. Results for a three layer structure showing the conditions for constructive and destructive interference interactions are discussed in details. It is shown that the interference interaction can occur in the vicinity of the overlapping resonance frequencies of the two spatially overlapping eigenmodes. The role of the phase characteristic of the eigenmodes at the resonance points in the interference phenomena is discussed. Different factors determining the phase behavior originating from either the incidence, or the characteristics of the scatterer itself are studied. These provide the ability to engineer the incidence, and the scatterer properties for achieving desired interference behavior. As a practical example for the application of this approach, reducing radiation loss of a plasmonic nanostructure through tailoring of structural parameters, and synthesis of proper incidence is presented. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a method for visual tracking based on local sparse representation. Image patches from the object and the background are split into image blocks to construct local representations. Within the subclass discriminant framework, a discriminative subspace is learned to distinguish the object image blocks from the background image blocks while preserving their multimodal structure. A dictionary is constructed using the centers of the object subclasses. With this dictionary, sparse coding is implemented on the projected vectors corresponding to the image blocks, and the sparse coefficients are concatenated to obtain a local sparse code as the feature that represents the image patch. Considering the subclass discriminant constraint and the sparsity constraint imposed on the sparse coding, the subspace learning and sparse representation problems are converted into a joint optimization problem with respect to a transformation matrix and sparse coefficients. To enhance the tracking accuracy, two dictionaries are devised, one to incorporate the original observations of the target and the other to incorporate the latest observations, thereby providing two templates to characterize the appearance of the target. Histogram intersection over the local sparse codes provides an evaluation of the confidence. Finally, the candidate with the maximal confidence is selected as the object image patch. Compared with several state-of-the-art algorithms, our method demonstrates a superior performance when applied to challenging sequences. [ABSTRACT FROM AUTHOR]

We propose a completely automatic approach for recognizing low resolution face images captured in uncontrolled environment. The approach uses multidimensional scaling to learn a common transformation matrix for the entire face which simultaneously transforms the facial features of the low resolution and the high resolution training images such that the distance between them approximates the distance had both the images been captured under the same controlled imaging conditions. Stereo matching cost is used to obtain the similarity of two images in the transformed space. Though this gives very good recognition performance, the time taken for computing the stereo matching cost is significant. To overcome this limitation, we propose a reference-based approach in which each face image is represented by its stereo matching cost from a few reference images. Experimental evaluation on the real world challenging databases and comparison with the state-of-the-art super-resolution, classifier based and cross modal synthesis techniques show the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

In the two-frame sensor calibration problem, the objective is to find rigid-body homogeneous transformation matrices $X,Y$ that best fit a set of equalities of the form A_i X = Y B_i$, i=1, \ldots, N$, where the are pairs of homogeneous transformations obtained from sensor measurements. The measurements are often subject to varying levels of noise and the resulting optimization can have numerous local minima that exhibit high sensitivity in the choice of optimization parameters. As a first contribution, we present a fast and numerically robust local optimization algorithm for the two-frame sensor calibration objective function. Using coordinate-invariant differential geometric methods that take into account the matrix Lie group structure of the rigid-body transformations, our local descent method makes use of analytic gradients and Hessians, and a strictly descending fast step-size estimate to achieve significant performance improvements. As a second contribution, we present a two-phase stochastic geometric optimization algorithm for finding a stochastic global minimizer based on our earlier local optimizer. Numerical studies demonstrate the considerably enhanced robustness and efficiency of our algorithm over existing unit quaternion-based methods. [ABSTRACT FROM AUTHOR]

This paper presents the development of an estimation algorithm for ballistic-target evasive acceleration during the terminal phase of interception. The proposed design is based on an application of the extended state observer, using target information acquired from a seeker to estimate target evasive acceleration. It is applicable to multiple-input multiple-output plants with variable observer gains applied in nonlinear coupled line-of-sight pitch and yaw dynamics. Design and stability analysis are evolved based on the theory of Lyapunov, with noncontinuous, piecewise, smoothly Lyapunov function candidates. [ABSTRACT FROM AUTHOR]

This paper presents an analytic coarse transfer alignment method based on inertial measurement vector matching for the inertial navigation system (INS) on vertically launched missiles from the ground. The alignment problem is transformed into the estimation of the relative attitude between the master INS (MINS) and slave INS (SINS) by decomposing the attitude matrix of SINS. As inspired by the ideology of the traditional analytic alignment method, the measurements from the accelerometers and gyroscopes of MINS and SINS are utilized to construct matching vectors to estimate the relative attitude between them without any initial information. Furthermore, the sensitivity of Euler angles with respect to the inertial sensor errors is analyzed according to the presented coarse transfer alignment principle. An algebraic expression for alignment error estimation is given, and thus the real-time precision evaluation for the presented coarse alignment method is achieved. It allows the system to switch to fine alignment in a timely and accurate manner. The simulation and flight test demonstrate that, compared with the quaternion-optimization-based alignment method proposed by Kang et al., the presented method has a smaller calculation cost and satisfactory convergence. The corresponding precision evaluation algorithm can describe the trend of true alignment error accurately, and is good enough to judge the moment for switching to the fine alignment. [ABSTRACT FROM AUTHOR]

This paper presents a framework for a semisupervised domain adaptation method for remote sensing image classification. Most of the representation-based domain adaptation methods attempt to find a total transformation matrix for all the samples from the source domain; however, they ignore the individual changes in each class, which often leads to the misalignment of the samples in each class between the two domains. This paper attempts to find new representations for the samples in different classes from the source domain by multiple linear transformations, which corresponds to the practical changes in each class to a higher degree. Furthermore, to avoid the influence of outliers and noise in the source domain samples, low-rank reconstruction is further applied to make the domain adaptation method more robust. In addition, in the stage of predicting the unlabeled samples by label propagation (LP), the proposed LP with instance weighting can effectively further reduce the negative effect of misleading samples from the source domain. The results obtained with a QuickBird data set and a hyperspectral data set confirm the effectiveness and reliability of the proposed method. [ABSTRACT FROM PUBLISHER]

Low-cost inertial/magnetic sensor units have been extensively used to determine sensor attitude information for a wide variety of applications, ranging from virtual reality, underwater vehicles, handheld navigation systems, to biomotion analysis and biomedical applications. In order to achieve precise attitude reconstruction, appropriate sensor calibration procedures must be performed in advance to process sensor readings properly. In this paper, we are aiming to calibrate different error parameters, such as sensor sensitivity/scale factor error, offset/bias error, nonorthogonality error, mounting error, and also soft iron and hard iron errors for magnetometers. Instead of estimating all of these parameters individually, these errors are combined together as the combined bias and transformation matrix. Two-step approaches are proposed to determine the combined bias and transformation matrix separately. For the accelerometer and magnetometer, the combined bias is determined by finding an optimal ellipsoid that can best fit the sensor readings, and the transformation matrix is then derived through a two-step iterative algorithm by exploring the intrinsic relationship among sensor readings. For the gyroscope, the combined bias can be easily determined by placing the sensor node stationary. For the transformation matrix estimation, the intrinsic relationship among gyroscope readings is explored again, and an unscented Kalman filter is employed to determine such matrix. The calibration methods are then applied to our sensor nodes, and the good performance of the orientation estimation has illustrated the effectiveness of the proposed sensor calibration methods. [ABSTRACT FROM PUBLISHER]

Besides Karatsuba’s algorithm, optimal Toeplitz matrix-vector product (TMVP) formulae is another approach to design GF(2^n) subquadratic multipliers. However, when GF(2^n) elements are represented using a polynomial basis or its generalization—shifted polynomial basis—this approach is currently appliable only to fields GF(2^n) generated by an irreducible trinomial or a special type of irreducible pentanomials, but not to a general irreducible pentanomial. The reason is that no transformation matrix, which transforms the Mastrovito matrix into a Toeplitz matrix, has been found. In this article, we propose such a transformation matrix and its inverse matrix for an arbitrary irreducible pentanomial. [ABSTRACT FROM AUTHOR]

Micromagnetometers, together with inertial sensors, are widely used for attitude estimation for a wide variety of applications. However, appropriate sensor calibration, which is essential to the accuracy of attitude reconstruction, must be performed in advance. Thus far, many different magnetometer calibration methods have been proposed to compensate for errors such as scale, offset, and nonorthogonality. They have also been used for obviate magnetic errors due to soft and hard iron. However, in order to combine the magnetometer with inertial sensor for attitude reconstruction, alignment difference between the magnetometer and the axes of the inertial sensor must be determined as well. This paper proposes a practical means of sensor error correction by simultaneous consideration of sensor errors, magnetic errors, and alignment difference. We take the summation of the offset and hard iron error as the combined bias and then amalgamate the alignment difference and all the other errors as a transformation matrix. A two-step approach is presented to determine the combined bias and transformation matrix separately. In the first step, the combined bias is determined by finding an optimal ellipsoid that can best fit the sensor readings. In the second step, the intrinsic relationships of the raw sensor readings are explored to estimate the transformation matrix as a homogeneous linear least-squares problem. Singular value decomposition is then applied to estimate both the transformation matrix and magnetic vector. The proposed method is then applied to calibrate our sensor node. Although there is no ground truth for the combined bias and transformation matrix for our node, the consistency of calibration results among different trials and less than $3^\circ$ root mean square error for orientation estimation have been achieved, which illustrates the effectiveness of the proposed sensor calibration method for practical applications. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a generalized analog network coding (GANC) scheme for a non-orthogonal multiple-access relay channel (MARC), where two sources transmit their information simultaneously to the destination with the help of a relay. In the GANC scheme, the relay receives interfered signals from the two sources and generates signals to be transmitted with a relay function. We focus on the design of the optimal relay function to achieve the minimum pair-wise error probability (PEP) of the system. Specifically, we first covert the relay function optimization problem to a transformation matrix (TM) design problem by presenting the received complex signals as signal matrices composed of real and imaginary parts. Then, we propose an optimization criteria, i.e., maximizing the minimal squared Euclidean distance (MMSED), to improve the PEP performance, since the PEP is determined by the Euclidean distance of the received constellation at destination. Next, we prove that the MMSED can be equivalently converted to a convex problem by introducing an intermediate matrix. We solve this convex problem by using the Lagrangian method and obtain the closed-form expression of the optimal TM. We further improve the PEP performance by optimizing transmission power of the two sources. Simulation results show that the proposed GANC scheme has a better PEP performance compared to other alternative schemes. [ABSTRACT FROM AUTHOR]

Scagnostics (Scatterplot Diagnostics) were developed by Wilkinson et al. based on an idea of Paul and John Tukey, in order to discern meaningful patterns in large collections of scatterplots. The Tukeys' original idea was intended to overcome the impediments involved in examining large scatterplot matrices (multiplicity of plots and lack of detail). Wilkinson's implementation enabled for the first time scagnostics computations on many points as well as many plots. Unfortunately, scagnostics are sensitive to scale transformations. We illustrate the extent of this sensitivity and show how it is possible to pair statistical transformations with scagnostics to enable discovery of hidden structures in data that are not discernible in untransformed visualizations. [ABSTRACT FROM PUBLISHER]

This paper presents a new method for the calculation of smooth frequency-dependent transmission-line (TL) transformation matrices. The proposed method, based on the Levenberg–Marquardt algorithm, solves an equivalent real-valued approach of the generalized complex eigenproblem. The implemented formulation incorporates a robust convergence criterion and is applicable to all TL configurations, due to the included numerically well-defined computational scheme. Smooth modal transformation matrices are calculated for overhead and underground TL configurations under different representations of the imperfect earth. Results are compared and validated with the corresponding results obtained from the Newton–Raphson and the sequential quadratic programming methods, revealing the accuracy, efficiency, and robustness of the proposed formulation, even in cases where the other methods fail. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an implementation of a fuzzy system whose parameters are mutable according to the context. The construction of the system is done via two steps. First, we build a based type-1 Takagi–Sugeno–Kang (TSK) fuzzy system whose membership functions will be later adjusted to the situation by means of contextual transformation to reflect the influence of context in the interpretation of fuzzy sets. Second, an iterative algorithm is performed to identify the transformation matrix, which is used to scale the membership functions of the reference-based fuzzy sets in each of the contexts. The identification of the premise part of the based fuzzy system is performed via a combination of an island model parallel genetic algorithm and a space search memetic algorithm, while the identification of the consequent parameters of the system is done via an improved QR Householder least-squares method. The proposed system is evaluated using the well-known Mackey–Glass time-series prediction benchmark dataset and has shown better accuracy than any other previous works concerning the same problem. [ABSTRACT FROM AUTHOR]

In this paper, we provide specific and practical approaches to associate uncertainty with \4 \times \4 transformation matrices, which is a common representation for pose variables in 3-D space. We show constraint-sensitive means of perturbing transformation matrices using their associated exponential-map generators and demonstrate these tools on three simple-yet-important estimation problems: 1) propagating uncertainty through a compound pose change, 2) fusing multiple measurements of a pose (e.g., for use in pose-graph relaxation), and 3) propagating uncertainty on poses (and landmarks) through a nonlinear camera model. The contribution of the paper is the presentation of the theoretical tools, which can be applied in the analysis of many problems involving 3-D pose and point variables. [ABSTRACT FROM PUBLISHER]

In this study, scattering from impedance bodies positioned at the edge of a perfectly electrically conducting wedge is investigated. In the treatment of the problem, eigenfunction expansion in terms of spherical vector wave functions is employed. A complete dyadic Green's function for the spherical impedance boss at the edge is developed. It is observed that the scattering is highly enhanced by the edge guided waves. Additionally, using T-matrix method, the solution is extended to the general case of irregularly shaped scatterers. The T-matrix solution is verified by applying it to the case of a spherical scatterer and results are compared with the dyadic Green's function solution. [ABSTRACT FROM PUBLISHER]

We present an explicit and numerically exact method for determining the T matrix of an arbitrarily shaped PEC object directly from a MoM impedance matrix that is generated with the Rao-Wilton-Glisson basis function for use in multiple-scattering calculations. [ABSTRACT FROM AUTHOR]

Spatial oscillations in neutron flux distribution resulting from xenon reactivity feedback are a matter of concern in large nuclear reactors. If the spatial oscillations in power distribution are not controlled, power density and rate of change of power at some locations in the reactor core may exceed their respective limits causing increase in chances of fuel failure. Hence, during the design stages of any large nuclear reactor, it is essential to identify the existence of spatial instabilities and to design suitable control strategy for regulating the spatial power distribution. This paper presents a method to design and analyze the effect of sliding mode control (SMC) for spatial control of Advanced Heavy Water Reactor (AHWR). The AHWR model considered here is of 90th order with 5 inputs and 18 outputs. In this paper, numerically ill-conditioned system of AHWR is separated into 73rd order ‘slow’ subsystem and 17th order ‘fast’ subsystem and SMC is designed from slow subsystem. Further, using simple linear transformation matrices, SMC for full system is constructed. Also, it is proved that slow subsystem SMC results in a sliding mode motion for full system. Dynamic simulations has been carried out using nodal core model of AHWR to show effectiveness and robustness of proposed method. [ABSTRACT FROM PUBLISHER]

A T-matrix method is proposed to solve the mixed boundary inverse scattering problem, i.e., perfect electric conductors (PEC) and dielectric scatterers are simultaneously reconstructed under the two-dimensional transverse magnetic (TM) illumination setting. Both the dipole and monopole elements of the T-matrix are chosen to accurately describe the scattering behavior of the mixed boundary problem. Criteria of utilizing the monopole element of T-matrix to distinguish the PEC from dielectric scatterers are presented. Apart from synthetic data, the experimental data from Fresnel dataset is also used to verify the validity of the proposed method, showing that it works well in sub-wavelength setting and is quite robust against noise. The pros and cons of the proposed T-matrix method are further discussed. [ABSTRACT FROM PUBLISHER]

We consider multiple scattering among different groups of vias with each group of vias sharing one antipad in planar waveguide. A transformation is used that converts the 2-D discretization and 2-D surface integration of the product of Green's functions and magnetic surface currents into 1-D discretization and 1-D integration of surface charges on the vias and on the ground plane. This is used to calculate the incident fields onto the vias. Based on the incident fields, the Foldy–Lax equations can be solved to calculate the circuit parameters for the problem. We show that the results are superior to the previously used finite difference method. In addition, the group T-matrix method is used to represent a group of vias to account for the scattering among different groups of vias. Results are illustrated for various cases of multiple vias up to 20 GHz. Results show the accuracy of the method even to very closely spaced vias when they are separated by merely 1 mil. Numerical results are in excellent agreement with ANSOFT HFSS. [ABSTRACT FROM AUTHOR]

In this paper, a new balanced-to-balanced power divider/combiner is proposed. By using matrix transformation, two three-port networks for the odd- and even-mode circuit models are deduced, based on the constraint rules of the mixed-mode S-parameters. In order to satisfy the two required scattering matrices simultaneously, the resistances of lumped elements, the characteristic impedances and electrical length of transmission lines are selected appropriately. Then, a planar microstrip structure is designed to realize the proposed balanced-to-balanced power divider/combiner with equal power division. The theoretical, simulated and measured results all show a good mixed-mode performance. In the measurement, the maximum differential-mode transmission coefficient is -\ 3.2 dB, the best differential-mode isolation is 47.2 dB, and the fractional bandwidth of its operating band is approximately 20.8%. [ABSTRACT FROM PUBLISHER]