Matrix Inversion Operation Research Articles

Finite-field coupling via learning the charge response kernel

Response of the electronic density at the electrode–electrolyte interface to the external field (potential) is fundamental in electrochemistry. In density-functional theory, this is captured by the so-called charge response kernel (CRK). Projecting the CRK to its atom-condensed form is an essential step for obtaining the response charge of atoms. In this work, the atom-condensed CRK is learnt from the molecular polarizability using machine learning (ML) models and subsequently used for the response-charge prediction under an external field (potential). As the machine-learnt CRK shows a physical scaling of polarizability over the molecular size and does not (necessarily) require the matrix-inversion operation in practice, this opens up a viable and efficient route for introducing finite-field coupling in the atomistic simulation of electrochemical systems powered by ML models.

국제 표준과 버스 임피던스 매트릭스를 이용한 고조파 해석 알고리즘에 관한 연구

Widespread interests in environmental issues are growing. Following this trend, the proportion of renewable energy resources in the grid is increasing. Renewable energy is connected to the grid as distributed generation (DG) using converters or inverters. Therefore, harmonic analysis in the system is essential. In this paper, we present an algorithm for harmonic analysis. Harmonics are analyzed using bus impedance matrix that does not require inverse matrix operation. And this algorithm includes a tap-change transformer. This allows you to analyze complex power systems and expands the versatility of the algorithm. And by presenting harmonic analysis methods according to international standards (i.e. IEC, IEEE 519-1,2), the ability of the algorithm has been expanded. The case study validates the algorithm by comparing the harmonic calculation results over the bus admittance matrix with the calculation results over the proposed bus impedance matrix in various scenarios (eg IEEE 14, 30 bus test feeder).

Balance control based on six-dimensional spatial mechanics and velocity adjustment through region intervention and foot landing for quadruped robot

AbstractCurrently, the body balance control algorithm of a quadruped robot executing trot gait motion is more complex and computationally intensive, which is not conducive to improving the real-time control performance of the robot. This paper proposes a six-dimensional spatial mechanics decoupling algorithm to enhance the balance control accuracy during trot gait while optimizing the computational effort. A 6 × 6 matrix is established to describe the relationship between six ground reaction forces of the diagonal supporting leg and six spatial forces and torques controlling robot degrees of freedom, which is optimized to reach the full rank. Decoupling calculation is adopted to obtain required ground reaction forces by matrix inverse operation, and forces are converted to joint motor torques utilizing the Jacobian matrix. The trajectory of the swing leg foot is generated based on cubic interpolation, and the robot motion speed is adjusted by selecting the landing point. This paper also proposes a region intervention control method based on center of mass projection to regulate the moving speed while ensuring the balance of the robot. Finally, the algorithm is verified by simulation using open source software Webots. The results show that when the robot moves at an average speed of 0.5 m/s, the lateral displacement change of the robot is less than 0.009 m, the height change is less than 0.003 m, and the rotating angles around the x, y, and z axes are less than 0.0036 rad, 0.0013 rad, and 0.001 rad, respectively.

A general adaptive ridge regression method for generalized linear models: an iterative re-weighting approach

This article is concerned with the problem of variable selection and estimation for high dimensional generalized linear models. In this article, we introduce a general iteratively reweighted adaptive ridge regression method (GAR). We show that the GAR estimator possesses oracle property and grouping effect. A data-driven parameter γ is introduced in the GAR method to adapt the different cases of the true model. Then, such an adaptive parameter γ is adequately taken into consideration to establish a γ-dependent sufficient condition to guarantee the oracle property and the grouping effect. Furthermore, to apply the GAR method more efficiently, a coordinate-wise Newton algorithm is employed to successfully avoid the inverse matrix operation and the numerical instability caused by iteration. Extensive numerical simulation results show that the GAR method outperforms the commonly used methods, and the GAR method is tested on the gastric cancer dataset for further illustration.

Low-Complexity Detectors for Uplink Massive MIMO Systems Leveraging Truncated Polynomial Expansion

In this work, we propose low-complexity detectors for massive multiple-input multiple-output (MIMO) systems. Particularly, we leverage variants of truncated polynomial expansion (TPE) in order to reduce the computational complexity of the signal detection in the uplink direction. Linear detectors such as zero-forcing (ZF) and minimum mean square error (MMSE) involve expensive matrix-matrix multiplication and matrix inversion operations. TPE-based detectors are appropriate candidates for approximating these linear detectors. However, tuning the normalization factor of TPE-based detectors may require calculating the minimum and the maximum eigenvalues of the channel Gram matrix. These calculations become computationally expensive for some massive MIMO systems, especially for systems with a large ratio of single-antenna user terminals to the number of antennas at the base station, i.e., loading factor. We propose to tune the normalization factor using appropriate approximations for the extreme eigenvalues. The proposed TPE-based detectors exhibit a bit error performance similar to that of the TPE-based detector with the optimal normalization factor. Moreover, our proposed detectors achieve the error performance of ZF and MMSE for different loading factors of spatially correlated and uncorrelated massive MIMO channels. The computational complexity of the proposed detector is proportional to the number of base station antennas and the number of users.

OGI-SLAM2: A Hybrid Map SLAM Framework Grounded in Inertial-Based SLAM

Indoor localization using mobile sensors has gained momentum lately. However, indoor pedestrian localization with low-cost IMU has not been practically applied, and the main challenge is that it is difficult for low-cost IMU to obtain high-precision localization performance over a long period of time. In this paper, we propose a multi-source fusion indoor pedestrian autonomous localization framework combining landmark maps and occupancy grid maps. Combining the ideas of optimization and occupancy grid map-based inertial SLAM algorithm(OGI-SLAM), we maintain the short- and medium-term localization accuracy with OGI-SLAM, and achieve long-term localization accuracy improvement with keypoint maps. Without prior knowledge of the map, we use user motion features and environmental features to extract keypoints in the trajectory and construct keypoint descriptors. Combining the uncertainty of system location and the similarity of environmental features, we propose a keypoint extraction and association method to solve the problem of inaccurate particle filtering loop closing with low-cost IMU. In addition, a two-step trajectory optimization method is proposed, which uses bundle adjustment to correct the positioning error of keypoints and models the error correction of common points between keypoints as affine transformation, avoiding the large matrix inversion operation in the optimization process. Simulations and field trial evaluations show that the system is able to achieve a maximum positioning accuracy of 1.64 meters with low-performance IMU on board, representing a 57% maximum improvement in positioning accuracy compared to OGI-SLAM. This highlights the promise of OGI-SLAM2 as an unconventional indoor positioning method.

Sparsity-Aware OCT Volumetric Data Restoration Using Optical Synthesis Model

In this study, a novel restoration model for the data of optical coherence tomography (OCT) is proposed. An OCT device acquires a tomographic image of a specimen at the scale of a few micrometers using a near-infrared laser and has been frequently adopted to measure the structures of bio-tissues. In certain applications, OCT devices face the problem of extremely weak reflected light and require the help of image processing to estimate the distribution of reflected light hidden in various noises. OCT identifies tomographic structures by searching for peak interference locations and their intensities. Therefore, the challenge of OCT data restoration involves the problem of identifying the interference function and its deconvolution. In this study, a restoration method is given by reducing the problem to a regularized least-squares problem with a hard constraint for the latent refractive index distributions, and an algorithm is derived using a primal-dual splitting (PDS) framework. The PDS has the advantage of requiring no inverse matrix operation and is able to handle high-dimensional data. The significance of the proposed method is verified through simulations using artificial data, followed by an experiment conducted using actual observation of <inline-formula><tex-math notation="LaTeX">$64 \times 64 \times 5000$</tex-math></inline-formula> sized voxels.

Fast and in-situ correction of camera channel crosstalk based on Fourier transform of carrier fringes in multi-colour interferometry

To deal with the light intensity crosstalk between R, G and B channels of colour camera in multi-colour interferometry, we present a fast and in-situ correction method based on Fourier transform of carrier fringes. The crosstalk coefficients of camera channels are obtained in the Fourier frequency domain of captured colour carrier fringes, and the crosstalk is corrected by matrix inverse operation. Simulations and experiments verify that this method has advantages of simple implementation, fast correction speed and high measurement accuracy, and it effectively achieves in-situ correction without removing the camera.

A Geometric Layout Method for Synchronous Pseudolite Positioning Systems Based on a New Weighted HDOP

The positioning accuracy of a ground-based system in an indoor environment is closely related to the geometric configuration of pseudolites. This paper presents a simple closed-form equation for computing the weighted horizontal dilution of precision (WHDOP) with four eigenvalues, which can reduce the amount of calculation. By comparing the result of WHDOP with traditional matrix inversion operation, the effectiveness of WHDOP of the proposed simple calculation method is analyzed. The proposed WHDOP has a linear relationship with the actual static positioning result error in an indoor environment proved by the Pearson analysis method. Twenty positioning points are randomly selected, and the positioning variance and WHDOP of each positioning point have been calculated. The correlation coefficient of WHDOP and the positioning variance is calculated to be 0.82. A pseudolite system layout method based on a simulated annealing algorithm is proposed by using WHDOP, instead of Geometric dilution of precision (GDOP). In this paper, the constraints of time synchronization are discussed. In wireless connection system, the distance between master station and slave station should be kept within a certain range. Specifically, for a given indoor scene, many positioning target points are randomly generated in this area by using the Monte Carlo method. The mean WHDOP value of all positioning points corresponding to the synchronous pseudolite layout is used as the objective function. The results of brute force search are compared with the method, which proves the accuracy of the new algorithm.

Aplikasi Operasi Matriks pada Perancangan Simulasi Metode Hill Cipher Menggunakan Microsoft Excel

&lt;p&gt;&lt;em&gt;One of several algorithms in cryptography is the Hill Cpher method. This method is used in randomizing the contents of the message using a password key in the form of a matrix with the order MXM. The product in this research is a simulation design to explain how a plaintext message is converted into cipher text with encryption and decryption processes and vice versa from ciphertext to paintext through multiplication and inverse matrix operations. using Microsoft Excel (MS Excel). In this study, a matrix with order 2x2 and modulo 26 was used. This simulation design shows how the work process visually for each step in the process of changing the message content in the Hill Cipher method. It is hoped that the results of this study can be used as a learning medium by the community, especially students and lecturers, to increase understanding and broaden their horizons about the Hill Cipher method in cryptography lectures.&lt;/em&gt;&lt;em&gt;&lt;/em&gt;&lt;/p&gt;

Hybrid precoding algorithm for massive MIMO system with imperfect channel knowledge

Millimeter wave MIMO system offers orders of magnitude high data rate due to the excess bandwidth available then conventional MIMO system. But, at the cost of excessive free space losses that highly influence the transmission at very high millimeter wave frequencies. The resulting small Wavelength at the millimeter wave frequency can overcome the path losses using beam forming gain offered by the massive antennas which is known as pre-coding. In millimeter wave massive MIMO system, hybrid pre-coding is the technique that combines analog pre-coding and digital pre-coding to reduce the requirement of high number of RF chains and thus energy consumption. Hybrid beam forming uses number of RF chains equal to the number of simulations users being served rather than using separate RF chains in the case of digital pre-coding. In designing analog and digital pre-coders, large number of calculations that uses complex mathematical process such as block diagonalization, SVD for channel matrix inversion required for the computation of pre-coder weight vector computation. In this paper, we propose low complexity hybrid pre-coding algorithm using simple linear approximation algorithms for matrix inversion operations. We first used the simple inversion algorithm in the computation of analog beam forming matrix without any SVD or direct inversion of matrices. Then, the same is being used in digital pre-coding matrix. In the proposed algorithm, there is no need for the complicated operations as SVD as in traditional pre coding algorithms.

Efficient HLS Implementation of Fast Linear Discriminant Analysis Classifier

Linear discriminant analysis(LDA) classification is widely used in the current field of machine learning and data mining. However, its computational complexity tends to cause high processing latency when implemented on Field Programmable Gate Array (FPGA), especially for high dimensional data. This letter proposes a method to reduce computational complexity, which uses principal component analysis (PCA) to obtain the most representative characteristics of the original data for projection. Instead of the original data, the dimension reduced data obtained by the projection will be used for classification. Moreover, when there is only one main characteristic value, not only the matrix inversion operation is avoided, but also a large number of matrix multiplication operations are simplified. The implementation of the classifier on FPGA is realized using High Level Synthesis(HLS), which can effectively save hardware development time. The results show that the method has an encouraging performance in reducing the execution time of the algorithm on FPGA, while the accuracy of the classifier can also be guaranteed.

The Threshold Optimization of the Canonical Piecewise Linear Function-Based Model With a Modified Quadratic SPSA

The canonical piecewise linear (CPWL) function-based model has been proposed for behavioral modeling of power amplifiers (PAs) because it can provide good modeling accuracy and low complexity. In the CPWL, thresholds are preselected as different constants, which are usually based on experience. The letter focuses on the threshold optimization of the CPWL, and a modified quadratic simultaneous perturbation stochastic approximation (SPSA) algorithm is employed to estimate the coefficients and optimize thresholds of the CPWL-based model. This method is more suitable for hardware implementation than the conventional least square (LS) by coefficient iterations rather than matrix inversion operations. Experimental results show that, compared with the LS, the proposed approach achieves comparable modeling and digital predistortion (DPD) performance of the CPWL-based model with fewer thresholds and coefficients after threshold optimization when a wideband PA is excited by a Long-Term Evolution (LTE)-Advanced signal of 100-MHz bandwidth.

A Low-Complexity Double EP-Based Detector for Iterative Detection and Decoding in MIMO

We propose a new iterative detection and decoding (IDD) algorithm for multiple-input multiple-output (MIMO) based on expectation propagation (EP) with application to massive MIMO scenarios. Two main results are presented. We first introduce EP to iteratively improve the Gaussian approximations of both the estimation of the posterior by the MIMO detector and the soft output of the channel decoder. With this novel approach, denoted by double-EP (DEP), the convergence is very much improved with a computational complexity just two times the one of the linear minimum mean square error (LMMSE) based IDD, as illustrated by the included experiments. Besides, as in the LMMSE MIMO detector, when the number of antennas increases, the computational cost of the matrix inversion operation required by the DEP becomes unaffordable. In this work we also develop approaches of DEP where the mean and the covariance matrix of the posterior are approximated by using the Gauss-Seidel and Neumann series methods, respectively. This low-complexity DEP detector has quadratic complexity in the number of antennas, as the low-complexity LMMSE techniques. Experimental results show that the new low-complexity DEP achieves the performance of the DEP as the ratio between the number of transmitting and receiving antennas decreases.

WITHDRAWN: Iterative SIC algorithm based detection for multiuser MIMO SC-FDMA uplink system

Abstract In this article, an iterative successive interference cancellation (SIC) method is investigated for uplink multiple input multiple output (MIMO) single carrier frequency division multiple access (SC-FDMA). The real challenge of wireless communication is reliable symbol detection in MIMO SC-FDMA system. An iterative SIC detection method is a prominent technique which acquires low complexity and near -optimal performance for MIMO systems. MIMO SC-FDMA system with renowned multiuser linear data estimation methods are minimum mean square error (MMSE) and zero forcing (ZF) which are frequently employed in single-input single- output detector scheme owing to its affordable estimation and noteworthy performance improvement. Nevertheless, this technique performs matrix inverse calculation whose matrix size related to set of subcarriers utilized in the scheme, generally, it has around thousands. In realistic scenario, matrix inversion operations turn to very high the computational complexity. Therefore, in this contribution proposes an iterative SIC algorithm which achieves near optimal performance with lower complexity. The performance of linear receiver scheme and iterative SIC algorithm is simulated for diverse antennas configuration in MIMO SC-FDMA systems. As a results illustrate that iterative SIC algorithm outperforms conventional linear detection techniques. The analysis of the new detection approach observes good performance and the reduced complexity detection in MIMO SC-FDMA systems.

Finite‐time distributed block‐decomposed information filter for nonlinear systems with colored measurement noise

AbstractThis paper considers the distributed filtering problem for discrete‐time nonlinear systems with colored measurement noise obeying a nonlinear autoregressive process in sensor networks. A novel block‐decomposed information‐type filter for such systems is proposed in a centralized fusion structure, by using the statistical linear regression to deal with model nonlinearities and the measurement difference approach to overcome the noise correlation caused by colored measurement noises. Meanwhile, with the help of block matrix inverse operation to realize the high‐dimensional block matrix decomposition, the information vector and information matrix of the original system state in the designed information filter is directly estimated recursively, so as to own good numerical stability. Then, the finite‐time distributed implementation of the proposed filter is put forward, where the final filtering estimate in each sensor node is consistent with the centralized filtering result, by ensuring that each sensor node directly obtains the average values of shared variables in the sensor network through finite iterations of average consensus. Finally, the posterior Cramér–Rao lower bound is derived to show the proposed filter reaches the optimal theoretical performance bound in the premise of statistical linear regression and Gaussian posterior probability density approximation. A target tracking example with colored measurement noise obeying a linear and a nonlinear autoregressive processes validates the proposed method.

Fast just-in-time-learning recursive multi-output LSSVR for quality prediction and control of multivariable dynamic systems

Aiming at quality prediction and control of blast furnace (BF) ironmaking process characterized by complicated nonlinear time-varying dynamics, this paper proposes a just-in-time-learning (JITL) recursive multi-output least squares support vector regression (JITL-R-M-LSSVR) algorithm with fast nonlinear local learning capability for multivariable dynamic systems. The proposed fast JITL-R-M-LSSVR effectively combines the online local learning of JITL with the multi-output LSSVR (M-LSSVR) based on multi-task transfer learning, and focuses on how to ensure the rapid verification of the local model during online learning of M-LSSVR, and how to perform model pruning while recursively updating the model parameters to improve the calculation efficiency. To this end, the proposed algorithm uses a derived multi-output incremental learning algorithm to recursively update model parameters online in a gentle way, which has better modeling stability and smoothness than the traditional way that discards old models. At the same time, when the model is pruned, a novel multi-output reverse decremental learning algorithm is proposed to adaptively delete the modeling data, so as to effectively control the sample size and reduces the calculation cost. In particular, the model verification of the proposed algorithm only needs to construct the M-LSSVR modeling matrix and the matrix inverse operation once, and the matrix after deleting each modeling sample can be easily obtained by reverse decremental learning of the original modeling matrix, which can achieve fast and efficient model verification. Finally, the effectiveness and practicability of the proposed method are verified by applying it to prediction modeling and predictive control of the molten iron quality in BF ironmaking process.

The ORLS-Based DoA Estimation for Unknown Mixtures of Uncorrelated and Coherent Signals Under Unknown Number of Sources

In this letter, the order recursive least squares (ORLS) is applied to the azimuth-only ULA to probe the DoA estimation under the unknown number of external sources. In the ORLS-based method, the iterative measured matrix equations are feasibly constructed by combining the two spatial modified Yule-Walker (MYW) systems of linear equations and are required to remain Hankel-block-matrix structure of augmented matrices after arrangement order of the unknowns and the maximum number of detectable sources are preset. Under the stationary assumption on source signals and noises, the remarkable advantage of the proposed method lies in that it can theoretically provide the zero LS error as iteration times is equal to the number of sources. The zero LS error is an evident mark to judge the number of sources, especially for the scenario of the unknown noise variances. The proposed method is free of uncorrelated and coherent signals and the corresponding various mixtures and remains computationally efficient in estimation owing to no eigenvalue decomposition (EVD) and matrix inversion operation. The effectiveness of the determination of the number and azimuth angles of sources versus the different SNRs and numbers of snapshots is numerically confirmed.

Inverse determination of multiple heat sources’ release history in indoor environments

The heat source of an air-conditioned room has an important effect on the indoor environment. The release rates of heat sources are related to the comfort of the designed thermal environment, so they must be determined. Traditional design methods rely on iterative guess-and-correct, which consumes resources and time and cannot meet the needs of modern design. This study aims to establish an inverse model of Tikhonov regularization and least square optimization by using computational fluid dynamics (CFD), so that researchers can accurately determine the time release rate of multiple heat sources with known parameters. The temporal release rates can then be solved based on the inverse matrix operation with the temperature series at different discrete times. The study speeds up the solving process and expresses the temperature as the convolution integral between the temperature response of the thermal response factor and the arbitrary release rate. The results show that applying the above method to the quantization of the temporal release rates of three heat sources in a three-dimensional cavity can correctly determine the temporal release rates of multiple heat sources. The errors between the inversely determined release rates and the actual release rates are less than 40%.

A mass-conservative predictor-corrector solution to the 1D Richards equation with adaptive time control

The predictor-corrector-type (P-C) numerical solution to the 1D Richards equation only requires one matrix inversion operation per time step, making it attractive in terms of computational cost. However, the mass conservation could be violated at the saturated-unsaturated interface. A new post-allocation procedure is designed for the P-C method, which redistributes moisture after the corrector step to achieve strict mass balance. A novel adaptive time-stepping strategy is proposed to further improve model efficiency and robustness. It adjusts time step size based on both moisture difference and the Courant number. The proposed solution method and time control strategies are tested and compared with an analytical solution, the previous P-C solution and other existing iterative solutions. The new method shows good conservation property and good agreements to the existing solutions. Compared to the iterative methods that occasionally experience convergence issues, the proposed P-C method is more robust. The new time-control strategy improves computational efficiency compared to the original P-C method, but it remains less efficient than iterative methods for most of the tested scenarios because of its explicit treatment of the corrector step.