In this paper, an improvement to the mid-point method is contributed for finding the square root of a matrix as well as its inverse. To this aim, an iteration scheme to find this matrix function is constructed, and its error and stability estimates a...
This paper develops and analyzes new high-order iterative schemes for the effective evaluation of the matrix square root (MSR). By leveraging connections between the matrix sign function and the MSR, we design stable algorithms that exhibit fourth-or...
This paper develops a new rational fixed-point iteration for
In this paper, we propose a high accuracy fingerprint-based localization scheme for the Internet of Things (IoT). The proposed scheme employs mathematical concepts based on sparse representation and matrix completion theories. Specifically, the propo...
Motivated by the close relationship between the matrix square root and the matrix sign function, this paper develops a new high-order iterative framework for computing the principal square root of a matrix and its inverse. The proposed approach is de...
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Padé approximation, sometimes accompanied by the Schur decomposition. In this work, we present a Taylor serie...
In quantum information science, it is very important to solve the eigenvalue problem of the Gram matrix for quantum signals. This allows various quantities to be calculated, such as the error probability, mutual information, channel capacity, and the...
The article examines the results of testing a series of samples, where the joint operation of wooden elements is ensured by a composite material based on fiberglass. A method for ensuring joint operation is adopted according to the insert scheme on t...
The research focuses on connections of wooden structural elements with composite materials based on fiberglass. An overview of existing research and regulatory technical documents in the field of connections between wooden elements and composite mate...
Accurate state of charge (SOC) estimation is helpful for battery management systems to extend batteries’ lifespan and ensure the safety of batteries. However, due to the pseudo-positive definiteness of the covariance matrix and noise statistics...
In this paper, we study the asymptotic and transient dynamics of a predator–prey model with square root functional responses and random perturbation. Firstly, the mean square stability matrix is obtained from the stability theory of stochastic...
In this paper, we focus on the asymptotic and transient dynamics of the studied ecosystem and measure the response to perturbation of the stochastic ratio-dependent predator–prey model. The method we use is mainly based on the Kronecker product and n...
Simultaneous Localization and Mapping (SLAM) is an effective method for estimating and correcting the pose of the mobile robot. However, a large amount of external noise and observed outliers in complex unknown environments often lead to a decrease i...
To address the problem of low accuracy for the regular filter algorithm in SINS/DVL integrated navigation, a square-root unscented information filter (SR-UIF) is presented in this paper. The proposed method: (1) adopts the state probability approxima...
The stress and deformation sensitivity analysis of high earth-rock dams requires knowledge of the statistical mean and standard deviation of deformation parameters of dam materials. However, these parameters are typically determined through grouped t...
This paper focuses on an improved square root unscented Kalman filter (SRUKF) and its application for rotor speed and position estimation of permanent magnet synchronous motor (PMSM). The approach, which combines the SRUKF and strong tracking filter,...
Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscent...
Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal nov...
State of charge (SOC) is a key parameter for lithium-ion battery management systems. The square root cubature Kalman filter (SRCKF) algorithm has been developed to estimate the SOC of batteries. SRCKF calculates 2n points that have the same weights a...
In the process of the attitude measurement for a steering drilling system, the measurement of the attitude parameters may be uncertain and unpredictable due to the influence of server vibration on bits. In order to eliminate the interference caused b...
This paper proposes an efficient and practical implementation of the Maximum Likelihood Ensemble Filter via a Modified Cholesky decomposition (MLEF-MC). The method works as follows: via an ensemble of model realizations, a well-conditioned and full-r...
The accuracy of X-ray fluorescence spectrometry in quantitative element analysis depends on the particular sample composition (so-called matrix effects). Counteracting these effects requires a large number of calibration samples similar in compositio...
In this paper, we investigate the possibility of recognizing a superposition of wave aberrations from a focal pattern based on a matrix of partial sums. Due to the peculiarities of the focal pattern, some types of the considered superpositions are re...
This paper deals with the problem of multi-target tracking in a distributed camera network using the square-root cubature information filter (SCIF). SCIF is an efficient and robust nonlinear filter for multi-sensor data fusion. In camera networks, mu...
On resource-constrained edge hardware, fixed-point Transformer inference is constrained by GEMM kernels and non-GEMM normalization paths. In LayerNorm and Softmax, division, inverse square root, and denominator reciprocal operations complicate fixed-...
In this work, we obtain a new formula for Fibonacci’s family m-step sequences. We use our formula to find the nth term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recur...
To improve the current indoor positioning algorithms, which have insufficient positioning accuracy, an ultra-wideband (UWB) positioning algorithm based on the Levenberg–Marquardt algorithm with improved Kalman filtering is proposed. An alternat...
Aperture space telescopes are widely used in space debris size information detection and celestial body detection work. For the problem of limited space inside the optical system of large aperture telescopes, a space telescope mounting method based o...
Compressed sensing (CS) is being widely used to compress and reconstruct data for processing electrocardiogram (ECG) signals obtained through Wireless Body Area Networks. However, the conventional measurement matrix generator and compression computat...
This paper focuses on the tracking problem of multiple targets with multiple sensors in a nonlinear cluttered environment. To avoid Jacobian matrix computation and scaling parameter adjustment, improve numerical stability, and acquire more accurate e...
The distinctive quality of Sichuan south-road dark tea (SSDT) is gradually disappearing with processing innovation. Here, near-infrared (NIR) spectroscopy (NIRS) and spectrofluorometric techniques were utilized to determine the spectral characteristi...
In zinc smelting solution, because the concentration of zinc is too high, the spectral signals of trace copper are masked by the spectral signals of zinc, and their spectral signals overlap, which makes it difficult to detect the concentration of tra...
This paper investigates the problem of source localization using signal time-of-arrival (TOA) measurements in the presence of unknown start transmission time. Most state-of-art methods are based on convex relaxation technologies, which possess global...
We report a theoretical derivation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing...
IMU preintegration technology has been widely used in the optimization-based sensor fusion framework, in order to avoid reintegrating the high-frequency IMU measurements at each iteration and maintain the ability of bias correction when bias estimati...
In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modifi...
We report on the fabrication of shellac thin films on silicon substrates by matrix-assisted pulsed laser evaporation (MAPLE) using methanol as matrix. Very adherent, dense, and smooth films were obtained by MAPLE with optimized deposition parameters,...
In flat spacetime, the Dirac equation is the “square root” of the Klein–Gordon equation in the sense that, by applying the square of the Dirac operator to the Dirac spinor, one recovers the equation duplicated for each component of...
The observational covariance matrix, whose diagonal square root is currently named radiometric noise, is one of the most important elements to characterize a given instrument. It determines the precision of measurements and their possible spectral in...
Dynamic information such as the position and velocity of the target detected by marine radar is frequently susceptible to external measurement white noise generated by the oscillations of an unmanned surface vehicle (USV) and target. Although the Sag...
This paper studies a nonnegative square-root diffusion subject to finite-activity multiplicative jumps whose multipliers follow a Gamma distribution. The analysis develops the mathematical foundation that is needed before moment calculations can be u...
This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structur...
A space-time variational method is developed for retrieving upper-level vortex winds from geostationary satellite rapid infrared scans over hurricanes. In this method, new vortex-flow-dependent correlation functions are formulated for the radial and...
The Brazilian Northeast (BNE) is located in the tropical region of Brazil. It is bounded by the Atlantic Ocean, and its climate and vegetation are strongly affected by continental plateaus. The plateaus keep the humid air masses to the east and are r...
Hyperspectral pansharpening is an effective technique to obtain a high spatial resolution hyperspectral (HS) image. In this paper, a new hyperspectral pansharpening algorithm based on homomorphic filtering and weighted tensor matrix (HFWT) is propose...
To model multivariate, possibly heavy-tailed data, we compare the multivariate normal model (N) with two versions of the multivariate Student model: the independent multivariate Student (IT) and the uncorrelated multivariate Student (UT). After recal...
This paper focuses on the coupling relationships between the optical constants (n: refractive index; k: extinction coefficient) and Mueller matrix elements, as well as between the morphological parameters (σ: root mean square roughness; τ:...
This paper proposes a robust navigation method based on a robust square-root cubature Kalman filter (RSRCKF) to address the accuracy divergence of integrated navigation systems caused by drilling-induced slippage and the mismatch between the tail-cab...
In real estate valuation using the Hedonic Price Model (HPM) estimated via Ordinary Least Squares (OLS) regression, subjectivity and measurement errors in the independent variables violate the Gauss–Markov theorem assumption of a non-random coe...
Precision positioning in orchards relies on Global Navigation Satellite System and Inertial Navigation System (GNSS/INS) integration. However, dense foliage often causes GNSS blockages, degrading accuracy and robustness. This paper proposes an optimi...
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