Fast Phased Array Calibration Method Based on Multiple Measuring Probes

<p>Autonomous driving has spurred the development of sensor fusion techniques, which combine data from multiple sensors to improve system performance. In particular, a localization system based on sensor fusion, such as Visual Simultaneous Localization and Mapping (VSLAM), plays a crucial role in environment perception and serves as the foundation for decision-making and motion control in intelligent vehicles. The accuracy of extrinsic calibration parameters between the camera and IMU is of utmost importance for precise positioning in VSLAM systems. However, existing calibration methods are often time-consuming, rely on complex optimization techniques, and are sensitive to noise and outliers, leading to potential degradation in system performance. To address these challenges, this paper presents a fast and accurate camera-IMU calibration method based on space coordinate transformation constraints and SVD (Singular Value Decomposition) tricks. The method involves constructing constraint equations by ensuring the equality of rotation and transformation matrices between camera frames and IMU coordinates at different time instances. Subsequently, the external parameters of the camera-IMU system are solved using quaternion transformation and SVD techniques. To validate the proposed method, experiments were conducted using the ROS (Robot Operating System) platform, where camera images and velocity, acceleration, and angular velocity data from the IMU were recorded in a ROS bag file. The results demonstrate that the proposed method achieves reliable camera-IMU calibration parameters, requiring less tuning time and exhibiting reduced uncertainty.</p>

The traditional hand-eye calibration needs to take the calibration target image acquired by the vision system and the corresponding robot pose information as input, the process is complicated, and there is a risk of calibration failure when the data are not corresponding. To solve these problems, a fast hand-eye calibration method is proposed. According to the principle that a certain point in space has the same three-dimensional (3D) coordinates in its coordinate system after the motion of the coordinate system, to control the end of the robot to carry out multiple translation and rotational motion, the traditional hand-eye calibration model AX=XB is simplified into AX=B. The hand-eye calibration matrix can be quickly solved only by the transformation between the camera coordinate system and the calibration target coordinate system. The experimental results show that the proposed method is simple, fast and high accuracy. It can be applied to eye-in-hand system and eye-to-hand system.

This paper presents a fast background digital calibration method for pipelined analog-to-digital converters (ADCs) that is robust and converges fast. To avoid the problem of input signal amplitude limitation, the proposed calibration technique takes advantage of the digital redundancy architecture by injecting pseudo-random noise (PN) in the sub-ADC. A split ADC architecture combined with a switch array control unit is also proposed to minimize the correlation between the input signal and the injecting PN signal. Simulation result shows, when the capacitor error is 0.1%, and the gain error between the two channel is 1%, the calibration time is about 217 samples simulated with 15-bit accuracy with a 0.32/−0.33 LSB DNL and a 0.50/−0.24 LSB INL, and the SNDR is 91.5 dB, the SFDR is 110.3 dB.

We have developed a fast detector calibration method, which is capable of calibration of monolithic crystal detectors fast and conveniently. This method could potentially be used to achieve the DOI calibration information of a thick detector. Compared with traditional calibration method, this calibration technique doesnt require a well-collimated pencil beams, and can calibrate a detector in reduced time with fan beams. After the collection of the calibration reference dataset, we propose a data-processing method called common-data subset (CDS) method to acquire the reference datasets as if they were acquired using a pencil beam or even as if there is a single-point light source scanning inside the scintillator. If using fan beams, only 2N scans (in x and y directions) are necessary to calibrate the whole detector surface instead of doing N2 scans using pencil gamma-ray beam. For calibration of the DOI information, 3N scans are necessary, within which the last set of N scans are done with slant beams. Monte-Carlo simulation has been done to support the feasibility of this method, which enables simple, fast and robust calibration for monolithic crystal detectors.

The issue of this paper is a fast and robust online calibration method for a multi laser tracking system (MLTS). The MLTS is able to track the movement of a retro-reflector that can be mounted on an arbitrary target. After introducing the MLTS and its functionality, the algorithm based on trilateration is depicted. The key issues applying the trilateration are varying parameters, which are dependent on the initial position of the target. In order to solve this problem a fast and robust calibration algorithm is proposed. The applied optimization algorithm, a Gauss-Newton approach, is explained, implemented and tested on a real time control system. After describing the calibration process the MLTS is explored by reference to measurements. The results are discussed and affecting factors are stated.

Free vibration analysis of cylindrical shells using the Haar wavelet method

The near-field calibration can be performed indoors, avoiding to be affected by the environment and security concerns which makes it has important research value. Nevertheless, the application is limited by the calibration efficiency and precision. A near-field calibration method based on code division multiple-access (CDMA) scheme is proposed in this paper to decrease calibration time and improve the calibration precision. In the proposed method, the calibrating signal associated with each antenna is distinguished by a unique spread-spectrum code sequence instead of the continuous wave (CW). The relationship between calibration accuracy and signal to noise ratio (SNR) is obtained by derivation, and the simulation results verify the correctness of theoretical derivation results. If the SNR is higher than 15dB, the calibration accuracy of the amplitude/phase can reach 0.1 decibel (dB) and 1 degree (deg), respectively. The proposed method can be good applied to the large-scale phased array antennas calibration.

This paper is concerned with the solution of ill-conditioned Systems of Linear Equations (SLE's) via the solution of equivalent SLE's which are well-conditioned. A matrix is first constructed from that of the given ill-conditioned system. Then, an adequate right-hand side is computed to make up the instance of an equivalent system. Formulae and algorithms for computing an instance of this equivalent SLE and solving it will be given and illustrated. © 2011 The Korean Mathematical Society.

In the traditional observability analysis methods, only current and a few historical measurement values are considered. For the linear systems, the satisfactory analysis results can be obtained. However, for the nonlinear systems, the analysis results are not completely in accordance with the navigation errors since the high-order nonlinearity of the navigation system is not embodied on the observability matrix. In order to solve this problem, a fractional differentiation-based observability analysis method is developed. Considering the fact that the fractional differentiation with respect to time is characterized by long-term memory effects, the fractional derivative of the measurement model with respect to time is considered. By this means, more historical measurement data can be exploited. And then the fractional differentiation-based observability matrix, which reflects the high-order nonlinearity of the navigation system, is constructed. Finally, as the condition number is not directly proportional to the positioning error, to evaluate the navigation performance, the exponent weighted condition number is developed, where small condition numbers have large weight. The simulation results demonstrate that the fractional differentiation-based observability analysis method is sensitive to the orbital elements in the nonlinear X-ray pulsar navigation system, and has small calculation load. In addition, compared to the traditional observability analysis methods, it is observed that its analysis result matches well with the X-ray pulsar navigation performance.

We propose a fast and robust method for calibrating Spatial Light Modulators (SLMs) based on polarization phase-shifting interferometry. Our method effectively calibrates the SLM by addressing both the static aberration and nonlinear phase response, utilizing specially designed gray images loaded sequentially onto the SLM. Notably, we introduce a novel kinoform that effectively eliminates the influence of tilt phase shift between two shots of the polarization camera. This results in a highly accurate phase aberration map and phase modulation curve with exceptional stability, making it an ideal method to calibrate the SLM with exceptional efficiency and precision in real applications.

This paper aims to provide an insight on the mechanism for the fast convergence of multigrid (MG) V-cycle algorithms. With this goal, the Fourier transform analysis is implemented to compute quantitatively the frequency spectrum of components of the residual resulted from the MG iterations. MG method has been extensively employed to solve large-scale systems of algebraic equations. Hence, one needs to understand its fast convergence property and scalability mechanism before applying MG method to a system equation, which affects the computational efficiency directly. In a first step, a number of novel features of the MG algorithm are studied, including the relationships among the iteration numbers needed for converged solutions, condition number of the system matrix and the grid-spacing in this paper. In a second step, the complexity of the MG method is researched, and various numerical experiments have been conducted in solving algebraic equations of models in finite element method for both heat transfer problems and solid mechanics problems. It is found that if the number of iterations in different grids is fixed, the optimal iteration mode is determined according to the attenuation of the high-frequency and low-frequency components of the residual. Our results also show that the complexity of the MG method is close to [Formula: see text], meaning that it is a close-to-linear scalable solver, which echoes the findings given by other literature. This study has revealed an important insight that the linear scalability is achieved by mitigating the negative effects (stagnation in convergence) of the large condition number of the system matrix created on the finest grid, using a sequence of coarser grids with smaller and smaller condition numbers.

Camera calibration is a prerequisite for spatial position measurement. The fish-eye camera can increase the field of view, but at the same time, the distortion it brings is more serious. It is difficult to obtain high accuracy when using traditional methods to calibrate the fish-eye camera. Therefore, this paper proposes a fast calibration method for fisheye cameras, which makes the calibration process convenient and fast, and improves the calibration accuracy. The camera is fixed on a high-precision two-dimensional turntable, and the turntable rotates according to the set law through a fully automatic program. At the same time, the camera captures the bright spots in the collimator and extracts the pixel coordinates of its centroid. Collect several sets of data, use the bicubic interpolation method to expand the data, find the relationship between the pixel coordinates of the centroid of the bright spot and the rotation angle of the turntable. Finally, the three-dimensional space coordinates can be obtained by binocular vision triangulation to verify the calibration accuracy. The above method bypasses the traditional camera optical imaging model and distortion model, but uses traversal and interpolation. Experiments show that the accuracy of this method can reach the centimeter level in long-distance, large field of view, and severely distorted scenes.

High precision calibration is a key procedure to ensure image measurement system has accuracy measurement results. In the micro-domain applications, such as IC packaging, optical microscopes form a critical component. Although many calibration techniques exist for macroscopic camera-lens system, there is a dearth of literature on optical microscope calibration. Optical microscope calibration has unique characteristics that are quite different from normal camera calibration, including (1) unique calibration parameters; (2) calibration patterns that must be parallel to the image plane, and (3) restriction to single-plane calibration. In this paper, a fast calibration method based on linear relations between the digital image coordinate system and the calibration sample coordinate system is proposed for optical microscopes. We select 2-D dot array calibration plate which where etched on a glass plate as calibration sample. Experiments have been performed and calibration errors have been analyzed.

Since it is well-known that the Vandermonde matrix is ill-conditioned, this paper surveys the choices of other bases. These bases are data-dependent and are categorized into discretely $ell^2$-orthonormal and continuously $L^2$-orthonormal bases. The first one is defined via a decomposition of the Vandermonde matrix while the latter is given by a decomposition of the Gramian matrix corresponding to monomial bases. A discussion of various matrix decomposition (e.g. Cholesky, QR and SVD) provides a variety of different bases with different properties. Special attention is given to duality. Numerical results show that the matrices of values of the new bases have smaller condition numbers than the common monomial bases. It can also be pointed out that the new introduced bases are good candidates for interpolation.

In this paper, we develop an h-p version of finite element method for one-dimensional fractional differential equation $-_{0}D_{x}^{\alpha }u+Au=f(x)$ with Dirichlet boundary condition. First, we introduce the existence and uniqueness of the considered problem and show the wellposedness of the corresponding weak form. To solve the mentioned equation, the classical hierarchical polynomials are employed as the trial basis functions. Then, we develop a kind of novel test basis functions for the Petrov-Galerkin finite element method such that the stiffness matrix becomes an identity matrix and the coefficient matrix often has a small condition number. Moreover, we give some properties of the developed test basis functions, and discuss the implementation of the developed finite element method in detail. It is shown that the implementation of our method is easier than that of other finite (and spectral) element methods. Finally, we give a numerical example, and the numerical results show the effectiveness of the develped method.