Search results for: Calibration estimation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1199

Search results for: Calibration estimation

1199 Mathematical Programming on Multivariate Calibration Estimation in Stratified Sampling

Authors: Dinesh Rao, M.G.M. Khan, Sabiha Khan

Abstract:

Calibration estimation is a method of adjusting the original design weights to improve the survey estimates by using auxiliary information such as the known population total (or mean) of the auxiliary variables. A calibration estimator uses calibrated weights that are determined to minimize a given distance measure to the original design weights while satisfying a set of constraints related to the auxiliary information. In this paper, we propose a new multivariate calibration estimator for the population mean in the stratified sampling design, which incorporates information available for more than one auxiliary variable. The problem of determining the optimum calibrated weights is formulated as a Mathematical Programming Problem (MPP) that is solved using the Lagrange multiplier technique.

Keywords: Calibration estimation, Stratified sampling, Multivariate auxiliary information, Mathematical programming problem, Lagrange multiplier technique.

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1198 A Calibration Device for Force-Torque Sensors

Authors: Nicolay Zarutskiy, Roman Bulkin

Abstract:

The paper deals with the existing methods of force-torque sensor calibration with a number of components from one to six, analyzed their advantages and disadvantages, the necessity of introduction of a calibration method. Calibration method and its constructive realization are also described here. A calibration method allows performing automated force-torque sensor calibration both with selected components of the main vector of forces and moments and with complex loading. Thus, two main advantages of the proposed calibration method are achieved: the automation of the calibration process and universality.

Keywords: Automation, calibration, calibration device, calibration method, force-torque sensors.

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1197 Vehicle Velocity Estimation for Traffic Surveillance System

Authors: H. A. Rahim, U. U. Sheikh, R. B. Ahmad, A. S. M. Zain

Abstract:

This paper describes an algorithm to estimate realtime vehicle velocity using image processing technique from the known camera calibration parameters. The presented algorithm involves several main steps. First, the moving object is extracted by utilizing frame differencing technique. Second, the object tracking method is applied and the speed is estimated based on the displacement of the object-s centroid. Several assumptions are listed to simplify the transformation of 2D images from 3D real-world images. The results obtained from the experiment have been compared to the estimated ground truth. From this experiment, it exhibits that the proposed algorithm has achieved the velocity accuracy estimation of about ± 1.7 km/h.

Keywords: camera calibration, object tracking, velocity estimation, video image processing

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1196 Accuracy of Displacement Estimation and Selection of Capacitors for a Four Degrees of Freedom Capacitive Force Sensor

Authors: Chisato Murakami, Makoto Takahashi

Abstract:

Force sensor has been used as requisite for knowing information on the amount and the directions of forces on the skin surface. We have developed a four-degrees-of-freedom capacitive force sensor (approximately 20×20×5 mm3) that has a flexible structure and sixteen parallel plate capacitors. An iterative algorithm was developed for estimating four displacements from the sixteen capacitances using fourth-order polynomial approximation of characteristics between capacitance and displacement. The estimation results from measured capacitances had large error caused by deterioration of the characteristics. In this study, effective capacitors had major information were selected on the basis of the capacitance change range and the characteristic shape. Maximum errors in calibration and non-calibration points were 25%and 6.8%.However the maximum error was larger than desired value, the smallness of averaged value indicated the occurrence of a few large error points. On the other hand, error in non-calibration point was within desired value.

 

Keywords: Force sensors, capacitive sensors, estimation, iterative algorithms.

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1195 A Method of Planar-Template- Based Camera Self-Calibration for Single-View

Authors: Yue Zhao, Chao Li

Abstract:

Camera calibration is an important step in 3D reconstruction. Camera calibration may be classified into two major types: traditional calibration and self-calibration. However, a calibration method in using a checkerboard is intermediate between traditional calibration and self-calibration. A self is proposed based on a square in this paper. Only a square in the planar template, the camera self-calibration can be completed through the single view. The proposed algorithm is that the virtual circle and straight line are established by a square on planar template, and circular points, vanishing points in straight lines and the relation between them are be used, in order to obtain the image of the absolute conic (IAC) and establish the camera intrinsic parameters. To make the calibration template is simpler, as compared with the Zhang Zhengyou-s method. Through real experiments and experiments, the experimental results show that this algorithm is feasible and available, and has a certain precision and robustness.

Keywords: Absolute conic, camera calibration, circle point, vanishing point.

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1194 Dead-Reckoning Error Calibration using Celling Looking Vision Camera

Authors: Jae-Young Choi, Sung-Gaun Kim

Abstract:

This paper suggests a calibration method to reduce errors occurring due to mobile robot sliding during location estimation using the Dead-reckoning. Due to sliding of the mobile robot caused between its wheels and the road surface while on free run, location estimation can be erroneous. Sliding especially occurs during cornering of mobile robot. Therefore, in order to reduce these frequent sliding errors in cornering, we calibrated the mobile robot-s heading values using a vision camera and templates of the ceiling.

Keywords: Dead-reckoning, Localization, Odomerty, Vision Camera

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1193 Determining the Criteria and their Importance Level of Calibration Supplier Selection

Authors: Ayse Gecer, Nihal Erginel

Abstract:

Quality control is the crucial step for ISO 9001 Quality System Management Standard for companies. While measuring the quality level of both raw material and semi product/product, the calibration of the measuring device is an essential requirement. Calibration suppliers are in the service sector and therefore the calibration supplier selection is becoming a worthy topic for improving service quality. This study presents the results of a questionnaire about the selection criteria of a calibration supplier. The questionnaire was applied to 103 companies and the results are discussed in this paper. The analysis was made with MINITAB 14.0 statistical programs. “Competence of documentations" and “technical capability" are defined as the prerequisites because of the ISO/IEC17025:2005 standard. Also “warranties and complaint policy", “communication", “service features", “quality" and “performance history" are defined as very important criteria for calibration supplier selection.

Keywords: Calibration, criteria of calibration supplier selection, calibration supplier selection, questionnaire

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1192 Evaluation of Manual and Automatic Calibration Methods for Digital Tachographs

Authors: Sarp Erturk, Levent Eyigel, Cihat Celik, Muhammet Sahinoglu, Serdar Ay, Yasin Kaya, Hasan Kaya

Abstract:

This paper presents a quantitative analysis on the need for automotive calibration methods for digital tachographs. Digital tachographs are mandatory for vehicles used in people and goods transport and they are an important aspect for road safety and inspection. Digital tachographs need to be calibrated for workshops in order for the digital tachograph to display and record speed and odometer values correctly. Calibration of digital tachographs can be performed either manual or automatic. It is shown in this paper that manual calibration of digital tachographs is prone to errors and there can be differences between manual and automatic calibration parameters. Therefore automatic calibration methods are imperative for digital tachograph calibration. The presented experimental results and error analysis clearly support the claims of the paper by evaluating and statistically comparing manual and automatic calibration methods.

Keywords: Digital tachograph, road safety, tachograph calibration, tachograph workshops.

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1191 Calibration Method for an Augmented Reality System

Authors: S. Malek, N. Zenati-Henda, M. Belhocine, S. Benbelkacem

Abstract:

In geometrical camera calibration, the objective is to determine a set of camera parameters that describe the mapping between 3D references coordinates and 2D image coordinates. In this paper, a technique of calibration and tracking based on both a least squares method is presented and a correlation technique developed as part of an augmented reality system. This approach is fast and it can be used for a real time system

Keywords: Camera calibration, pinhole model, least squares method, augmented reality, strong calibration.

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1190 Robust Camera Calibration using Discrete Optimization

Authors: Stephan Rupp, Matthias Elter, Michael Breitung, Walter Zink, Christian Küblbeck

Abstract:

Camera calibration is an indispensable step for augmented reality or image guided applications where quantitative information should be derived from the images. Usually, a camera calibration is obtained by taking images of a special calibration object and extracting the image coordinates of projected calibration marks enabling the calculation of the projection from the 3d world coordinates to the 2d image coordinates. Thus such a procedure exhibits typical steps, including feature point localization in the acquired images, camera model fitting, correction of distortion introduced by the optics and finally an optimization of the model-s parameters. In this paper we propose to extend this list by further step concerning the identification of the optimal subset of images yielding the smallest overall calibration error. For this, we present a Monte Carlo based algorithm along with a deterministic extension that automatically determines the images yielding an optimal calibration. Finally, we present results proving that the calibration can be significantly improved by automated image selection.

Keywords: Camera Calibration, Discrete Optimization, Monte Carlo Method.

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1189 Calibration of Parallel Multi-View Cameras

Authors: M. Ali-Bey, N. Manamanni, S. Moughamir

Abstract:

This paper focuses on the calibration problem of a multi-view shooting system designed for the production of 3D content for auto-stereoscopic visualization. The considered multiview camera is characterized by coplanar and decentered image sensors regarding to the corresponding optical axis. Based on the Faugéras and Toscani-s calibration approach, a calibration method is herein proposed for the case of multi-view camera with parallel and decentered image sensors. At first, the geometrical model of the shooting system is recalled and some industrial prototypes with some shooting simulations are presented. Next, the development of the proposed calibration method is detailed. Finally, some simulation results are presented before ending with some conclusions about this work.

Keywords: Auto-stereoscopic display, camera calibration, multi-view cameras, visual servoing

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1188 Automatic Camera Calibration for Images of Soccer Match

Authors: Qihe Li, Yupin Luo

Abstract:

Camera calibration plays an important role in the domain of the analysis of sports video. Considering soccer video, in most cases, the cross-points can be used for calibration at the center of the soccer field are not sufficient, so this paper introduces a new automatic camera calibration algorithm focus on solving this problem by using the properties of images of the center circle, halfway line and a touch line. After the theoretical analysis, a practicable automatic algorithm is proposed. Very little information used though, results of experiments with both synthetic data and real data show that the algorithm is applicable.

Keywords: Absolute conic, camera calibration, circular points, line at infinity.

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1187 Research of Linear Camera Calibration Based on Planar Pattern

Authors: Jin Sun, Hongbin Gu

Abstract:

An important step in three-dimensional reconstruction and computer vision is camera calibration, whose objective is to estimate the intrinsic and extrinsic parameters of each camera. In this paper, two linear methods based on the different planes are given. In both methods, the general plane is used to replace the calibration object with very good precision. In the first method, after controlling the camera to undergo five times- translation movements and taking pictures of the orthogonal planes, a set of linear constraints of the camera intrinsic parameters is then derived by means of homography matrix. The second method is to get all camera parameters by taking only one picture of a given radius circle. experiments on simulated data and real images,indicate that our method is reasonable and is a good supplement to camera calibration.

Keywords: camera calibration, 3D reconstruction, computervision

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1186 The Hyperbolic Smoothing Approach for Automatic Calibration of Rainfall-Runoff Models

Authors: Adilson Elias Xavier, Otto Corrêa Rotunno Filho, Paulo Canedo de Magalhães

Abstract:

This paper addresses the issue of automatic parameter estimation in conceptual rainfall-runoff (CRR) models. Due to threshold structures commonly occurring in CRR models, the associated mathematical optimization problems have the significant characteristic of being strongly non-differentiable. In order to face this enormous task, the resolution method proposed adopts a smoothing strategy using a special C∞ differentiable class function. The final estimation solution is obtained by solving a sequence of differentiable subproblems which gradually approach the original conceptual problem. The use of this technique, called Hyperbolic Smoothing Method (HSM), makes possible the application of the most powerful minimization algorithms, and also allows for the main difficulties presented by the original CRR problem to be overcome. A set of computational experiments is presented for the purpose of illustrating both the reliability and the efficiency of the proposed approach.

Keywords: Rainfall-runoff models, optimization procedure, automatic parameter calibration, hyperbolic smoothing method.

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1185 A Novel Digital Calibration Technique for Gain and Offset Mismatch in TIΣΔ ADCs

Authors: Ali Beydoun, Van-Tam Nguyen, Patrick Loumeau

Abstract:

Time interleaved sigma-delta (TIΣΔ) architecture is a potential candidate for high bandwidth analog to digital converters (ADC) which remains a bottleneck for software and cognitive radio receivers. However, the performance of the TIΣΔ architecture is limited by the unavoidable gain and offset mismatches resulting from the manufacturing process. This paper presents a novel digital calibration method to compensate the gain and offset mismatch effect. The proposed method takes advantage of the reconstruction digital signal processing on each channel and requires only few logic components for implementation. The run time calibration is estimated to 10 and 15 clock cycles for offset cancellation and gain mismatch calibration respectively.

Keywords: sigma-delta, calibration, gain and offset mismatches, analog-to-digital conversion, time-interleaving.

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1184 On Best Estimation for Parameter Weibull Distribution

Authors: Hadeel Salim Alkutubi

Abstract:

The objective of this study is to introduce estimators to the parameters and survival function for Weibull distribution using three different methods, Maximum Likelihood estimation, Standard Bayes estimation and Modified Bayes estimation. We will then compared the three methods using simulation study to find the best one base on MPE and MSE.

Keywords: Maximum Likelihood estimation , Bayes estimation, Jeffery prior information, Simulation study

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1183 Uncertainty Propagation and Sensitivity Analysis During Calibration of an Integrated Land Use and Transport Model

Authors: Parikshit Dutta, Mathieu Saujot, Elise Arnaud, Benoit Lefevre, Emmanuel Prados

Abstract:

In this work, propagation of uncertainty during calibration process of TRANUS, an integrated land use and transport model (ILUTM), has been investigated. It has also been examined, through a sensitivity analysis, which input parameters affect the variation of the outputs the most. Moreover, a probabilistic verification methodology of calibration process, which equates the observed and calculated production, has been proposed. The model chosen as an application is the model of the city of Grenoble, France. For sensitivity analysis and uncertainty propagation, Monte Carlo method was employed, and a statistical hypothesis test was used for verification. The parameters of the induced demand function in TRANUS, were assumed as uncertain in the present case. It was found that, if during calibration, TRANUS converges, then with a high probability the calibration process is verified. Moreover, a weak correlation was found between the inputs and the outputs of the calibration process. The total effect of the inputs on outputs was investigated, and the output variation was found to be dictated by only a few input parameters.

Keywords: Uncertainty propagation, sensitivity analysis, calibration under uncertainty, hypothesis testing, integrated land use and transport models, TRANUS, Grenoble.

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1182 Frequency Estimation Using Analytic Signal via Wavelet Transform

Authors: Sudipta Majumdar, Akansha Singh

Abstract:

Frequency estimation of a sinusoid in white noise using maximum entropy power spectral estimation has been shown to be very sensitive to initial sinusoidal phase. This paper presents use of wavelet transform to find an analytic signal for frequency estimation using maximum entropy method (MEM) and compared the results with frequency estimation using analytic signal by Hilbert transform method and frequency estimation using real data together with MEM. The presented method shows the improved estimation precision and antinoise performance.

Keywords: Frequency estimation, analytic signal, maximum entropy method, wavelet transform.

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1181 X-Corner Detection for Camera Calibration Using Saddle Points

Authors: Abdulrahman S. Alturki, John S. Loomis

Abstract:

This paper discusses a corner detection algorithm for camera calibration. Calibration is a necessary step in many computer vision and image processing applications. Robust corner detection for an image of a checkerboard is required to determine intrinsic and extrinsic parameters. In this paper, an algorithm for fully automatic and robust X-corner detection is presented. Checkerboard corner points are automatically found in each image without user interaction or any prior information regarding the number of rows or columns. The approach represents each X-corner with a quadratic fitting function. Using the fact that the X-corners are saddle points, the coefficients in the fitting function are used to identify each corner location. The automation of this process greatly simplifies calibration. Our method is robust against noise and different camera orientations. Experimental analysis shows the accuracy of our method using actual images acquired at different camera locations and orientations.

Keywords: Camera Calibration, Corner Detector, Saddle Points, X-Corners.

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1180 Development of Perez-Du Mortier Calibration Algorithm for Ground-Based Aerosol Optical Depth Measurement with Validation using SMARTS Model

Authors: Jedol Dayou, Jackson Hian Wui Chang, Rubena Yusoff, Ag. Sufiyan Abd. Hamid, Fauziah Sulaiman, Justin Sentian

Abstract:

Aerosols are small particles suspended in air that have wide varying spatial and temporal distributions. The concentration of aerosol in total columnar atmosphere is normally measured using aerosol optical depth (AOD). In long-term monitoring stations, accurate AOD retrieval is often difficult due to the lack of frequent calibration. To overcome this problem, a near-sea-level Langley calibration algorithm is developed using the combination of clear-sky detection model and statistical filter. It attempts to produce a dataset that consists of only homogenous and stable atmospheric condition for the Langley calibration purposes. In this paper, a radiance-based validation method is performed to further investigate the feasibility and consistency of the proposed algorithm at different location, day, and time. The algorithm is validated using SMARTS model based n DNI value. The overall results confirmed that the proposed calibration algorithm feasible and consistent for measurements taken at different sites and weather conditions.

Keywords: Aerosol optical depth, direct normal irradiance, Langley calibration, radiance-based validation, SMARTS.

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1179 Influence of Temperature Variations on Calibrated Cameras

Authors: Peter Podbreznik, Božidar Potocnik

Abstract:

The camera parameters are changed due to temperature variations, which directly influence calibrated cameras accuracy. Robustness of calibration methods were measured and their accuracy was tested. An error ratio due to camera parameters change with respect to total error originated during calibration process was determined. It pointed out that influence of temperature variations decrease by increasing distance of observed objects from cameras.

Keywords: camera calibration, perspective projection matrix, epipolar geometry, temperature variation.

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1178 A Calibration Approach towards Reducing ASM2d Parameter Subsets in Phosphorus Removal Processes

Authors: N.Boontian

Abstract:

A novel calibration approach that aims to reduce ASM2d parameter subsets and decrease the model complexity is presented. This approach does not require high computational demand and reduces the number of modeling parameters required to achieve the ASMs calibration by employing a sensitivity and iteration methodology. Parameter sensitivity is a crucial factor and the iteration methodology enables refinement of the simulation parameter values. When completing the iteration process, parameters values are determined in descending order of their sensitivities. The number of iterations required is equal to the number of model parameters of the parameter significance ranking. This approach was used for the ASM2d model to the evaluated EBPR phosphorus removal and it was successful. Results of the simulation provide calibration parameters. These included YPAO, YPO4, YPHA, qPHA, qPP, μPAO, bPAO, bPP, bPHA, KPS, YA, μAUT, bAUT, KO2 AUT, and KNH4 AUT. Those parameters were corresponding to the experimental data available.

Keywords: ASM2d, calibration approach, iteration methodology, sensitivity, phosphorus removal

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1177 Bi-Lateral Comparison between NIS-Egypt and NMISA-South Africa for the Calibration of an Optical Time Domain Reflectometer

Authors: Osama Terra, Mariesa Nel, Hatem Hussein

Abstract:

Calibration of Optical Time Domain Reflectometer (OTDR) has a crucial role for the accurate determination of fault locations and the accurate calculation of loss budget of long-haul optical fibre links during installation and repair. A comparison has been made between the Egyptian National Institute for Standards (NIS-Egypt) and the National Metrology institute of South Africa (NMISA-South Africa) for the calibration of an OTDR. The distance and the attenuation scales of a transfer OTDR have been calibrated by both institutes using their standards according to the standard IEC 61746-1 (2009). The results of this comparison have been compiled in this report.

Keywords: OTDR calibration, recirculating loop, concatenated method, standard fibre.

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1176 Bi-Lateral Comparison between NIS-Egypt and NMISA-South Africa for the Calibration of an Optical Spectrum Analyzer

Authors: Osama Terra, Hatem Hussein, Adriaan Van Brakel

Abstract:

Dense wavelength division multiplexing (DWDM) technology requires tight specification and therefore measurement of wavelength accuracy and stability of the telecommunication lasers. Thus, calibration of the used Optical Spectrum Analyzers (OSAs) that are used to measure wavelength is of a great importance. Proficiency testing must be performed on such measuring activity to insure the accuracy of the measurement results. In this paper, a new comparison scheme is introduced to test the performance of such calibrations. This comparison scheme is implemented between NIS-Egypt and NMISA-South Africa for the calibration of the wavelength scale of an OSA. Both institutes employ reference gas cell to calibrate OSA according to the standard IEC/ BS EN 62129 (2006). The result of this comparison is compiled in this paper.

Keywords: OSA calibration, HCN gas cell, DWDM technology, wavelength measurement.

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1175 Fast Wavelength Calibration Algorithm for Optical Spectrum Analyzers

Authors: Thomas Fuhrmann

Abstract:

In this paper an algorithm for fast wavelength calibration of Optical Spectrum Analyzers (OSAs) using low power reference gas spectra is proposed. In existing OSAs a reference spectrum with low noise for precise detection of the reference extreme values is needed. To generate this spectrum costly hardware with high optical power is necessary. With this new wavelength calibration algorithm it is possible to use a noisy reference spectrum and therefore hardware costs can be cut. With this algorithm the reference spectrum is filtered and the key information is extracted by segmenting and finding the local minima and maxima. Afterwards slope and offset of a linear correction function for best matching the measured and theoretical spectra are found by correlating the measured with the stored minima. With this algorithm a reliable wavelength referencing of an OSA can be implemented on a microcontroller with a calculation time of less than one second.

Keywords: correlation, gas reference, optical spectrum analyzer, wavelength calibration

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1174 Identifying the Kinematic Parameters of Hexapod Machine Tool

Authors: M. M. Agheli, M. J. Nategh

Abstract:

Hexapod Machine Tool (HMT) is a parallel robot mostly based on Stewart platform. Identification of kinematic parameters of HMT is an important step of calibration procedure. In this paper an algorithm is presented for identifying the kinematic parameters of HMT using inverse kinematics error model. Based on this algorithm, the calibration procedure is simulated. Measurement configurations with maximum observability are decided as the first step of this algorithm for a robust calibration. The errors occurring in various configurations are illustrated graphically. It has been shown that the boundaries of the workspace should be searched for the maximum observability of errors. The importance of using configurations with sufficient observability in calibrating hexapod machine tools is verified by trial calibration with two different groups of randomly selected configurations. One group is selected to have sufficient observability and the other is in disregard of the observability criterion. Simulation results confirm the validity of the proposed identification algorithm.

Keywords: Calibration, Hexapod Machine Tool (HMT), InverseKinematics Error Model, Observability, Parallel Robot, ParameterIdentification.

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1173 Distance Estimation for Radar Systems Using DS-UWB Signals

Authors: Youngpo Lee, Seokho Yoon

Abstract:

In this paper, we propose a distance estimation scheme for radar systems using direct sequence ultra wideband (DS-UWB) signals. The proposed distance estimation scheme averages out the noise by accumulating the correlator outputs of the radar, and thus, helps the radar to employ a short-length DS-UWB signal reducing the correlation processing time. Numerical results confirm that the proposed distance estimation scheme provides a better estimation performance and a reduced correlation processing time compared with those of the conventional DS-UWB radars.

Keywords: Radar, DS-UWB, distance estimation, correlation accumulation.

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1172 Method of Parameter Calibration for Error Term in Stochastic User Equilibrium Traffic Assignment Model

Authors: Xiang Zhang, David Rey, S. Travis Waller

Abstract:

Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Keywords: Parameter calibration, sequential quadratic programming, Stochastic User Equilibrium, traffic assignment, transportation planning.

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1171 A Novel Frequency Offset Estimation Scheme for OFDM Systems

Authors: Youngpo Lee, Seokho Yoon

Abstract:

In this paper, we propose a novel frequency offset estimation scheme for orthogonal frequency division multiplexing (OFDM) systems. By correlating the OFDM signals within the coherence phase bandwidth and employing a threshold in the frequency offset estimation process, the proposed scheme is not only robust to the timing offset but also has a reduced complexity compared with that of the conventional scheme. Moreover, a timing offset estimation scheme is also proposed as the next stage of the proposed frequency offset estimation. Numerical results show that the proposed scheme can estimate frequency offset with lower computational complexity and does not require additional memory while maintaining the same level of estimation performance.

Keywords: OFDM, frequency offset estimation, threshold.

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1170 An Estimation of Variance Components in Linear Mixed Model

Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ2 of the original model is equal to the least-squares estimation (LSE) about σ2 of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree.

Keywords: Linear mixed model, Random effects, Parameter estimation, Stein function.

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