Scale Factor Correction Research Articles

Effect of backscattering on nonlinear distortions of the scale factor of a laser gyro with a rectangular bias

We report the results of measurements of nonlinear scale factor corrections, resulting from the backscattering effect in a laser gyro with a rectangular bias. It is shown that taking conservative and dissipative backscattering components into account allows one to obtain analytical relationships that adequately describe the frequency response of a laser gyroscope over the entire working range of angular velocities. Using these relationships to correct the frequency response of a laser gyroscope makes it possible to reduce the value of nonlinear corrections to 1 – 2 ppm.

Stability of the Calibration of Scintrex Relative Gravimeters as Inferred from 12 Years of Measurements on a Large Amplitude Calibration Line in Iran

In spite of the large stability of the fused quartz elastic system, which is utilized in modern relative gravimeters such as Scintrex CG-5, precise gravity measurements need regular calibration mostly because of weak changes in time of the elastic properties of the spring. Calibration of the relative gravimeters is important to avoid the systematic error of scale in relevant observations. In this study, due to the establishment of a large amplitude (of about 1200 mGal) calibration line in Iran, the stability of three CG-3 M and three CG-5 gravimeters has been continuously investigated based on the results of a 12 year (2005–2017) observations. The absolute gravity values at calibration stations were measured during the period 2005–2007 and more recently in 2017–2018 (for most of the stations) with absolute FG5 gravimeters. The results show that the Scintrex gravimeters exhibit different behaviors on the calibration line. The accuracy of determining the calibration coefficient of the gravimeters was better than 40 ppm. According to our results there is no effect of the gravity amplitude itself on the calibration factors. CG-5 #83 and CG-5 #87 have the largest changes in calibration factor (more than 1000 ppm) over the 12 year observation period while CG-3 M #20 and CG-3 M #60 have the smallest range (less than 200 ppm). The misclosure of relative gravity measurements in the first-order gravity network of Iran has been calculated before and after calibration corrections and it is shown that applying the scale factor correction reduced significantly the misclosures on the gravity network.

Low-cost IMU and odometer tightly coupled integration with Robust Kalman filter for underground 3-D pipeline mapping

Abstract A low-cost IMU and odometer integration system is developed in this paper for underground pipeline mapping. A tightly coupled integration between IMU and odometer is implemented to decrease the error caused by the odometer installation attitude error and scale factor error. Besides this, a novel approach to this application of using a Robust Kalman filter is developed to remove the effect of odometer measurement outliers due to the wheel-slip. Compared with the loosely coupled integration method, the use of loosely coupled integration with scale factor correction, tightly coupled integration and tightly coupled with Robust Kalman filter provide a horizontal position improvement of 11%, 41% and 43%, respectively. Similarly, the height accuracy is improved by 14%, 50% and 57%. Moreover, after applying the Robust Kalman filter, the positioning error caused by wheel-slip is reduced to 0.61 m in the horizontal plan, and 0.11 m in the height.

Cell Averaging CFAR Detector with Scale Factor Correction through the Method of Moments for the Log-Normal Distribution

Se presenta el nuevo detector LN-MoM-CA-CFAR que tiene una desviación reducida en la tasa de probabilidad de falsa alarma operacional con respecto al valor concebido de diseño. La solución corrige un problema fundamental de los procesadores CFAR que ha sido ignorado en múltiples desarrollos. En efecto, la mayoría de los esquemas previamente propuestos tratan con los cambios bruscos del nivel del clutter mientras que la presente solución corrige los cambios lentos estadísticos de la señal de fondo. Se ha demostrado que estos tienen una influencia marcada en la selección del factor de ajuste multiplicativo CFAR, y consecuentemente en el mantenimiento de la probabilidad de falsa alarma. Los autores aprovecharon la alta precisión que se alcanza en la estimación del parámetro de forma Log-Normal con el MoM, y la amplia aplicación de esta distribución en la modelación del clutter, para crear una arquitectura que ofrece resultados precisos y con bajo costo computacional. Luego de un procesamiento intensivo de 100 millones de muestras Log-Normal, se creó un esquema que, mejorando el desempeño del clásico CA-CFAR a través de la corrección continua de su factor de ajuste, opera con una excelente estabilidad alcanzando una desviación de solamente 0,2884 % para la probabilidad de falsa alarma de 0,01.

Scale factor correction for Gaussian beam truncation in second moment beam radius measurements

Charged-couple devices (CCD) and complementary metal oxide semiconductor (CMOS) image sensors, in conjunction with the second moment radius analysis method, are effective tools for determining the radius of a laser beam. However, the second moment method heavily weights sensor noise, which must be dealt with using a thresholding algorithm and a software aperture. While these noise reduction methods lower the random error due to noise, they simultaneously generate systematic error by truncating the Gaussian beam’s edges. A scale factor that is invariant to beam ellipticity and corrects for the truncation of the Gaussian beam due to thresholding and the software aperture has been derived. In particular, simulations showed an order of magnitude reduction in measured beam radius error when using the scale factor—irrespective of beam ellipticity—and further testing with real beam data demonstrated that radii corrected by the scale factor are independent of the noise reduction parameters. Thus, through use of the scale factor, the accuracy of beam radius measurements made with a CCD or CMOS sensor and the second moment are significantly improved.

A process to graphically demonstrate distance errors associated with local ground-based coordinate systems

This paper describes an empirical process for graphically illustrating, using any particular distance accuracy specification, boundaries where significant errors could be introduced in derived ground distances as a result of using local ground-based coordinate systems. The process involves selecting three-dimensional points across the project site, replacing their heights with combined scale factor corrections, and creating contours to represent potential distance errors. The resultant contour map shows potential distance errors in parts per million for comparison with accuracy specifications. The effectiveness will depend on the spacing of the selected points and the topography of the project site, but on most projects today closely spaced three dimensional points are readily available. The benefits were demonstrated on an example site, with the conclusion that the process is robust and effective, and will have applications on many large scale construction sites, residential estates, and other surveys where local ground-based coordinate systems may be used.

Scale factor characteristics of laser gyroscopes of different sizes.

The scale factor correction characteristics of two ring laser gyroscopes of different sizes are investigated systematically in this paper. The variation in the scale factor can reach 144 or 70 ppm for square gyroscopes with arm lengths of 8.4 cm or 15.6 cm, respectively, during frequency tuning. A dip in the scale factor is observed at the line center of the gain characteristic for both gyroscope sizes. When a different longitudinal mode is excited, the scale factor behavior remains the same, but the scale factor values differ slightly from those derived from geometric prediction. The scale factor tends to decrease with increasing discharge current, but the sensitivity of the scale factor to variations in the excitation decreases with increasing discharge current.

Odometer Module for Mobile Robot with Position Error Estimation

Abstract: In this article, an odometry module for a mobile robot with probabilistic position estimation is proposed. The localization processing is based on Extended Kalman Filter (EKF) from which only prediction phase is used. This configuration is prepared for a possible later extension with Global navigation satellite system (GNSS). Scale factor correction and University of Michigan Benchmark test (UMBmark) measurements were concluded to correct model parameters of the robot. The correction outcome was tested on an experiment with simultaneous Global Positioning System (GPS) and odometry localization. The realized differential drive mobile robot has an optical encoder for each wheel. They are connected to STM32F4 development board which calculates the odometric data and sends them with a time-stamp from GPS module over the Bluetooth to PC. Visualization and control program was created to log and store the odometric data and also to set up the odometric parameters in the firmware of the microcontroller.

Attitude estimation and sensor identification utilizing nonlinear filters based on a low-cost MEMS magnetometer and sun sensor

A combination of low-cost micro-electoro-mechanical sensors (MEMSs) and nonlinear attitude estimation algorithm techniques can provide an inexpensive and accurate system for navigation and attitude determination. The features of MEMSs are their light weight and small size; hence, the MEMSs have found significant attention in low-cost navigation and control systems [1]. A common disadvantage of these sensors is the significant errors that accompany the corresponding measurements. The accuracy obtained using MEMSs depends on a number of factors, such as scale factor, bias, and random noise corrections [2]. However, these low-cost sensors suffer from large noise and errors, making calibration and error identification of critical importance [3].

Design, manufacture and geometric verification of rapid prototyped microfluidic encapsulations by computed tomography

This paper presents the dimensional verification of encapsulations used to package microfluidic devices manufactured using a 3D printer of photopolymerisable resin. This characterisation has been performed by computed tomography (CT) by comparing newly manufactured encapsulations and samples that have been subjected to test conditions. Thus, it has been possible to draw conclusions both on the deviations of the nominal geometry of the encapsulations and on how this might affect their performance. This paper presents a scheme of dimensional verification from the point clouds obtained by CT. Finally, a combined threshold and scale factor correction technique of the tomography images is shown. This method is based on the simultaneous measurement of objective and master parts with known geometry. The results reveal the improvements achievable in the accuracy, given a particular machine configuration. The conclusions facilitate the improvement of the geometric design of these devices regarding their behaviour under test conditions.

일라이트 폴리타입 정량분석법의 최적화

본 연구에서는 배경값 보정 및 크기보정을 포함하여 오차요인을 크게 줄이고, WILDFIRE(C)를 통해 최적화된 이론값과 실측값의 일치정도 (R%, (<TEX>${\sum}$</TEX>|이론값-측정값|/이론값)/<TEX>$n{\times}100$</TEX>)를 정량값으로 제시하고, 그 값을 최소화하는 반복과정을 통해 일라이트 폴리타입 함량을 정량하는 개선된 full-pattern-fitting법을 제안하여 일정 함량을 갖는 혼합시료를 대상으로 검증하고, 기존의 Grathoff and Moore법과 비교하였다. 개선된 full-pattern-fitting법은 대상시료 내 불순물로 인한 각 폴리타입 함량오차에도 불구하고, 기존의 full-pattern-fitting법 보다 개선된 최대 3.6% 이내의 오차를 보였다. Grathoff and Moore법과의 비교에서 대상시료 모두에서 Grathoff and Moore법 적용결과는 <TEX>$2M_1$</TEX> 폴리타입의 상대함량이 고평가되어 나타났으며, 이용한 피크별 매우 큰 정량값 차이를 보이는 반면, 본 연구의 개선된 full-pattern-fitting법 적용 결과는 10% 이내의 낮은 R% 값을 갖는 폴리타입 상대함량값을 보이는 것으로 나타나, 높은 신뢰도의 정량결과를 제공할 수 있음을 확인하였다. We proposed the revised full-pattern-fitting method of illite polytype quantification with background correction and scale factor correction of WILDFIRE(C) simulated pattern, and R% value ((<TEX>${\sum}$</TEX>|simulated-measured|/simulated)/ <TEX>$n{\times}100$</TEX>) calculation, and then verified the reliability of this method by applying for the test sample (<TEX>$2M_1$</TEX>:1M<TEX>$$\frac{._-}{.}$$</TEX>1:1), and by comparing the result with Grathoff and Moore method (1996). We confirmed that the proposed method showed the error range of less than 3.6%, which is much lower than the previous full-pattern-fitting methods, in spite of the impurities of the test sample. In the comparison with Grathoff and Moore method for 2 tested samples, we obtained the relatively higher <TEX>$2M_1$</TEX> contents using Grathoff and Moore method, whereas we obtained the reliable results with less than 10% of R% values.

Cerebral blood flow with [15O]water PET studies using an image-derived input function and MR-defined carotid centerlines

Full quantitative analysis of brain PET data requires knowledge of the arterial input function into the brain. Such data are normally acquired by arterial sampling with corrections for delay and dispersion to account for the distant sampling site. Several attempts have been made to extract an image-derived input function (IDIF) directly from the internal carotid arteries that supply the brain and are often visible in brain PET images. We have devised a method of delineating the internal carotids in co-registered magnetic resonance (MR) images using the level-set method and applying the segmentations to PET images using a novel centerline approach. Centerlines of the segmented carotids were modeled as cubic splines and re-registered in PET images summed over the early portion of the scan. Using information from the anatomical center of the vessel should minimize partial volume and spillover effects. Centerline time-activity curves were taken as the mean of the values for points along the centerline interpolated from neighboring voxels. A scale factor correction was derived from calculation of cerebral blood flow (CBF) using gold standard arterial blood measurements. We have applied the method to human subject data from multiple injections of [15O]water on the HRRT. The method was assessed by calculating the area under the curve (AUC) of the IDIF and the CBF, and comparing these to values computed using the gold standard arterial input curve. The average ratio of IDIF to arterial AUC (apparent recovery coefficient: aRC) across 9 subjects with multiple (n = 69) injections was 0.49 ± 0.09 at 0–30 s post tracer arrival, 0.45 ± 0.09 at 30–60 s, and 0.46 ± 0.09 at 60–90 s. Gray and white matter CBF values were 61.4 ± 11.0 and 15.6 ± 3.0 mL/min/100 g tissue using sampled blood data. Using IDIF centerlines scaled by the average aRC over each subjects’ injections, gray and white matter CBF values were 61.3 ± 13.5 and 15.5 ± 3.4 mL/min/100 g tissue. Using global average aRC values, the means were unchanged, and intersubject variability was noticeably reduced. This MR-based centerline method with local re-registration to [15O]water PET yields a consistent IDIF over multiple injections in the same subject, thus permitting the absolute quantification of CBF without arterial input function measurements.

VARIOMETRIC TESTS FOR ACCELEROMETER SENSORS

Abstract. We present a comprehensive review of several variometric tests recently carried out on a home-made measurement system composed of a tern of low-cost accelerometer sensors of MEMS (Micro-Electro-Mechanical Systems) type equipped with autonomous electric supply and wireless transmission. The most important parameters characterizing the systematic errors, i.e. bias, scale factor and thermal correction factor, have been evaluated by calibration tests based upon the so-called "six -positions" static test proposed by the IEEE 517 Standard. In this way the system optimal configuration has been defined in terms of data acquisition frequency and of scale factor. In addition to such tests, partly documented elsewhere, the results of some sensitivity tests on the influence of external environmental factors are also presented. With the aim of employing the proposed MEMS-based system as a device for monitoring the onset of slope landslides, some further tests have been carried out in order to measure the inclination of rigid objects which the sensors have been fixed to. The most significant results of the tests are illustrated and discussed.

Reducing magnetic zero drift by optimizing proportions of neon dual isotopes in laser gyros

The relationships among the proportions of the neon dual isotopes ratio, scale factor corrections (SFCs), light intensities, environmental magnetic field and magnetic zero drift are discussed in detail by numerical simulations. The results show that the unification of the optimal operating point (OP) and the frequency stabilization operating point (FSP) is achievable by adjusting the proportions of neon dual isotopes accurately and tuning the cavity length with frequency stabilization system exactly. In that case, the left-rotation and right-rotation gyros can obtain the same SFC, which can decrease the magnetic sensitivity of the laser gyro efficiently. The Zeeman effect zero drift and the Faraday bias zero drift are both reduced by two orders of magnitude, while the magnetic shielding requirement of laser tube is decreased by 1–2 orders of magnitude.

An Improved High-Accuracy CORDIC Algorithm for DSC in Endoscopic Ultrasonography System

An Improved High-Accuracy CORDIC (COordinate Rotation Digital Computer) algorithm for digital scan conversion is presented in this paper to enhance the accuracy and speed of coordinate conversion for Endoscopic Ultrasonography. Several optimization methods are carried out to make coordinate conversion implemented more exactly with fewer resources of FPGA. In the paper, the Cartesian coordinates are re-demarcated to save LE (Logic Element) resources of FPGA. The bit width of data, the scale factor correction and the convergence range are all optimized to improve the accuracy of the algorithm. Further more, a special processing for the near-field data is carried out to reduce the errors of digital scan conversion. With a full pipeline structure implemented on FPGA, the Improved High-Accuracy CORDIC algorithm is validated by both simulation and real-time ultrasound imaging experiment, making the accuracy enhanced and the image quality improved.

Calibration shifts in Scintrex CG‐3M gravimeters with an application to detection of microgravity changes at Iwo‐tou caldera, Japan

ABSTRACTCalibration shift seriously influences gravity values measured using Scintrex CG‐3M gravimeters. We calibrated three Scintrex CG‐3M gravimeters three times (1999, 2003 and 2006) over eight years, using a calibration line with a gravity difference of 1.38 Gal. The scale factor correction coefficients (calibration factors) obtained here range from 0.9998–1.0005. The calibration factors vary with time by 89 ppm, −102 ppm and −126 ppm between the 1999–2003 surveys. The calibration shifts of two of the three gravimeters decreased to about 20 ppm or less in the second interval, the other remained about the same (142 ppm). The results indicate that they shifted at rates on the order of 10 ppm/year even several years after manufacturing. The large shift in calibration factors indicates that they must be corrected using calibrations done before and after the measurements to perform microgravity measurements when gravity differences between a reference gravity site and survey sites are on the order of a hundred milligals (mGal) or more. The results also indicate that the calibration factors change gradually with time, so their interpolation provides a good practical approximation for a specific survey time. We applied the time‐dependent calibration factors to microgravity monitoring at the Iwo‐tou caldera, Japan, where the gravity difference between the base site on the island and the reference site on Honshu (the mainland of Japan) is about 870 mGal mainly due to the 11° latitude difference. Gravity surveys were conducted every two years from 1998–2006. The correction of scale factors estimated from the repeated calibration surveys leads to satisfactory measurements, in which the average of the absolute differences between two Scintrex CG‐3M instruments in five surveys is reduced from 207μGal to 19μGal; for three of those surveys, it is less than 10 μGal. This result demonstrates the importance of repeated calibration surveys.

Scale-factor corrections in the optical inertial sensor

In the operations of optical inertial sensors, geometric variations due to temperature and operation environments cause thermoelastic deformations of their components, which lead to changes in the area and perimeter of their resonator block. The fluctuations in the geometric scale factor are corrected by the piezoelectric actuator. This article presents the numerical formulation of the elastic behaviour of each piezoelectric actuator, and the numerical formulations are verified through comparisons with the results of a finite element simulation.

Scale-factor corrections in large ring lasers

The authors report on fluctuations of the geometric scale factor of a very large ring laser situated 30m underground in the Cashmere Cavern in Christchurch (New Zealand). Variations in temperature and atmospheric pressure cause thermoelastic deformations to the cavern, which lead to changes of the area and perimeter of the ring laser structure. In situ beam monitoring has been used to partially correct for these effects.

Non-Collinear Magnetic Structure of TbB4

Non-Collinear Magnetic Structure of TbB₄

Application-specific instruction set processor for SoC implementation of modern signal processing algorithms

A novel application-specific instruction set processor (ASIP) for use in the construction of modern signal processing systems is presented. This is a flexible device that can be used in the construction of array processor systems for the real-time implementation of functions such as singular-value decomposition (SVD) and QR decomposition (QRD), as well as other important matrix computations. It uses a coordinate rotation digital computer (CORDIC) module to perform arithmetic operations and several approaches are adopted to achieve high performance including pipelining of the micro-rotations, the use of parallel instructions and a dual-bus architecture. In addition, a novel method for scale factor correction is presented which only needs to be applied once at the end of the computation. This also reduces computation time and enhances performance. Methods are described which allow this processor to be used in reduced dimension (i.e., folded) array processor structures that allow tradeoffs between hardware and performance. The net result is a flexible matrix computational processing element (PE) whose functionality can be changed under program control for use in a wider range of scenarios than previous work. Details are presented of the results of a design study, which considers the application of this decomposition PE architecture in a combined SVD/QRD system and demonstrates that a combination of high performance and efficient silicon implementation are achievable.