Vertical Position Error Research Articles

On-machine precision form truing of arc-shaped diamond wheels

In order to realize the efficient and precision truing of arc-shaped diamond wheel for precision grinding of spherical, aspherical and free-form surfaces, a novel on-machine precision form truing of resin and metal bonded arc-shaped diamond wheels is proposed utilizing rotary green silicon carbon (GC) rod. Through this on-machine rotary GC rod (ORGCR) mutual-wear truing, any required radius of wheel arc profile could be formed by programmed truing paths, meanwhile, the vertical direction position error of the wheel center could be corrected after truing. Firstly, the principle of ORGCR mutual-wear truing for arc-shaped diamond wheel was introduced, and new evaluation methods of truing performance and truing ratio were provided. Then the truing performance and truing ratio were observed for different grains and bond of arc-shaped diamond wheels, the effects of ORGCR mutual-wear truing parameters on profile radius and form accuracy of wheels were investigated. Finally, the convex aspherical surface of single crystal silicon was ground by trued arc-shaped diamond wheel. The experimental results showed that the resin and metal bonded diamond wheels could be efficiently and precisely trued with high truing ratio. The form error of wheel arc profile reached 2.5–6μm/3mm which decreased about 90% compared to pre-truing wheel. Besides, the diamond grains were well distributed on the wheel surface, and protruded out of the wheel bond after truing. The precision aspherical surface of single crystal silicon with the form accuracy PV of 507nm and the average roughness Ra of 57.1nm was achieved by parallel grinding with the trued D7 resin bonded wheel.

Network RTK 항체의 불연속 위치 결정 개선을 위한 기준국 셀간 미지정수 차이 조정 연구

Abstract One-way Network-RTK(Real Time Kinematics) is considered as a method which can satisfy moving vehicle’s recently-required high accuracy and mobility. When we use one-way Network RTK for vehicle navigation, multiple cells-based system is required to provide the service continuously in wide area. The rover which moves through various cells inevitably experiences a correction discontinuity, which is not eliminated by the DD(Double Difference) method and to cause 13cm(horizontal) and 48cm(vertical) position error. We suggest three solutions to reduce this discontinuity, which are identification of master RS with neighbor networks, duplication of communication module to receive corrections from other cells, and ambiguity adjustment between neighbor cells. All of our suggestions reduce the error to 1/4 wavelength in measurement and 3cm in position-domain, and we suggest the ambiguity adjustment is the best when we consider the extendibility of service area and the cost of rover device.Key words : Network RTK, Ambiguity Difference, Reference Station Network Cell, Continuous Positioning

Wide Area RTK: A satellite navigation system based on precise real‐time ionospheric modelling

The Wide Area Real Time Kinematic (WARTK) is an augmentation system concept for multi‐frequency users based on precise real‐time ionospheric modeling. It is able to provide a high accuracy and integrity GNSS positioning service over continental areas using the infrastructure of a network of permanent ground monitor stations, such as the European Geostationary Navigation Overlay Service (EGNOS) network of Ranging and Integrity Monitoring Stations (RIMS) in Europe. In this way, it allows an additional benefit to be obtained from these reference stations, that is, the network has the potential to support two independent systems: a satellite‐based augmentation system, such as EGNOS, and a high‐precision positioning service, based on WARTK. Indeed, thanks to the accuracy of the ionospheric corrections provided, WARTK users have available in real‐time an extra constraint per satellite between the carrier phase ambiguities, which helps solve them quickly. Once such ambiguities have been solved, the GNSS user obtains navigation accurate to within 20 cm at the 95th percentile (about 10 cm RMS). Moreover, this precise positioning is achieved in a few minutes (with two frequency signals) or in a single epoch, after initial convergence of the tropospheric delay (with three frequency signals), even up to hundreds of kilometers away from the nearest reference station. While previous WARTK research has been devoted to implementing the concept and assessing its feasibility, considering in particular the accuracy achievable, the work reported in this paper focused on consolidating the results by analyzing a large and representative data set, and on deeper analysis of the integrity issue. It was carried out in the context of the Multi‐constellation Regional System (MRS) project, within the European Space Agency GNSS Evolution Programme, with the aim of designing a high accuracy service for GPS and/or Galileo. Three months of actual data, from more than 25 permanent GPS stations in Europe, have been processed (some of them as a roving user), for high‐, mid‐ and low‐solar cycle conditions (in 2002, 2004 and 2006 respectively). In addition, several ionospheric storms occurred during the selected periods, withDstvalues reaching up to −150 nT. Results based on these data show that user domain integrity was maintained for baselines of up to 400 km. At the 95th percentile, the daily horizontal and vertical position errors were 20 and 30 cm, respectively, and the corresponding protection levels were about 1 and 2 m. The convergence time was around 5 minutes with actual GPS constellation data. The benefits of using a multi‐constellation system were also studied, with simulated GPS and three‐frequency Galileo data, showing that it is possible to reduce the convergence time to a few seconds.

Accuracy of positioning three types of self-ligating brackets compared with a conventionally ligating bracket

The aim of this study was to determine whether the morphology of three different self-ligating brackets affects the accuracy of their positioning when compared with a conventionally ligating bracket. An ex vivo prospective comparison of the accuracy of positioning self-ligating brackets with conventionally ligating brackets. Orthodontic Department, Eastman Dental Institute, London, UK. Twenty-five clinicians with 2 or more years experience of bracket placement bonded four identical typodont malocclusions with Damon MX(TM), In-Ovation System R(TM) and SmartClip(TM) self-ligating brackets and also Victory Series(TM) conventionally ligating brackets. Four hundred brackets of each type were positioned. Vertical, horizontal and angular bracket position errors were assessed by reference to the FA point and FACC respectively, using digital images and image analysis software. Method error analysis showed no evidence of bias and minimal random error. The Victory Series brackets were the most accurately positioned. Although the amount of positioning error for all the self-ligating brackets was small, a greater number were positioned outside vertical and horizontal tolerance limits compared to the conventionally ligated brackets (P<0·001). The Damon MX bracket type was nearly 10 times more likely to be inaccurately placed relative to the FA point compared with the Victory Series bracket. The differences relating to angular positioning error were not statistically significant (P>0·05). The findings indicate that the positioning of three types of self-ligating brackets was less accurate than the conventional pre-adjusted edgewise bracket, when using a direct bonding technique. This may have implications for their clinical application.

Mid-Field Calibration Technology on the Phased Array Antenna

Transmit and receive performances are up to the amplitude and phase distributions over the aperture in the phased array antenna. The Mid-field Calibration Technology (MFCT) is analysed in theory, and vertical position error and horizontal position error are discussed in the pattern evaluation. Simultaneously, MFCT is applied to the experimental antenna array, and theory and experimental results have verified the effects of MFCT.

Electrode placement configurations for 3D EIT

This paper investigates several configurations for placing electrodes on a 3D cylindrical medium to reconstruct 3D images using 16 electrode EIT equipment intended for use with a 2D adjacent drive protocol. Seven different electrode placement configurations are compared in terms of the following figures of merit: resolution, radial and vertical position error, image magnitude, immunity to noise, immunity to electrode placement errors, and qualitative evaluation of image artefacts. Results show that for ideal conditions, none of the configurations considered performed significantly better than the others. However, when noise and electrode placement errors were considered the planar electrode placement configuration (two rings of vertically aligned electrodes with electrodes placed sequentially in each ring) had the overall best performance. Based on these results, we recommend planar electrode placement configuration for 3D EIT lung imaging of the thorax.

On the Probability of Collision Between Climbing and Descending Aircraft

The probability of coincidence (which is a upper bound for the probability of collision) is calculated for aircraft on arbitrary straight flight paths with constant speed: either aircraft may be climbing, descending, or in level flight and they may cross at any angle. Gaussian statistics with equal or distinct rms deviations for the two aircraft are used to calculate the probability of coincidence as a function of time in the first instance, with a correction factors for 1) the more accurate generalized error distribution; 2) asymmetry in vertical position errors. The time and distance of closest approach are used to calculate the position for maximum probability of coincidence. The cumulative probability of coincidence over all time is calculated, and expressed as a probability of coincidence per unit distance and per unit time: the latter is compared with the International Civil Aviation Organization target level of safety. Examples are given of the effect on coincidence probabilities of the seven parameters of the problem: velocities and glide slopes of each aircraft, crossing angle in horizontal projection, vertical separation, and rms position error.

Characterization of symmetric [3 x 3] directional couplers fabricated by direct writing with a femtosecond laser oscillator

We demonstrate and characterize symmetric [3x3] three-dimensional directional couplers fabricated in glass using a high-pulse energy femtosecond laser oscillator. The characteristics of the [3x3] directional couplers closely agree with the theoretical prediction, except for small errors caused by the fabrication process. We show that deviations from symmetry are dominated by vertical position errors of the coupling waveguide.

An Evaluation of Atmospheric Models for GPS data Retrieval by Output from a Numerical Weather Model

Atmospheric delays in GPS processing are estimated by fitting parameters of atmospheric models to the observed delays. GPS-related error sources include multipath effects and phase center variations, as well as uncertainties in atmospheric models. An atmospheric model must accurately capture the delay distribution if errors are to be minimized. Large GPS position errors occurred on 7 March 1997 on the Izu Peninsula and at Hatsu-shima, about 100 km southwest of Tokyo, concomitant with a mountain lee wave. The coinciding of the large position errors and the mountain lee wave suggests that small-scale fluctuations in water vapor and air density associated with lee waves could cause large position errors. This study used a high-resolution non-hydrostatic model to simulate the mountain lee wave. Slant delays for the GPS satellites were calculated from the reproduced water vapor and air density fields using a ray-tracing method. The atmospheric delays are obtained by fitting the atmospheric models to the reproduced slant delays, instead of the actual delay data. The atmospheric models were evaluated by determining the difference in position error between the reproduced delays and the model-fitted delays. The mountain lee wave case was used to evaluate three different atmospheric models. The first, the “constant model”, has only zenith delay as an unknown parameter. Large position errors occurred when the constant model was used to fit the data in this case. The “linear gradient model”, adds two horizontal gradient parameters to the zenith parameter, and yielded significantly reduced horizontal position errors. Horizontal and vertical position errors were reduced further with a “second order model”, which adds second-order terms. Evaluation of the atmospheric models using the mountain lee wave case indicated that 1) the linear gradient model cannot express complicated atmospheric disturbances; and, 2) a second-order model reduces horizontal and vertical position errors.

Limitations in DGPS positioning accuracies at low latitudes during solar maximum

While it is possible to mitigate the impact of ionospheric effects on Global Positioning System (GPS) positioning applications through differential techniques, residual errors may persist in regions of steep TEC gradients. An enhancement of absolute TEC and large‐scale gradients is observed at low latitudes near the equatorial anomaly. This effect is significant in the equinoctial months during periods of solar maximum. In this paper, differential GPS (DGPS) positioning accuracies in the anomaly region are investigated during the period of solar maximum 1999–2000, using as data the L1 pseudoranges. TEC gradients of 30 TECU per 100 km are observed during March 2000, with corresponding horizontal and vertical position errors of approximately 25–30 m (95% confidence level) for single baseline processing. Positioning accuracies are improved by a factor of 5 for a wide area DGPS approach.

Marine magnetotellurics for petroleum exploration, Part II: Numerical analysis of subsalt resolution

In areas where seismic imaging of the base of salt structures is difficult, seaborne electromagnetic techniques offer complementary as well as independent structural information. Numerical models of 2-D and 3-D salt structures demonstrate the capability of the marine magnetotelluric (MT) technique to map the base of the salt structures with an average depth accuracy of better than 10%. The mapping of the base of the salt with marine MT is virtually unaffected by internal variation within the salt. Three‐dimensional anticlinal structures with a horizontal aspect ratio greater than two can be interpreted adequately via two‐dimensional inversions. Marine MT can distinguish between salt structures which possess deep vertical roots and those which do not. One measure of the relative accuracy of MT and seismic methods can be made by considering the vertical and lateral position errors in the locations of interfaces caused by neglecting velocity anisotropy in migration. For the shallow part of the section where two‐way travel times are on the order of 1 s, the vertical and lateral position errors in the locations of salt‐sediment interfaces from 2-D MT inversion is more than twice the expected migration error in reflectors in transversely isotropic sediments, such as those in the Gulf of Mexico. Deeper in the section where two‐way times are on the order of 4 s, lateral position errors in migration become comparable to those of the MT inverse, whereas seismic vertical position errors remain more than a factor of two smaller than MT errors. This analysis shows that structural mapping accuracy would be improved using MT and seismic together.

Relationship between navigation vertical error, VDOP, and pseudo-range error in GPS

At a specified position and time, vertical position error is related to satellite ranging errors by the relationship Z=VDOP*URE where URE is the user range equivalent error, VDOP is the vertical dilution of precision, and Z is the vertical position error. This relationship is developed and it is shown that it is statistically correct even when position and time are variables. Expressions are given for the density, cumulative distribution, and standard deviation of Z in terms of the distributions of VDOP and URE. Vertical position error is investigated at several locations and the results compared with published work. A simple method for converting VDOP distributions to distributions of vertical accuracy as an alternative to computer simulation is presented. >