A comparison of GPS, VLBI and model estimates of ocean tide loading displacements

In recent years, ocean tide loading displacements (OTLD) have been measured using the Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI). This study assesses the accuracy of GPS measurements of OTLD by comparison with VLBI measurements and estimates derived from numerical ocean tide models. A daily precise point positioning (PPP) analysis was carried out on ∼11 years of GPS data for each of 25 sites that have previous OTLD estimates based on data from co-located VLBI sites. Ambiguities were fixed to integer values where possible. The resulting daily estimates of OTLD, at eight principal diurnal and semi-diurnal tidal frequencies, were combined to give GPS measurements of OTLD at each site. The 3D GPS and VLBI measurements of OTLD were compared with estimates computed (by convolution with Green’s functions) from five modern ocean tide models (CSR4.0, FES2004, GOT00.2, NAO99b and TPXO6.2). The GPS/model agreement is shown to be similar to the VLBI/model agreement. In the important radial direction, the GPS/model misfit is shown to be smaller than the VLBI/model misfit for seven of the eight tidal constituents; the exception being the K2 constituent. Fixing of GPS carrier-phase ambiguities to integer values resulted in a marginal improvement to the GPS/model agreement. Statistically, it is shown there is no significance to the difference between the fit of the GPS and VLBI measurements of OTLD to modelled values. Equally, differences in fit of either the complete set of GPS or VLBI estimates to the five sets of model-derived values cannot be identified with statistical significance. It is thus concluded that, overall, we cannot distinguish between GPS and VLBI measurements of OTLD, and that at the global scale, present ocean tide models are accurate to within the current measurement noise of these techniques.     

Assessing the accuracy of predicted ocean tide loading displacement values

The accuracy of ocean tide loading (OTL) displacement values has long been assumed to be dominated by errors in the ocean tide models used, with errors due to the convolution scheme used considered very small (2–5%). However, this paper shows that much larger convolution errors can arise at sites within approximately 150 km of the coastline, depending on the method used to refine the discrete regularly spaced grid cells of the ocean tide model to better fit the coastline closest to the site of interest. If the local water mass redistribution approach is implemented, as used in the OLFG/OLMPP software recommended in the IERS 2003 conventions, OTL height displacement errors of up to around 20% can arise, depending on the ocean tide model used. Bilinear interpolation only, as used in the SPOTL and CARGA softwares for example, is shown from extensive global and regional comparisons of OTL displacement values derived from the different methods and softwares to be more appropriate. This is verified using GPS observations. The coastal refinement approach used in the OLFG/OLMPP software was therefore changed in August 2007 to use bilinear interpolation only. It is shown that with this change, OTL displacement values computed using OLFG/OLMPP, SPOTL and CARGA invariably agree to the millimetre level for coastal sites, and better than 0.2 mm for sites more than about 150 km inland.     

An estimate of the errors in gravity ocean tide loading computations

The error contributions within the ocean tide loading (OTL) convolution integral computation were determined to be able to estimate the numerical accuracy of the gravity OTL values. First, the comparison of four OTL programs by different authors (CONMODB, GOTIC2, NLOADF and OLFG/OLMPP) at ten globally distributed gravity stations using exactly the same input values shows discrepancies between 2% and 5%. A new program, called CARGA, was written that is able to reproduce the results of these programs to a level of 0.1%. This has given us the ability to state with certainty the cause of the discrepancies among the four programs. It is shown that by choosing an appropriate interpolation of the Green’s function, refinement of the integration mesh and a high-resolution coastline, an accuracy level of better than 1% can be obtained for stations in Europe. Besides this numerical accuracy, there are errors in the ocean tide model such as a 1% uncertainty in the mean value of the sea-water density and the lack of conservation of tidal water mass, which can produce offsets of around 0.04 μgal.     

The gravitational effect of ocean tide loading at high latitude coastal stations in Norway

Gravity measurements close to the ocean are strongly affected by ocean tide loading (OTL). The gravitational OTL effect consists of three parts, i.e. a change in gravity caused by direct attraction from the variable water-masses, by displacement of the observing point due to the load, and by redistribution of masses due to crustal deformation. We compare the OTL gravitational effect of several global models to observed time-series of gravity to identify the best model for four arctic observation sites. We also investigate if the global models are sufficient for correcting gravity observations. The NAO99b model fits the observations best at three stations. At two stations (Tromsø and Bodø) the global models explain the variability in the observations well. At the other two (Honningsvåg and Andøya), a significant periodic signal remains after the OTL correction has been applied. We separate two of the gravitational effects, the direct attraction and the change in gravity due to displacement, to study the local effects. Simple geometric models of the water load and independent measurements from local tide-gauges are used to calculate these effects. This leads to improved correspondence with the OTL signal, hence demonstrating the importance of careful modelling of local effects for correction of gravity observations in coastal stations.     

海潮模型对连续跟踪参考站数据解算的影响——以福建省为例

针对在近海或海洋区域进行高精度全球定位系统测量中海潮负荷的影响,该文通过GAMIT对福建省的连续跟踪参考站数据进行了解算,并对解算结果进行了进一步的探讨。结果表明,海潮负荷对近海的连续跟踪参考站的影响在U方向上能达到亚毫米级,而且与测站与海的距离、基线的长度,以及基准站的选择都有一定的关系。在解算福建省的连续跟踪参考站数据时,海潮负荷的影响是可以忽略的,均可满足大多数的工程需要。对于如何更好地消除海潮负荷的影响,以满足更高精度的要求,还值得进一步的探讨。     

The M 2 ocean tide loading wave in Alaska: vertical and horizontal displacements, modelled and observed

Crustal deformations caused by surface load due to ocean tides are strongly dependent on the surface load closest to the observation site. In order to correctly model this ocean loading effect near irregular coastal areas, a high-resolution coastline is required. A test is carried out using two GPS sites located in Alaska, where the ocean tide loading effect is large and consequently observed easily by relative positioning with GPS. The selected sites are Fair (Fairbanks) and Chi3 (located on an island that separates Prince William Sound from the Gulf of Alaska). Processing of hourly baseline solutions between Fair and Chi3 over a period of 49 days yields a significant ocean tide loading effect. The data are processed using different strategies for the tropospheric delay correction. However, the best results are obtained when 1-h ZTD (Zenith Tropospheric Delay) parameters for hourly solutions are used. In this case ocean tide loading is not absorbed into the ZTD parameters. Hence, ocean tide loading can be well resolved in the GPS data analysis. In addition, the M ₂ ocean tide wave in the Gulf of Alaska has a very large amplitude. Although the horizontal M ₂ ocean tide loading amplitude in general is only about 1/4 of the vertical M ₂ ocean tide loading amplitude, the differential horizontal M ₂ ocean tide loading displacements are nevertheless measurable using differential GPS (DGPS). When using the GOT99.2 ocean tide model and taking the coastal structure into account, the predicted differential vertical M ₂ amplitude and Greenwich phase lag due to ocean tide loading are 19.3 mm and 110.2 degrees respectively, while GPS measurements yield 21.3 ± 1.0 mm and 99.7±2.8 degrees. Similarly, the predicted differential horizontal M ₂ amplitude and Greenwich phase lag (in the north–south direction) are 4.5 mm and –77.0 degrees, while GPS yields 5.4 ± 0.3 mm and –106.3±3.3 degrees. Only the north-south component of the differential horizontal M ₂ ocean tide loading wave is considered, because the east–west component is too small for the processed baseline and not detectable using DGPS.     

海潮负荷效应对我国及周边IGS站的影响

针对近海区域海潮变化复杂且海潮负荷效应显著,而全球海潮模型在近海区域精度较低的问题,该文提出了将全球海潮模型NAO.99b和区域模型osu.chinasea.2010相结合,分析海潮对中国大陆及周边地区IGS站的影响。使用GAMIT软件解算IGS站实测数据,通过海潮负荷计算软件SPOTL对解算结果进行改正,并对改正效果进行对比和分析。结果表明,海潮负荷对中国及周边区域站点的影响主要体现在垂直方向,对一些站点的影响可以达到厘米级;海潮负荷对站点坐标的改正效果明显,特别是日本的种子岛站改正效果接近30%;站点改正效果从沿海到内陆逐渐减弱。     

Ocean tide loading (OTL) displacements from global and local grids: comparisons to GPS estimates over the shelf of Brittany, France

In this paper we examine OTL displacements detected by GPS stations of a dedicated campaign and validate ocean tide models. Our area of study is the continental shelf of Brittany and Cotentin in France. Brittany is one of the few places in the world where tides provoke loading displacements of ∼10–12 cm vertically and a few cm horizontally. Ocean tide models suffer from important discrepancies in this region. Seven global and regional ocean tide models were tested: FES2004 corrected for K2, TPXO.7.0, TPXO.6.2, GOT00.2, CSR4.0, NAO.99b and the most recent regional grids of the North East Atlantic (NEA2004). These gridded amplitudes and phases of ocean tides were convolved in order to get the predicted OTL displacements using two different algorithms. Data over a period of 3.5 months of 8 GPS campaign stations located on the north coast of Brittany are used, in order to evaluate the geographical distribution of the OTL effect. We have modified and implemented new algorithms in our GPS software, GINS 7.1. GPS OTL constituents are estimated based on 1-day batch solutions. We compare the observed GPS OTL constituents of M₂, S₂, N₂ and K₁ waves with the selected ocean tide models on global and regional grids. Large phase-lag and amplitude discrepancies over 20° and 1.5 cm in the vertical direction in the semi-diurnal band of M₂ between predictions and GPS/models are detected in the Bay of Mont St-Michel. From a least squares spectral analysis of the GPS time-series, significant harmonic peaks in the integer multiples of the orbital periods of the GPS satellites are observed, indicating the existence of multipath effects in the GPS OTL constituents. The GPS OTL observations agree best with FES2004, NEA2004, GOT00.2 and CSR4.0 tide models.     

山东地区GPS测量中的海潮负荷影响

针对影响山东地区GPS测量精度的重要因素之一——海潮负荷,不同海潮模型在山东沿海地区差异较大的问题,该文以山东CORS数据为例,基于FES2004、NAO99b、CSR4.0、GOT00.2 4种全球海潮模型,使用GAMIT软件,分析了海潮负荷对山东地区GPS定位及基线解算的影响。通过对比分析,海潮负荷对山东地区GPS定位的影响主要体现在U方向上,振幅达到厘米级;海潮负荷对山东沿海定位的影响大于山东内陆,U方向达到了2cm,为内陆地区2倍以上;海潮负荷对基线解算的影响与基线方位和基线两端测站负荷差异有关,其中差异较大的基线U方向的影响接近8mm;除GOT00.2海潮模型以外,不同模型对山东地区较长观测时段的GPS数据解算结果的影响并无太大差异,但对于短时观测或实时的GPS高精度定位,半日分潮迟角的精度还有待提高,因此有必要精细化山东区域海潮模型。     

GPS抗干扰方法综述

全球定位系统提供的低能级信号易受干扰。这些干扰或对抗导致GPS丢失信息，因而成为威胁GPS的严重问题。本文探讨对抗或干扰对GPS的威胁，从策略，干扰源和GPS接收机角度谈抗干扰方法，侧重分析减少GPS干扰的技术。     

GPS滑坡监测系统在铁路桥桥墩稳定性监测中的应用

结合对铁路桥桥墩的实际监测应用,介绍了GPS滑坡监测系统的工作原理和性能特点,阐述了现场安装过程中的许多重点问题及其对监测效果的影响,并结合实际测量数据论证了该系统应用于滑坡监测的可行性和优势所在。     

World-wide synthetic tide parameters for gravity and vertical and horizontal displacements

The response of the Earth’s crust to the direct effect of lunisolar gravitational forcing is known as the body tide. The body tide is superimposed by surface-loading forces due to the pressure of the periodically varying ocean tide acting on the Earth, called ocean tide loading (OTL). Both body tide and OTL can be decomposed into components of the same frequency known as tidal parameters. However, OTL is more complicated than body tides because of the dynamic effects of the ocean. Estimating OTL requires a model of the ocean tides and knowledge of the elastic properties of the solid Earth. Thus, synthetic tide parameters (amplitude factors and phase leads) have been developed here on a world-wide grid for gravity and positional displacements. The body tide contributions were added to the oceanic contribution to provide the Earth tide response. The accuracy and reliability of the synthetic tidal parameters have been estimated by comparing observed gravity and vertical-displacement tide parameters with those interpolated from our synthetic model, which shows good agreement. Tests also indicate that the synthetic tide parameters provide realistic gravimetric and displacements for practical use in tidal prediction.     

利用GPS数据对城市三角控制网进行分析

讨论了利用GPS基线对三角点之间的数据内符性和精度进行检验的方法,并对该方法可能的误差项进行了综合分析,用实例验证了提出的方法是可行的。     

航天GPS接收机设计

航天GPS接收机为航天器提供航迹、姿态、时问和相对距离等导航信息，提高航天嚣运行的自主性。文中介绍了清华宇航中。航天GPS接收的硬件和软件设计，给出测试结果和分析。     

基于GPS/DR的车辆定位系统设计与实现

在介绍了目前存在的车辆定位技术的基础上,提出了一种基于GPS/DR定位技术的车辆定位系统的设计框架,详细描述了框架内各个部分的功能和实现细节;并基于该框架开发了一个简单的系统,其具备车辆定位系统的基本功能。实际应用效果表明该系统是合理的,具有一定的实用价值。     

GPS技术在像控测量中的应用

继阐述GPS技术已有方法在像控测量中的优缺点后,提出了应用非差相位精密单点定位技术进行像控测量的新方法。通过实例验证了此方法的可行性和高效性,并得出了一些对生产实际有益的结论。     

Accuracy assessment of GPS navigation augmented by SAR and LiDAR-derived Digital Elevation Models

Remotely sensed Digital Elevation Models (DEM) can be used to augment a standalone Global Positioning System (GPS) by adding an extra range observation which measures the distance to the Earth centre. This method so called height aiding can reduce the number of GPS satellites required to get a 3D position fix from four to three and hence improve the performance of the GPS navigation algorithm in terms of accuracy, reliability and availability. Up until now, the accuracy of height aided GPS navigation using higher resolution Synthetic Aperture Radar (SAR) and Light Detection and Ranging (LiDAR)-derived elevation data has not been fully evaluated in a broad spectrum of navigation scenarios. This article provides a robust and accurate analysis on how much range error is introduced by height aiding using 5 m spacing SAR and 1 m spacing LiDAR-derived DEMs under in-car and personal navigation situations. Based on the experimental results obtained from both dynamic and static tests, suggestions have been made on what level of vertical and positional accuracy can be achieved as well as the related DEM quality issues for navigation purposes.     

相对差分GPS精度分析

近年来,全球定位系统(GPS)以其精度高、速度快、经济方便等优点,在布设各种形式的控制网、变形监测及精密工程测量等诸多方面都得到迅速广泛的应用。但由于美国的SA和AS政策,使其精度下降,因此各国都在研究如何提高其精度,本文就此问题给出一些观点。     

基于GPS矢量观测信息的姿态确定算法

用于GPS姿态确定的矢量化算法可等价于两级最优问题。第一级把GPS载波相位观测量转换为矢量观测量。第二级是Wahba问题,即从矢量观测量获得最佳姿态解。Wahba问题可用四元数法求解,如QUEST方法。本文采用基于小角度的迭代法求解Wahba问题。在均衡星座或均衡基线务件下,两级最优解亦是全局最优解。实验结果表明迭代解的精度与QUEST解相同。实验中也应用了改进的TRIAD算法以比较两级最优解。