有色噪声对东南极区域GPS测站三维速度估计的影响

近年来,有研究发现在GPS测站坐标时间序列中既存在白噪声,也存在有色噪声。为了研究有色噪声对东南极区域GPS测站三维速度估计的影响,本文使用GAMIT/GLOBK10.5软件对东南极区域6个连续GPS测站2005—2014年的实测数据进行解算和平差,并利用最大似然法（MLE）分别估计了在两种假设噪声模型条件下的测站三维运动速度及其不确定性。结果表明：在进行参数估计时,考虑两种有色噪声（闪烁噪声和随机游走噪声）对东南极区域GPS测站三维速度估计的量级影响不大,水平方向最大影响量级为0.3 mm/a,垂直方向最大影响量级为0.8 mm/a;但如果不考虑有色噪声,会严重低估参数估计的真实不确定性。     

An assessment of Bernese GPS software precise point positioning using IGS final products for global site velocities

We assess the use of precise point positioning (PPP) within the Bernese GPS software (BSW) Version 5.0 over the period from 2000 to 2005. In our strategy, we compute a set of daily PPP solutions for international GNSS service (IGS) reference frame (IGb00) sites by fixing IGS final satellite orbits and clock products, followed by a Helmert transformation of these solutions into ITRF2000, forming a set of continuous position time series over the entire time span. We assess BSW PPP by comparing our set of transformation parameters with those produced by the IGS analysis centre coordinator (ACC) and our position time series with those of the Jet Propulsion Laboratory (JPL) and the Scripps Orbit and Permanent Array Centre at the Scripps Institute of Oceanography (SIO). The distributions of the north (N), east (E) and up (U) daily position differences are characterized by means and SD of +2.2 ± 4.8, −0.6 ± 7.9 and +4.8 ± 17.3 mm with respect to JPL, and of +0.1 ± 4.4, −0.1 ± 7.4 and −0.1 ± 11.8 mm with respect to SIO. Similarly, we find sub-millimetre mean velocity differences and SD for the N, E and U components of 0.9, 1.5 and 2.2 mm/year with JPL, and of 1.2, 1.6 and 2.3 mm/year with SIO. A noise analysis using maximum likelihood estimation (MLE) shows that when estimating global site velocities from our position time series, the series need to be on average up to 1.3 times longer than those of JPL and SIO, before an uncertainty of less than 0.5 mm/year is obtained.     

南极IGS跟踪站观测所得的坐标时间序列

介绍了南极洲和南极洲上的IGS跟踪站的概况,处理了其2006年和2007年的GPS观测数据,分析了坐标分量的时间序列及各站的运动趋势。     

Effects of azimuthal multipath asymmetry on long GPS coordinate time series

Carrier phase multipath is currently one source of unmodeled signals that may bias GPS coordinate time series significantly. We investigate the effect of simulated carrier phase multipath on time series of several sites covering the period 2002.0–2008.0 and spanning a range of observation geometries. High-, mid-, and low-latitude IGS sites are investigated as well as sites with significant signal obstructions. We examine the effect of multipath in different sectors of the sky, considering time-constant, horizontal reflectors at each of 0.1, 0.2, and 1.5 m below the antenna. The differences between a horizontally uniform multipath source are analyzed, and it is shown that positioning errors are generally larger when unmodeled carrier phase multipath is azimuthally heterogeneous. Using the adopted multipath model, height biases reach ±1 mm in case of the symmetric multipath and ±5 mm for the asymmetric multipath but this increases to being ±10 mm in the worst case. In addition to mean bias, low-frequency variations in the bias also exist, including periodic signals and leading to velocity biases of up to ±0.1 mm/year in the symmetric case and ±1 mm/year in the asymmetric case over the considered period. In contrast to the generally slowly varying observation geometry that is typically experienced, we show the effects of an abrupt change in geometry due to receiver/antenna hardware changes; in the case considered, we see changed pattern of temporal variation in the bias in addition to an instantaneous offset.     

基于滑动L2优化准则的GPS坐标时间序列重构

GPS坐标时间序列中不仅包含白噪声,还包含闪烁噪声、随机漫步噪声等有色噪声,这些噪声将影响GPS应用的可靠性,甚至可能对一些地球物理现象做出错误的解释,因此降低GPS坐标时间序列中有色噪声的影响、提高GPS精度是一个重要和基本的问题。提出了一种滑动L₂优化估计方法(ML₂),通过选取合适的窗口建立L₂优化模型,再利用交替迭代乘子法求解每段时间序列的优化问题,并逐年滑动得到整段GPS坐标时间序列的估计。实验结果表明,ML₂方法与奇异谱分析、小波分解、滑动普通最小二乘法相比具有更好的重构效果。     

地表质量负载对格陵兰岛区域GPS站点坐标时序特征的影响

选取ITRF2008框架下格陵兰岛区域12个GPS站2013年1月-2016年12月期间的日解坐标时间序列作为研究对象,并利用极大似然估计分析地表质量负载改正前后各站点的噪声特性、速度场及周期项振幅。结果表明：站点最优噪声模型主要为白噪声+幂律噪声与白噪声+闪烁噪声,地表质量负载形变修正GPS坐标时序后,明显增加U方向闪烁噪声的成分,平均降低其速度约0.36 mm/a,对水平方向影响较小;同时分别降低高程方向44.1%、14.2%的1 a项、0.5 a项振幅,相反,却增加了水平方向的周期项振幅。     

云南地区GPS基准站噪声模型分析

以云南地区陆态网27个全球定位系统(GPS)基准站在2011-2017年不同时间跨度的观测数据为例,使用赤池信息量和贝叶斯信息量估计准则(AIC/BIC)对解算结果进行分析,从而确定其最优有色噪声模型.结果表明,不同时间跨度基准站各坐标分量上噪声特性主要体现为白+闪烁噪声(WN+FN)、幂律噪声(PL)模型组合.部分基准站在北向和垂向的最优噪声模型会随着观测时间的累积而改变,PL模型所占比例有所下降,WN+FN模型所占比例有所上升.当时间跨度大于5 a时,基准站噪声模型的稳定性显著提高.随着坐标时间序列积累时长的增加,未知噪声分量出现的可能性也相应提高.     

Sub-daily noise in horizontal GPS kinematic time series due to thermal tilt of GPS monuments

The sub-daily noise in horizontal global positioning system (GPS) kinematic time series arising from monument tilts is quantitatively evaluated using tiltmeter data at GPS stations from the Japanese nationwide global navigation satellite system network. The estimated tilt-induced monument displacements show characteristics that are typical of those caused by thermal tilts of the monuments. The root mean square of the displacements is typically a few millimetres, with notable inter-seasonal variations. The stacked amplitude spectra of the monument displacements have peaks at the tidal bands S1 and S2, and their higher tones. The peaks at the S1 and S2 bands in the amplitude spectra are reduced by 41 and 43 % for the north–south component and 36 and 53 % for the east–west component, respectively, after correcting for the monument displacements. The monument displacements due to the thermal tilts of the monuments may also be a favourable candidate for sub-daily noise at the S1 and S2 bands found in other GPS networks.     

利用GPS基准站数据浅析我国地壳垂直运动

应用国内GPS基准站1999-2005年共？年的垂直位移时间序列数据,浅析我国的地壳垂直运动。粗略地分析GPS基准站的垂向位移分量时间序列,表明地壳垂直运动受到多种因素的影响。     

A first look at the effects of ionospheric signal bending on a globally processed GPS network

This study provides a first attempt at quantifying potential signal bending effects on the GPS reference frame, coordinates and zenith tropospheric delays (ZTDs). To do this, we homogeneously reanalysed data from a global network of GPS sites spanning 14 years (1995.0–2009.0). Satellite, Earth orientation, tropospheric and ground station coordinate parameters were all estimated. We tested the effect of geometric bending and dTEC bending corrections, which were modelled at the observation level based, in part, on parameters from the International Reference Ionosphere 2007 model. Combined, the two bending corrections appear to have a minimal effect on site coordinates and ZTDs except for low latitude sites. Considering five days (DOY 301–305, 28 October–1 November 2001) near ionospheric maximum in detail, they affect mean ZTDs by up to ~1.7 mm at low latitudes, reducing to negligible levels at high latitudes. Examining the effect on coordinates in terms of power-spectra revealed the difference to be almost entirely white noise, with noise amplitude ranging from 0.3 mm (high latitudes) to 2.4 mm (low latitudes). The limited effect on station coordinates is probably due to the similarity in the elevation dependence of the bending term with that of tropospheric mapping functions. The smoothed z-translation from the GPS reference frame to ITRF2005 changes by less than 2 mm, though the effect combines positively with that from the second order ionospheric refractive index term. We conclude that, at the present time, and for most practical purposes, the geometric and dTEC bending corrections are probably negligible at current GPS/reference frame precisions.     

GPS坐标时间序列噪声估计及相关性分析

比较分析了极大似然估计法、最小二乘方差分量估计法以及最小范数二次无偏估计法对GPS站坐标时间序列噪声的估计效果,确定最小范数二次无偏估计法为最优的噪声方差估计方法。在此基础上对中国及其周边区域20个IGS站坐标时间序列中各方向噪声方差进行一元线性回归分析。结果表明,中国及其周边区域IGS站不同方向的噪声间具有中等强度以上的相关性,其中N方向闪烁噪声与其他方向闪烁噪声的相关性要强于白噪声。水平方向的噪声振幅能够解释垂直方向噪声振幅变化的40%~60%,而N方向噪声振幅能够解释E方向噪声振幅变化的60%~80%,获得的线性回归方程具有使用价值。     

Combination of GNSS and SLR observations using satellite co-locations

Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and allows the estimation of SLR station coordinates at the level of 1–2 cm. The SLR observations to GNSS satellites provide the scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119 mm and −13 mm on average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in the range of a few centimeters up to 5 cm. Scale differences of 0.9 ppb are seen between GNSS and SLR.     

顾及MLE的IGS坐标时间序列噪声模型特性分析

以30个GPS基准站坐标序列为对象,提出分别采用赤池信息量准则(AIC)与贝叶斯信息准则(BIC)噪声模型估计准则判定GPS时间序列噪声特性,对比分析GPS时间序列噪声模型特性,探讨不同噪声模型对GPS站速度及其不确定度的影响.结果表明GPS站坐标序列噪声模型主要表现为FN+WN、PL及FN+RW+WN噪声模型特性;FN+WN噪声模型对GPS站速度估计值的影响相对较小,但在U分量影响最为明显;此外,RW对站速度不确定度的影响不可忽略,正确获取模型参数估计的实际不确定度及改正噪声分量对于合理应用GPS坐标时间序列数据具有重要的意义.     

Comparison of Absolute and Relative Antenna Phase Center Variations

Three major GPS antenna calibration methods are available toda: the relative field calibrations using the GPS data collected on short baselines, the absolute field calibrations, where the GPS antenna is rotated and tilted by a robot, and calibration measurements in an anechoic chamber. Mean antenna offsets and the elevation-dependent phase center variations of GPS antennas determined by all three techniques are compared to assess their accuracy. The analysis of global GPS data with these sets of calibration values reveals that the offsets and variations of the satellite antenna phase centers have to be considered, too, to obtain a consistent picture. ? 2001 John Wiley & Sons, Inc.     

Estimates of ocean tide loading displacements and its impact on position time series in Hong Kong using a dense continuous GPS network

Three-dimensional ocean tide loading (OTL) displacements of eight diurnal and semidiurnal constituents at 12 sites in Hong Kong were estimated using 3–7 years of continuous global positioning system (GPS) observations. OTL displacements were estimated using the precise point positioning (PPP) technique on a daily basis and then combined. The OTL displacements obtained by GPS were compared with predictions using seven recent global ocean tide models. The effect of OTL displacements on GPS position time series was also investigated. The study shows that the GPS-derived OTL displacements (excluding K1 and K2 constituents) agree best with those predicted by the GOT4.7 and NAO99b models. The GPS/model agreement is generally at the sub-millimeter level, except for S2, K1, and K2 constituents with relatively large errors. After systematic biases between the GPS and model values are removed, the misfits of all sites for M2, S2, N2, O1, P1, and Q1 are less than 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while larger misfits (within 2.5 mm) are observed for K1 and K2. Integer ambiguity fixing slightly improves the east component of OTL displacement estimates. The study also finds that GPS-derived OTL corrections, instead of model predicts, can be used in daily data processing with the exception of K1 and K2. Including K2 corrections, a secular vertical rate of up to 1 mm/year in position time series can be induced, which needs to be confirmed by further studies.     

GPS position time-series analysis based on asymptotic normality of M-estimation

The efficacy of robust M-estimators is a well-known issue when dealing with observational blunders. When the number of observations is considerably large—long time series for instance—one can take advantage of the asymptotic normality of the M-estimation and compute reasonable estimates for the unknown parameters of interest. A few leading M-estimators have been employed to identify the most likely functional model for GPS coordinate time series. This includes the simultaneous detection of periodic patterns and offsets in the GPS time series. Estimates of white noise, flicker noise, and random walk noise components are also achieved using the robust M-estimators of (co)variance components, developed in the framework of the least-squares variance component estimation (LS-VCE) theory. The method allows one to compute confidence interval for the (co)variance components in asymptotic sense. Simulated time series using white noise plus flicker noise show that the estimates of random walk noise fluctuate more than those of flicker noise for different M-estimators. This is because random walk noise is not an appropriate noise structure for the series. The same phenomenon is observed using the results of real GPS time series, which implies that the combination of white plus flicker noise is well described for GPS time series. Some of the estimated noise components of LS-VCE differ significantly from those of other M- estimators. This reveals that there are a large number of outliers in the series. This conclusion is also affirmed by performing the statistical tests, which detect (large) parts of the outliers but can also leave parts to be undetected.     

MATLAB Tools for viewing GPS velocities and time series

Over the past decade, many Global Positioning System (GPS) networks have been installed to monitor tectonic motions around the world. Some of these networks contain hundreds of sites spread across active tectonic margins where the differences in velocities across the network can be 50–100 mm/year. For networks that have been running for a number of years, the uncertainty in the velocity estimates can be less than 1 mm/year. In some cases the vertical motions can also be significant and of importance. Often, the time series of the motions of the GPS sites show complex non-linear behavior, and in all cases the statistical model of the time series is more complex than simple white noise. In this article, we describe a set of Matlab tools developed for use with the GAMIT/GLOBK GPS data analysis system (King 2002; King and Herring 2002) that allow interactive viewing and manipulation of GPS velocities and time series with a Matlab-based graphical user interface (GUI). The formats of the data files used by the tools are specific to GAMIT/GLOBK, but they are simple ASCII files that can be generated from other file formats. The tools are referred to as GGMatlab.The GPS Toolbox is a column dedicated to highlighting algorithms and source code utilized by GPS Engineers and scientists. If you have an interesting program or software package you would like to share with our readers, please pass it along; e-mail it to us at gps-toolbox@ngs.noaa.gov/. To comment on any of the source code discussed here, or to download source code, visit our website at . This column is edited by Stephen Hilla, National Geodetic Survey, NOAA, Silver Spring, Maryland, and Mike Craymer, Geodetic Survey Division, Natural Resources Canada, Ottawa, Ontario, Canada. For the sidebar, see the Volume 6, Number 4, 2003 issue of the GPS Toolbox column.     

中国大陆GPS基准站的时间序列特征

利用1999年3月至2002年3月期间“中国地壳运动观测网络”25个GPS基准站与周边国家IGS站的观测资料，进行了时间序列分析研究，并对提高GPS基准站的观测精度进行了探讨。结果表明，GPS基准站的时间序列具有一定的周期性，高程分量的周期性最为明显，GPS点位高程时间序列拟舍曲线的波峰和波谷出现的时间表现为区域性的不同。     

Calibrating adaptive antenna arrays for high-integrity GPS

A major challenge in using GPS guidance for aircraft final approach and landing is to reject interference that can jam reception of the GPS signals. Antenna arrays, which use space–time adaptive processing (STAP), significantly improve the signal to interference plus noise ratio, but at the possible expense of distorting the received signals, leading to timing biases that may degrade navigation performance. Rather than a sophisticated calibration approach to remove biases introduced by STAP, this paper demonstrates that a relatively compact calibration strategy can substantially reduce navigation biases, even under elevated interference conditions. Consequently, this paper develops an antenna bias calibration strategy for two classes of adaptive array algorithm and validates this method using both simulated and experimental data with operational hardware in the loop. A proof-of-concept system and an operational prototype are described, which implement the adaptive antenna algorithms and deterministic corrections. This investigation demonstrates that systems with adaptive antenna arrays can approach the accuracy and integrity requirements for automatic aircraft landing, and in particular for sea-based landing on board aircraft carriers, while simultaneously providing significant attenuation of interference. Evidence suggests that achieving these goals is possible with minimal restrictions on system hardware configuration—specifically, limitations on the permissible level of antenna anisotropy and the use of sufficient analog-to-digital converter resolution.