Multivariate Monitoring with GPS Observations and Auxillary Multisensor Data

In a multisensor measurement or monitorin environment, p variables are measured simultaneously. The measured data are correlated and can be monitored to identify special causes of variation in order to establish control and to obtain reference samples to use as a basis in determining the control limits for future observations. One common method is to construct a multivariate control chart based on Hotelling's T² statistic. When the monitoring process is at the start-up stage, F and chi-square distributions are used to construct the necessary control limits. An example from a seven-day GPS data sample measured concurrently with the accelerometer response, wind velocity and temperature illustrates that this technique can improve the interpretation of GPS results. Moreover, the computational complexity is reduced through a reduction in the data dimensionality. ? 2002 Wiley Periodicals, Inc.     

Full-scale structural monitoring using an integrated GPS and accelerometer system

Accurate in situ measurement of the full-scale structural responses, especially tall buildings, under severe loading conditions is an important requirement for validating their design, evaluating their construction as well as facilitating their maintenance. Traditionally such response has been measured using accelerometers. However, it is impossible to measure the static and quasi-static components of motion with acceleration sensors. An integrated system comprising of RTK-GPS and accelerometers has been developed with the objective of assessing full-scale structural responses by exploiting the complementary characteristics of GPS and accelerometer sensors. The data used in this paper were obtained from GPS and accelerometer sensors installed on a 108-m-high steel tower in Tokyo, together with other sensors such as anemometer and strain gauge. The seismic and wind-induced responses of the tower were analyzed using the Fast Fourier Transformation (FFT) and compared to results from finite element modeling (FEM). In order to study the system reliability, the correlated signals were extracted by applying a digital filtering technique. Then the filtered data sets were converted to displacement (in the case of accelerometer data) and acceleration (in the case of GPS data) through double integration and double differentiation, respectively, for the purpose of direct comparison and to further fuse data from the two different sensors. The results agree with each other very well, although the static and quasi-static components are missing from the accelerometer-derived results. The redundancy of the monitoring system therefore has been achieved.     

External atmospheric corrections in geodetic very-long-baseline interferometry

Three methods to correct for the atmospheric propagation delay in very-long-baseline interferometry (VLBI) measurements were investigated. In the analysis, the NASA R&D experiments from January 1993 to June 1995 were used. The methods were compared in correcting for the excess propagation delay due to water vapour, the “wet” delay, at one of the sites, the Onsala Space Observatory on the west coast of Sweden. The three methods were: (1) estimating the wet delay using the VLBI data themselves; (2) inferring the wet delay from water vapour radiometer (WVR) data, and (3) using independent estimates based on data from the global positioning system (GPS). Optimum elevation cutoff angles were 22^∘ and 26^∘ when using WVR and GPS data, respectively. The results were found to be similar in terms of reproducibility of the estimated baseline lengths. The shortest baselines tend to benefit from external measurements, whereas the lack of improvement in the longer baselines may be partly due to the large amount of data thrown away when removing observations at low elevation angles. Over a 2 week period of intensive measurements, the two methods using external data showed an overall improvement, for all baseline lengths, compared to the first method. This indicates that there are long-term systematic errors in the wet delay data estimated using WVR and GPS data. Received: 27 October 1998 / Accepted: 20 May 1999     

基于经验模态分解的GPS基线解算模型

非建模系统误差是影响高精度GPS基线解算精度的一个重要因素,文章给出基于经验模态分解的GPS基线解算模型,有效消弱系统误差对基线解的影响。在现有经验模态分解理论的基础上,定义经验模态分解的多尺度分解与重构结构,并由此给出基于经验模态的系统趋势分离模型,依据累积标准化模量的均值随尺度的变化确定系统误差与噪声分离尺度的选择标准。给出基于经验模态分解的GPS基线解算的技术路线,首先计算GPS相位双差观测方程的浮点解残差序列,分离出系统误差并用于修正GPS双差观测值,重新计算双差浮点解,采用Lambda算法固定整周模糊度,计算固定基线解,从而消弱系统误差对基线解算的影响,提高基线固定解的可靠性。并采用实测GPS数据验证模型,F-ratio指数与W-ratio指数表明系统误差消弱后,基线固定解可靠性得到明显提高,重新计算的残差序列表明系统误差得到很好的消弱。     

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.     

Adaptive wavelet transform based on cross-validation method and its application to GPS multipath mitigation

Global positioning system (GPS) multipath disturbance is a bottleneck problem that limits the accuracy of precise GPS positioning applications. A method based on the technique of cross-validation for automatically identifying wavelet signal layers is developed and used for separating noise from signals in data series, and applied to mitigate GPS multipath effects. Experiments with both simulated data series and real GPS observations show that the method is a powerful signal decomposer, which can successfully separate noise from signals as long as the noise level is lower than about half of the magnitude of the signals. A multipath correction model is derived based on the proposed method and the sidereal day-to-day repeating property of GPS multipath signals to remove multipath effects on GPS observations and to improve the quality of the GPS measurements.     

A case study of using Raman lidar measurements in high-accuracy GPS applications

This paper investigates the impact of rapid small-scale water vapor fluctuations on GPS height determination. Water vapor measurements from a Raman lidar are used for documenting the water vapor heterogeneities and correcting GPS signal propagation delays in clear sky conditions. We use data from four short observing sessions (6 h) during the VAPIC experiment (15 May–15 June 2004). The retrieval of wet delays from our Raman lidar is shown to agree well with radiosonde retrievals (bias and standard deviation (SD) were smaller than 1 and 2.8 mm, respectively) and microwave radiometers (from two different instruments, bias was 6.0/−6.6 mm and SD 1.3/3.8 mm). A standard GPS data analysis is shown to fail in accurately reproducing fast zenith wet delay (ZWD) variations. The ZWD estimates could be improved when mean post-fit phase residuals were removed. Several methodologies for integrating zenith lidar observations into the GPS data processing are also presented. The final method consists in using lidar wet delays for correcting a priori the GPS phase observations and estimating a scale factor for the lidar wet delays jointly with the GPS station position. The estimation of this scale factor allows correcting for a mis-calibration in the lidar data and provides in the same way an estimate of the Raman lidar instrument constant. The agreement of this constant with an independent determination using radiosonde data is at the level of 1–4%. The lidar wet delays were derived by ray-tracing from zenith pointing measurements: further improvement in GPS positioning is expected from slant path lidar measurements that would properly account for water vapor anisotropy.     

Precise ionosphere-free single-frequency GNSS positioning

Ionospheric delays can be efficiently eliminated from single-frequency data using a combination of carrier phases and code ranges. Unfortunately, GPS and GLONASS ranges are relatively noisy which can limit the use of the positioning method. Nevertheless, position standard deviations are in the range of 6–8 cm (horizontal) and 7–9 cm (3d) obtained from diurnal data batches from selected IGS reference stations can be further reduced to 2–3 cm (3d) for weekly smoothed averages. GPS data sets collected in Ghana (Africa) reveal a typical level of 10 cm of deviation that must be anticipated under average conditions. Looking at the future of GNSS, the European Galileo system will, in contrast to GPS, provide the broadband signal E5 that is by far less affected by multipath thus providing rather precise range measurements. Simulated processing runs featuring both high ionospheric and tropospheric delay variations show a 3d position precision of 4 cm even for a data batch as short as just 1 h, whereas GPS L1/Galileo E1 performance is close to 13 cm for the same data set.     

Investigating the propagation mechanism of unmodelled systematic errors on coordinate time series estimated using least squares

The propagation of unmodelled systematic errors into coordinate time series computed using least squares is investigated, to improve the understanding of unexplained signals and apparent noise in geodetic (especially GPS) coordinate time series. Such coordinate time series are invariably based on a functional model linearised using only zero and first-order terms of a (Taylor) series expansion about the approximate coordinates of the unknown point. The effect of such truncation errors is investigated through the derivation of a generalised systematic error model for the simple case of range observations from a single known reference point to a point which is assumed to be at rest by the least squares model but is in fact in motion. The systematic error function for a one pseudo-satellite two-dimensional case, designed to be as simple but as analogous to GPS positioning as possible, is quantified. It is shown that the combination of a moving reference point and unmodelled periodic displacement at the unknown point of interest, due to ocean tide loading, for example, results in an output coordinate time series containing many periodic terms when only zero and first-order expansion terms are used in the linearisation of the functional model. The amplitude, phase and period of these terms is dependent on the input amplitude, the locations of the unknown point and reference point, and the period of the reference point's motion. The dominant output signals that arise due to truncation errors match those found in coordinate time series obtained from both simulated data and real three-dimensional GPS data.     

The northern European geoid: a case study on long-wavelength geoid errors

 The long-wavelength geoid errors on large-scale geoid solutions, and the use of modified kernels to mitigate these effects, are studied. The geoid around the Nordic area, from Greenland to the Ural mountains, is considered. The effect of including additional gravity data around the Nordic/Baltic land area, originating from both marine, satellite and ground-based measurements, is studied. It is found that additional data appear to increase the noise level in computations, indicating the presence of systematic errors. Therefore, the Wong–Gore modification to the Stokes kernel is applied. This method of removing lower-order terms in the Stokes kernel appears to improve the geoid. The best fit to the global positioning system (GPS) leveling points is obtained with a degree of modification of approximately 30. In addition to the study of modification errors, the results of different methods of combining satellite altimetry gravity and other gravimetry are presented. They all gave comparable results, at the 6-cm level, when evaluated for the Nordic GPS networks. One dimensional (1-D) and 2-D fast Fourier transform (FFT) methods are also compared. It is shown that even though methods differ by up to 6 cm, the fit to the GPS is essentially the same. A surprising conclusion is that the addition of more data does not always produce a better geoid, illustrating the danger of systematic errors in data. Received: 4 July 2001 / Accepted: 21 February 2002     

GOCE gradiometer: estimation of biases and scale factors of all six individual accelerometers by precise orbit determination

A method has been implemented and tested for estimating bias and scale factor parameters for all six individual accelerometers that will fly on-board of GOCE and together form the so-called gradiometer. The method is based on inclusion of the individual accelerometer observations in precise orbit determinations, opposed to the baseline method where so-called common-mode accelerometer observations are used. The method was tested using simulated data from a detailed GOCE system simulator. It was found that the observations taken by individual accelerometers need to be corrected for (1) local satellite gravity gradient (SGG), and (2) rotational terms caused by centrifugal and angular accelerations, due to the fact that they are not located in the satellite’s center of mass. For these corrections, use is made of a reference gravity field model. In addition, the rotational terms are derived from on-board star tracker observations. With a perfect a priori gravity field model and with the estimation of not only accelerometer biases but also accelerometer drifts, scale factors can be determined with an accuracy and stability better than 0.01 for two of the three axes of each accelerometer, the exception being the axis pointing along the long axis of the satellite (more or less coinciding with the flight direction) for which the scale factor estimates are unreliable. This axis coincides with the axis of drag-free control, which results in a small variance of the signal to be calibrated and thus an inaccurate determination of its scale factor in the presence of relatively large (colored) accelerometer observation errors. In the presence of gravity field model errors, it was found that still an accuracy and stability of about 0.015 can be obtained for the accelerometer scale factors by simultaneously estimating empirical accelerations.     

基于GPS与GIS集成的车辆导航系统设计与实现

介绍了基于GPS与GIS集成的车辆导航系统设计与实现 ,探讨了导航系统中电子地图的空间数据组织 ,提出了GPS信号与GIS路网数据匹配、快速的邮路选择、最佳路径选择、地图随驾驶方向快速实时旋转技术及语音提示、语音识别技术的使用。     

The impact of accelerometry on CHAMP orbit determination

 The contribution of the STAR accelerometer to the CHAMP orbit precision is evaluated and quantified by means of the following results: orbital fit to the satellite laser ranging (SLR) observations, GPS reduced-dynamic vs SLR dynamic orbit comparisons, and comparison of the measured to the modeled non-gravitational accelerations (atmospheric drag in particular). In each of the four test periods in 2001, five CHAMP arcs of 2 days' length were analyzed. The mean RMS-of-fit of the SLR observations of the orbits computed with STAR data or the non-gravitational force model were 11 and 24 cm, respectively. If the accelerometer calibration parameters are not known at least at the few percent level, the SLR orbit fit deteriorates. This was tested by applying a 10% error to the along-track scale factor of the accelerometer, which increased the SLR RMS-of-fit on average to 17 cm. Reference orbits were computed employing the reduced-dynamic technique with GPS tracking data. This technique yields the most accurate orbit positions thanks to the estimation of a large number of empirical accelerations, which compensate for dynamic modeling errors. Comparison of the SLR orbits, computed with STAR data or the non-gravitational force model, to the GPS-based orbits showed that the SLR orbits employing accelerometer observations are twice as accurate. Finally, comparison of measured to modeled accelerations showed that the level of geomagnetic activity is highly correlated with the atmospheric drag model error, and that the largest errors occur around the geomagnetic poles. Received: 7 May 2002 / Accepted: 18 November 2002 Correspondence to: S. Bruinsma Acknowledgments. The TIGCM results were obtained from the CEDAR database. This study was supported by the Centre National d'Etudes Spatiales (CNES). The referees are thanked for their helpful remarks and suggestions.     

A combined algorithm of improving INS error modeling and sensor measurements for accurate INS/GPS navigation

Although the integrated system of a differential global positioning system (DGPS) and an inertial navigation system (INS) had been widely used in many geodetic navigation applications, it has sometimes a major limitation. This limitation is associated with the frequent occurrence of DGPS outages caused by GPS signal blockages in certain situations (urban areas, high trees, tunnels, etc.). In the standard mechanization of INS/DGPS navigation, the DGPS is used for positioning while the INS is used for attitude determination. In case of GPS signal blockages, positioning is provided using the INS instead of the GPS until satellite signals are obtained again with sufficient accuracy. Since the INS has a very short-time accuracy, the accuracy of the provided INS navigation parameters during these periods decreases with time. However, the obtained accuracy in these cases is totally dependent on the INS error model and on the quality of the INS sensor data. Therefore, enhanced navigation parameters could be obtained during DGPS outages if better inertial error models are implemented and better quality inertial measurements are used. In this paper, it will be shown that better INS error models are obtained using autoregressive processes for modeling inertial sensor errors instead of Gauss–Markov processes that are implemented in most of the current inertial systems and, on the other hand, that the quality of inertial data is improved using wavelet multi-resolution techniques. The above two methods are discussed and then a combined algorithm of both techniques is applied. The performance of each method as well as of the combined algorithm is analyzed using land-vehicle INS/DGPS data with induced DGPS outage periods. In addition to the considerable navigation accuracy improvement obtained from each single method, the results showed that the combined algorithm is better than both methods by more than 30%.     

Single frequency processing of Ørsted GPS radio occultation measurements

The Global Positioning System (GPS) radio occultation measurements obtained using the TurboRogue GPS receiver on the Danish satellite Ørsted have been processed using the single frequency method. Atmospheric profiles of refractivity and temperature are derived and validated against numerical weather prediction data from the European Centre for Medium-Range Weather Forecast (ECMWF). Results from the Ørsted GPS measurement campaign in February 2000 indicate that the single frequency method can provide retrievals with accuracy comparable to that of using two frequencies. From comparisons between measured dry temperature profiles and corresponding dry temperature profiles derived from ECMWF analysis fields, we find a mean difference of less than 0.5 K and a standard deviation of 2–4 K between 500 and 30 hPa in height. Above 30 hPa the impact of the ionosphere becomes more dominant and more difficult to eliminate using the single frequency method, and the results show degraded accuracy when compared to previous analysis results of occultation data from other missions using the dual frequency method. At latitudes less than 40° (denoted low latitudes), the standard deviation is generally smaller than at latitudes higher than 40° (denoted high latitudes). A small temperature bias is observed centered at 200 hPa for low latitudes and at 300 hPa for high latitudes. This indicates that the ECMWF analyses do not adequately resolve the tropopause temperature minimum. In the lowest part of the troposphere an observed warm bias is thought to be due to erroneous tracking of the GPS signal in cases of atmospheric multipath propagation.     

Precise estimation of residual tropospheric delays using a regional GPS network for real-time kinematic applications

 A new method called Trop_NetAdjust is described to predict in real time the residual tropospheric delays on the GPS carrier phase observables using the redundant measurements from a network of GPS reference stations. This method can not only enhance the effectiveness and reliability of real-time kinematic users within the network, but also provide a valid approach to tropospheric parameter variation forecasting. Trop_NetAdjust is theoretically based upon LS prediction criteria and enables the prediction of residual tropospheric delays remaining after a standard model has been applied to the raw GPS measurements. Two cases are analyzed, namely a first case when the delay is required for an existing satellite at a new point within the network and a second case when the delay is required for a new satellite. Field tests were conducted using data collected in a network of 11 reference stations covering a 400×600 km region in southern Norway. The results were analyzed in the measurement domain (ionospheric-free double-difference residuals) and showed improvements of 20 to 65% RMS errors using Trop_NetAdjust. The estimates of the Trop_NetAdjust prediction accuracy were also obtained using the covariance analysis method. The agreement was consistently better than 30% when compared with data from a real network. Received: 28 February 2000 / Accepted: 9 January 2001     

Atmospheric turbulence theory applied to GPS carrier-phase data

Turbulent irregularities in the lower atmosphere cause physical correlations between Global Positioning System (GPS) carrier-phase measurements. Based on turbulence theory, a variance–covariance model is developed in this paper that reflects these correlations. The main result shows that the obtained fully-populated variance–covariance matrices depend not only on the satellite-station geometry, but also on the prevailing atmospheric conditions, which are parameterised by, e.g., the von Karman spectrum of refractivity fluctuations and the wind velocity vector. It is shown that the amount of the correlation between two GPS carrier-phase observations is inversely related to the separation distance of the corresponding ray paths through the turbulent atmosphere. Furthermore, the wind velocity and direction play a key role in the correlation.     

2005珠峰GPS测量大地高确定

珠峰大地高确定是计算珠峰海拔高程一个关键环节。2005珠峰GPS测量大地高确定主要包括青藏地区GPS监测网、珠峰地区GPS控制网和珠峰峰顶GPS联测三部分;并利用GPS峰顶联测数据直接计算大地高。本文结合珠峰峰顶GPS观测自然环境恶劣的特点,分析比较了各种计算方案,确定了一种较为合理的解算珠峰大地高的GPS数据处理方法,获得了较为满意的珠峰大地高计算结果。     

Identification of GPS positioning solutions deteriorated by signal degradations using a fuzzy inference system

The accuracy of GPS positioning based on pseudorange measurements under signal degradation environments is limited by poor satellite geometry and signal distortions due to diffraction and multipath. As a result, the GPS position solutions could become unreliable. Those deteriorated solutions should be identified and not used for navigation. For that purpose, methods for reliable identification of deteriorated GPS positioning solutions from a navigation receiver should be developed. In this paper, a fuzzy inference system is proposed to classify the quality of GPS positioning solutions. The input for the system includes the signal quality evaluated by the difference between the measured and expected carrier-to-noise density ratio (C/N0) and the satellites geometry strength evaluated by the dilution of precision (DOP) number. The proposed fuzzy inference system is developed based on the human knowledge and understanding of the problem under consideration and is further optimized using data acquired from the field. The test results indicate that the proposed method can be used for reliable identification of deteriorated GPS position solutions affected by signal degradations.     

Development and testing of a new ray-tracing approach to GNSS carrier-phase multipath modelling

Multipath is one of the most important error sources in Global Navigation Satellite System (GNSS) carrier-phase-based precise relative positioning. Its theoretical maximum is a quarter of the carrier wavelength (about 4.8 cm for the Global Positioning System (GPS) L1 carrier) and, although it rarely reaches this size, it must clearly be mitigated if millimetre-accuracy positioning is to be achieved. In most static applications, this may be accomplished by averaging over a sufficiently long period of observation, but in kinematic applications, a modelling approach must be used. This paper is concerned with one such approach: the use of ray-tracing to reconstruct the error and therefore remove it. In order to apply such an approach, it is necessary to have a detailed understanding of the signal transmitted from the satellite, the reflection process, the antenna characteristics and the way that the reflected and direct signal are processed within the receiver. This paper reviews all of these and introduces a formal ray-tracing method for multipath estimation based on precise knowledge of the satellite–reflector–antenna geometry and of the reflector material and antenna characteristics. It is validated experimentally using GPS signals reflected from metal, water and a brick building, and is shown to be able to model most of the main multipath characteristics. The method will have important practical applications for correcting for multipath in well-constrained environments (such as at base stations for local area GPS networks, at International GNSS Service (IGS) reference stations, and on spacecraft), and it can be used to simulate realistic multipath errors for various performance analyses in high-precision positioning.