Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

The global positioning system (GPS) has become an essential tool for the high precision navigation and positioning. The quality of GPS positioning results mainly depends on the model’s formulations regarding GPS observations, including both a functional model, which describes the mathematical relationships between the GPS measurements and unknown parameters, and a stochastic model, which reflects the physical properties of the measurements. Over the past two decades, the functional models for GPS measurements have been investigated in considerable detail. However, the stochastic models of GPS observation data are simplified, assuming that all the GPS measurements have the same variance and are statistically independent. Such assumptions are unrealistic. Although a few studies of GPS stochastic models were performed, they are restricted to short baselines and short time session lengths. In this paper, the stochastic modeling for GPS long-baseline and zenith tropospheric delay (ZTD) estimates with a 24-h session is investigated using the residual-based and standard stochastic models. Results show that using the different stochastic modelling methods, the total differences can reach as much as 3–6 mm in the baseline component, especially in the height component, and 10 mm in the ZTD estimation. Any misspecification in the stochastic models will result in unreliable GPS baseline and ZTD estimations. Using the residual-based stochastic model, not only the precision of GPS baseline and ZTD estimation is obviously improved, but also the baseline and ZTD estimations are closer to the reference value.     

Optimal combination of InSAR and GPS for measuring interseismic crustal deformation

High spatial resolution measurements of interseismic deformation along major faults are critical for understanding the earthquake cycle and for assessing earthquake hazard. We propose a new remove/filter/restore technique to optimally combine GPS and InSAR data to measure interseismic crustal deformation, considering the spacing of GPS stations in California and the characteristics of interseismic signal and noise using InSAR. To constrain the longer wavelengths (>40 km) we use GPS measurements, combined with a dislocation model, and for the shorter wavelength information we rely on InSAR measurements. Expanding the standard techniques, which use a planar ramp to remove long wavelength error, we use a Gaussian filter technique. Our method has the advantage of increasing the signal-to-noise ratio, controlling the variance of atmosphere error, and being isotropic. Our theoretical analysis indicates this technique can improve the signal-to-noise ratio by up to 20%. We test this method along three segments of the San Andreas Fault (Southern section near Salton Sea, Creeping section near Parkfield and Mojave/Big Bend section near Los Angeles), and find improvements of 26%, 11% and 8% in these areas, respectively. Our data shows a zone of uplift to the west of the Creeping section of the San Andreas Fault and an area of subsidence near the city of Lancaster. This work suggests that after only 5 years of data collection, ALOS interferograms will provide a major improvement in measuring details of interseismic deformation.     

The contribution of radar interferometry to the assessment of landslide hazards

Interferometric analysis of repeat pass radar images (InSAR) enables the mapping of slope movements with high accuracy, being of great relevance for the assessment of landslide risk. The InSAR method is briefly explained, with emphasis on data processing for landslide motion mapping. Constraints of the method are discussed, mainly resulting from temporal decorrelation of the radar signal in vegetated areas. Application examples for InSAR mapping of very slow slope movements, using SAR data of the European Earth Observation Satellite ERS, are shown for a mass waste above an alpine traffic route and for slope deformation in a mountain village. The comparison with GPS measurements of surface motion shows RMSE = 3.7 mm a⁻¹ between the InSAR and GPS retrieved motion, where part of this difference is attributed to the different observation periods. The investigations demonstrate the good capability of InSAR for detecting and monitoring surface deformation on mountain slopes, thus providing valuable support for landslide inventories and risk assessment.     

异形光斑的高精度光束偏转角度测量

大气湍流通常会造成激光光斑畸变为不规则的异形光斑,针对目前四象限探测器(QD)对空间光通信中不规则光斑偏转角度测量精度不足的问题,提出了一种基于多源信息融合的高精度光束偏转角度测量方法.该方法通过对QD及电荷耦合元件(CCD)的数据信息进行融合分析,在保持QD高分辨率和高响应速度的基础上,提高QD对不规则光斑偏转角的测...     

DORIS and GPS monitoring of the Gavdos calibration site in Crete

Due to its specific geographical location as well as its geodetic equipment (DORIS, GNSS, microwave transponder and tide gauges), the Gavdos station in Crete, Greece is one of the very few sites around the world used for satellite altimetry calibration. To investigate the quality of the Gavdos geodetic coordinates and velocities, we analyzed and compared here DORIS and GPS-derived results obtained during several years of observations. The DORIS solution is the latest ignwd11 solution at IGN, expressed in ITRF2008, while the GPS solution was obtained using the GAMIT software package. Current results show that 1–2 mm/yr agreement can be obtained for 3-D velocity, showing a good agreement with current geophysical models. In particular, the agreement obtained for the vertical velocity is around 0.3–0.4 mm/yr, depending on the terrestrial reference frame. As a by-product of these geodetic GPS and DORIS results, Zenith Tropospheric Delays (ZTDs) estimations were also compared in 2010 between these two techniques, and compared to ECMWF values, showing a 6.6 mm agreement in dispersion without any significant difference between GPS and DORIS (with a 97.6% correlation), but with a 13–14 mm agreement in dispersion when comparing to ECMWF model (with only about 90% correlation for both techniques). These tropospheric delay estimations could also provide an external calibration of the tropospheric correction used for the geophysical data of satellite altimetry missions.     

The Western Crete geodetic infrastructure: Long-range power-law correlations in GPS time series using Detrended Fluctuation Analysis

The Global Positioning System makes it possible, nowadays, to measure crustal displacements with unprecedented accuracy. These measurements can improve our understanding of the spatio-temporal evolution of motion along tectonic plate boundaries, as well as deepen our comprehension for the nature of earthquake fault behavior and earthquake cycle. The Hellenic subduction zone and the earthquake-prone Crete, with large crustal motions of 3–4 cm/yr, may provide such a natural laboratory for this type of investigation. In this work, we examine the statistical structure and behavior of time series, as produced by permanent GPS sites, established on the islands of Crete and Gavdos.     

基于多源图像弱监督学习的3D人体姿态估计

3D人体姿态估计是计算机视觉领域一大研究热点,针对深度图像缺乏深度标签,以及因姿态单一造成的模型泛化能力不高的问题,创新性地提出了基于多源图像弱监督学习的3D人体姿态估计方法。首先,利用多源图像融合训练的方法,提高模型的泛化能力;然后,提出弱监督学习方法解决标签不足的问题;最后,为了提高姿态估计的效果,改进了残差模块的设计。实验结果表明:改善的网络结构在训练时间下降约28%的情况下,准确率提高0.2%,并且所提方法不管是在深度图像还是彩色图像上,均达到了较好的估计结果。      

基于双频GPS观测的简化动力学最小二乘批处理精密定轨

星载双频GPS载波相位和伪距观测量已成为低轨卫星获取精确三维位置和速度信息的主要方式. 本文以非差消电离载波相位和伪距组合作为观测量,应用简化动力学最小二乘批处理方法进行地球低轨卫星的精密定轨,并给出完整定轨流程. 采用逐段常量的经验加速度对动力学模型误差进行补偿,描述了经验加速度敏感矩阵及稀疏带状矩阵求逆的有效计算方法. 利用GRACE-A卫星GPS观测数据对定轨位置精度进行分析,结果显示,三维位置定轨精度优于5cm,经验加速度在径向、切向和法向上的补偿水平不超过40nm·s-2,大气阻力系数和辐射光压系数的估计值符合物理实际,星载接收机钟差大致呈线性并具有短周期小波动.      

Vertical motions in Thailand after the 2004 Sumatra–Andaman Earthquake from GPS observations and its geophysical modelling

Following previous findings from ongoing GPS research in Thailand since 2004 we continue to exploit the GPS technique to monitor and model land motions induced by the Sumatra–Andaman Earthquake. Our latest results show that up to the end of 2010, Thailand has been co-seismically displaced and is subsequently undergoing a post-seismic horizontal deformation with total displacements (co-seismic plus post-seismic) ranging from 10.5 to 74.7 cm. We observed the largest horizontal displacements in the southern part of Thailand and moderate and small displacements in the central and northern parts. In addition to horizontal displacements throughout Thailand, continuous GPS measurements show that large parts of Thailand are subsiding at rates up to 1 cm/yr. It is the first time that such vertical post-seismic deformations at large distances (650–1500 km away from the Earthquake’s epicentre) have been recorded. We have investigated the physical processes leading to the observed subsidence. While after-slip on the subduction interface induces negligible or even slightly positive vertical motions, relaxation in the asthenosphere is associated with a sizable subsidence. Predictions from a 3D finite element model feature an asthenosphere with an effective viscosity of the order of 3 * 10¹⁸ Pas, fit the horizontal post-seismic data and the observed subsidence well. This model is then used to predict the subsidence over the whole seismic cycle. The subsidence should go on with a diminishing rate through the next two decades and its final magnitude should not exceed 10 cm in the Bangkok area.     

Tomographic reconstruction of the ionospheric electron density as a function of space and time

Electron density distribution is the major determining parameter of the ionosphere. Computerized Ionospheric Tomography (CIT) is a method to reconstruct ionospheric electron density image by computing Total Electron Content (TEC) values from the recorded Global Positioning Satellite System (GPS) signals. Due to the multi-scale variability of the ionosphere and inherent biases and errors in the computation of TEC, CIT constitutes an underdetermined ill-posed inverse problem. In this study, a novel Singular Value Decomposition (SVD) based CIT reconstruction technique is proposed for the imaging of electron density in both space (latitude, longitude, altitude) and time. The underlying model is obtained from International Reference Ionosphere (IRI) and the necessary measurements are obtained from earth based and satellite based GPS recordings. Based on the IRI-2007 model, a basis is formed by SVD for the required location and the time of interest. Selecting the first few basis vectors corresponding to the most significant singular values, the 3-D CIT is formulated as a weighted least squares estimation problem of the basis coefficients. By providing significant regularization to the tomographic inversion problem with limited projections, the proposed technique provides robust and reliable 3-D reconstructions of ionospheric electron density.     

Noise analysis of continuous GPS coordinate time series for CMONOC

The Crustal Movement Observation Network of China (CMONOC) is one of the major scientific infrastructures, mainly using Global Positioning System (GPS) measurements, to monitor crustal deformation in the Chinese mainland. In this paper, decade-long coordinate time series of 26 continuous GPS sites of CMONOC are analyzed for their noise content using maximum likelihood estimation (MLE). We study the noise properties of continuous GPS time series of CMONOC for the unfiltered, filtered solutions and also the common mode signals in terms of power law plus white noise model. In the spatial filtering, we remove for every time series a common mode error that was estimated from a modified stacking of position residuals from other sites within ∼1000 km of the selected site. We find that the common mode signal in our network has a combination of spatially correlated flicker noise and a common white noise with large spatial extent. We demonstrate that for the unfiltered solutions of CMONOC continuous GPS sites the main colored noise is a flicker process, with a mean spectral index of ∼1. For the filtered solutions, the main colored noise is a general power law process, indicating that a major number of the filtered regional solutions have a combination of noise sources or local effects. The velocity uncertainties from CMONOC continuous GPS coordinate time series may be underestimated by factors of 8–16 if a pure white noise model is assumed. In addition, using a white plus flicker noise model, the median values of velocity errors for the unfiltered solutions are 0.16 (north), 0.17 (east) and 0.58 (vertical) mm/yr, and the median values for the filtered solutions are 0.09 (north), 0.10 (east) and 0.40 (vertical) mm/yr.     

Accuracy assessment of single and double difference models for the single epoch GPS compass

The single epoch GPS compass is an important field of study, since it is a valuable technique for the orientation estimation of vehicles and it can guarantee a total independence from carrier phase slips in practical applications. To achieve highly accurate angular estimates, the unknown integer ambiguities of the carrier phase observables need to be resolved. Past researches focus on the ambiguity resolution for single epoch; however, accuracy is another significant problem for many challenging applications. In this contribution, the accuracy is evaluated for the non-common clock scheme of the receivers and the common clock scheme of the receivers, respectively. We focus on three scenarios for either scheme: single difference model vs. double difference model, single frequency model vs. multiple frequency model and optimal linear combinations vs. traditional triple-frequency least squares. We deduce the short baseline precision for a number of different available models and analyze the difference in accuracy for those models. Compared with the single or double difference model of the non-common clock scheme, the single difference model of the common clock scheme can greatly reduce the vertical component error of baseline vector, which results in higher elevation accuracy. The least squares estimator can also reduce the error of fixed baseline vector with the aid of the multi-frequency observation, thereby improving the attitude accuracy. In essence, the “accuracy improvement” is attributed to the difference in accuracy for different models, not a real improvement for any specific model. If all noise levels of GPS triple frequency carrier phase are assumed the same in unit of cycles, it can be proved that the optimal linear combination approach is equivalent to the traditional triple-frequency least squares, no matter which scheme is utilized. Both simulations and actual experiments have been performed to verify the correctness of theoretical analysis.     

基于经验加速度的低轨卫星轨道预报新方法

研究将定轨过程中的经验加速度应用于地球低轨卫星轨道预报的新方法. 利用GPS伪距观测数据和简化动力学最小二乘批处理方法对地球低轨卫星定 轨, 其中卫星位置、速度及大气阻力系数和辐射光压系数可以直接用于轨道预报. 作为简化动力学最重要特征的经验加速度呈现准周期、余弦曲线特点, 可通过 傅里叶级数拟合建模. 确定性动力学模型与补偿大气阻力模型误差的切向经验 加速度级数拟合模型组成增强型动力学模型用于提高轨道预报精度. 应用 GRACE-A星载GPS伪距观测数据和IGS超快星历定轨并进行轨道预报, 结果表明 轨道预报初值位置精度达到0.2m, 速度精度达到1×10-4m·s-1, 预报3天位置精度优于60m, 比只利用确定性动力学模型进行预报精度平 均提高2.3倍. 先定轨后预报的模式可用在星上自主精确导航系统中.      

Stochastic modelling considering ionospheric scintillation effects on GNSS relative and point positioning

Global Navigation Satellite Systems (GNSS), in particular the Global Positioning System (GPS), have been widely used for high accuracy geodetic positioning. The Least Squares functional models related to the GNSS observables have been more extensively studied than the corresponding stochastic models, given that the development of the latter is significantly more complex. As a result, a simplified stochastic model is often used in GNSS positioning, which assumes that all the GNSS observables are statistically independent and of the same quality, i.e. a similar variance is assigned indiscriminately to all of the measurements. However, the definition of the stochastic model may be approached from a more detailed perspective, considering specific effects affecting each observable individually, as for example the effects of ionospheric scintillation. These effects relate to phase and amplitude fluctuations in the satellites signals that occur due to diffraction on electron density irregularities in the ionosphere and are particularly relevant at equatorial and high latitude regions, especially during periods of high solar activity. As a consequence, degraded measurement quality and poorer positioning accuracy may result.     

Total electron content measurements in ionospheric physics

With the advent of modern global networks of dual-frequency Global Positioning System (GPS), total electron content (TEC) measurements along slant paths connecting GPS receivers and satellites at 22,000 km have become the largest data set available to ionospheric scientists. The TEC can be calculated from the time and phase delay in the GPS signal using the GPS Toolkit, but an unknown bias will remain. In addition, UHF/VHF radio beacons on board low-Earth-orbiting satellites can also be used to measure the electron content. However, the TEC measurements are obtained by integrating TEC differences between slant paths, but also contain biases. It is often necessary to use data assimilative algorithms like the Ionospheric Data Assimilation Three-Dimensional (IDA3D), and to treat both GPS- and LEO-beacon TEC measurements as relative data in order to conduct ionospheric studies.     

A realistic simulation framework to evaluate ionospheric tomography

Observation of the 3-dimensional (3-D) electron density of the ionosphere is useful to study large-scale physical processes in space weather events. Ionospheric data assimilation and ionospheric tomography are methods that can create an image of the 3-D electron density distribution. While multiple techniques have been developed over the past 30 years, there are relatively few studies that show the accuracy of the algorithms. This paper outlines a novel simulation approach to test the quality of an ionospheric tomographic inversion. The approach uses observations from incoherent scatter radar (ISR) scans and extrapolates them spatially to create a realistic ionospheric representation. A set of total electron content (TEC) measurements can then be simulated using real geometries from satellites and ground receivers. This data set, for which the ‘truth’ ionosphere is known, is used as input for a tomographic inversion algorithm to estimate the spatial distribution of electron density. The reconstructed ionospheric maps are compared with the truth ionosphere to calculate the difference between the images and the truth.To demonstrate the effectiveness of this simulation framework, an inversion algorithm called MIDAS (Multi-Instrument Data Analysis Software) is evaluated for three geographic regions with differing receiver networks. The results show the importance of the distribution and density of GPS receivers and the use of a realistic prior conditioning of the vertical electron density profile. This paper demonstrates that when these requirements are met, MIDAS can reliably estimate the ionospheric electron density. When the region under study is well covered by GPS receivers, as in mainland Europe or North America, the errors in vertical total electron content (vTEC) are smaller than 1 TECu (2–4%) . In regions with fewer and more sparsely distributed receivers, the errors can be as high as 20–40%. This is caused by poor data coverage and poor spatial resolution of the reconstruction, which has an important effect on the calibration process of the algorithm.     

A new method for improving the performance of an ionospheric model developed by multi-instrument measurements based on artificial neural network

There are remarkable ionospheric discrepancies between space-borne (COSMIC) measurements and ground-based (ionosonde) observations, the discrepancies could decrease the accuracies of the ionospheric model developed by multi-source data seriously. To reduce the discrepancies between two observational systems, the peak frequency (foF2) and peak height (hmF2) derived from the COSMIC and ionosonde data are used to develop the ionospheric models by an artificial neural network (ANN) method, respectively. The averaged root-mean-square errors (RMSEs) of COSPF (COSMIC peak frequency model), COSPH (COSMIC peak height model), IONOPF (Ionosonde peak frequency model) and IONOPH (Ionosonde peak height model) are 0.58 MHz, 19.59 km, 0.92 MHz and 23.40 km, respectively. The results indicate that the discrepancies between these models are dependent on universal time, geographic latitude and seasons. The peak frequencies measured by COSMIC are generally larger than ionosonde’s observations in the nighttime or middle-latitudes with the amplitude of lower than 25%, while the averaged peak height derived from COSMIC is smaller than ionosonde’s data in the polar regions. The differences between ANN-based maps and references show that the discrepancies between two ionospheric detecting techniques are proportional to the intensity of solar radiation. Besides, a new method based on the ANN technique is proposed to reduce the discrepancies for improving ionospheric models developed by multiple measurements, the results indicate that the RMSEs of ANN models optimized by the method are 14–25% lower than the models without the application of the method. Furthermore, the ionospheric model built by the multiple measurements with the application of the method is more powerful in capturing the ionospheric dynamic physics features, such as equatorial ionization, Weddell Sea, mid-latitude summer nighttime and winter anomalies. In conclusion, the new method is significant in improving the accuracy and physical characteristics of an ionospheric model based on multi-source observations.     

Modeling the ionospheric gradient by using VSS base functions and GPS data over Iran

The spatial and temporal variations of ionosphere play an important role in positioning and navigation by the space geodetic techniques. Therefore, the ionospheric gradient should be calculated, analyzed, and applied in both space and time. Spatial gradients of the ionosphere have remarkable delay on the propagation of electromagnetic waves. This study intends to propose a new method for simultaneous modeling of the spatial gradients of ionosphere and VTECs in the local scale for Iran. Vector Spherical Slepian (VSS) base functions are used for the development of this method.Five VSS models with the maximal degrees of L = 30, 35, 40, 45 and 50 are taken into account. For implementing the VSS method, 24 permanent GPS stations from the Iranian Permanent GPS Network (IPGN) have been used. The unknown coefficients are estimated with the observations of these stations with least squares technique. Four other stations are used for evaluating the accuracy of the models. Repeatability of baselines is the measure that is used for this purpose. Based on the results obtained, L = 40 is the optimum degree for the VSS model with this input data over Iran.The baselines’ repeatability showed that ionospheric gradients have more influence on the north–south component. Moreover, the spatial gradient is negligible in the east–west and up-down component when a short baseline is processed. In other words, this kind of ionospheric modeling has significant application for baseline, which is longer than 1000 km. In the study, proposed method has improved the long baselines' solution by more than 12%, 18% and 10% in east–west, north–south and up-down components, respectively.     

Bayesian network-based extraction of lunar impact craters from optical images and DEM data

Impact craters are among the most noticeable geomorphological features on the planetary surface and yield significant information about terrain evolution and the history of the solar system. Thus, the recognition of impact craters is an important branch of modern planetary studies. Aiming at addressing problems associated with the insufficient and inaccurate detection of lunar impact craters, a decision fusion method within the Bayesian network (BN) framework is developed in this paper to handle multi-source information from both optical images and associated digital elevation model (DEM) data. First, we implement the edge-based method for efficiently searching crater candidates which are the image patches that can potentially contain impact craters. Secondly, the multi-source representations of an impact crater derived from both optical images and DEM data are proposed and constructed to quantitatively describe the two-dimensional (2D) and three-dimensional (3D) morphology, consisting of Histogram of Oriented Gradient (HOG), Histogram of Multi-scale Slope (HMS) and Histogram of Multi-scale Aspect (HMA). Finally, a BN-based framework integrates the multi-source representations of impact craters, which can provide reductant and complementary information, for distinguishing craters from non-craters. To evaluate the effectiveness and robustness of the proposed method, experiments were conducted on three lunar scenes using both orthoimages from the Lunar Reconnaissance Orbiter (LRO) and DEM data acquired by the Lunar Orbiter Laser Altimeter (LOLA). Experimental results demonstrate that integrating optical images with DEM data significantly decreases the number of false positives compared with using optical images alone, with F₁-score of 84.8% on average. Moreover, compared with other existing fusion methods, our proposed method was quite advantageous especially for the detection of small-scale craters with diameters less than 1000 m.     

一种基于自适应滤波的GPS滚转角估计方法

全球定位系统（GPS）测姿技术主要是利用GPS载波相位和信号功率2种方法，但是测量信息单一且独立，针对旋转载体的测姿问题，提出一种基于自适应滤波的GPS滚转角估计方法，通过融合GPS接收机天线信号功率和多普勒频率信息测量载体滚转角和滚转角速度。利用当前统计模型对滚转角和滚转角速度测量进行系统建模，根据滚转角预测估计值选取量测量，并提出自适应滤波，采用滚转角加速度估计自适应滤波算法，实现了对系统噪声方差阵的自适应调整，避免了滚转角加速度最值的选取问题，降低了噪声的影响。通过仿真验证了基于自适应滤波的GPS滚转角估计方法的可行性，结果表明该方法的测量精度高于无迹卡尔曼滤波（UKF）。