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1.
Continuously operating reference stations (CORS) are increasingly used to deliver real-time and near-real-time precise positioning services on a regional basis. A CORS network-based data processing system uses either or both of the two types of measurements: (1) ambiguity-resolved double-differenced (DD) phase measurements, and (2) phase bias calibrated zero-differenced (ZD) phase measurements. This paper describes generalized, network-based geometry-free models for three carrier ambiguity resolution (TCAR) and phase bias estimation with DD and ZD code and phase measurements. First, the geometry-free TCAR models are constructed with two Extra-Widelane (EWL)/Widelane (WL) virtual observables to allow for rapid ambiguity resolution (AR) for DD phase measurements without distance constraints. With an ambiguity-resolved WL phase measurement and the ionospheric estimate derived from the two EWL observables, an additional geometry-free equation is formed for the third virtual observable linearly independent of the previous two. AR with the third geometry-free model requires a longer period of observations for averaging than the first two, but is also distance-independent. A more general formulation of the geometry-free model for a baseline or network is also introduced, where all the DD ambiguities can be more rigorously resolved using the LAMBDA method. Second, the geometry-free models for calibration of three carrier phase biases of ZD phase measurements are similarly defined for selected virtual observables. A network adjustment procedure is then used to improve the ZD phase biases with known DD integer constraints. Numerical results from experiments with 24-h dual-frequency GPS data from three US CORS stations baseline lengths of 21, 56 and 74 km confirm the theoretical predictions concerning AR reliability of the network-based geometry-free algorithms.
Chris RizosEmail:
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2.
Construction of anisotropic covariance functions using Riesz-representers   总被引：1，自引：1，他引：0  
A reproducing-kernel Hilbert space (RKHS) of functions harmonic in the set outside a sphere with radius R 0, having a reproducing kernel K 0(P,Q) is considered (P, Q, and later P n being points in the set of harmonicity). The degree variances of this kernel will be denoted σ0 n . The set of Riesz representers associated with the evaluation functionals (or gravity functionals) related to distinct points P n ,n = 1,…,N, on a two-dimensional surface surrounding the bounding sphere, will be linearly independent. These functions are used to define a new N-dimensional RKHS with kernel (a n >0)
If the points all are located on a concentric sphere with radius R 1>R 0, and form an ε-net covering the sphere, and a n are suitable area elements (depending on N), then this kernel will converge towards an isotropic kernel with degree variances
Consequently, if K N (P,Q) is required to represent an isotropic covariance function of the Earth's gravity potential, COV(P,Q), σ0 n can be selected so that σ n becomes equal to the empirical degree variances. If the points are chosen at varying radial distances R n >R 0, then an anisotropic kernel, or equivalent covariance function representation, can be constructed. If the points are located in a bounded region, the kernel may be used to modify the original kernel
Values of anisotropic covariance functions constructed based on these ideas are calculated, and some initial ideas are presented on how to select the points P n . Received: 24 September 1998 / Accepted: 10 March 1999  相似文献   

3.
A constrained LAMBDA method for GPS attitude determination   总被引：4，自引：0，他引：4  
An improved method to obtain fixed integer ambiguity in GPS attitude determination is presented. Known conditions are utilized as constraints to acquire attitude information when the float solution and its variance–covariance matrix are not accurate enough. The searching ellipsoidal region is first expanded to compensate for errors caused by the inaccurate float solution. Then the constraints are used to shrink the region to a proper size, which maintains the true integer ambiguity. Experimental results demonstrate that this scheme gives a fast search time and a higher success rate in determining the fixed integer ambiguity than the unconstrained method. The accuracy of attitude angles is also improved.
Bo WangEmail:
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4.
Single-frequency precise point positioning with optimal filtering   总被引：7，自引：0，他引：7  
The accuracy of standalone GPS positioning improved significantly when Selective Availability was turned off in May 2000. With the availability of various public GPS related products including precise satellite orbits and clocks, and ionosphere maps, a single-frequency standalone user can experience even a further improvement of the position accuracy. Next, using carrier phase measurements becomes crucial to smoothen the pseudorange noise. In this contribution, the most critical sources of error in single-frequency standalone positioning will be reviewed and different approaches to mitigate the errors will be considered. An optimal filter (using also carrier phase measurements) will be deployed. The final approach will then be evaluated in a decently long static test with receivers located in different regions of the world. Kinematic experiments have also been performed in various scenarios including a highly dynamic flight trial. The accuracy, in general, can be confirmed at 0.5 m horizontal and 1 m vertical, with static tests. Ultimate results demonstrate an accuracy close to 2 dm (95%) for the horizontal position components and 5 dm (95%) for the vertical in the flight experiment.
Anh Quan LeEmail:
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5.
A unified scheme for processing GPS dual-band phase observations   总被引：3，自引：4，他引：3  
A unified computational scheme is presented for sequential least-squares processing ofGPS dual-band carrier-beat-phase observations in network-mode positioning with orbit relaxation, and in orbit determination applications. This scheme is applicable to any spatial and temporal distribution of stations and satellites during a particularGPS experiment. Full covariance matrices can be specified for carrier-beat-phases and for weighted constraints on the ionosphere in order to improve phase ambiguity resolution. Physically meaningful choices for these covariance matrices are developed.  相似文献   

6.
The now classical collocation method in geodesy has been derived byH. Moritz (1970; 1973) within an appropriate Mixed Linear Model. According toB. Schaffrin (1985; 1986) even a generalized form of the collocation solution can be proved to represent a combined estimation/prediction procedure of typeBLUUE (Best Linear Uniformly Unbiased Estimation) for the fixed parameters, and of type inhomBLIP (Best inhomogeneously LInear Prediction) for the random effects with not necessarily zero expectation. Moreover, “robust collocation” has been introduced by means of homBLUP (Best homogeneously Linear weakly Unbiased Prediction) for the random effects together with a suitableLUUE for the fixed parameters. Here we present anequivalence theorem which states that the robust collocation solution in theoriginal Mixed Linear Model can identically be derived as traditionalLESS (LEast Squares Solution) in amodified Mixed Linear Model without using artifacts like “pseudo-observations”. This allows us a nice interpretation of “robust collocation” as an adjustment technique in the presence of “weak prior information”.  相似文献   

7.
In radio signal-based observing systems, such as Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR), the water vapor in the atmosphere will cause delays during the signal transmission. Such delays vary significantly with terrain elevation. In the case when atmospheric delays are to be eliminated from the measured raw signals, spatial interpolators may be needed. By taking advantage of available terrain elevation information during spatial interpolation process, the accuracy of the atmospheric delay mapping can be considerably improved. This paper first reviews three elevation-dependent water vapor interpolation models, i.e., the Best Linear Unbiased Estimator in combination with the water vapor Height Scaling Model (BLUE + HSM), the Best Linear Unbiased Estimator coupled with the Elevation-dependent Covariance Model (BLUE + ECM), and the Simple Kriging with varying local means based on the Baby semi-empirical model (SKlm + Baby for short). A revision to the SKlm + Baby model is then presented, where the Onn water vapor delay model is adopted to substitute the inaccurate Baby semi-empirical model (SKlm + Onn for short). Experiments with the zenith wet delays obtained through the GPS observations from the Southern California Integrated GPS Network (SCIGN) demonstrate that the SKlm + Onn model outperforms the other three. The RMS of SKlm + Onn is only 0.55 cm, while those of BLUE + HSM, BLUE + ECM and SKlm + Baby amount to 1.11, 1.49 and 0.77 cm, respectively. The proposed SKlm + Onn model therefore represents an improvement of 29–63% over the other known models.  相似文献   

8.
Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.  相似文献   

9.
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10.
In a linear Gauss–Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov–Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result. The delay in publishing this paper is due to a number of unfortunate complications. It was first submitted as a multi-author paper in two parts. Due to some miscommunication among the original authors, it was reassigned to one of the J Geod special issues, but later reassigned at this author’s request to a standard issue of J Geod. This compounded with a difficulty to find willing reviewers to slow the process. We apologize to the author.  相似文献   

11.
In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation spectra are introduced and estimated for the series to detect the regular and modulated dominant frequencies of the periodic patterns. Two significant periodic patterns are the diurnal and annual signals with periods of 24/n hours and 365.25/n days (n = 1, 2, …), which are the Fourier series decomposition of the regular daily and yearly periodic variations of the ionosphere. The spectrum shows a cluster of periods near 27 days, thereby indicating irregularities at this solar cycle period. A series of peaks, with periods close to the diurnal signal and its harmonics, are evident in the spectrum. In fact, the daily signal harmonics of ω i  = 2πi are modulated with the annual signal harmonics of ω j  = 2πj/365.25 as ω ijM  = 2πi(1 ± j/365.25i). Among them, at low and midlatitudes, the largest variations belong to the diurnal signal modulated to the semiannual signal. Some preliminary results on the modulated part are presented. The maximum ranges of the modulated daily signal are ±15 TECU and ±6 TECU at high and low solar periods, respectively. A model consisting of purely harmonic functions plus modulated ones is capable of studying known regular anomalies of the ionosphere, which is currently in progress.  相似文献   

12.
Artificial neural networks (ANNs) were used to predict the differential global positioning system (DGPS) pseudorange and carrier phase correction information. Autoregressive moving average (ARMA) and autoregressive (AR) models were bounded with neural networks to provide predictions of the correction. The neural network was employed to realize time-varying implementation. Online training for real-time prediction of the carrier phase enhances the continuity of service of the differential correction signals and, therefore, improves the positioning accuracy. When the correction signal from the DGPS was lost, the artificial neural networks predicted the correction data with good accuracy for the navigation system during a limited period. Comparisons of the prediction results using the two models are given.
Young Jae LeeEmail:
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13.
BDS网络RTK中距离参考站整周模糊度单历元解算方法   总被引：1，自引：1，他引：0  
提出了一种BDS网络RTK中距离(50~100 km)参考站间的双频载波相位整周模糊度单历元解算方法。该方法首先利用B1、B2载波相位整周模糊度间的线性关系选取B1、B2载波相位整周模糊度备选值。利用双频载波相位整周模糊度备选值计算双差电离层延迟误差,根据参考站各卫星电离层延迟误差间的空间关系,使用双差电离层延迟误差构建双差电离层延迟误差的线性计算模型。通过双差电离层延迟误差线性计算模型的建立搜索和确定B1、B2载波相位的整周模糊度。经CORS网实测数据试验算例的验证,该方法只需一个历元的观测数据即可确定参考站间双差B1、B2载波相位整周模糊度,且不受周跳影响。  相似文献   

14.
In this paper we study the following mixed boundary value problem
where is the reference ellipsoid, and T the disturbing potential. With the help of the variational principles of partial differential equations and the expression of ellipsoidal harmonic series, we give a linear system related to the coefficients of the ellipsoidal harmonic series. Hence the solution of the problem can be obtained in the form of ellipsoidal harmonic series, which supplies us an important theoretical basis for making use of data given by satellite altimetry measurements more efficiently. Received: 16 January 1996; Accepted: 22 January 1997  相似文献   

15.
While there is a large literature on the form of epidemic waves in the time domain, models of their structure and shape in the spatial domain remain poorly developed. This paper concentrates on the changing spatial distribution of an epidemic wave over time and presents a simple method for identifying the leading and trailing edges of the spatial advance and retreat of such waves. Analysis of edge characteristics is used to (a) disaggregate waves into ‘swash’ and ‘backwash’ stages, (b) measure the phase transitions of areas from susceptible, S, through infective, I, to recovered, R, status (S → I → R) as dimensionless integrals and (c) estimate a spatial version of the basic reproduction number, R 0. The methods used are illustrated by application to measles waves in Iceland over a 60-year period from 1915 to 1974. Extensions of the methods for use with more complex waves are possible through modifying the threshold values used to define the start and end points of an event.
Peter HaggettEmail:
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16.
With the increasing global distribution of high rate dual-frequency global positioning system (GPS) receivers, the production of a real-time atmospheric constituent definition, total electron content (TEC), has become a beneficial contributor to the modeling applications used in the assessment of GPS position accuracy and the composition of the ionosphere, plasmasphere, and troposphere. Historically, TEC measurements have been obtained through post processing techniques to produce the quality of data necessary for modeling applications with rigorous error estimate requirements. These procedures necessitated the collection of large volumes of data to address the various abnormalities in the computation of TEC associated with the use of greater data quality controls and source selection while real-time modeling environments must rely on autonomous controls and filtration techniques to prevent the production of erroneous model results. In this paper we present methods for processing TEC in real time, which utilize several procedures including the application of an ionospheric model to automatically perform quality control on the TEC output and the computational techniques used to address receiver multipath, faulty receiver observations, cycle-slips, segmented processing, and receiver calibrations. The resulting TEC measurements are provided with rigorous error estimates validated using the vertical TEC from the Jason satellite mission.
Nelson A. BonitoEmail:
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17.
In Global Navigation Satellite System (GNSS) positioning, the receiver measures the pseudorange with respect to each observable navigation satellite and determines the position and clock bias. In addition to the GPS, several other navigation satellite constellations including Glonass, Galileo and Compass can/will also be used to provide positioning, navigation, and timing information. The paper is concerned with the solvability of the navigation problem when the receiver attempts to process measurements from different constellations. As two different constellations may not be time-synchronized, the navigation problem involves the determination of position of the receiver and clock bias with respect to each constellation. The paper describes an analytic approach to account for the two-constellation navigation problem with three measurements from one constellation and two measurements from another constellation. It is shown that the two-constellation GNSS navigation problem becomes the solving of a set of two simultaneous quadratic equations or, equivalently, a quartic equation. Furthermore, the zero-crossover of the leading coefficient and the sign of the discriminant of the quartic equation are shown to play a significant role in governing the solvability, i.e., the existence and uniqueness of the navigation solutions.
Jyh-Ching JuangEmail:
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18.
Existing algorithms for GPS ambiguity determination can be classified into three categories, i.e. ambiguity resolution in the measurement domain, the coordinate domain and the ambiguity domain. There are many techniques available for searching the ambiguity domain, such as FARA (Frei and Beutler in Manuscr Geod 15(4):325–356, 1990), LSAST (Hatch in Proceedings of KIS’90, Banff, Canada, pp 299–308, 1990), the modified Cholesky decomposition method (Euler and Landau in Proceedings of the sixth international geodetic symposium on satellite positioning, Columbus, Ohio, pp 650–659, 1992), LAMBDA (Teunissen in Invited lecture, section IV theory and methodology, IAG general meeting, Beijing, China, 1993), FASF (Chen and Lachapelle in J Inst Navig 42(2):371–390, 1995) and modified LLL Algorithm (Grafarend in GPS Solut 4(2):31–44, 2000; Lou and Grafarend in Zeitschrift für Vermessungswesen 3:203–210, 2003). The widely applied LAMBDA method is based on the Least Squares Ambiguity Search (LSAS) criterion and employs an effective decorrelation technique in addition. G. Xu (J Glob Position Syst 1(2):121–131, 2002) proposed also a new general criterion together with its equivalent objective function for ambiguity searching that can be carried out in the coordinate domain, the ambiguity domain or both. Xu’s objective function differs from the LSAS function, leading to different numerical results. The cause of this difference is identified in this contribution and corrected. After correction, the Xu’s approach and the one implied in LAMBDA are identical. We have developed a total optimal search criterion for the mixed integer linear model resolving integer ambiguities in both coordinate and ambiguity domain, and derived the orthogonal decomposition of the objective function and the related minimum expressions algebraically and geometrically. This criterion is verified with real GPS phase data. The theoretical and numerical results show that (1) the LSAS objective function can be derived from the total optimal search criterion with the constraint on the fixed integer ambiguity parameters, and (2) Xu’s derivation of the equivalent objective function was incorrect, leading to an incorrect search procedure. The effects of the total optimal criterion on GPS carrier phase data processing are discussed and its practical implementation is also proposed.  相似文献   

19.
Many kinematic GPS applications rely on high accuracy, which usually requires the ambiguities to be fixed. Normally, a reference station in the rover’s vicinity is needed for successful ambiguity resolution. Alternatively, a network surrounding the rover and allowing one to derive area correction parameters is needed. Unfortunately, both approaches are not feasible in certain situations. This paper is a contribution to precise kinematic positioning over long baselines. Atmospheric refraction becomes critical in the error budget, but progress has been made to use numerical weather models to derive tropospheric corrections, for instance. The spatial correlation of both ionospheric and tropospheric propagation delays is investigated in this paper and special attention is paid on the systematic error behavior of tropospheric refraction. The principles developed are applied to an extended reliability test of the ambiguities. Finally, it is demonstrated in positioning experiments that kinematic positioning retrieval with fixed ambiguities is actually possible for baselines between 150 and 300 km with an accuracy of approximately 2 cm in post-mission processing.
Torben SchülerEmail: Phone: +49-89-60042587Fax: +49-89-60043019
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20.
Income distribution dynamics and cross-region convergence in Europe   总被引：3，自引：3，他引：0  
This paper presents a continuous version of the model of distribution dynamics to analyse the transition dynamics and implied long-run behaviour of the EU-27 NUTS-2 regions over the period 1995–2003. It departs from previous research in two respects: first, by introducing kernel estimation and three-dimensional stacked conditional density plots as well as highest density regions plots for the visualisation of the transition function, based on Hyndman et al. (J Comput Graph Stat 5(4):315–336, 1996), and second, by combining Getis’ spatial filtering view with kernel estimation to explicitly account for the spatial dimension of the growth process. The results of the analysis indicate a very slow catching-up of the poorest regions with the richer ones, a process of shifting away of a small group of very rich regions, and highlight the importance of geography in understanding regional income distribution dynamics.
Manfred M. FischerEmail:
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