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1.
In this contribution we consider the time-averaged GPS single-baseline model and study in a qualitative sense its relation with the geometry-free model and the geometry-based model. The least-squares estimators of the model are derived and their properties discussed. Special attention is given to the ambiguity search space, since it plays such a crucial role in the problem of integer ambiguity estimation and validation. Easy-to-evaluate, closed-form expressions are presented for the volumes of the ambiguity search spaces that belong to the geometry-free model, the single-epoch geometry-based model and the time-averaged model. By means of an eigenvalue analysis, the geometry of the ambiguity search spaces is revealed and its impact on the search for the integer least-squares ambiguities discussed. Received: 3 April 1996; Accepted: 6 January 1997  相似文献   

2.
This contribution is the last of four parts and deals with the link between baseline precision and ambiguity reliability. It is shown analytically how and to what extent the baseline-ambiguity correlation is related to the gain in baseline precision, to the volume of the ambiguity search space, and to the impact of potential integer ambiguity biases. Also, an ambiguity DOP measure is introduced together with its closed-form formulae for the three different single-baseline models. Received: 16 July 1996 / Accepted: 14 November 1996  相似文献   

3.
S. Han 《Journal of Geodesy》1997,71(6):351-361
An integrated method for the instantaneous ambiguity resolution using dual-frequency precise pseudo-range and carrier-phase observations is suggested in this paper. The algorithm combines the search procedures in the coordinate domain, the observation domain and the estimated ambiguity domain (and therefore benefits from the integration of their most positive elements). A three-step procedure is then proposed to enhance the reliability of the ambiguity resolution by: (1) improving the stochastic model for the double-differenced functional model in real time; (2) refining the criteria which distinguish the integer ambiguity set that generates the minimum quadratic form of residuals from that corresponding to the second minimum one; and (3) developing a fault detection and adaptation procedure. Three test scenarios were considered, one static baseline (11.3 km) and two kinematic experiments (baseline lengths from 5.2 to 13.7 km). These showed that the mean computation time for one epoch is less than 0.1 s, and that the success rate reaches 98.4% (compared to just 68.4% using standard ratio tests). Received: 5 June 1996; Accepted: 16 January 1997  相似文献   

4.
 The problem of phase ambiguity resolution in global positioning system (GPS) theory is considered. The Bayesian approach is applied to this problem and, using Monte Carlo simulation to search over the integer candidates, a practical expression for the Bayesian estimator is obtained. The analysis of the integer grid points inside the search ellipsoid and their evolution with time, while measurements are accumulated, leads to the development of a Bayesian theory based on a mathematical mixture model for the ambiguity. Received: 29 March 2001 / Accepted: 3 September 2001  相似文献   

5.
A canonical theory for short GPS baselines. Part I: The baseline precision   总被引：5，自引：4，他引：1  
The present contribution is the first of four parts. It considers the precision of the floated and the fixed baseline. A measure is introduced for the gain in baseline precision which is experienced when the carrier phase double-differenced ambiguities are treated as integers instead of as reals. The properties of this measure are analyzed, and it is shown by means of principal angles how it relates to the change over time of the relative receiver-satellite geometry. We also present canonical forms of the baseline variance matrices for different measurement scenarios. These canonical forms make the relation between the various variance matrices transparent and thus present a simple way of studying their relative merits. Received: 16 July 1996; Accepted: 14 November 1996  相似文献   

6.
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   

7.
In this contribution we analyse in a qualitative sense for the geometry-free model the dependency of the location, the size and the shape of the ambiguity search space on different factors of the stochastic model. For this purpose a rather general stochastic model is used. It includes time-correlation, cross-correlation, satellite elevation dependency and the use of an a priori weighted ionospheric model, having the ionosphere-fixed model and the ionosphere-float model as special cases. It is shown that the location is invariant for changes in the cofactor matrix of the phase observables. This also holds true for the cofactor matrix of the code observables in the ionosphere-float case. As for time-correlation and satellite elevation dependency, it is shown that they only affect the size of the search space, but not its shape and orientation. It is also shown that the least-squares ambiguities, their variance matrix and its determinant, for, respectively, the ionosphere-fixed model, the ionosphere-float model and the ionosphere-weighted model, are all related through the same scalar weighted mean, the weight of which is governed by the variance ratio of the ionospheric delays and the code observables. A closed-form expression is given for the area of the search space in which all contributing factors are easily recognized. From it one can infer by how much the area gets blown up when the ionospheric spatial decorrelation increases. This multiplication factor is largest when one switches from the ionosphere-fixed model to the ionosphere-float model, in which case it is approximately equal to the ratio of the standard deviation of phase with that of code. The area gives an indication of the number of grid points inside the search space. Received: 11 November 1996 / Accepted: 21 March 1997  相似文献   

8.
On the GPS widelane and its decorrelating property   总被引：2，自引：1，他引：2  
In this contribution we consider the popular widelaning technique from the viewpoint of ambiguity decorrelation. It enables us to cast the technique into the framework of the least-squares ambiguity decorrelation adjustment (LAMBDA) and to analyse its relative merits. In doing so, we will provide answers to the following three questions. Does the widelane decorrelate? Does it explicitly appear in the automated transformation step of the LAMBDA method? Can one do better than the widelane? It is shown that all three questions can be answered in the affirmative. This holds true for the ionosphere-fixed case, the ionosphere-float case, as well as for the ionosphere-weighted case. Received: 11 November 1996 / Accepted: 23 April 1997  相似文献   

9.
Success probability of integer GPS ambiguity rounding and bootstrapping   总被引：26，自引：7，他引：19  
Global Positioning System ambiguity resolution is usually based on the integer least-squares principle (Teunissen 1993). Solution of the integer least-squares problem requires both the execution of a search process and an ambiguity decorrelation step to enhance the efficiency of this search. Instead of opting for the integer least-squares principle, one might also want to consider less optimal integer solutions, such as those obtained through rounding or sequential rounding. Although these solutions are less optimal, they do have one advantage over the integer least-squares solution: they do not require a search and can therefore be computed directly. However, in order to be confident that these less optimal solutions are still good enough for the application at hand, one requires diagnostic measures to predict their rate of success. These measures of confidence are presented and it is shown how they can be computed and evaluated. Received: 24 March 1998 / Accepted: 8 June 1998  相似文献   

10.
In this contribution GPS statistics are presented for the case that the relative receiver-satellite geometry is included in the single baseline model and for the case that the relative receiver-satellite geometry is excluded. It is shown that the statistics are linked through a particular form of a phased adjustment. Based on the stepwise approach of a phased adjustment, the impact of using satellite geometry or dispensing with it, on the least-squares estimators, on the teststatistics and their associated reliability, and on the integer ambiguity estimation, is presented and analyzed. Received 1 March 1996; Accepted 22 July 1996  相似文献   

11.
The present contribution is the second of four parts. It considers the precision and correlation of the least-squares estimators of the carrier phase ambiguities. It is shown how the precision and correlation of the double-differenced ambiguities as well as of the widelane ambiguities are effected by the observation weights, by the number of satellites tracked, by the number of observation epochs used, and by the change over time of the relative receiver-satellite geometry. Also the ability of the widelane transformation to decorrelate and to improve the precision is investigated. Received: 16 July 1996 / Accepted: 14 November 1996  相似文献   

12.
 Carrier phase ambiguity resolution is the key to fast and high-precision GNSS (Global Navigation Satellite System) kinematic positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. Very high success rates are therefore required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower the success rate and thus increase the chance of unsuccessful ambiguity resolution. The performance of integer ambiguity estimation in the presence of such biases is studied. Particular attention is given to integer rounding, integer bootstrapping and integer least squares. Lower and upper bounds, as well as an exact and easy-to-compute formula for the bias-affected success rate, are presented. These results will enable the evaluation of the bias robustness of ambiguity resolution. Received: 28 September 2000 / Accepted: 29 March 2001  相似文献   

13.
A new approach to GPS ambiguity decorrelation   总被引：13，自引：1，他引：12  
Ambiguity decorrelation is a useful technique for rapid integer ambiguity fixing. It plays an important role in the least-squares ambiguity decorrelation adjustment (Lambda) method. An approach to multi-dimension ambiguity decorrelation is proposed by the introduction of a new concept: united ambiguity decorrelation. It is found that united ambiguity decorrelation can provide a rapid and effective route to ambiguity decorrelation. An approach to united ambiguity decorrelation, the HL process, is described in detail. The HL process performs very well in high-dimension ambiguity decorrelation tests. Received: 9 March 1998 / Accepted: 1 June 1999  相似文献   

14.
Grid point search algorithm for fast integer ambiguity resolution   总被引：1，自引：0，他引：1  
A Grid Point Search Algorithm (GRIPSA) for fast integer ambiguity resolution is presented. In the proposed algorithm, after the orthogonal transformation of the original ambiguity parameters, the confidence ellipsoid of the new parameters is represented by a rectangular polyhedron with its edges parallel to the corresponding axes. A cubic grid covering the whole polyhedron is then identified and transformed back to the original coordinate system. The integer values of the corresponding transformed grid points are obtained by rounding off the transformed values to their nearest integer values. These values are then tested as to whether they are located inside the polyhedron. Since the identification of the grid points in the transformed coordinate system greatly reduces the search region of the integer ambiguities, marked improvements are obtained in the computational effort. Received: 13 October 1997 / Accepted: 9 June 1998  相似文献   

15.
The least-squares ambiguity decorrelation adjustment is a method for fast GPS double-difference (DD) integer ambiguity estimation. The performance of the method will be discussed, and although it is stressed that the method is generally applicable, attention is restricted to short-baseline applications in the present contribution. With reference to the size and shape of the ambiguity search space, the volume of the search space will be introduced as a measure for the number of candidate grid points, and the signature of the spectrum of conditional variances will be used to identify the difficulty one has in computing the integer DD ambiguities. It is shown that the search for the integer least-squares ambiguities performs poorly when it takes place in the space of original DD ambiguities. This poor performance is explained by means of the discontinuity in the spectrum of conditional variances. It is shown that through a decorrelation of the ambiguities, transformed ambiguities are obtained which generally have a flat and lower spectrum, thereby enabling a fast and efficient search. It is also shown how the high precision and low correlation of the transformed ambiguities can be used to scale the search space so as to avoid an abundance of unnecessary candidate grid points. Numerical results are presented on the spectra of conditional variances and on the statistics of both the original and transformed ambiguities. Apart from presenting numerical results which can typically be achieved, the contribution also emphasizes and explains the impact on the method's performance of different measurement scenarios, such as satellite redundancy, single vs dual-frequency data, the inclusion of code data and the length of the observation time span. Received: 31 October 1995 / Accepted: 21 March 1997  相似文献   

16.
采用方向余弦矩阵描述姿态,建立GPS/陀螺组合姿态确定系统模型,由矩阵Kalman滤波方法解算整周模糊度的浮点解,然后再利用MCLambda方法得到整周模糊度固定解。仿真实验结果表明,附加方向余弦矩阵约束的Kalman滤波方法可以有效地提高整周模糊度浮点解的精度,使得整周模糊度的固定成功率和效率均得到提高,尤其是在GPS观测条件较差的情况下。  相似文献   

17.
In current global positioning system (GPS) ambiguity resolution practice there is not yet a rigorous procedure in place to diagnose its expected performance and to evaluate the probabilistic properties of the computed baseline. The necessary theory to bridge this gap is presented. Probabilistic statements about the `fixed' GPS baseline can be made once its probability distribution is known. This distribution is derived for a class of integer ambiguity estimators. Members from this class are the ambiguity estimators that follow from `integer rounding', `integer bootstrapping' and `integer least squares' respectively. It is also shown how this distribution differs from the one which is usually used in practice. The approximations involved are identified and ways of evaluating them are given. In this comparison the precise role of GPS ambiguity resolution is clarified. Received: 3 August 1998 / Accepted: 4 March 1999  相似文献   

18.
The parameter distributions of the integer GPS model   总被引：6，自引：0，他引：6  
 A parameter estimation theory is incomplete if no rigorous measures are available for describing the uncertainty of the parameter estimators. Since the classical theory of linear estimation does not apply to the integer GPS model, rigorous probabilistic statements cannot be made with reference to the classical results. The fact that integer parameters are involved in the estimation process forces a reappraisal of the propagation of uncertainty. It is with this purpose in mind that the joint and marginal distributional properties of both the integer and non-integer parameters of the GPS model are determined. These joint distributions can also be used to determine the distribution of functions of the parameters. As an important example, the distribution of the vector of ambiguity residuals is determined. Received: 30 January 2001 / Accepted: 31 July 2001  相似文献   

19.
M. C. Kim 《Journal of Geodesy》1997,71(12):749-767
The fundamental geometry of satellite ground tracks and their crossover problem are investigated. For idealized nominal ground tracks, the geometry is governed by a few constant parameters whose variations lead to qualitative changes in the crossover solutions. On the basis that the theory to locate crossovers has not been studied in sufficient detail, such changes are described in regard to the number of crossover solutions in conjunction with their bifurcations. Employing the spinor algebra as a tool for establishing the ground-track crossing condition, numerical methodologies to locate crossovers appearing in general dual-satellite ground-track configurations are also presented. The methodologies are applied to precisely determined orbital ephemerides of the GEOSAT, ERS-1, and TOPEX/POSEIDON altimeter satellites. Received: 19 November 1996 / Accepted: 12 May 1997  相似文献   

20.
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