Rapid GPS ambiguity resolution for short and long baselines

 A method of quick initial carrier cycle ambiguity resolution is described. The method applies to high-quality dual-band global positioning system observations. Code measurements on both frequencies must be available. The rapidity of the method is achieved through smoothing pseudoranges by phase observables and forming linear combinations between the phase observables. Two cases are investigated. Case 1: ionospheric bias is neglected (short distances); and case 2: the bias is taken into account (longer distances, more than, say, 10 km). The method was tested on six baselines, from 1 to 31 km long. In most cases, single-epoch ambiguity resolution was achieved. Received: 6 October 1999 / Accepted: 4 March 2002     

A new method for three-carrier GNSS ambiguity resolution

A new method for resolving the carrier-phase integer ambiguity in Global Navigation Satellite Systems (GNSS) is presented: the MOdified Cholesky factorization for Ambiguity (MOCA) resolution. The characteristics and features of this method are described and results obtained using a software simulator and an emulator are presented to validate its efficiency. The results are then compared to those obtained using another existing method and good performance of the MOCA method in new GNSS systems is shown. Furthermore, the proposed method yields accurate results even when short time spans are used or when there are poor estimations of measurement error, making it immune to non-ideal conditions and ultimately a practical solution for real applications.     

An integer ambiguity resolution procedure for GPS/pseudolite/INS integration

In order to achieve a precise positioning solution from GPS, the carrier-phase measurements with correctly resolved integer ambiguities must be used. Based on the integration of GPS with pseudolites and Inertial Navigation Systems (INS), this paper proposes an effective procedure for single-frequency carrier-phase integer ambiguity resolution. With the inclusion of pseudolites and INS measurements, the proposed procedure can speed up the ambiguity resolution process and increase the reliability of the resolved ambiguities. In addition, a recently developed ambiguity validation test, and a stochastic modelling scheme (based on-line covariance matrix estimation) are adapted to enhance the quality of ambiguity resolution. The results of simulation studies and field experiments indicate that the proposed procedure indeed improves the performance of single-frequency ambiguity resolution in terms of both reliability and time-to-fix-ambiguity.     

A discrimination test procedure for ambiguity resolution on-the-fly

Ambiguity validation tests include the acceptance test and discrimination test, which are both important steps in the Global Positioning System ambiguity resolution process. An ambiguity discrimination test procedure based on a test statistic which is constructed by the difference (not the ratio as used in current procedures) between the minimum and second minimum quadratic form of the residuals in ambiguity identification, and its standard deviation, is proposed. The distribution function of the proposed test statistic is theoretically identified as a standard normal distribution when the known a priori variance factor is used, or as a Student's t distribution when the estimated variance factor is used. With this procedure, the ambiguity discrimination test is based on a more rigorous test statistic whose critical value can be calculated with any chosen level of significance. Test results indicate that the proposed ambiguity discrimination test procedure is reliable for use in ambiguity resolution on-the-fly. Received: 17 December 1997 / Accepted: 30 June 1998     

基于LAMBDA和DC算法的GPS单历元整周模糊度的快速确定

仅利用LAMBDA方法求解GPS单历元整周模糊度成功率不高,并且当接收卫星数较多时搜索空间较大。为此,采用TIKHONOV正则化方法削弱单历元模型法方程的病态性,并且基于协方差矩阵选择部分宽巷模糊度,先采用LAMBDA方法进行搜索,再利用高解算效率的DC算法解算剩余宽巷模糊度,最后通过两组不同线性组合的逆变换直接求取原始观测值L1和L2的整周模糊度。实验和计算表明,方法显著提高整周模糊度的搜索效率,并且提高模糊度搜索成功率。     

一种GPS整周模糊度单历元解算方法

仅利用单历元的载波相位观测值进行整周模糊度解算,观测方程秩亏,给单历元模糊度解算带来很大困难.因此,本文提出一种单历元确定GPS整周模糊度的方法.利用单历元测码伪距观测值和双频载波相位观测值组成双差观测方程,根据方差矩阵对宽巷模糊度进行分组,采用基于LABMDA方法的逐步解算方法来确定双差相位观测值的宽巷模糊度.确定宽...     

Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods

This paper investigates single epoch ambiguity resolution performance using Galileo four frequency data. Two commonly used ambiguity resolution methods are used in the tests, including the Cascade Ambiguity Resolution (CAR) and the Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) methods. For CAR method, four optimal combinations are carefully selected according to their wavelength to noise ratios and success rate for ambiguity fixing. The test results show, in general, the LAMBDA method performs better than the CAR method. The speed of ambiguity resolution is closely related to the carrier phase measurement precision. With carrier phase measurement precision of 3 mm, single epoch ambiguity resolution can be achieved at every epoch with simulated 1-s interval 24-h Galileo data (total epochs 86,400). With the increase of carrier phase noise, ambiguity resolution performances become worse. When the noise level is increased to 12 mm, single epoch ambiguity resolution can only be achieved about 50% of epochs.     

Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning

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     

Network-based geometry-free three carrier ambiguity resolution and phase bias calibration

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.

基于白噪声滤波技术及零空间约束的单频GPS模糊度解算方法

给出了一种适合单频GPS接收机的快速模糊度解算方法，利用白噪声技术提高了浮点解的精度，以基于零空间约束的累积残差和伪性能指标的比例检验法为主要的搜索策略，加速弃伪存真的过程，实验结果表明方法能快速、稳定的解算初始整周模糊度。     

GPS单频伪距相位平滑的离散性分析

基于Hatch滤波方法进行伪距相位平滑的研究,对GPS单频伪距相位平滑的离散性进行理论分析,给出移动窗口分段平滑方法的处理方案.采用自编软件,利用IGS跟踪站数据,对单频伪距相位平滑的离散性进行数据验证;对基于Hatch滤波的移动窗口分段平滑方法的可行性和效果进行分析,结果表明:移动窗口分段平滑方法可以较好地控制单频伪...     

The least-squares ambiguity decorrelation adjustment: its performance on short GPS baselines and short observation spans

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     

A comparison of P code and high performance C/A code GPS receivers for on the fly ambiguity resolution

Carrier phase ambiguity resolution on the fly is investigated using two receiver technologies, namely dual-frequency P code and high performance, single frequency, C/A code receivers. Both receiver types were used simultaneously in a series of land kinematic trials. A least-squares search technique is used to find the correct double difference carrier phase ambiguities. Both C/A and single frequency P code technologies are found to be equivalent and capable of resolving the integer ambiguities on the fly using some 30 to 200 seconds of data under benign multipath conditions. Successful ambiguity resolution on the fly results in cm-level accuracy kinematic positioning. The ambiguity resolution time required and success rate are however found to be strongly dependent on the level of carrier phase multipath and, as a consequence, on the error variance assigned to the carrier phase measurements. The use of widelaning with the dual frequency P code results in ambiguity resolution in seconds. The performance of widelaning is also superior in a comparatively high carrier phase multipath environment.     

综合变形特征及双频约束的模糊度单历元搜索算法

利用变形监测中变形量在一定范围内、主要变形方向已知等变形特征,结合双频之间模糊度约束关系,提出了一种适用于动态变形监测的双频单历元GPS整周模糊度搜索的算法。新算法还采用DOP值与信噪比相结合,进行卫星分组,进一步缩小了模糊度搜索空间,从而大大地提高了模糊度搜索的成功率和速度。通过振动监测实验表明:对变形量在1m范围内的变形监测,该算法的效果显著,成功率高达99%以上。     

GPS单频伪距相位平滑及其单点定位的精度分析

本文基于Hatch滤波方法进行GPS单频伪距相位平滑及其单点定位的研究,针对单频伪距相位平滑的离散性,给出了移动窗口分段平滑方法的具体处理方案,并研制了相应的软件模块。采用自编软件,利用IGS跟踪站观测数据,以静态模拟动态的方式,对GPS单频伪距进行了相位平滑处理和动态单点定位计算,并对单频相位平滑伪距及其单点定位的精度进行了分析。计算结果验证了本文基于Hatch滤波和移动窗口分段平滑的单频伪距相位平滑方法的可行性和有效性。     

Ionospheric calibration of single frequency VLBI and GPS observations using dual GPS data

Summary The ionospheric effect is one of the main sources of error in Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) high precision geodesy. Although the use of two frequencies allows the estimation of this effect, in some cases dual observations are not possible due to the available equipment or the type of observation. This paper presents the ionospheric calibration of single frequency VLBI and GPS observations based on the ionospheric electron content estimated from dual frequency GPS data. The ionospheric delays obtained with this procedure and the VLBI baseline length results have been compared with those obtained with dual frequency data. For the European geodetic VLBI baselines, both solutions agree at the 3–5 parts in 10^–9 level. The noise introduced by the GPS-based calibration is in the order of 3 cm for the VLBI observables and of 10 cm for the GPS observables.     

Efficiency of carrier-phase integer ambiguity resolution for precise GPS positioning in noisy environments

Precise GPS positioning relies on tracking the carrier-phase. The fractional part of carrier-phase can be measured directly using a standard phase-locked loop, but the integer part is ambiguous and the ambiguity must be resolved based on sequential carrier-phase measurements to ensure the required positioning precision. In the presence of large phase-measurement noise, as can be expected in a jamming environment for example, the amount of data required to resolve the integer ambiguity can be large, which requires a long time for any generic integer parameter estimation algorithm to converge. A key question of interest in significant applications of GPS where fast and accurate positioning is desired is then how the convergence time depends on the noise amplitude. Here we address this question by investigating integer least-sqaures estimation algorithms. Our theoretical derivation and numerical experiments indicate that the convergence time increases linearly with the noise variance, suggesting a less stringent requirement for the convergence time than intuitively expected, even in a jamming environment where the phase noise amplitude is large. This finding can be useful for practical design of GPS-based systems in a jamming environment, for which the ambiguity resolution time for precise positioning may be critical.     

附有长度约束的模糊度解算方法比较

整周模糊度解算方法的合理选择是GNSS定向处理中的关键问题,针对此问题,该文对GNSS定向中的LAMBDA_C和CLAMBDA两种附有基线长约束的模糊度固定方法的性能进行了详细的对比分析。结果显示,相对于经典的基于Ratio检验的LAMBDA算法,LAMBDA_C和CLAMBDA均可提高模糊度固定率和正确率,尤其是在单频单系统下提高效果更为显著;CLAMBD的总体固定效果略优于LAMBDA_C,但后者的解算效率更高。     

GPS单频精密单点定位的研究实现

本文研究建立了电离层参数估计的单频精密单点定位的数学模型,并综合考虑各项误差模型改正,运用卡尔曼滤波算法,开发了单频精密单点定位程序,最后利用实测数据进行实验。实验结果表明:静态平面、高程方向精度均优于0.15m,动态精度优于0.3m。     

BDS静态精密单点定位模糊度固定解精度分析

针对BDS单系统未校准相位延迟(UPD)估计以及不同时长精密单点定位(PPP)模糊度固定对定位精度影响的问题,该文选取56个测站估计UPD,利用未参与UPD计算的8个测站进行不同时长BDS静态PPP模糊度固定实验。结果表明:BDS星间单差宽巷和窄巷UPD在连续时段内具有一定的稳定性,其估计精度满足用于PPP模糊度固定要求。时长越短模糊度固定率越低。以IGS周解为参考值,不同时长模糊度固定解较浮点解三维定位精度均提高12%以上,时长越短模糊度固定解精度提高越显著。因此,模糊度固定是提高BDSPPP定位精度的重要手段。