Single receiver phase ambiguity resolution with GPS data

Global positioning system (GPS) data processing algorithms typically improve positioning solution accuracy by fixing double-differenced phase bias ambiguities to integer values. These “double-difference ambiguity resolution” methods usually invoke linear combinations of GPS carrier phase bias estimates from pairs of transmitters and pairs of receivers, and traditionally require simultaneous measurements from at least two receivers. However, many GPS users point position a single local receiver, based on publicly available solutions for GPS orbits and clocks. These users cannot form double differences. We present an ambiguity resolution algorithm that improves solution accuracy for single receiver point-positioning users. The algorithm processes dual- frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites. We constrain (rather than fix) linear combinations of local phase biases to improve compatibility with global phase bias estimates. For this precise point positioning, no other receiver data are required. When tested, our algorithm significantly improved repeatability of daily estimates of ground receiver positions, most notably in the east component by approximately 30% with respect to the nominal case wherein the carrier biases are estimated as real values. In this “static” test for terrestrial receiver positions, we achieved daily repeatability of 1.9, 2.1 and 6.0 mm in the east, north and vertical (ENV) components, respectively. For kinematic solutions, ENV repeatability is 7.7, 8.4, and 11.7 mm, respectively, representing improvements of 22, 8, and 14% with respect to the nominal. Results from precise orbit determination of the twin GRACE satellites demonstrated that the inter-satellite baseline accuracy improved by a factor of three, from 6 to 2 mm up to a long-term bias. Jason-2/Ocean Surface Topography Mission precise orbit determination tests results implied radial orbit accuracy significantly below the 10 mm level. Stability of time transfer, in low-Earth orbit, improved from 40 to 7 ps. We produced these results by applying this algorithm within the Jet Propulsion Laboratory’s (JPL’s) GIPSY/OASIS software package and using JPL’s orbit and clock products for the GPS constellation. These products now include a record of the wide-lane and phase bias estimates from the underlying global network of GPS stations. This implies that all GIPSY–OASIS positioning users can now benefit from this capability to perform single-receiver ambiguity resolution.     

The Reliability of GPS Ambiguity Resolution

GPS ambiguity resolution is the process of resolving the unknown cycle ambiguities of double-difference (DD) carrier-phase data as integers. It is the key to fast and high-precision relative GPS positioning. Critical in the application of ambiguity resolution is its reliability. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. High success rates are required for ambiguity resolution to be reliable. In this contribution we will introduce and evaluate such diagnostic measures. They complement existing methods of ambiguity resolution and allow the user and/or analyst to infer their reliability. ? 1999 John Wiley & Sons, Inc.     

Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm

GPS Single-epoch Real-Time Kinematic positioning is immune to cycle slips and can be immediately re-initialized after loss-of-lock, providing high availability. This technique requires reliable ambiguity resolution: incorrect ambiguities can cause position errors of several meters, and failed ambiguity resolution reduces availability. However, a bias or inaccuracy in a single phase observation can prevent successful resolution of the whole set of ambiguities. Partial ambiguity resolution allows a subset of ambiguities to be resolved with greater probability of success than the full set. A new algorithm for resolving a subset of ambiguities with validation from previous epochs is described. If normal ambiguity resolution fails, all ambiguity subsets are generated and ordered with the best subsets first. Each subset is then resolved in turn. Fixed subsets are validated against values from previous epochs; this validation procedure greatly reduces the proportion of epochs with incorrect ambiguities. An additional algorithm is described that uses the fixed ambiguities as precise ranges to resolve the remaining unfixed ambiguities. In order to test these new algorithms, GPS data were collected from static and ship-based GPS receivers around Harwich harbor and processed from reference stations at distances up to 111 km. In the static tests the distance over which a 90% ambiguity resolution success rate for dual-frequency data was achieved was increased from 15 to 76 km. However, in some cases, the processing time was too long for this algorithm to be practical without a time-based cut-off. There is also a risk of incorrect ambiguities being propagated, particularly for single-frequency processing. In a ship-based test, the distance over which sufficient availability to support harbor navigation was achieved using single-epoch dual-frequency RTK was increased from 1 to 66 km.     

BDS/GPS单历元短基线动对动定位性能分析

针对在城市峡谷环境下观测卫星较少、观测质量差和周跳频繁,导致动对动定位过程中双差模糊度不连续的问题,提出了一种GPS/BDS组合系统的单历元模糊度解算方法。通过GPS/BDS组合定位提高了卫星的可用数量,利用单历元模糊度固定减弱了周跳频繁带来的影响。实验采用GPS/BDS组合的7组数据,分析了在不同高度角下动对动定位单历元解的模糊度固定率、解算失败率、粗差率和定位精度。结果表明,GPS/BDS组合动对动定位单历元模糊度解算方法,在高遮挡的城市峡谷环境仍然可以取得较好的定位结果。     

The probability distribution of the GPS baseline for a class of integer ambiguity estimators

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     

GPS and GLONASS Integration: Modeling and Ambiguity Resolution Issues

The integration of GPS with GLONASS may be considered a major milestone in satellite-based positioning, because it can dramatically improve the reliability and productivity of said positioning. However, unlike GPS, GLONASS satellites transmit signals at different frequencies, which result in significant complexity in terms of modeling and ambiguity resolution for integrated GPS and GLONASS positioning systems. In this paper, a variety of mathematical and stochastic modeling methodologies and ambiguity resolution strategies are analyzed, and some remaining research challenges are identified. The exercise, of developing mathematical models and processing methodologies for integrated systems based on more than one satellite system, is a valuable one as it identified crucial issues concerned with the combination of any two or more microwave positioning systems, be they satellite-based or terrestrial. Hence these are experiences that can be applied to future projects that might integrate GPS with Galileo, or GLONASS and Galileo, or all three. ? 2001 John Wiley & Sons, Inc.     

Ambiguity resolution in precise point positioning with hourly data

Precise point positioning (PPP) has become a powerful tool for the scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station in PPP has been considered difficult, due to the receiver- and satellite-dependent uncalibrated hardware delays (UHD). However, recent studies show that if these UHD can be determined accurately in advance within a network of stations, then ambiguity resolution at a single station becomes possible. In this study, the method proposed by Ge et al. J Geod 82(7):389–399, 2007 is adopted with a refinement in which only one single-difference narrow-lane UHD between a pair of satellites is determined within each full pass over a regional network. This study uses the EUREF (European Reference Frame) Permanent Network (EPN) to determine the UHD from Day 245 to 251 in 2007. Then 12 International GNSS Service stations inside the EPN and 15 outside the EPN are used to conduct ambiguity resolution in hourly PPP. It is found that the mean positioning accuracy in all hourly solutions for the stations inside the EPN is improved from (3.8, 1.5, 2.8) centimeters to (0.5, 0.5, 1.4) centimeters for the East, North and Up components, respectively. For the stations outside the EPN, some of which are over 2,000 km away from the nearest EPN stations, the mean positioning accuracy in the East, North and Up directions still achieves (0.6, 0.6, 2.0) centimeters, respectively, when the EPN-based UHD are applied to these stations. These results demonstrate that ambiguity resolution at a single station can significantly improve the positioning accuracy in hourly PPP. Particularly, UHD can be even applied to a station which is up to thousands of kilometers from the UHD-determination network, potentially showing a great advantage over current network-based GPS augmentation systems. Therefore, it is feasible and beneficial for the operators of GPS regional networks and providers of PPP-based online services to provide these UHD estimates as an additional product.     

Kinematic precise point positioning at remote marine platforms

Precise kinematic differential positioning using the global positioning system (GPS) at a marine platform usually requires a relatively short distance (e.g. <500 km) to a land-based reference station. As an alternative, precise point positioning (PPP) is normally considered free from this limiting requirement. However, due to the prerequisite of network-based satellite products, PPP at a remote marine platform may still be affected by its distance to the reference network. Hence, this paper investigates this scenario by configuring rings of reference stations with different radii centered on a to-be-positioned marine platform. Particularly, we applied ambiguity resolution at a single station to PPP by estimating uncalibrated phase delays (UPDs). We used three rings of reference stations centered on a vessel, with radii of roughly 900, 2,000 and 3,600 km, to determine satellite clocks and UPDs independently. For comparison, we also performed differential positioning based on a single reference station with baseline lengths of about 400, 1,700 and 2,800 km. We demonstrate that, despite the increasing ring-network radius to a few 1,000 km, the overall change in accuracy of the satellite clocks that are used at the vessel is smaller than 0.02 ns, and the RMS values of differences between the three sets of narrow-lane UPD estimates are around 0.05 cycles only. Moreover, the kinematic positioning accuracy of PPP is affected by the increasing ring-network radius, but can still achieve several centimeters after ambiguity resolution when the vessel is over a few 1,000 km away from the ring network, showing better performance than that of differential positioning. Therefore, we propose that ambiguity-fixed PPP can be used at remote marine platforms that support precise oceanographic and geophysical applications in open oceans.     

一种基于多频模糊度快速解算方法的BDS/GPS中长基线RTK定位模型

随着全球卫星导航系统（global navigation satellite system,GNSS）进入多系统时代,空中导航卫星的可见卫星数不断增加,中国北斗卫星导航系统（BeiDou navigation satellite system,BDS）已开始面向用户提供三频导航信号,这都有利于改善单历元实时动态定位（real-time kinematic,RTK）的精度和可靠性。中长基线单历元RTK通常采用电离层无关组合算法,但是该方法将观测噪声进行了放大,模糊度固定成功率随着基线长度的增加而明显降低。提出一种BDS/GPS（global positioning system）中长基线单历元多频RTK定位算法,先以较高成功率快速固定BDS的两个超宽巷模糊度,继而通过简单变换得到BDS宽巷模糊度,然后将其辅助提高GPS宽巷模糊度固定成功率,最后采用将电离层延迟误差参数化的策略以提高BDS/GPS窄巷模糊度固定成功率。结合实测数据进行验证分析,结果表明本文算法是可行的。     

IRNSS/NavIC and GPS: a single- and dual-system L5 analysis

The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) become fully operational. In this contribution, for the fully operational IRNSS as a stand-alone system and also in combination with GPS, we provide a first assessment of L5 integer ambiguity resolution and positioning performance. While our empirical analyses are based on the data collected by two JAVAD receivers at Curtin University, Perth, Australia, our formal analyses are carried out for various onshore locations within the IRNSS service area. We study the noise characteristics (carrier-to-noise density, measurement precision, time correlation), the integer ambiguity resolution performance (success rates and ambiguity dilution of precision), and the positioning performance (ambiguity float and ambiguity fixed). The results show that our empirical outcomes are consistent with their formal counterparts and that the GPS L5-data have a lower noise level than that of IRNSS L5-data, particularly in case of the code data. The underlying model in our assessments varies from stand-alone IRNSS (L5) to IRNSS \(+\) GPS (L5), from unconstrained to height-constrained and from kinematic to static. Significant improvements in ambiguity resolution and positioning performance are achievable upon integrating L5-data of IRNSS with GPS.     

Stochastic assessment of GPS carrier phase measurements for precise static relative positioning

 Global positioning system (GPS) carrier phase measurements are used in all precise static relative positioning applications. The GPS carrier phase measurements are generally processed using the least-squares method, for which both functional and stochastic models need to be carefully defined. Whilst the functional model for precise GPS positioning is well documented in the literature, realistic stochastic modelling for the GPS carrier phase measurements is still both a controversial topic and a difficult task to accomplish in practice. The common practice of assuming that the raw GPS measurements are statistically independent in space and time, and have the same accuracy, is certainly not realistic. Any mis-specification in the stochastic model will inevitably lead to unreliable positioning results. A stochastic assessment procedure has been developed to take into account the heteroscedastic, space- and time-correlated error structure of the GPS measurements. Test results indicate that the reliability of the estimated positioning results is improved by applying the developed stochastic assessment procedure. In addition, the quality of ambiguity resolution can be more realistically evaluated. Received: 13 February 2001 / Accepted: 3 September 2001     

建筑塔机臂尖GNSS动态监测模型设计

鉴于传统的人工周期巡检方式存在诸多弊端,本文设计了一种基于卫星定位的建筑塔机臂尖动态监测模型。以GPS为例建立单历元快速定位模型,给出利用DUFCOM和DC算法相组合的整周模糊度快速确定算法（FARSE）的实现流程;提出了一种基于历元位置偏差的臂尖垂向位移监测参数及预警参数构造方法。初步试验结果表明,利用GPS单历元快速定位模型解算获得了平面精度优于2 cm、高程精度优于4 cm的定位结果;基于该定位结果,从监测参数和预警参数两个角度验证了本文模型设计的有效性。     

基于多普勒测速的GPS单历元动态定位算法

在传统的GPS单历元动态定位参数估计中,由于先验约束信息较少,模糊度求解和定位性能往往较低。据此,研究了多普勒测速在GPS单历元动态定位中的应用,提出了一种附有GPS多普勒测速信息约束的坐标更新方法,即利用移动载体先验坐标和多普勒测速信息预测当前历元坐标。考虑到该方法进行坐标更新的精度较高和传统单点定位坐标更新的稳健性较强等特点,在此基础上给出了相应的单历元整周模糊度参数求解策略,进一步提高了该方法的定位性能。试验结果表明,所提出的算法相对于传统的无速度信息坐标约束的GPS单历元动态定位算法,其模糊度浮点解精度、模糊度固定率和平均定位精度均有了进一步提高,尤其是在观测卫星数较少、卫星几何结构较差的情况下更为明显。     

Position-domain integrity risk-based ambiguity validation for the integer bootstrap estimator

Integrity monitoring for ambiguity resolution is of significance for utilizing the high-precision carrier phase differential positioning for safety–critical navigational applications. The integer bootstrap estimator can provide an analytical probability density function, which enables the precise evaluation of the integrity risk for ambiguity validation. In order to monitor the effect of unknown ambiguity bias on the integer bootstrap estimator, the position-domain integrity risk of the integer bootstrapped baseline is evaluated under the complete failure modes by using the worst-case protection principle. Furthermore, a partial ambiguity resolution method is developed in order to satisfy the predefined integrity risk requirement. Static and kinematic experiments are carried out to test the proposed method by comparing with the traditional ratio test method and the protection level-based method. The static experimental result has shown that the proposed method can achieve a significant global availability improvement by 51% at most. The kinematic result reveals that the proposed method obtains the best balance between the positioning accuracy and the continuity performance.     

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.     

Carrier phase-based integrity monitoring for high-accuracy positioning

Pseudorange-based integrity monitoring, for example receiver autonomous integrity monitoring (RAIM), has been investigated for many years and is used in various applications such as non-precision approach phase of flight. However, for high-accuracy applications, carrier phase-based RAIM (CRAIM), an extension of pseudorange-based RAIM (PRAIM) must be used. Existing CRAIM algorithms are a direct extension of PRAIM in which the carrier phase ambiguities are estimated together with the estimation of the position solution. The main issues with the existing algorithms are reliability and robustness, which are dominated by the correctness of the ambiguity resolution, ambiguity validation and error sources such as multipath, cycle slips and noise correlation. This paper proposes a new carrier phase-based integrity monitoring algorithm for high-accuracy positioning, using a Kalman filter. The ambiguities are estimated together with other states in the Kalman filter. The double differenced pseudorange, widelane and carrier phase observations are used as measurements in the Kalman filter. This configuration makes the positioning solution both robust and reliable. The integrity monitoring is based on a number of test statistics and error propagation for the determination of the protection levels. The measurement noise and covariance matrices in the Kalman filter are used to account for the correlation due to differencing of measurements and in the construction of the test statistics. The coefficient used to project the test statistic to the position domain is derived and the synthesis of correlated noise errors is used to determine the protection level. Results from four cases based on limited real data injected with simulated cycle slips show that residual cycle slips have a negative impact on positioning accuracy and that the integrity monitoring algorithm proposed can be effective in detecting and isolating such occurrences if their effects violate the integrity requirements. The CRAIM algorithm proposed is suitable for use within Kalman filter-based integrated navigation systems.

Quality assessment of GPS rapid static positioning with weighted ionospheric parameters in generalized least squares

Precise GPS positioning requires the processing of carrier-phase observations and fixing integer ambiguities. With increasing distance between receivers, ambiguity fixing becomes more difficult because ionospheric and tropospheric effects do not cancel sufficiently in double differencing. A popular procedure in static positioning is to increase the length of the observing session and/or to apply atmospheric (ionospheric) models and corrections. We investigate the methodology for GPS rapid static positioning that requires just a few minutes of dual-frequency GPS observations for medium-length baselines. Ionospheric corrections are not required, but the ionospheric delays are treated as pseudo-observations having a priori values and respective weights. The tropospheric delays are reduced by using well-established troposphere models, and satellite orbital and clock errors are eliminated by using IGS rapid products. Several numerical tests based on actual GPS data are presented. It is shown that the proposed methodology is suitable for rapid static positioning within 50–70 km from the closest reference network station and that centimeter-level precision in positioning is feasible when using just 1 min of dual-frequency GPS data.     

Precise GPS Positioning by Applying Ionospheric Corrections from an Active Control Network

In this article, initial results are presented of a method to improve fast carrier phase ambiguity resolution over longer baselines (with lengths up to about 200 km). The ionospheric delays in the global positioning system (GPS) data of these long baselines mainly hamper successful integer ambiguity resolution, a prerequisite to obtain precise positions within very short observation time spans. A way to correct the data for significant ionospheric effects is to have a GPS user operate within an active or permanently operating network use ionospheric estimates from this network. A simple way to do so is to interpolate these ionospheric estimates based on the expected spatial behaviour of the ionospheric delays. In this article such a technique is demonstrated for the Dutch Active Control Network (AGRS.NL). One hour of data is used from 4 of the 5 reference stations to obtain very precise ionospheric corrections after fixing of the integer ambiguities within this network. This is no problem because of the relatively long observation time span and known positions of the stations of the AGRS.NL. Next these interpolated corrections are used to correct the GPS data from the fifth station for its ionospheric effects. Initial conclusions about the performance of this technique are drawn in terms of improvement of integer ambiguity resolution for this baseline. ? 1999 John Wiley & Sons, Inc.     

GPS载波相位测量中的几个重要问题

利用GPS载波相位信息可以达到精密导航定位。对GPS载波测量时整周模糊解算方法和周跳的检测与恢复进行了研究。阐述了解模糊的Extradwinding技术和模糊函数法,重点研究了利用卡尔曼滤波技术实现“on-the-fly”解模糊算法。     

BDS／GPS中长基线宽巷准厘米级RTK算法

针对常规实时动态（RTK）定位技术中长基线初始化时间较长、定位结果不稳定的问题,提出了一种基于部分模糊度固定策略的BDS/GPS宽巷卡尔曼滤波RTK定位方法,从充分发挥宽巷观测值波长较长和宽巷模糊度易于固定的优势,避免低高度角卫星对模糊度解算的影响,从而提高中长基线情况下的模糊度固定率. 同时采用附加宽巷模糊度参数的卡尔曼滤波方法计算浮点解,以固定高于设置模糊度解算截止高度角的卫星进行定位,并解算电离层活动较剧烈的25~76 km的中长基线. 通过3组试验,结果表明,BDS/GPS双系统联合定位宽巷模糊度固定率均接近100%,76 km基线模糊度固定率达到99.9%,定位精度达到厘米级或准厘米级.