A modified geometry- and ionospheric-free combination for static three-carrier ambiguity resolution

The reliability of the classical geometry- and ionospheric-free (GIF) three-carrier ambiguity resolution (TCAR) degrades when applied to long baselines of hundreds of kilometers. To overcome this deficiency, we propose two new models, which are used sequentially to resolve wide-lane (WL) and narrow-lane (NL) ambiguities and form a stepwise ambiguity resolution (AR) strategy. In the first model, after a successful extra-wide-lane AR, the pseudorange and phase observations are combined to estimate WL ambiguities, in which the residual ionospheric delays and geometry effects are eliminated. In the second model, using the resolved ambiguities from the first step, the two WL ambiguities are combined to remove ionospheric and geometry effects. The unknown coefficients in the two models are determined in such that they minimize the formal errors in the ambiguity estimates to optimize the ambiguity estimation. Using experimental BeiDou triple-frequency observations, we evaluate our method and identify three advantages. First, the two models use double-differenced phase observations that are not differences across frequency. Second, the two models are entirely free from ionospheric delay and geometry effects. Third, the unknown estimates in the two models satisfy the minimum noise condition, which makes the formal errors in the float NL ambiguity estimates much lower than those obtained with common GIF TCAR methods, thereby directly and significantly increasing the success rate of AR compared to the cascaded integer resolution method and two other GIF combinations.     

Network-based triple-frequency carrier phase ambiguity resolution between reference stations using BDS data for long baselines

Network-based ambiguity resolution (AR) between reference stations is the prerequisite to realize a precise real-time kinematic positioning service. With the help of BDS triple-frequency signals, we can efficiently deal with the ionospheric delay and tropospheric delay, and achieve rapid and reliable AR. To overcome the inaccurate ionospheric delay estimated by the geometry-free three carrier ambiguity resolution (GF TCAR) technique, which leads to failure in the original ambiguity resolution, we propose an ionospheric-free (IF) TCAR method to resolve the ambiguity between the reference stations over long baselines. Taking full advantage of the known positions of the reference stations, the easily resolved extra-wide-lane (EWL) ambiguity, and the IF phase combinations, we can reliably fix the wide-lane (WL) ambiguity. A Kalman filter is applied to estimate precise IF ambiguities and the original ambiguity is resolved with the fixed WL ambiguity. A numerical analysis with triple-frequency BDS data from three long baselines of a CORS network is provided to compare the AR performance of GF TCAR with that of IF TCAR. The results show that both methods can reliably resolve the WL ambiguity with a remarkable correctly-fixed rate of higher than 99%, and the reliably-fixed rates of the IF TCAR slightly increase from 92.19, 94.67 and 94.61–98.26, 99.54 and 97.51% for the three baselines. Herein “correctly-fixed” and “reliably-fixed” mean the difference between the float ambiguity and the true one are less than ± 0.5 and ± 0.25 cycles, respectively. On the other hand, the AR performance of the original signals with the IF TCAR method is much better than that with the GF TCAR method attaining a 100% correctly-fixed rate, while the GF TCAR method can hardly fix the original ambiguity with the largest bias being as much as 4 cycles because of the amplified systematic bias.     

Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization

Recent research has demonstrated that the undifferenced integer ambiguities can be recovered using products from a network solution. The standard dual-frequency PPP integer ambiguity resolution consists of two aspects: Hatch-Melbourne-Wübbena wide-lane (WL) and ionosphere-free narrow-lane (NL) integer ambiguity resolution. A major issue affecting the performance of dual-frequency PPP applications is the time it takes to fix these two types of integer ambiguities, especially if the WL integer ambiguity resolution suffers from the noisy pseudorange measurements and strong multipath effects. With modernized Global Navigation Satellite Systems, triple-frequency measurements will be available to global users and an extra WL (EWL) model with very long wavelength can be formulated. Then, the easily resolved EWL integer ambiguities can be used to construct linear combinations to accelerate the PPP WL integer ambiguity resolution. Therefore, we propose a new reliable procedure for the modeling and quality control of triple-frequency PPP WL and NL integer ambiguity resolution. First, we analyze a WL integer ambiguity resolution model based on triple-frequency measurements. Then, an optimal pseudorange linear combination which is ionosphere-free and has minimum measurement noise is developed and used as constraint in the WL and the NL integer ambiguity resolution. Based on simulations, we have investigated the inefficiency of dual-frequency WL integer ambiguity resolution and the performance of EWL integer ambiguity resolution. Using almanacs of GPS, Galileo and BeiDou, the performances of the proposed triple-frequency WL and NL models have been evaluated in terms of success rate. Comparing with dual-frequency PPP, numerical results indicate that the proposed triple-frequency models can outperform the dual-frequency PPP WL and NL integer ambiguity resolution. With 1 s sampling rate, generally, only several minutes of data are required for reliable triple-frequency PPP WL and NL integer ambiguity resolution. Under benign observation situations and good geometries, the integer ambiguity can be reliably resolved even within 10 s.     

Performance analysis of triple-frequency ambiguity resolution with BeiDou observations

We investigate triple-frequency ambiguity resolution performance using real BeiDou data. We test four ambiguity resolution (AR) methods which are applicable to triple-frequency observations. These are least squares ambiguity decorrelation adjustment (LAMBDA), GF-TCAR (geometry-free three-carrier ambiguity resolution), GB-TCAR (geometry-based three-carrier ambiguity resolution) and GIF-TCAR (three-carrier ambiguity resolution based on the geometry-free and ionospheric-free combination). A comparison between LAMBDA, GF-TCAR and GB-TCAR was conducted over three short baselines and two medium baselines. The results indicated that LAMBDA is optimal in both short baseline and medium baseline cases. However, the performances of GB-TCAR and LAMBDA differ slightly for short baselines. Compared with GF-TCAR, which uses the geometry-free model, the GB-TCAR using the geometry-based model improves the AR performance significantly. Compared with dual-frequency observations, the LAMBDA AR results show a significant improvement when using triple-frequency observations over short baselines. The performance of GIF-TCAR is evaluated using multi-epoch observations. The results indicated that multi-path errors on carrier phases will have a significant influence on GIF-TCAR AR results, which leads to different GIF-TCAR AR performance for different type of satellites. For GEO (Geostationary Orbit) satellites, the ambiguities can barely be correctly fixed because the multi-path errors on carrier phases are very systematic. For IGSO (Inclined Geosynchronous Orbit) and MEO (Medium Earth Orbit) satellites, when the elevation cutoff angle is set as 30°, several tens to several hundreds of epochs are needed for correctly fixing the narrow lane ambiguities. The comparison of positioning performance between dual-frequency observations and triple-frequency observations was also conducted. The results indicated that a minor improvement can be achieved by using triple-frequency observations compared with using dual-frequency observations.     

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.     

ERTK: extra-wide-lane RTK of triple-frequency GNSS signals

Triple-frequency signals have thus far been available for all satellites of BeiDou and Galileo systems and for some GPS satellites. The main benefit of triple-frequency signals is their formation of extra-wide-lane (EWL) combinations whose ambiguities can be instantaneously fixed for several 10–100 km baselines. Yet, this benefit has not been fully exploited and only used as a constraint for narrow-lane (NL) ambiguity resolution (AR) in most previous studies. In this study, we comprehensively investigate the real-time kinematic (RTK) capabilities of EWL observations, also referred to as EWL RTK (ERTK). We begin by mathematically expressing the ease of EWL AR and the difficulty of NL AR, respectively, using a numerical demonstration. We then present the mathematical models for ERTK including the ionosphere-ignored, ionosphere-float and ionosphere-smoothed types. The experiments are conducted using a four-station network of real triple-frequency BeiDou data with baseline lengths from 33 to 75 km. The results show that the ionosphere-ignored ERTK achieves real-time solutions with a horizontal accuracy of about 10 cm. Although the ionosphere-float ERTK solutions are very noisy, they can be quickly improved at the centimetre level by further applying the ionosphere-smoothed model. Note that such accurate results are very promising and already satisfy many applications without complicated NL AR. To the best of our knowledge, this is the first comprehensive study to make full use of EWL observations of triple-frequency signals on RTK.     

基于无几何电离层滤波模型的北斗三号系统相位周跳与中断修复方法

高精度位置服务依赖模糊度正确固定的载波相位观测值,而复杂环境的相位周跳和中断给模糊度固定和数据处理带来了巨大挑战。北斗三号系统向全球播发四频和五频信号,为提升周跳处理性能提供了机遇。本文建立了探测多频超宽巷周跳的伪距-相位无几何组合模型,以及探测窄巷周跳的相位-相位无几何组合模型,并以周跳探测成功概率最大为准则确定了多频最优超宽巷和窄巷组合。由于电离层延迟制约了数据中断和电离层变化剧烈情况下的窄巷周跳探测,进而建立了顾及电离层延迟的窄巷周跳探测滤波模型。试验结果表明,对30 s采样间隔,基于无几何组合模型探测周跳的成功率均优于96%;对于3 min的数据中断,基于无几何组合模型的周跳探测成功率仅为70%,但补偿电离层延迟的滤波模型将成功率提升至95%以上。     

北斗三频电离层延迟及码硬件延迟解算方法

准确固定非差模糊度是利用相位观测量获取高精度电离层延迟的关键。三频观测条件下常规的处理策略需依次固定超宽巷、宽巷以及窄巷模糊度,通常利用MW（melbourne-wubbena）组合解算宽巷模糊度时易受到码硬件延迟和观测噪声的影响而固定错误。利用北斗三频数据和GIM（grid ionosphenimap）产品,通过固定的超宽巷模糊度以及构造相位无几何组合解算宽巷模糊度,进而重构得到高精度电离层延迟,并且分离了码硬件延迟总量。结果表明,GIM模型辅助条件下宽巷模糊度固定成功率能达到100%,且消除了系统性偏差;电离层重构值与GIM模型改正值存在约1 m的差异,等效精度约6TECU;分离的码硬件延迟变化平稳,标准偏差不超过0.3 m。     

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.

一种顾及电离层延迟信息的长基线北斗三频模糊度解算方法

北斗卫星导航系统播发3个频点的导航信号,有利于载波相位模糊度解算。鉴于传统的三频模糊度解算方法由于受基线距离的限制难以在中长基线情形下可靠地固定模糊度,本文提出一种适用于北斗卫星系统中长基线模糊度固定的新方法。实验结果表明,改进的新算法不受基线长度的约束,在保证超宽巷、宽巷模糊度正确固定的同时,宽巷模糊度估值误差在0.3周以内;窄巷模糊度估值误差在3周以内。相比于传统算法,新方法的改进效果较好。     

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。     

Triple-frequency carrier ambiguity resolution for Beidou navigation satellite system

The Chinese Beidou system, also known as Compass, has entered its trial operational stage and can already provide services for triple-frequency users. Using triple-frequency signals is expected to be of great benefit for ambiguity resolution. Based on error characteristic analysis of the Beidou frequencies, we introduce the procedure of selecting the best combinations of triple-frequency signals. The geometry-based model and geometry-free model of triple-frequency signals are presented. Three triple-frequency carrier ambiguity resolution (TCAR) methods are described, which include the cascading rounding method, the stepwise AR method and the modified stepwise AR method. In order to evaluate the performance of these methods, observations from baselines of various lengths were collected using Beidou triple-frequency receivers and were processed epoch-by-epoch using the three methods. The same observation data were also processed in a dual-frequency mode for comparison. The results show that, compared to the dual-frequency based solution, the single epoch ambiguity resolution success rate with triple frequency improved nearly 30 % for the short baselines (<20 km) and 100 % for the mid-length baselines (20–50 km) using the proposed modified stepwise AR method.     

一种改进的基于 BDS 三频非差观测的周跳实时探测与修复模型

BDS三频观测条件下可以组合得到具有优良特性的虚拟载波观测量,有利于改善非差观测数据的周跳实时探测与修复。文中提出一种基于BDS三频非差数据的周跳实时探测与修复模型:首先,采用消电离层无几何HMW组合观测量探测和修复EWL周跳;然后,将经过修复的EWL观测量与WL组合消除几何相关项,忽略电离层延迟残差进而确定WL周跳;最后采用经过修复的WL观测量与NL组合形成无几何观测量,并通过优化载波相位组合确定电离层延迟的变化量以探测和计算NL周跳,并通过简单变换得到原始载波观测量的周跳值。通过实测BDS三频数据对模型可行性进行验证分析,结果表明,即使在30s的采样率以及电离层活动活跃条件下,该模型都可有效实时探测和修复各类周跳。     

北斗RNSS-RDSS组合模糊度解算方法

电离层延迟较大是基线较长情况下的模糊度解算需要解决的关键问题。当基线较长时,由于基准站和流动站的电离层相关性弱使得双差电离层残差较大,易导致模糊度解算所需时间长且成功率不高。本文提出了一种模糊度解算方法,该方法将北斗无线电测定业务(radio determination satellite system,RDSS)的下行S频段信号测量值与无线电导航业务(radio navigation satellite system,RNSS)信号测量值组合来削弱电离层的影响。首先,通过RDSS信号测量值与RNSS信号测量值一起进行频率组合研究,确定了几组电离层延迟系数小且总噪声波长比(total noise level,TNL)较小的组合。然后,利用这些组合形成几何无关和电离层无关模型解算GEO卫星的窄巷模糊度。最后利用已知窄巷模糊度的GEO卫星测量值辅助求解非GEO卫星的窄巷模糊度。利用实测北斗星历对提出的方法进行了仿真验证,结果表明,本文方法可以从整体上提高模糊度解算的速度和成功率。     

一种机载GNSS高精度定位算法

提出部分模糊度固定的加权电离层模型提高大范围全球卫星导航系统(GNSS)航空定位的精度、可靠性及连续性.该方法的主要思路包括:自适应调整大气扰动等误差影响以实现短基线与长基线两类解算模式之间的灵活切换;施加虚拟电离层观测约束信息,提高基线动态定位的浮点解精度;采用部分模糊度固定方法有效挖掘若干模糊度参数的整周约束.试验表明,提出的方法可提高模糊固定效率与定位精度,克服传统方法有效观测信息利用率不足、定位精度较差、可靠性不高以及连续性较差的问题.实验结果表明,部分模糊度固定算法可在2 min内固定95%以上宽巷模糊度解算与80%以上窄巷模糊度,约20 min后可固定所有模糊度.     

GNSS ambiguity resolution with controllable failure rate for long baseline network RTK

Many large-scale GNSS CORS networks have been deployed around the world to support various commercial and scientific applications. To make use of these networks for real-time kinematic positioning services, one of the major challenges is the ambiguity resolution (AR) over long inter-station baselines in the presence of considerable atmosphere biases. Usually, the widelane ambiguities are fixed first, followed by the procedure of determination of the narrowlane ambiguity integers based on the ionosphere-free model in which the widelane integers are introduced as known quantities. This paper seeks to improve the AR performance over long baseline through efficient procedures for improved float solutions and ambiguity fixing. The contribution is threefold: (1) instead of using the ionosphere-free measurements, the absolute and/or relative ionospheric constraints are introduced in the ionosphere-constrained model to enhance the model strength, thus resulting in the better float solutions; (2) the realistic widelane ambiguity precision is estimated by capturing the multipath effects due to the observation complexity, leading to improvement of reliability of widelane AR; (3) for the narrowlane AR, the partial AR for a subset of ambiguities selected according to the successively increased elevation is applied. For fixing the scalar ambiguity, an error probability controllable rounding method is proposed. The established ionosphere-constrained model can be efficiently solved based on the sequential Kalman filter. It can be either reduced to some special models simply by adjusting the variances of ionospheric constraints, or extended with more parameters and constraints. The presented methodology is tested over seven baselines of around 100 km from USA CORS network. The results show that the new widelane AR scheme can obtain the 99.4 % successful fixing rate with 0.6 % failure rate; while the new rounding method of narrowlane AR can obtain the fix rate of 89 % with failure rate of 0.8 %. In summary, the AR reliability can be efficiently improved with rigorous controllable probability of incorrectly fixed ambiguities.     

基于北斗三频的BDS/GPS宽巷模糊度逐级单历元固定方法

利用北斗三频超宽巷模糊度波长较长易于固定的优势,提出一种基于北斗三频的BDS/GPS宽巷模糊度逐级单历元固定方法。首先利用载波和伪距组合固定BDS(0,-1,1)和(1,4,-5)两个超宽巷模糊度,根据固定后的超宽巷模糊度变换得到BDS宽巷模糊度(1,-1,0),然后将BDS宽巷模糊度作为约束条件与GPS宽巷观测方程联立得到GPS宽巷模糊度浮点解和其方差协方差阵,最后采用LAMBDA算法实现GPS宽巷模糊度的固定。实验结果表明,BDS超宽巷组合可实现100%固定,采用BDS约束GPS宽巷模糊度固定时ratio值均大于2,大于5的占97.8%以上,因此文中提出的方法可实现BDS/GPS双系统宽巷模糊度单历元固定,有效提升GNSS模糊度解算的时效性。     

Rapid re-convergences to ambiguity-fixed solutions in precise point positioning

Integer ambiguity resolution at a single receiver can be achieved if the fractional-cycle biases are separated from the ambiguity estimates in precise point positioning (PPP). Despite the improved positioning accuracy by such integer resolution, the convergence to an ambiguity-fixed solution normally requires a few tens of minutes. Even worse, these convergences can repeatedly occur on the occasion of loss of tracking locks for many satellites if an open sky-view is not constantly available, consequently totally destroying the practicability of real-time PPP. In this study, in case of such re-convergences, we develop a method in which ionospheric delays are precisely predicted to significantly accelerate the integer ambiguity resolution. The effectiveness of this method consists in two aspects: first, wide-lane ambiguities can be rapidly resolved using the ionosphere-corrected wide-lane measurements, instead of the noisy Melbourne–Wübbena combination measurements; second, narrow-lane ambiguity resolution can be accelerated under the tight constraints derived from the ionosphere-corrected unambiguous wide-lane measurements. In the test at 90 static stations suffering from simulated total loss of tracking locks, 93.3 and 95.0% of re-convergences to wide-lane and narrow-lane ambiguity resolutions can be achieved within five epochs of 1-Hz measurements, respectively, even though the time latency for the predicted ionospheric delays is up to 180 s. In the test at a mobile van moving in a GPS-adverse environment where satellite number significantly decreases and cycle slips frequently occur, only when the predicted ionospheric delays are applied can the rate of ambiguity-fixed epochs be dramatically improved from 7.7 to 93.6% of all epochs. Therefore, this method can potentially relieve the unrealistic requirement of a continuous open sky-view by most PPP applications and improve the practicability of real-time PPP.     

Spatial–temporal characteristic of BDS phase delays and PPP ambiguity resolution with GEO/IGSO/MEO satellites

GPS precise point positioning (PPP) ambiguity resolution (AR) can improve the positioning accuracy and shorten the convergence time. However, for the BeiDou Satellite Navigation System (BDS), the problems of satellite-induced code bias, imperfections in the error models and the inadequate accuracy of orbit products limit the applications of the BDS PPP AR system, which requires more than 6 h to achieve the first ambiguity-fixed solution. In this study, the accuracy of a wide-lane (WL) uncalibrated phase delay (UPD) is improved after careful consideration of the code bias and multipath. Meanwhile, the accuracy of the BDS float ambiguity is also improved by multi-GNSS fusion and improved precise orbit and clock products, which are critical for high-quality narrow-lane (NL) UPD estimations. With three tracking networks of different scales, including Hong Kong, the Crustal Movement Observation Network of China (CMONOC) and the multi-GNSS experiment (MGEX) networks, the spatial–temporal characteristics of WL and NL UPDs for BDS GEO/IGSO/MEO satellites are analyzed, and the PPP AR is performed. Numerous results show that WL and NL UPDs with a standard deviation (STD) of less than 0.15 cycles can be achieved for BDS GEO satellites, while a STD of less than 0.1 cycles can be obtained for IGSO and MEO satellites. With the precise UPD estimation, for the first time, the BDS PPP rapid ambiguity resolution for GEO/IGSO/MEO satellites is achieved. We found that the average time to first fix (TTFF) of the BDS PPP AR is shortened significantly, to approximately 40 min for Hong Kong and the CMONOC, while the TTFF was 57.4 min for the MGEX networks. With ambiguity resolution, the accuracy of the daily BDS PPP in the east, north and vertical directions improves from 1.74 cm, 1.08 cm, and 5.52 cm to 0.72 cm, 0.54 cm, and 3.21 cm for the Hong Kong network, 2.24 cm, 2.31 cm, and 5.64 cm to 1.18 cm, 0.79 cm, and 3.30 cm for the CMONOC, and 2.71 cm, 1.80 cm, and 6.00 cm to 1.58 cm, 1.15 cm, and 4.33 cm for the MGEX networks. Significant improvement is also achieved for kinematic PPP, with improvements of 40.41%, 34.33% and 37.17% in the east, north and vertical directions for the MGEX networks, respectively.     

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.