FirCAR算法的OTF快速定位方法

根据GNSS不同频率间整周模糊度的约束关系,提出一种基于多频整周模糊度间关系约束的模糊度新算法(dual-frequency integer relationship constrained ambiguity resolution,FirCAR)。FirCAR可快速动态解算出高高度角卫星的整周模糊度,将已经固定的整周模糊度视为高精度的伪距观测值应用到下一步的浮点解重算中。结合模糊度搜索算法,如LAMBDA,在模糊度搜索方面的高效性,根据重算后的浮点解进一步解算其他未固定的模糊度解。模糊度固定成功后,即可实现OTF(on the fly)快速定位。实测数据表明,FirCAR算法在静态和动态观测条件下,模糊度初始化所用的平均观测历元数分别为1.04和1.10。与常规的模糊度搜索算法的对比试验表明,结合FirCAR算法模糊度固定所用的观测历元数分别减少了39%和18%。     

Triple-frequency GPS precise point positioning with rapid ambiguity resolution

At present, reliable ambiguity resolution in real-time GPS precise point positioning (PPP) can only be achieved after an initial observation period of a few tens of minutes. In this study, we propose a method where the incoming triple-frequency GPS signals are exploited to enable rapid convergences to ambiguity-fixed solutions in real-time PPP. Specifically, extra-wide-lane ambiguity resolution can be first achieved almost instantaneously with the Melbourne-Wübbena combination observable on L2 and L5. Then the resultant unambiguous extra-wide-lane carrier-phase is combined with the wide-lane carrier-phase on L1 and L2 to form an ionosphere-free observable with a wavelength of about 3.4 m. Although the noise of this observable is around 100 times the raw carrier-phase noise, its wide-lane ambiguity can still be resolved very efficiently, and the resultant ambiguity-fixed observable can assist much better than pseudorange in speeding up succeeding narrow-lane ambiguity resolution. To validate this method, we use an advanced hardware simulator to generate triple-frequency signals and a high-grade receiver to collect 1-Hz data. When the carrier-phase precisions on L1, L2 and L5 are as poor as 1.5, 6.3 and 1.5 mm, respectively, wide-lane ambiguity resolution can still reach a correctness rate of over 99 % within 20 s. As a result, the correctness rate of narrow-lane ambiguity resolution achieves 99 % within 65 s, in contrast to only 64 % within 150 s in dual-frequency PPP. In addition, we also simulate a multipath-contaminated data set and introduce new ambiguities for all satellites every 120 s. We find that when multipath effects are strong, ambiguity-fixed solutions are achieved at 78 % of all epochs in triple-frequency PPP whilst almost no ambiguities are resolved in dual-frequency PPP. Therefore, we demonstrate that triple-frequency PPP has the potential to achieve ambiguity-fixed solutions within a few minutes, or even shorter if raw carrier-phase precisions are around 1 mm. In either case, we conclude that the efficiency of ambiguity resolution in triple-frequency PPP is much higher than that in dual-frequency PPP.     

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 assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning

The first results of the short baseline single-epoch kinematic positioning based on dual-frequency real BeiDou/GPS data are presented. The performance of the BeiDou/GPS single-epoch positioning is demonstrated in both static and kinematic modes and compared with corresponding GPS-only performance. It is shown that the availability and reliability of the single-frequency BeiDou/GPS and dual-frequency BeiDou single-epoch kinematic positioning are comparable to those of the dual-frequency GPS. The fixed rate and reliability of ambiguity resolution for the single- and dual-frequency BeiDou/GPS are remarkably improved as compared to that of GPS-only, especially in case of high cutoff elevations. For positioning accuracy with fixed ambiguities, the BeiDou/GPS single-epoch solutions are improved by 23 and 4 % relative to the GPS-only case for two short baseline tests of 8 km, respectively. These results reveal that dual-frequency BeiDou real-time kinematic (RTK) is already applicable in Asia–Pacific areas and that single-frequency BeiDou/GPS RTK is also achievable but only with initialization of several seconds. More promisingly, the dual-frequency BeiDou/GPS RTK can overcome the difficulties with GPS-only RTK under the challenging conditions assuming, of course, that the additional BeiDou satellites are visible.     

Single-Epoch Ambiguity Resolution for Real-Time GPS Attitude Determination with the Aid of One-Dimensional Optical Fiber Gyro

High-accuracy real-time GPS-based attitude determination requires that integer ambiguities be resolved very quickly so that the attitude angles can be output with minimum delay. This article describes an attitude determination algorithm that can resolve integer ambiguities instantaneously, relative to one antenna of a multi-antenna array configuration. The carrier phase and pseudorange observations are used with fixed baseline length constraints and fiberoptic gyro data. Real-time stochastic model improvement using empirical elevation-dependent standard deviation function and an estimated scale factor are a feature of this algorithm. Integer ambiguity search using the LAMBDA method, sophisticated validation criteria, and an adaptive procedure has also been implemented within the software. An experiment was carried out using four Leica dual-frequency GPS receivers (but only the L1 carrier phase and pseudorange data were used) and a low-cost fiberoptic on a car. The results indicate that integer ambiguities can be resolved on a single-epoch basis with a 98.9% success rate. ? 1999 John Wiley & Sons, Inc.     

基于部分固定策略的多系统长距离基准站间模糊度快速解算

基准站间整周模糊度的快速准确固定是实现网络RTK高精度快速定位的前提。对于GPS/GLONASS/BDS组合系统长基线,模糊度维数大幅度增加,加之观测噪声、大气残余误差等因素的影响,很难快速准确地固定所有模糊度,尤其是低高度角卫星模糊度。提出了一种基于部分固定策略的GPS/GLONASS/BDS组合网络长基线部分模糊度快速解算方法,以截止高度角、模糊度固定成功率以及Ratio值为主要参数,优选模糊度固定子集,以实现长距离基准站间模糊度快速固定。通过实测GPS/GLONASS/BDS三系统长基线数据的实验验证,部分模糊度固定方法可有效避免低高度角卫星对模糊度固定的影响,从而显著提高模糊度固定时的成功率及Ratio值,缩短长距离基准站间模糊度准确固定所需的时间。     

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.     

Reliable single-epoch ambiguity resolution for short baselines using combined GPS/BeiDou system

GNSS single-epoch real-time kinematic (RTK) positioning depends on correct ambiguity resolution. If the number of observed satellites in a single epoch is insufficient, which often happens with a standalone GNSS system, the ambiguity resolution is difficult to achieve. China’s BeiDou Navigation Satellite System has been providing continuous passive positioning, navigation and timing services since December 27, 2012, covering China and the surrounding area. This new system will increase the number of satellites in view and will have a significant effect on successful ambiguity resolution. Since the BeiDou system is similar to GPS, the procedure of data processing is easier than that for the Russian GLONASS system. We briefly introduce the time and the coordinate system of BeiDou and also the BeiDou satellite visibility in China, followed by the discussion on the combined GPS/BeiDou single-epoch algorithm. Experiments were conducted and are presented here, in which the GPS/BeiDou dual-frequency static data were collected in Wuhan with the baseline distance varying from 5 to 13 km, and processed in separate and combined modes. The results indicate that, compared to a standalone GPS or BeiDou system, the combined GNSS system can increase the successful ambiguity fixing rate for single epochs and can also improve the precision of short baselines determination.     

Improved network-based single-epoch ambiguity resolution using centralized GNSS network processing

Network real-time kinematic (NRTK) positioning is today’s industry standard for high-precision applications. Once network ambiguities are fixed, the network engine processes simultaneous observations from a number of continuously operating reference stations to compute corrections for users operating within the network area. Users are treated as passive nodes of the network. However, if two-way communication is available, then users could transmit their observations to the central processing facility where the network can treat them as active nodes, densifying the existing network infrastructure. This multiple rover network (MRN) concept exploits the additional information provided by users in a GNSS network. One application is to use the shorter inter-receiver distances to improve the success rate of single-epoch ambiguity resolution. This is also the goal of the subset ambiguity resolution algorithm, which improves the single-epoch success rate by allowing a subset of ambiguities to be resolved. We present an enhanced processing strategy to complement centimeter-level single-epoch NRTK positioning. This approach combines a single-baseline and an MRN solution with the partial ambiguity resolution algorithm and is only possible for a centralized GNSS network architecture. The algorithm is tested against the standard network ambiguity resolution strategy of full-set ambiguity fixing with respect to the nearest reference station. A 24-h dataset from the Southern California Integrated GNSS network is used with a configuration of three reference stations and four users. The enhanced solution achieves a mean ambiguity resolution success rate of 83% over all four users and all epochs, compared to 32% for the conventional technique.     

Enhancement of the accuracy of single-epoch GPS positioning for long baselines by local ionospheric modelling

Single-epoch relative GPS positioning has many advantages, especially for monitoring dynamic targets. In this technique, errors occurring in previous epochs cannot affect the position accuracy at the current epoch, but careful processing is required, and resolving carrier phase ambiguities is essential. Statistical ambiguity resolution functions have been used to determine the best values of these ambiguities. The function inputs include as a minimum the known base station position, the approximate roving antenna “seed” position, and the dual-frequency carrier phase measurements from both receivers. We investigate different solutions to find the ambiguity function inputs that achieve the highest ambiguity resolution success rate. First, we address the rover seed position. A regionally filtered undifferenced pseudorange coordinate solution proves better than a double-differenced one. Multipath errors approximately repeat themselves every sidereal day in the case of static or quasi-static antennas; applying a sidereal filter to the pseudorange-derived positions mitigates their effects. Second, we address the relative carrier phase measurements, which for medium to long baselines are significantly affected by ionospheric propagation errors imperfectly removed during differencing. In addition to the International GNSS Service ionospheric model, we generate a local pseudorange-based ionospheric correction. Applying this correction improves the quality of the phase measurements, leading to more successful ambiguity resolution. Temporally smoothing the correction by means of a Kalman filter further improves the phase measurements. For baselines in the range 60–120 km, the mean absolute deviation of single-epoch coordinates improves to 10–20 cm, from 30–50 cm in the default case.     

Enhancing differential GPS using regional ionospheric error models

Distance-dependent errors due to ionospheric refraction complicate ambiguity resolution and limit the accuracy attainable in GPS baseline determination. This paper presents an approach for modelling these errors from the observations of several permanent GPS-stations surrounding the area of interest. Regional ionospheric correction models are produced epoch-by-epoch and satellite-by-satellite. It is shown that after their application, observation residuals, fractional parts of estimated ambiguities, and single-frequency coordinate errors are greatly reduced, thus improving ambiguity resolution even under disturbed ionospheric conditions, with short observation sessions, in the case of baseline lengths of more than 10 km, and with singlefrequency and dual-frequency data.     

Precise GRACE baseline determination using GPS

Precision relative navigation is an essential aspect of spacecraft formation flying missions, both from an operational and a scientific point of view. When using GPS as a relative distance sensor, dual-frequency receivers are required for high accuracy at large inter-satellite separations. This allows for a correction of the relative ionospheric path delay and enables double difference integer ambiguity resolution. Although kinematic relative positioning techniques demonstrate promising results for hardware-in-the-loop simulations, they were found to lack an adequate robustness in real-world applications. To overcome this limitation, an extended Kalman Filter modeling the relative spacecraft dynamics has been developed. The filter processes single difference GPS pseudorange and carrier phase observations to estimate the relative position and velocity along with empirical accelerations and carrier phase ambiguities. In parallel, double difference carrier phase ambiguities are resolved on both frequencies using the least square ambiguity decorrelation adjustment (LAMBDA) method in order to fully exploit the inherent measurement accuracy. The combination of reduced dynamic filtering with the LAMBDA method results in smooth relative position estimates as well as fast and reliable ambiguity resolution. The proposed method has been validated with data from the gravity recovery and climate experiment (GRACE) mission. For an 11-day data arc, the resulting solution matches the GRACE K-Band Ranging System measurements with an accuracy of 1 mm, whereby 83% of the double difference ambiguities are resolved.     

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to real-time kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution, an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance–covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.     

纳伪概率可控的四舍五入法及其在RTK模糊度固定中的应用

RTK模糊度固定通常采用序贯四舍五入方法,该方法只固定能可靠固定的部分模糊度,因此控制四舍五入的纳伪概率是实现RTK可靠性的关键。从含多个备选假设的假设检验理论出发,研究纳伪概率可控的四舍五入方法,根据风险水平和实数解的质量自适应地确定四舍五入取整区域,从而有效地控制整数固定的纳伪概率。并结合GNSS应用中两种特殊情况,发展两种简单实用的应用策略。采用基线长94.6 km的CORS站GPS双频数据进行网络RTK模糊度固定试验,分析本文纳伪概率可控的四舍五入方法的效果。结果表明,纳伪概率可控的四舍五入方法的固定率与传统四舍五入方法的固定率相当,且较传统方法更能有效地控制纳伪概率,提高整数解的可靠性。     

Assessment of PPP integer ambiguity resolution using GPS,GLONASS and BeiDou (IGSO,MEO) constellations

Although integer ambiguity resolution (IAR) can improve positioning accuracy considerably and shorten the convergence time of precise point positioning (PPP), it requires an initialization time of over 30 min. With the full operation of GLONASS globally and BDS in the Asia–Pacific region, it is necessary to assess the PPP–IAR performance by simultaneous fixing of GPS, GLONASS, and BDS ambiguities. This study proposed a GPS + GLONASS + BDS combined PPP–IAR strategy and processed PPP–IAR kinematically and statically using one week of data collected at 20 static stations. The undifferenced wide- and narrow-lane fractional cycle biases for GPS, GLONASS, and BDS were estimated using a regional network, and undifferenced PPP ambiguity resolution was performed to assess the contribution of multi-GNSSs. Generally, over 99% of a posteriori residuals of wide-lane ambiguities were within ±0.25 cycles for both GPS and BDS, while the value was 91.5% for GLONASS. Over 96% of narrow-lane residuals were within ±0.15 cycles for GPS, GLONASS, and BDS. For kinematic PPP with a 10-min observation time, only 16.2% of all cases could be fixed with GPS alone. However, adding GLONASS improved the percentage considerably to 75.9%, and it reached 90.0% when using GPS + GLONASS + BDS. Not all epochs could be fixed with a correct set of ambiguities; therefore, we defined the ratio of the number of epochs with correctly fixed ambiguities to the number of all fixed epochs as the correct fixing rate (CFR). Because partial ambiguity fixing was used, when more than five ambiguities were fixed correctly, we considered the epoch correctly fixed. For the small ratio criteria of 2.0, the CFR improved considerably from 51.7% for GPS alone, to 98.3% when using GPS + GLONASS + BDS combined solutions.     

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.     

0.99999999 confidence ambiguity resolution with GPS and Galileo

In this short contribution it is demonstrated how integer carrier phase cycle ambiguity resolution will perform in near future, when the US GPS gets modernized and the European Galileo becomes operational. The capability of ambiguity resolution is analyzed in the context of precise differential positioning over short, medium and long distances. Starting from dual-frequency operation with GPS at present, particularly augmenting the number of satellites turns out to have beneficial consequences on the capability of correctly resolving the ambiguities. With a 'double' constellation, on short baselines, the confidence of the integer ambiguity solution increases to a level of 0.99999999 or beyond. Electronic Publication     

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.     

一种用于GPS整周模糊度OTF求解的整数白化滤波改进算法

提出一种用于整周模糊度OTF求解的整数白化滤波改进算法。该算法首先对整周模糊度的协方差矩阵进行整数白化滤波处理 ,以降低整周模糊度间的相关性 ,然后构造搜索空间来判定是否需要进行搜索。如果需要 ,则通过搜索来确定变换后的整周模糊度 ;如果不需要 ,则通过直接取整来确定整周模糊度 ,进而得到原始的整周模糊度和基线分量的固定解。初步试验结果显示 ,采用改进方法解算整周模糊度可以提高成功率和解算效率