联合GEO/IGSO/MEO的北斗PPP模糊度固定方法与试验分析

由于北斗地球静止轨道（geostationary earth orbiting,GEO）卫星轨道精度较低且其观测值受多路径误差和伪距偏差影响严重,目前各分析中心尚未针对北斗GEO卫星提供长期稳定的相位小数偏差（uncalibrated phase delay,UPD）产品,北斗精密单点定位（precise point positioning,PPP）模糊度固定技术研究主要针对倾斜轨道（inclined geosynchronous orbiting,IGSO）和中地球轨道（medium earth orbiting,MEO）卫星。本文采用Wanninger和Beer的高度角模型消除了IGSO/MEO观测值伪距偏差,并通过小波变换提取低频分量修正伪距观测值的方法削弱了GEO卫星多路径和伪距偏差的影响。由于窄巷UPD估值受未模型化误差影响较大,本文改进了窄巷UPD估计的策略,该策略利用上一历元成功估计的窄巷UPD对当前历元的浮点模糊度进行改正,剔除了残差较大的浮点模糊度,修正固定错误的整周模糊度,从而提高了窄巷UPD的精度和稳定性。利用估计得到的UPD产品,本文实现了联合GEO、IGSO和MEO卫星的北斗非差PPP模糊度固定,并对其定位性能进行分析。结果表明：联合GEO、IGSO和MEO卫星的PPP固定解的首次固定时间和收敛时间均可以缩短到30 min以内;6 h后的E、N、U方向的定位误差由（1.35、0.35、2.75）cm减少到（1.07、0.26、2.24）cm,分别减少了20%、27%和18%。     

BDS三频与双频模糊度解算性能分析

全球导航卫星系统(GNSS)已进入多频多系统时代。针对两条短基线,对比分析BDS三频与BDS／GPS三频对于BDS双频与BDS／GPS双频在模糊度固定率、成功率及定位精度等方面的改善情况。结果表明,BDS三频与BDS／GPS三频可有效提高BDS双频与BDS／GPS双频的固定率和成功率,但BDS三频与BDS／GPS三频对于BDS双频与BDS／GPS双频的定位精度基本上没有改善。      

Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS,BDS, GLONASS,Galileo

This paper focuses on the precise point positioning (PPP) ambiguity resolution (AR) using the observations acquired from four systems: GPS, BDS, GLONASS, and Galileo (GCRE). A GCRE four-system uncalibrated phase delay (UPD) estimation model and multi-GNSS undifferenced PPP AR method were developed in order to utilize the observations from all systems. For UPD estimation, the GCRE-combined PPP solutions of the globally distributed MGEX and IGS stations are performed to obtain four-system float ambiguities and then UPDs of GCRE satellites can be precisely estimated from these ambiguities. The quality of UPD products in terms of temporal stability and residual distributions is investigated for GPS, BDS, GLONASS, and Galileo satellites, respectively. The BDS satellite-induced code biases were corrected for GEO, IGSO, and MEO satellites before the UPD estimation. The UPD results of global and regional networks were also evaluated for Galileo and BDS, respectively. As a result of the frequency-division multiple-access strategy of GLONASS, the UPD estimation was performed using a network of homogeneous receivers including three commonly used GNSS receivers (TRIMBLE NETR9, JAVAD TRE_G3TH DELTA, and LEICA). Data recorded from 140 MGEX and IGS stations for a 30-day period in January in 2017 were used to validate the proposed GCRE UPD estimation and multi-GNSS dual-frequency PPP AR. Our results show that GCRE four-system PPP AR enables the fastest time to first fix (TTFF) solutions and the highest accuracy for all three coordinate components compared to the single and dual system. An average TTFF of 9.21 min with \(7{^{\circ }}\) cutoff elevation angle can be achieved for GCRE PPP AR, which is much shorter than that of GPS (18.07 min), GR (12.10 min), GE (15.36 min) and GC (13.21 min). With observations length of 10 min, the positioning accuracy of the GCRE fixed solution is 1.84, 1.11, and 1.53 cm, while the GPS-only result is 2.25, 1.29, and 9.73 cm for the east, north, and vertical components, respectively. When the cutoff elevation angle is increased to \(30{^{\circ }}\), the GPS-only PPP AR results are very unreliable, while 13.44 min of TTFF is still achievable for GCRE four-system solutions.     

北斗三频精密单点定位模型比较及定位性能分析

在Trip软件的基础上实现了北斗三频无电离层两两组合、三频消电离层组合和三频非组合精密单点定位（precise point positioning,PPP）算法。利用12个陆态网观测站的北斗三频观测数据对3种三频PPP定位模型及传统的双频无电离层组合PPP模型的定位性能进行分析。试验结果表明,对大多数测站,3种三频PPP模型静态定位精度水平方向优于1 cm,高程方向优于2 cm,动态定位精度水平方向优于4 cm,高程方向优于6 cm;3种三频PPP模型静态收敛时间约为120 min,动态收敛时间约180 min;相比于传统的双频PPP模型,三频PPP模型的定位精度有所提高,其中,三频非组合模型静态单天解RMS在水平方向和高程方向分别提高36.1%和6.3%,动态单天解RMS在水平方向和高程方向分别提高9.1%和6.3%。     

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.     

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.     

GPS/BDS/Galileo三频精密单点定位模型及性能分析

在精细考虑伪距和载波相位硬件偏差时变特性的基础上,导出了更为严谨的非差非组合观测方程,并给出了非组合模式下两类GNSS偏差的数学表达形式.基于此,本文详细研究了3种常用的三频精密单点定位(PPP),即无电离层两两组合IF1213、单个无电离层组合IF123与非组合UC123函数模型的独立参数化方法,系统分析了3种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.     

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.     

整数相位钟法精密单点定位模糊度固定模型及效果分析

精密单点定位(PPP)模糊度固定方法有3种:星间单差法、整数相位钟法和钟差解耦法,但目前仅法国CNES公开发布用于整数相位钟法PPP模糊度固定的产品,因此研究基于整数相位钟法的用户端PPP模糊度固定模型很有必要.本文分析了整数相位钟法PPP模糊度固定模型,着重指出该模型与传统浮点解PPP模型的区别;提出一种顾及质量控制的逐级模糊度固定策略用于具体实施PPP模糊度固定.大量动态PPP解算试验表明:与浮点解PPP相比,固定解PPP具有更快的收敛速度且定位精度和稳定性更好.     

Instantaneous BDS + GPS undifferenced NRTK positioning with dynamic atmospheric constraints

As the Chinese BeiDou Navigation Satellite System (BDS) has become operational in the Asia-Pacific region, it is important to better understand and demonstrate the benefits of combining triple-frequency BDS with dual-frequency GPS observations for network-based real-time kinematic (NRTK) services. Undifferenced NRTK is a new NRTK service mode, it extends the concept of NRTK by not requiring reference station and specified reference satellite at the rover processing. In order to realize the undifferenced NRTK service, a strategy for real-time modeling the undifferenced (UD) augmentation information is given, in which the fixed double-differenced ambiguities are transformed into UD ones with the help of datum settings. Since this strategy is insensitive to existing ephemeris products, it is applicable to the services of current BDS regional reference networks. Furthermore, a processing scheme for ambiguity resolution (AR) with arbitrary-frequency observations is also presented in detail. An instantaneous and reliable BDS + GPS positioning service can be provided to the rovers in undifferenced NRTK processing mode. With the data collected at 31 stations from a continuously operating reference station network in Guangdong Province (GDCORS) of China, the efficiency of the proposed approaches using combined BDS and GPS observations is confirmed. For three rover stations during days 327–329, a total of 12,960 1-min tests were performed separately to demonstrate the performance of AR. Thanks to the dynamically refined priori information of residual tropospheric and ionospheric error, and the availability of more satellites and observations, the AR fixing rates of combined BDS and GPS systems improve by 13 to 65%, compared with those of the GPS-only system using the traditional WL-L1-IF scheme. The positioning accuracy has also significantly improved.     

Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.     

BDS网络RTK参考站三频整周模糊度解算方法

北斗卫星导航系统是目前唯一一个全星座提供三频观测数据的卫星导航定位系统,三频观测值有助于载波相位整周模糊度的快速、准确固定。本文提出了一种BDS网络RTK参考站三频整周模糊度解算方法。首先利用B2、B3频率的观测值及严格的模糊度固定标准确定超宽巷整周模糊度,将固定的超宽巷整周模糊度与其他宽巷整周模糊度的线性关系作为约束条件,然后估计宽巷整周模糊度、相对天顶对流层延迟误差和电离层延迟误差,并搜索确定宽巷整周模糊度。利用固定的宽巷整周模糊度与三频载波相位整周模糊度的整数线性关系,将线性关系加入载波相位整周模糊度参数估计观测模型中,然后确定载波相位整周模糊度。使用实测的CORS网BDS三频观测数据进行算法验证,结果表明,该方法可正确有效地实现参考站间三频载波相位整周模糊度的快速解算。     

Benefits of the third frequency signal on cycle slip correction

Cycle slip detection and correction are important issues when carrier phase observations are used in high-precision GNSS data processing and have, therefore, been intensively investigated. Along with the GNSS modernization, the cycle slip correction (CSC) problem has been raised to deal with more signals from multi-frequencies. We extend the geometry-based approach by integrating time-differenced pseudorange and carrier phase observations to estimate the integer number of triple-frequency cycle slips together with the receiver clock offset, ionospheric delay variations and receiver displacements. The Least-squares AMBiguity Decorrelation Adjustment method can be employed. The benefit of the third frequency observation on the cycle slip estimate is first investigated with simulation tests. The results show that adding the third frequency observation can significantly improve the model strength and that a reliable triple-frequency CSC with a theoretical success rate of higher than 99.9 % can still be achieved, even under the condition that the range or ionosphere delay variation is poorly defined. The performance of triple-frequency CSC is validated with real triple-frequency BDS data since all BDS satellites in orbit are transmitting triple-frequency signals. The results show that the fixing rate of CSC can reach 99.1 % in static precise point positioning (PPP) and 98.8 % in the kinematic case. PPP solutions with cycle slip-uncorrected and cycle slip-corrected data sets are compared to validate the correctness of triple-frequency CSC. The standard deviations of the PPP solution in east, north and vertical component, respectively, can be improved by 31.1, 30.7 and 37.6 % for static, and by 42.0, 53.8 and 39.7 % for kinematic after cycle slips are corrected. The performance of dual- and triple-frequency CSC is also compared. Results show that the performance of dual-frequency CSC is slightly worse than that of triple-frequency CSC. These results demonstrate that the performance of CSC can be significantly improved with triple-frequency observations.     

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.     

BDS参考站三频整周模糊度单历元确定方法

参考站载波相位整周模糊度的准确确定是实现BDS网络RTK定位的关键。本文研究了BDS参考站三频载波相位整周模糊度单历元确定方法。首先推导了参考站三频载波相位整周模糊度之间的多个整数线性关系,根据双频载波相位整周模糊度的整数线性关系,以及B1载波相位整周模糊度备选值,确定B1/B2和B1/B3载波相位整周模糊度的备选组合。然后利用不受误差影响的三频载波相位整周模糊度间整数线性关系,对整周模糊度备选值进行约束和确定。根据大气误差的空间相关性,采用以卫星高度角和方位角为依据的基准卫星选择方法,降低了对流层延迟误差残差对多频载波相位整周模糊度之间线性关系约束能力的影响。试验结果表明,本文方法能够实现参考站三频载波相位整周模糊度的单历元准确确定,且计算效率高,算法简单。     

北斗三频数据的两个无电离层组合轨道钟差估计及其应用

本文针对全球连续监测评估系统（iGMAS）和国际多系统GNSS试验计划（MGEX）两个观测网接收到不同频率北斗卫星数据的情况,提出了一种北斗卫星（BDS）3个频率（B1I、B2I、B3I）的两种无电离层组合（B1/B3和B1/B2）数据精密定轨（POD）和钟差估计（CE）方法。该方法可以统一处理上述两个观测网收到的北斗二代（BDS-2）,北斗三代试验系统（BDS-3e）和北斗三代全球系统（BDS-3g）3个频率的观测数据,并在一次程序运行中对所有北斗卫星进行联合处理,可有效提高一次运行的数据使用率,从而提高参数估计精度。采集了多天iGMAS、MGEX的GPS和BDS数据进行试验。结果表明,对BDS-3e+BDS-2+GPS联合定轨时,采用三频两组合方法后由于增强了观测几何,BDS轨道重叠RMS为15.9 cm,比传统双频法定轨精度提高11.3%。新方法引入了与卫星端3个频率相关的码偏差,该量多天估计结果稳定,证明了模型和方法可靠。将新方法用于BDS-3g+BDS-3e+BDS-2+GPS联合定轨,6颗BDS-3g的MEO卫星轨道重叠RMS为14.5 cm,钟差重叠RMS为0.43 ns,与BDS-3e的15.1 cm和0.49 ns相当。开展了北斗卫星精密单点定位（PPP）试验,结果显示增加了BDS-3g的6颗MEO的精密轨道和钟差后,测站定位精度水平为39.6 mm,天顶为37.8 mm,比仅用BDS-2和BDS-3e卫星定位精度提高了11.1%。     

北斗广域差分分米级定位的分区切换算法

从2017年1月开始,北斗系统在播发基本导航电文的同时,提供了包含实时轨道改正数、钟差改正数、电离层格网改正数和分区综合改正数四重广域差分参数,使得系统具备了基于系统广播的电文参数实现广域单站实时动态分米级定位的能力。实际应用表明,北斗系统播发的分区综合改正数存在中断的情况,使得实时定位存在因重新收敛而造成跳变的情况。本文分析了分区中断期间定位跳变产生的原因,提出一种适用于分区切换的广域差分分米级定位算法。采用中国境内7个北斗测站10d的静态数据和车载动态数据对新算法进行评估验证。结果表明,在分区改正数中断的情况下,分区切换算法得到的坐标误差与使用连续分区综合改正数结果一致,双频动态定位水平和高程方向分别小于0.3m和0.5m,平均三维定位精度优于0.5m;车载实时动态定位测试中,分区切换前后的单双频定位精度不受切换影响,与切换前保持一致。分区切换算法有效保证了分区改正数中断后北斗广域分米级实时动态定位的连续性。     

GNSS非组合PPP部分模糊度固定方法与结果分析

在精密单点定位(precise point positioning,PPP)技术中,模糊度固定错误将导致严重的定位偏差,为保证PPP模糊度实现更可靠的固定,需对模糊度子集的选取方式进行优化。提出了一种将质量控制与施密特正交化相结合的PPP部分模糊度固定方法。在全球导航卫星系统（global navigation satellite system,GNSS）多系统融合条件下, 选取多模GNSS实验数据,在非差非组合PPP模型中对比分析施密特正交化方法与高度角选星方法,并进行模糊度固定及定位性能验证。结果表明,施密特正交化方法相比高度角选星方法,各天与各站平均历元固定率在静态模式下分别提高了7.74%与11.46%,在仿动态模式下分别提高了7.90%与7.78%;各天与各站的首次固定时间在静态模式下分别提高了22.30%与25.42%,在仿动态模式下分别提高了20.44%与19.65%。在PPP模糊度固定和定位精度方面,多系统融合相比单BDS(BeiDou navigation satellite system)提升效果明显,在95%分位数条件下,水平和高程方向收敛时间分别平均减少20.00 min和19.00 min,水平和高程方向定位精度分别平均改善了1.50 cm和1.12 cm。在非差非组合PPP模型中,采用施密特正交化PPP部分模糊度固定方法可以显著提升模糊度固定性能,改善定位精度。