星间单差精密单点定位部分模糊度固定方法

针对传统的精密单点定位(PPP)技术由于收敛速度慢、获取高精度位置信息所需时间较长而无法满足用户对于快速高精度定位的需求的问题,该文采用了单差小数周偏差(FCB)产品固定模糊度的方法,以及部分模糊度固定的固定策略,来达到最优化使用固定解的PPP.通过对测站的数据的静态和仿动态实验分析验证,结果表明,进行部分模糊度固定的固定解定位精度要优于使用模糊度浮点解进行PPP得到的实数解的定位精度,收敛速度也有提升;而且相比于全模糊度固定策略,部分模糊度固定策略可以提升模糊度的历元固定率,使更多的固定模糊度的卫星可以参与定位,提升了定位的精度和收敛速度.     

基于整数钟的PPP非差模糊度固定方法

非差模糊度固定能够有效提高精密单点定位(PPP)的定位精度和收敛速度,是国内外卫星导航定位领域的研究热点。基于整数钟实现了PPP非差模糊度固定,在非差模糊度逐级固定中分别估计接收机宽巷偏差和窄巷偏差;对宽巷和窄巷模糊度进行改正,从而消除了接收机硬件延迟对模糊度的影响;同时采用取整成功率检验和ratio值检验,保证模糊度固定的可靠性。将以上方法应用到动态精密单点定位中,实验结果表明:仿动态条件下,模糊度正确固定后,东、北向定位精度达到mm级、天向定位精度优于5 cm;动态解算条件下,采用1 s采样间隔数据16 min左右即可实现模糊度的首次固定。PPP固定解在东、北、天3个方向的定位精度分别为1.5、2.7和1.3 cm,相比于浮点解分别提升了61%、40%和38%。     

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.     

GPS/Galileo精密单点定位模糊度解算与实验分析

针对提高多频模糊度固定解的GNSS精密单点定位的可靠性与稳定性的问题,该文基于实时非组合相位偏差产品,对三频非差非组合GPS/Galileo PPP的浮点解、固定解模型进行深入研究,并设计了3种定位策略,选取了17个MGEX跟踪站7d的实测数据,分析了三频非差模糊度固定解对静态、仿动态PPP定位精度与滤波收敛时间的影响。结果表明,滤波收敛后,与浮点解策略相比较,固定三频模糊度对高程、水平方向定位精度均有提高,在静态定位模式中提升幅度分别约为20.45%和37.50%,在仿动态定位模式中提升幅度分别约为22.41%和33.33%。在滤波收敛时间方面,相较于浮点解策略的收敛时间,静态与仿动态定位中模糊度固定策略的收敛时间分别提升了约12.57%和6.41%。     

基于部分整周模糊度固定的非差GPS精密单点定位方法

近年来,精密单点定位(PPP)模糊度固定技术不断发展,模糊度正确固定后可以提高短时间的定位精度。然而固定错误的模糊度,将引起严重的定位偏差,因此对PPP模糊度固定的成功率和可靠性进行研究很有必要。本文探讨了采用非差小数偏差(FCBs)改正的PPP模糊度固定方法;同时提出了一种分步质量控制的PPP部分模糊度固定(PAR)策略。通过欧洲CORS数据对该方法进行验证,结果表明:PPP模糊度固定可以提高小时解静态PPP定位精度。同时,采用部分模糊度固定策略,能够有效控制未收敛模糊度影响,提高用户端PPP模糊度固定成功率。     

利用参考站增强信息进行精密单点定位

提出一种基于参考站增强信息的精密单点定位（Precise Point Positioning,PPP)新算法。与其它方法的不同在于采用星间历元间差分技术,消除了模糊度和接收机钟差,避免模糊度参数的收敛或固定。应用基于参考站的增强信息 ,以减弱残余对流层延迟和潜在偏差对定位结果的影响。与传统PPP处理方法相比较,提出的新方法可以改善位置参数的收敛速度,定位精度也有一定程度的提高。     

精密单点定位模糊度快速固定算法

精密单点定位非差模糊度解算和收敛时间是制约其应用和发展的主要因素。本文从基本观测模型出发,将消电离层模糊度分解为宽巷和窄巷分别固定,并对固定方法做了改进,削弱了初始历元相关性对收敛速度的影响;提出非差相位延迟估计(PDE)解算模型,在不利用区域或全球参考站的前提下解算卫星与接收机相位延迟。通过对中国6个IGS站数据处理结果显示,93%的模糊度可以在20 min内固定。固定后定位精度在E,N和U方向上分别提高了63%,53%和24%;定位精度可以达到毫米至厘米级。对于数据质量较好的站点(如上海站)平面精度可达3 mm,模糊度固定后精密单点定位有了很大提高。     

非差FCB估计及其在PPP模糊度固定中的应用

模糊度固定能够显著提高精密单点定位(PPP)的精度和收敛速度,是国内外卫星导航定位领域的研究热点．本文通过最小二乘法分离接收机端和卫星端小数周偏差(FCB),恢复非差模糊度的整数特性,将得到的卫星端FCB提供给用户,能够实现非差模糊度固定的PPP．采用全球IGS跟踪站的观测数据进行非差FCB解算,实验结果表明,宽巷FCB的稳定性较好,一周内变化小于0.1周,而窄巷FCB一天内变化较大．将获得的FCB用于模糊度固定PPP实验,E、N、U三个方向的定位精度分别为0.7 cm、0.8 cm和2.1 cm,与浮点解PPP相比,分别提高68％、51％和37％,验证了本文估计的FCB用于模糊度固定PPP的定位性能      

GNSS载波相位整数等变估计及其PPP性能提升算法

精密单点定位技术能够提供全球高精度定位结果,其主要技术瓶颈在于定位收敛时间长,载波相位模糊度固定技术是加快PPP收敛速度、改善定位精度的主要手段之一。模糊度固定的可靠性问题在PPP定位中尤为突出,因为模糊度浮点解质量取决于服务端产品质量、接收机噪声特性和观测环境等多种因素,所以高可靠PPP模糊度固定技术仍然充满巨大挑战。为了保障PPP定位的可靠性,本文将最优整数等变估计(best integer equivariant,BIE)引入PPP模糊度估计过程中。BIE法利用GNSS模糊度整数解加权融合以获得最优的浮点模糊度估计值,可有效降低模糊度错误固定风险,同时又利用了模糊度整数解信息来提升模糊度估值精度,从而提升PPP定位精度,缩短模糊度收敛时间。本文选取了105个全球分布的MGEX测站对BIE估计PPP模糊度的性能进行验证,试验结果表明,与模糊度固定解相比,采用BIE估计PPP模糊度能够进一步改善坐标三分量(东、北、垂向)定位性能,收敛时间分别减少了37%、28%与31%,收敛后定位精度分别提高了9%、8%和3%。此外,BIE估计PPP模糊度定位结果的毛刺和阶跃现象更少。     

估计对流层延迟的单频RTK卡尔曼滤波算法

提出一种对流层估计方法实现单频RTK快速动态定位。用模型改正对流层干延迟,双差对流层湿延迟用测站对流层天顶延迟估计,并与流动站位置及站间单差模糊度组成双差方程进行卡尔曼滤波,得到单差模糊度浮点解及方差阵,通过星间求差得到双差模糊度浮点解及方差阵,结合MLAMBDA方法实时确定模糊度。试验验证单历元平面定位精度优于±3 cm,高程定位精度优于±10 cm。     

Rapid PPP ambiguity resolution using GPS+GLONASS observations

Integer ambiguity resolution (IAR) in precise point positioning (PPP) using GPS observations has been well studied. The main challenge remaining is that the first ambiguity fixing takes about 30 min. This paper presents improvements made using GPS+GLONASS observations, especially improvements in the initial fixing time and correct fixing rate compared with GPS-only solutions. As a result of the frequency division multiple access strategy of GLONASS, there are two obstacles to GLONASS PPP-IAR: first and most importantly, there is distinct code inter-frequency bias (IFB) between satellites, and second, simultaneously observed satellites have different wavelengths. To overcome the problem resulting from GLONASS code IFB, we used a network of homogeneous receivers for GLONASS wide-lane fractional cycle bias (FCB) estimation and wide-lane ambiguity resolution. The integer satellite clock of the GPS and GLONASS was then estimated with the wide-lane FCB products. The effect of the different wavelengths on FCB estimation and PPP-IAR is discussed in detail. We used a 21-day data set of 67 stations, where data from 26 stations were processed to generate satellite wide-lane FCBs and integer clocks and the other 41 stations were selected as users to perform PPP-IAR. We found that GLONASS FCB estimates are qualitatively similar to GPS FCB estimates. Generally, 98.8% of a posteriori residuals of wide-lane ambiguities are within \(\pm 0.25\) cycles for GPS, and 96.6% for GLONASS. Meanwhile, 94.5 and 94.4% of narrow-lane residuals are within 0.1 cycles for GPS and GLONASS, respectively. For a critical value of 2.0, the correct fixing rate for kinematic PPP is only 75.2% for GPS alone and as large as 98.8% for GPS+GLONASS. The fixing percentage for GPS alone is only 11.70 and 46.80% within 5 and 10 min, respectively, and improves to 73.71 and 95.83% when adding GLONASS. Adding GLONASS thus improves the fixing percentage significantly for a short time span. We also used global ionosphere maps (GIMs) to assist the wide-lane carrier-phase combination to directly fix the wide-lane ambiguity. Employing this method, the effect of the code IFB is eliminated and numerical results show that GLONASS FCB estimation can be performed across heterogeneous receivers. However, because of the relatively low accuracy of GIMs, the fixing percentage of GIM-aided GPS+GLONASS PPP ambiguity resolution is very low. We expect better GIM accuracy to enable rapid GPS+GLONASS PPP-IAR with heterogeneous receivers.     

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.     

A study on the dependency of GNSS pseudorange biases on correlator spacing

We provide a comprehensive overview of pseudorange biases and their dependency on receiver front-end bandwidth and correlator design. Differences in the chip shape distortions among GNSS satellites are the cause of individual pseudorange biases. The different biases must be corrected for in a number of applications, such as positioning with mixed signals or PPP with ambiguity resolution. Current state-of-the-art is to split the pseudorange bias into a receiver- and a satellite-dependent part. As soon as different receivers with different front-end bandwidths or correlator designs are involved, the satellite biases differ between the receivers and this separation is no longer practicable. A test with a special receiver firmware, which allows tracking a satellite with a range of different correlator spacings, has been conducted with live signals as well as a signal simulator. In addition, the variability of satellite biases is assessed through zero-baseline tests with different GNSS receivers using live satellite signals. The receivers are operated with different settings for multipath mitigation, and the changes in the satellite-dependent biases depending on the receivers’ configuration are observed.     

GLONASS phase bias estimation and its PPP ambiguity resolution using homogeneous receivers

Integer ambiguity resolution (IAR) appreciably improves the position accuracy and shortens the convergence time of precise point positioning (PPP). However, while many studies are limited to GPS, there is a need to investigate the performance of GLONASS PPP ambiguity resolution. Unfortunately, because of the frequency-division multiple-access strategy of GLONASS, GLONASS PPP IAR faces two obstacles. First, simultaneously observed satellites operate at different wavelengths. Second and most importantly, distinct inter-frequency bias (IFB) exists between different satellites. For the former, we adopt an undifferenced method for uncalibrated phase delay (UPD) estimation and proposed an undifferenced PPP IAR strategy. We select a set of homogeneous receivers with identical receiver IFB to perform UPD estimation and PPP IAR. The code and carrier phase IFBs can be absorbed by satellite wide-lane and narrow-lane UPDs, respectively, which is in turn consistent with PPP IAR using the same type of receivers. In order to verify the method, we used 50 stations to generate satellite UPDs and another 12 stations selected as users to perform PPP IAR. We found that the GLONASS satellite UPDs are stable in time and space and can be estimated with high accuracy and reliability. After applying UPD correction, 91 % of wide-lane ambiguities and 99 % of narrow-lane ambiguities are within (?0.15, +0.15) cycles of the nearest integer. After ambiguity resolution, the 2-hour static PPP accuracy improves from (0.66, 1.42, 1.55) cm to (0.38, 0.39, 1.39) cm for the north, east, and up components, respectively.     

A cycle slip fixing method with GPS + GLONASS observations in real-time kinematic PPP

A key limitation of precise point positioning (PPP) is the long convergence time, which requires about 30 min under normal conditions. Frequent cycle slips or data gaps in real-time operation force repeated re-convergence. Repairing cycle slips with GPS data alone in severely blocked environments is difficult. Adding GLONASS data can supply redundant observations, but adds the difficulty of having to deal with differing wavelengths. We propose a single-difference between epoch (SDBE) method to integrate GPS and GLONASS for cycle slip fixing. The inter-system bias can be eliminated by SDBE, thus only one receiver clock parameter is needed for both systems. The inter-frequency bias of GLONASS satellites also cancels in the SDBE, so cycle slips are preserved as integers, and the LAMBDA method is adopted to search for cycle slips. Data from 7 days of 20 globally distributed IGS sites were selected to test the proposed cycle slip fixing procedure with artificial blocking of the signal; cycle slips were introduced for all un-blocked satellites at each epoch. For a 30-s sampling interval, the average success rate of fixing can be improved from 73 to 98 % by adding GLONASS. Even for a 180-s sampling interval, GPS + GLONASS can achieve a success rate of 81 %. A real-time kinematic PPP experiment was also performed, and the results show that using GPS + GLONASS can achieve continuous high-accuracy real-time PPP without re-convergence.     

北斗星上多径对宽巷模糊度解算的影响分析

通过引入北斗星上多径参数,量化了北斗星上多径对宽巷模糊度解算的影响;从理论上分析了该影响量在非差、单差和双差条件下的特性,并采用零基线、短基线和长基线3组实测数据进行了分析与验证。结果表明:星上多径对非差宽巷模糊度估值的影响在三类卫星上表现出不同的特性,在MEO卫星上最大,可达1周;星间单差无法消除星上多径偏差影响,进而PPP宽巷模糊度的解算将受到影响;星上多径不会对零基线双差宽巷模糊度解算造成影响,对短基线双差宽巷模糊度解算的影响也可忽略,但长基线双差宽巷模糊度解算则受严重影响;星上多径会导致长基线双差宽巷模糊度平滑收敛缓慢,经改正后模糊度固定成功率能够显著提高,单历元取整成功率从52.7%提升到61.4%,平滑20个历元模糊度固定成功率即可从68.4%提升到95.5%。     

Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP

The main challenge of ambiguity resolution in precise point positioning (PPP) is that it requires 30 min or more to succeed in the first fixing of ambiguities. With the full operation of the BeiDou (BDS) satellite system in East Asia, it is worthwhile to investigate the performance of GPS + BDS PPP ambiguity resolution, especially the improvements of the initial fixing time and ambiguity-fixing rate compared to GPS-only solutions. We estimated the wide- and narrow-lane fractional-cycle biases (FCBs) for BDS with a regional network, and PPP ambiguity resolution was carried out at each station to assess the contribution of BDS. The across-satellite single-difference (ASSD) GPS + BDS combined ambiguity-fixed PPP model was used, in which the ASSD is applied within each system. We used a two-day data set from 48 stations. For kinematic PPP, the percentage of fixing within 10 min for GPS only (Model A) is 17.6 %, when adding IGSO and MEO of BDS (Model B), the percentage improves significantly to 42.8 %, whereas it is only 23.2 % if GEO is added (Model C) due to the low precision of GEO orbits. For static PPP, the fixing percentage is 32.9, 53.3 and 28.0 % for Model A, B and C, respectively. In order to overcome the limitation of the poor precision of GEO satellites, we also used a small network of 10 stations to analyze the contribution of GEO satellites to kinematic PPP. We took advantage of the fact that for stations of a small network the GEO satellites appear at almost the same direction, such that the GEO orbit error can be absorbed by its FCB estimates. The results show that the percentage of fixing improves from 39.5 to 57.7 % by adding GEO satellites.     

Performance analysis of integrated GPS/GLONASS carrier phase-based positioning

Due to the different signal frequencies for the GLONASS satellites, the commonly-used double-differencing procedure for carrier phase data processing can not be implemented in its straightforward form, as in the case of GPS. In this paper a novel data processing strategy, involving a three-step procedure, for integrated GPS/GLONASS positioning is proposed. The first is pseudo-range-based positioning, that uses double-differenced (DD) GPS pseudo-range and single-differenced (SD) GLONASS pseudo-range measurements to derive the initial position and receiver clock bias. The second is forming DD measurements (expressed in cycles) in order to estimate the ambiguities, by using the receiver clock bias estimated in the above step. The third is to form DD measurements (expressed in metric units) with the unknown SD integer ambiguity for the GLONASS reference satellite as the only parameter (which is constant before a cycle slip occurs for this satellite). A real-time stochastic model estimated by residual series over previous epochs is proposed for integrated GPS/GLONASS carrier phase and pseudo-range data processing. Other associated issues, such as cycle slip detection, validation criteria and adaptive procedure(s) for ambiguity resolution, is also discussed. The performance of this data processing strategy will be demonstrated through case study examples of rapid static positioning and kinematic positioning. From four experiments carried out to date, the results indicate that rapid static positioning requires 1 minute of single frequency GPS/GLONASS data for 100% positioning success rate. The single epoch positioning solution for kinematic positioning can achieve 94.6% success rate over short baselines (<6 km).