GLONASS频间码偏差特性分析及其在宽巷模糊度固定中的应用

受接收机类型、固件版本和天线的影响,GLONASS IFCB变化规律复杂且难以有效改正,导致GLONASS HMW组合包含系统性偏差,无法用于GLONASS宽巷模糊度固定。本文提出一种基于GLONASS HMW组合观测值残差的站间IFCB估计方法,并对站间IFCB变化特性进行分析。结果表明,站间IFCB长期稳定,少数相同类型硬件（包括接收机类型、固件版本和天线）站间IFCB可达0.5 m。为削弱伪距多路径效应对站间IFCB估值的影响,基于一个轨道重复周期的观测数据求得一组站间IFCB对实时观测值进行补偿,实现HMW组合平滑序列直接用于GLONASS宽巷模糊度实时固定。进行站间IFCB补偿后,基线宽巷模糊度固定正确率均在98%以上。     

Carrier-phase inter-frequency biases of GLONASS receivers

The frequency division multiplexing of the GLONASS signals causes inter-frequency biases in the receiving equipment. These biases vary considerably for receivers from different manufacturers and thus complicate or prevent carrier-phase ambiguity fixing. Complete and reliable ambiguity fixing requires a priori information of the carrier-phase inter-frequency bias differences of the receivers involved. GLONASS carrier-phase inter-frequency biases were estimated for 133 individual receivers from 9 manufacturers. In general, receivers of the same type and even receivers from the same manufacturer show similar biases, whereas the differences among manufacturers can reach up to 0.2 ns (more than 5 cm) for adjacent frequencies and thus up to 2.4 ns (73 cm) for the complete L1 or L2 frequency bands. A few individual receivers were identified whose inter-frequency biases behave differently as compared to other receivers of the same type or whose biases vary with time.     

An approach to GLONASS ambiguity resolution

 When processing global navigation satellite system (GLONASS) carrier phases, the standard double-differencing (DD) procedure cannot cancel receiver clock terms in the DD phase measurement equations due to the multiple frequencies of the carrier phases. Consequently, a receiver clock parameter has to be set up in the measurement equations in addition to baseline components and DD ambiguities. The resulting normal matrix unfortunately becomes singular. Methods to deal with this problem have been proposed in the literature. However, these methods rely on the use of pseudo-ranges. As pseudo-ranges are contaminated by multi-path and hardware delays, biases in these pseudo-ranges are significant, which may result in unreliable ambiguity resolution. A new approach is addressed that is not sensitive to the biases in the pseudo-ranges. The proposed approach includes such steps as converting the carrier phases to their distances to cancel the receiver clock errors, and searching for the most likely single-differenced (SD) ambiguity. Based on the results from the theoretical investigation, a practical procedure for GLONASS ambiguity resolution is presented. The initial experimental results demonstrate that the proposed approach is useable in cases of GLONASS and combined global positioning system (GPS) and GLONASS positioning. Received: 19 August 1998 / Accepted: 12 November 1999     

An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK

A user of heterogeneous GPS and GLONASS receiver pairs in differential positioning mode will experience ambiguity fixing challenges due to the presence of inter-channel biases. These biases cannot be canceled by differencing GLONASS observations, whether pseudorange or carrier phase. Fortunately, pre-calibration of GLONASS pseudorange and carrier phase observations can make ambiguity fixing for GPS/GLONASS positioning much easier. We propose an effective algorithm that transforms an RTK (real-time kinematic) solution in a mixed receiver baseline from a float to a fixed ambiguity solution. Carrier phase and code inter-channel biases are estimated from a zero baseline. Then, GLONASS both carrier phase and code observations are corrected accordingly. The results show that a mixed baseline can be transformed from a float (~100 %) to a fixed (more than 92 %) solution.     

长基线GLONASS模糊度固定方法及实验分析

格洛纳斯（Global Navigation Satellite System,GLONASS）采用了频分多址技术,接收机在接收不同卫星信号时会产生频间偏差,阻碍了GLONASS长基线模糊度固定,限制了其定位定轨的精度。提出了一种新的GLONASS模糊度固定方法。该方法基于全球电离层格网产品,根据频间偏差率的变化范围,采用搜索的方法和线性模型去除相位频间偏差对宽窄巷模糊度的影响,实现了GLONASS无电离层组合模糊度固定。利用平均基线长度为763 km的全球卫星导航系统（Global Navigation Satellite System,GNSS）服务站实验网数据对该方法进行分析,结果表明:连续30 d内,模糊度固定成功率最高为95.4%,最低为88.8%,平均为93.45%;模糊度固定后,北（north,N）、东（east,E）、高（up,U）各分量重复性和均方根误差（root mean square er-ror,RMSE）值均得到不同程度的改善,E分量重复性和RMSE值分别改善了20%和14%,改善效果最为明显。     

A review on the inter-frequency biases of GLONASS carrier-phase data

GLONASS ambiguity resolution (AR) between inhomogeneous stations requires correction of inter-frequency phase biases (IFPBs) (a “station” here is an integral ensemble of a receiver, an antenna, firmware, etc.). It has been elucidated that IFPBs as a linear function of channel numbers are not physical in nature, but actually originate in differential code-phase biases (DCPBs). Although IFPBs have been prevalently recognized, an unanswered question is whether IFPBs and DCPBs are equivalent in enabling GLONASS AR. Besides, general strategies for the DCPB estimation across a large network of heterogeneous stations are still under investigation within the GNSS community, such as whether one DCPB per receiver type (rather than individual stations) suffices, as tentatively suggested by the IGS (International GNSS Service), and what accuracy we are able to and ought to achieve for DCPB products. In this study, we review the concept of DCPBs and point out that IFPBs are only approximate derivations from DCPBs, and are potentially problematic if carrier-phase hardware biases differ by up to several millimeters across frequency channels. We further stress the station and observable specific properties of DCPBs which cannot be thoughtlessly ignored as conducted conventionally. With 212 days of data from 200 European stations, we estimated DCPBs per stations by resolving ionosphere-free ambiguities of \(\sim \)5.3 cm wavelengths, and compared them to the presumed truth benchmarks computed directly with L1 and L2 data on ultra-short baselines. On average, the accuracy of our DCPB products is around 0.7 ns in RMS. According to this uncertainty estimates, we could unambiguously confirm that DCPBs can typically differ substantially by up to 30 ns among receivers of identical types and over 10 ns across different observables. In contrast, a DCPB error of more than 6 ns will decrease the fixing rate of ionosphere-free ambiguities by over 20 %, due to their smallest frequency spacing and highest sensitivity to DCPB errors. Therefore, we suggest that (1) the rigorous DCPB model should be implemented instead of the classic, but inaccurate IFPB model; (2) DCPBs of sub-ns accuracy can be achieved over a large network by efficiently resolving ionosphere-free ambiguities; (3) DCPBs should be estimated and applied on account of their station and observable specific properties, especially for ambiguities of short wavelengths.     

单站多参数GLONASS码频间偏差估计及其对组合精密单点定位的影响

在分析传统GPS/GLONASS组合PPP数学模型中忽略GLONASS码IFB不足的基础上,提出一种基于"多参数"的组合PPP与码IFB估计算法。将"频间偏差"与"系统时差"参数进行合并,通过引入多个独立的"时频偏差"参数对组合PPP中的GLONASS码IFB进行函数模型补偿,同时可实现基于单个测站观测数据的码IFB精确估计。对配备6种GNSS品牌接收机的30个IGS站实测数据进行GLONASS码IFB估计与分析。结果表明:各品牌接收机不同频率通道的GLONASS码IFB可达数米,且表现出与频率的明显相关性,但难以通过简单函数建模为其提供精确的先验改正值;相同品牌接收机的GLONASS码IFB整体上具有相似的特性,而在个别测站会表现出异常特征;即使接收机类型、固件版本及天线类型完全相同的测站,GLONASS码IFB值也可能存在显著差异。新算法能实现对GLONASS码IFB的有效补偿,明显加快组合PPP的收敛速度。虽然引入多个附加参数会导致函数模型自由度减小,但对定位精度的影响有限,与传统"单参数"法进行组合PPP的定位精度相当。     

顾及码频间偏差的GPS/GLONASS实时卫星钟差估计

在进行GPS/GLONASS联合卫星钟差估计时,GLONASS码频间偏差（inter-frequency bias,IFB）因卫星频率间的差异而无法被测站接收机钟差参数吸收,其一部分将进入GLONASS卫星钟差估值中。通过引入多个"时频偏差"参数（inter-system and inter-frequency bias,ISFB）及附加基准约束对测站GLONASS码IFB进行函数模型补偿,实现其与待估卫星钟差参数的有效分离,并对所估计实时卫星钟差和实时精度单点定位（real-time precise point positioning,RT-PPP）进行精度评估。结果表明,在卫星钟差估计观测方程中忽略码IFB,会明显降低GLONASS卫星钟差估值精度;新方法能有效避免码IFB对卫星钟差估值的影响,所获得GPS、GLONASS卫星钟差与ESA（European Space Agency）事后精密钟差产品偏差平均均方根值分别小于0.2 ns、0.3 ns。利用实时估计卫星钟差进行静态RT-PPP,当观测时段长为2 h时,GPS单系统、GPS/GLONASS组合系统的3D定位精度优于10 cm,GLONASS单系统3D定位精度约为15 cm;三种模式24 h单天解的3D定位精度均优于5 cm。     

Influence of the GLONASS inter-frequency bias on differential code bias estimation and ionospheric modeling

GPS Solutions - Due to the application of frequency division multiple access, the signals of GLONASS satellites suffer from code and carrier phase inter-frequency biases (IFBs). In this study, the...     

A two-step ionospheric modeling algorithm considering the impact of GLONASS pseudo-range inter-channel biases

The Global Navigation Satellite System presents a plausible and cost-effective way of computing the total electron content (TEC). But TEC estimated value could be seriously affected by the differential code biases (DCB) of frequency-dependent satellites and receivers. Unlike GPS and other satellite systems, GLONASS adopts a frequency-division multiplexing access mode to distinguish different satellites. This strategy leads to different wavelengths and inter-frequency biases (IFBs) for both pseudo-range and carrier phase observations, whose impacts are rarely considered in ionospheric modeling. We obtained observations from four groups of co-stations to analyze the characteristics of the GLONASS receiver P1P2 pseudo-range IFB with a double-difference method. The results showed that the GLONASS P1P2 pseudo-range IFB remained stable for a period of time and could catch up to several meters, which cannot be absorbed by the receiver DCB during ionospheric modeling. Given the characteristics of the GLONASS P1P2 pseudo-range IFB, we proposed a two-step ionosphere modeling method with the priori IFB information. The experimental analysis showed that the new algorithm can effectively eliminate the adverse effects on ionospheric model and hardware delay parameters estimation in different space environments. During high solar activity period, compared to the traditional GPS + GLONASS modeling algorithm, the absolute average deviation of TEC decreased from 2.17 to 2.07 TECu (TEC unit); simultaneously, the average RMS of GPS satellite DCB decreased from 0.225 to 0.219 ns, and the average deviation of GLONASS satellite DCB decreased from 0.253 to 0.113 ns with a great improvement in over 55%.     

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.     

PERFORMANCE ANALYSIS OF INTEGRATED GPS/GLONASS CARRIER PHASE-BASED POSITIONING

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GLONASS inter-frequency phase bias rate estimation by single-epoch or Kalman filter algorithm

GPS Solutions - GLONASS double-differenced (DD) ambiguity resolution is hindered by the inter-frequency bias (IFB) in GLONASS observation. We propose a new algorithm for IFB rate estimation to...     

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).     

GLONASS pseudorange inter-channel biases and their effects on combined GPS/GLONASS precise point positioning

Combined GPS/GLONASS precise point positioning (PPP) can obtain a more precise and reliable position than GPS PPP. However, because of frequency division multiple access, GLONASS carrier phase and pseudorange observations suffer from inter-channel biases (ICBs) which will influence the accuracy and convergence speed of combined GPS/GLONASS PPP. With clear understanding of the characteristics of carrier phase ICBs, we estimated undifferenced GLONASS pseudorange ICBs for 133 receivers from five manufacturers and analyzed their characteristics. In general, pseudorange ICBs corresponding to the same firmware have strong correlations. The ICB values of two receivers with the same firmware may be different because of different antenna types, and their differences are closely related to frequency. Pseudorange ICBs should be provided for each satellite to obtain more precise ICBs as the pseudorange ICBs may vary even on the same frequency. For the solutions of standard point positioning (SPP), after pseudorange ICB calibration, the mean root mean square (RMS) improvements of GLONASS SPP reach up to 57, 48, and 53 % for the East, North, and Up components, while combined GPS/GLONASS SPP reach up to 27, 17, and 23 %, respectively. The combined GPS/GLONASS PPP after pseudorange ICB calibration evidently improved the convergence speed, and the mean RMS of PPP improved by almost 50 % during the convergence period.     

Improvements on the particle-filter-based GLONASS phase inter-frequency bias estimation approach

The carrier phase inter-frequency bias (IFB) of GLONASS between receivers of different types is usually not zero. This bias must be estimated and removed in data processing so that the integer double difference (DD) ambiguities can be fixed successfully. Recently, the particle filter approach has been proposed to estimate the IFB rate in real time. In this approach, the IFB rate samples are first generated and used to correct the phase IFB in the GLONASS observations. Then, the weights of the rate samples are updated with a function related to RATIO which is for ambiguity acceptance testing in integer ambiguity resolution. Afterwards, the IFB rate is estimated according to the weighted particles. This approach can estimate IFB accurately with short convergence time and without prior information. However, when the system noise is set too low, the estimated results are unstable due to the serious problem of particle diversity-loss, even though the system model is accurate. Additionally, the computational burden is dependent on the number of particles, which has to be optimized for the computation at hand. Therefore, this study proposes two improvements for the IFB estimation in regard to the above two aspects. The first improvement is to solve the noise setting problem by employing a regularized particle filter (RPF). The second improvement optimizes the number of particles in the resampling step according to the standard deviation (STD) of the weighted particles via a controlling function. The two improvements result in significantly better performances. The regularization method allows for the system noise to be set as zero without disturbing the estimates, and consequently, more precise estimates can be achieved. In addition, the approach using the controlling function for adapting the number of particles has comparable performance in precision but the computation load is largely reduced.     

实时GLONASS相位频间偏差粒子群优化估计方法

针对GLONASS相位频间偏差与模糊度线性相关所导致的难以对两者进行快速分离的问题,提出了一种实时GLONASS相位频间偏差估计方法。通过分析相位IFB与RATIO值之间的关系,将相位IFB估计问题归结为求解最优化问题,并将优化方法中的粒子群优化算法引入相位IFB估计中,该方法可在不增加待估参数数量以及先验信息的条件下,高效可靠地搜索出IFB变化率参数,实现GLONASS模糊度实时固定。测试结果表明,该方法在单历元解算条件下每历元平均搜索次数为32次,远低于基于粒子滤波的相位频间偏差估计方法的200次;在采用Kalman滤波方法进行解算条件下,每历元平均搜索次数仅为9次。无论采用单历元解还是滤波解,模糊度固定成功率均高于96.2%,模糊度固定解的最大坐标偏差均小于4 cm。     

Simultaneous estimation of GLONASS pseudorange inter-frequency biases in precise point positioning using undifferenced and uncombined observations

GLONASS precise point positioning (PPP) performance is affected by the inter-frequency biases (IFBs) due to the application of frequency division multiple access technique. In this contribution, the impact of GLONASS pseudorange IFBs on convergence performance and positioning accuracy of GLONASS-only and GPS + GLONASS PPP based on undifferenced and uncombined observation models is investigated. Through a re-parameterization process, the following four pseudorange IFB handling schemes were proposed: neglecting IFBs, modeling IFBs as a linear or quadratic polynomial function of frequency number, and estimating IFBs for each GLONASS satellite. One week of GNSS observation data from 132 International GNSS Service stations was selected to investigate the contribution of simultaneous estimation of GLONASS pseudorange IFBs on GLONASS-only and combined GPS + GLONASS PPP in both static and kinematic modes. The results show that considering IFBs can speed up the convergence of PPP using GLONASS observations by more than 20%. Apart from GLONASS-only kinematic PPP, the positioning accuracy of GLONASS-only and GPS + GLONASS PPP is comparable among the four schemes. Overall, the scheme of estimating IFBs for each GLONASS satellite outperforms the other schemes in both convergence time reduction and positioning accuracy improvement, which indicates that the GLONASS IFBs may not strictly obey a linear or quadratic function relationship with the frequency number.     

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.     

Method for real-time self-calibrating GLONASS code inter-frequency bias and improvements on single point positioning

Utilization of frequency-division multiple access (FDMA) leads to GLONASS pseudorange and carrier phase observations suffering from variable levels inter-frequency bias (IFB). The bias related with carrier phase can be absorbed by ambiguities. However, the unequal code inter-frequency bias (cIFB) will degrade the accuracy of pseudorange observations, which will affect positioning accuracy and convergence of precise point positioning (PPP) when including GLONASS satellites. Based on observations made on un-differenced (UD) ionospheric-free combinations, GLONASS cIFB parameters are estimated as a constant to achieve GLONASS cIFB real-time self-calibration on a single station. A total of 23 stations, with different manufacturing backgrounds, are used to analyze the characteristics of GLONASS cIFB and its relationship with variable receiver hardware. The results show that there is an obvious common trend in cIFBs estimated using broadcast ephemeris for all of the different manufacturers, and there are unequal GLONASS inter-satellite cIFB that match brand manufacture. In addition, a particularly good consistency is found between self-calibrated receiver-dependent GLONASS cIFB and the IFB products of the German Research Centre for Geosciences (GFZ). Via a comparative experiment, it is also found that the algorithm of cIFB real-time self-calibration not only corrects receiver-dependent cIFB, but can moreover eliminate satellite-dependent cIFB, providing more stable results and further improving global navigation satellite system (GNSS) point positioning accuracy. The root mean square (RMS) improvements of single GLONASS standard point positioning (SPP) reach up to 54.18 and 53.80% in horizontal and vertical direction, respectively. The study’s GLONASS cIFB self-estimation can realize good self-consistency between cIFB and stations, working to further promote convergence efficiency relative to GPS?+?GLONASS PPP. An average improvement percentage of 19.03% is observed, realizing a near-consistent accuracy with GPS?+?GLONASS fusion PPP.