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.     

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...     

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...     

顾及频率间偏差的GPS/GLONASS卫星钟差实时估计

GPS/GLONASS卫星钟差联合估计过程中,由于GLONASS系统采用频分多址技术区分卫星信号,因而会产生频率间偏差（IFB）^[1]。本文在GPS/GLONASS卫星定轨过程中的IFB参数特性分析的基础上,引入IFB参数,实现顾及频率间偏差的GPS/GLONASS卫星钟差实时估计。同时,为解决实时估计中待估参数过多导致的实时性较弱等问题,基于非差伪距观测值和历元间差分相位观测值改进实时估计数学模型,实现多系统卫星钟差的联合快速估计。结果表明：GPS/GLONASS联合估计时需引入IFB参数并优化其估计策略,采用MGEX和iGMAS跟踪站的实测数据进行实时钟差解算,快速估计方法可实现1.6 s逐历元快速、高精度估计,与GBM提供的最终精密卫星钟差相比,GPS卫星钟差实时精度约为0.210 ns,GLONASS卫星约为0.298 ns。     

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.     

GLONASS频间码偏差实时估计方法及其在RTK定位中的应用

GLONASS伪距频间偏差难以利用经验模型消除。在RTK定位解算中,尤其是需顾及大气延迟的中长距离异质基线,IFCB会降低模糊度收敛速度,甚至导致模糊度固定错误。本文基于双差HMW组合和消电离层组合,提出一种站间IFCB实时估计算法,实时获取各频段的非组合站间单差IFCB。试验结果表明,站间IFCB长期稳定,可达数个纳秒;在GPS/GLONASS观测值先验误差比值为3：5的条件下,未改正的IFCB可能导致基线GPS/GLONASS组合RTK定位性能比单GPS差。将本文提出算法应用于RTK定位,能够有效消除IFCB的影响,RTK模糊度浮点解精度、定位收敛速度和固定率都有明显改善,部分基线的RTK定位首次固定时间从9.2 s提高到2.1 s,固定解比率从84.5%提高到97.9%。     

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.     

Understanding the characteristic of GLONASS inter-frequency clock bias using both FDMA and CDMA signals

GPS Solutions - High-frequency global navigation satellite system (GNSS) observations are of great significance for structural health monitoring. At present, most studies on high-frequency GNSS...     

Fast estimation and analysis of the inter-frequency clock bias for Block IIF satellites

The inter-frequency bias of PRN25 was noticed by the scientific community and considered to be caused by thermal variations. The inter-frequency bias leads to an apparent inter-frequency clock bias (IFCB), which could be obtained using the difference of two ionosphere-free phase combinations (L1/L2 and L1/L5). We present an efficient approach derived from the epoch-differenced strategy for fast estimation of IFCBs for Block IIF satellites. For the analysis, data from 32 stations from the IGS network spanning 10 months (DOY 213, 2011–153, 2012) are processed. The processing times show that the epoch-differenced method is more efficient than the undifferenced one. In order to study the features of IFCB, a harmonic analysis is performed by using a FFT (fast Fourier transformation), and significant periodic variations with the periods of 12, 6 and 8 h are noticed. The fourth-order period is determined by comparing the performances of the model with different periods. After determination, a harmonics-based function of order 4 is used to model the IFCB, and the single-day amplitudes and phases are estimated for the 10 months from a least squares fit. Based on the estimated results, the characterization of IFCB is discussed. The algorithm is incorporated into the MGPSS software developed at SHAO (Shanghai Astronomical Observatory, Chinese Academy of Sciences) and used to monitor the IFCB variations of GPS and COMPASS systems in near real time.     

Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS

Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ? P2) and DCB (P1 ? P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 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.     

Combined GPS/GLONASS precise positioning for long-distance baselines

Combined GPS/GLONASS can increase the accuracy and reliability of positioning especially in some applications with many impediments. Due to the atmosphere delay, the commonly used methods for processing short distance baselines can not be implemented in long distance baselines. In this paper, a new data processing strategy for long distance baselines is proposed, which uses the properties of some combination observables of combined GPS/GLONASS and distance baselines may come to the order of 10?8 and combined GPS/GLONASS improves the accuracy over that of GPS-only positioning, which brings benefit to crust deformation monitoring and research on geodynamics.     

COMBINED GPS/GLONASS PRECISE POSITIONING FOR LONG-DISTANCE BASELINES

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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.     

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.     

GNSS多频融合精密单点定位频率间卫星钟偏差研究

全球导航卫星系统(GNSS)提供多频信号,多频融合已经成为一种趋势。在精密钟差估计(PCE)的过程中,卫星钟差参数会吸收卫星端稳定的伪距偏差和时变的相位偏差,这些偏差均与频率相关。因而使用不同的观测值进行PCE时,得到的卫星钟差估值是不同的,它们之间的差值被定义为频率间卫星钟偏差(IFCB)。按组成成分,IFCB可以分成伪距相关的IFCB(CIFCB)和相位相关的IFCB(PIFCB)两部分。国际GNSS服务(IGS)提供的精密卫星钟差产品是基于双频消电离层(IF)组合观测值生成的。由于IFCB的存在,导致IGS卫星钟差产品不能直接应用于多频精密单点定位(PPP)。IFCB的精确考虑已经成为多频PPP的一个关键问题。本研究旨在对IFCB特性和估计方法开展系统深入的研究,并评估其对多频PPP解的影响。     

Assessment of code bias variations of BDS triple-frequency signals and their impacts on ambiguity resolution for long baselines

GPS Solutions - Carrier phase ambiguity resolution over long baselines is challenging in BDS data processing. This is partially due to the variations of the hardware biases in BDS code signals and...