Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution

Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.     

Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution

The Global Positioning System (GPS) and Galileo will transmit signals on similar frequencies, that is, the L1–E1 and L5–E5a frequencies. This will be beneficial for mixed GPS and Galileo applications in which the integer carrier phase ambiguities need to be resolved, in order to estimate the positioning unknowns with centimeter accuracy or better. In this contribution, we derive the mixed GPS + Galileo model that is based on “inter-system” double differencing, that is, differencing the Galileo phase and code observations relative to those corresponding to the reference or pivot satellite of GPS. As a consequence of this, additional between-receiver inter-system bias (ISB) parameters need to be solved as well for both phase and code data. We investigate the size and variability of these between-receiver ISBs, estimated from L1 and L5 observations of GPS, as well as E1 and E5a observations of the two experimental Galileo In-Orbit Validation Element (GIOVE) satellites. The data were collected using high-grade multi-GNSS receivers of different manufacturers for several zero- and short-baseline setups in Australia and the USA. From this analysis, it follows that differential ISBs are only significant for receivers of different types and manufacturers; for baselines formed by identical receiver types, no differential ISBs have shown up; thus, implying that the GPS and GIOVE data are then fully interoperable. Fortunately, in case of different receiver types, our analysis also indicates that the phase and code ISBs may be calibrated, since their estimates, based on several datasets separated in time, are shown to be very stable. When the single-frequency (E1) GIOVE phase and code data of different receiver types are a priori corrected for the differential ISBs, the short-baseline instantaneous ambiguity success rate increases significantly and becomes comparable to the success rate of mixed GPS + GIOVE ambiguity resolution based on identical receiver types.     

Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases

Double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can be fixed to integers if the associated differential inter-system biases (DISBs) are well known. In this case, only one common pivot satellite is sufficient for inter-system ambiguity resolution. This will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning especially when only a few satellites are observed. However, for GPS and current operational BDS-2, there are no overlapping frequencies. Due to the influence of different frequencies, the inter-system DD ambiguities still cannot be fixed to integers even if the DISBs are precisely known. In this contribution, we present an inter-system differencing model for combined GPS and BDS single-frequency RTK positioning through real-time estimation of DISBs. The stability of GPS L1 and BDS B1 DISBs is analyzed with different receiver types. Along with parameterization and using the short-term stability of DISBs, the DD ambiguities between GPS and BDS pivot satellites and the between-receiver single-difference ambiguity of the GPS pivot satellite can be estimable jointly with the differential phase DISB term from epoch to epoch. Then the inter-system differencing model can benefit from the near time-constant DISB parameters and thus has better multi-epoch positioning performance than the classical intra-system differencing model. The combined GPS and BDS single-frequency RTK positioning performance is evaluated with various simulated satellite visibilities. It will be shown that compared with the classical intra-system differencing model, the proposed model can effectively improve the positioning accuracy and reliability, especially for severely obstructed situations with only a few satellites observed.     

顾及系统间偏差的BDS/GPS单钟差定位法

在多系统定位中,因接收机硬件延迟难以与钟差分离,导致传统方法需要对每个系统考虑一个接收机钟差项,使得在遮挡环境下存在因卫星少参数多,导致定位结果不可靠的问题。针对这一不足,研究一种顾及系统间偏差的BDS/GPS双系统单钟差定位算法。在卫星数足够时利用传统方法估计系统间偏差参数,当卫星数过少时,将已获得的参数作为已知量,从而只估计一个钟差参数。采用Trimble NetR9与UBLOX M8T两种接收机数据对算法进行验证,以提高截止高度角的方式模拟遮挡环境。实验结果表明,相较于传统方法,当卫星数过少时,Trimble NetR9平面和高程分别提高118.8%(1.374 m)与41.3%(1.434 m),UBLOX M8T平面和高程分别提高9.5%(0.654 m)与242.9%(10.165 m),可更好地应用于导航领域。     

GPS/BDS接收机端系统偏差实时估计方法

针对GPS-BDS系统偏差会导致GPS和BDS系统间的混合双差模糊度不具有整数特性,且其不完全稳定的问题,该文提出一种GPS/BDS系统偏差实时在线估计方法。通过将双差模糊度以单差模糊度之差的形式进行求解,然后再将以周为单位的单差模糊度投影为双差模糊度,以此消除GPS和BDS不同波长的影响;在此基础上,采用Kalman滤波对系统偏差进行实时动态估计。实验结果表明,该方法采用较少历元的观测数据便可使系统偏差收敛,并且收敛后十分稳定,可以将其作为校正参数;加入系统偏差改正的GPS/BDS紧组合定位在恶劣环境下表现良好,可将模糊度固定平均所需时间缩短29%,模糊度固定成功率提高45%。     

A new practical approach to GNSS high-dimensional ambiguity decorrelation

Based on both the lower and the upper triangular Cholesky decomposition algorithms, the (inverse) lower triangular Cholesky integer transformation and the (inverse) upper triangular Cholesky integer transformation are defined, and the (inverse) paired Cholesky integer transformation is proposed. Then, for the case of high-correlation ambiguity, a multi-time (inverse) paired Cholesky integer transformation is given. In addition, a simple and practical criterion is presented to solve the uniqueness problem of the integer transformation. It is verified by an example that (1) the (inverse) paired Cholesky integer transformation is very convenient and very efficient in practical computation; (2) the (inverse) paired Cholesky integer transformation is better than both the (inverse) lower triangular Cholesky integer transformation and the (inverse) upper triangular Cholesky integer transformation; and that (3) the inverse paired Cholesky integer transformation outperforms the paired Cholesky integer transformation slightly in the most cases.     

Seven possible states of geospatial data with respect to map projection and definition: a novel pedagogical device for GIS education

ABSTRACT

Conceptually, the theory and implementation of “map projection” in geographic information system (GIS) technology is difficult to comprehend for most introductory students and novice users. Compounding this difficulty is the concept of a “map projection file” that defines map projection parameters of geo-spatial data. The problem of the “missing projection file” appears ubiquitous for all users, especially in practice where data is widely shared. Another common problem is inadvertent misapplication of the “Define Projection” tool that can result in a GIS dataset with an incorrectly defined map projection file. GIS education should provide more guidance in differentiating the concepts of map projection versus projection files by increasing understanding and minimizing common errors. A novel pedagogical device is introduced in this paper: the seven possible states of GIS data with respect to map projection and definition. The seven possible states are: (1) a projected coordinate system (PCS) that is correctly defined, (2) a PCS that is incorrectly defined, (3) a PCS that is undefined, (4) a geographic coordinate system (GCS) that is correctly defined, (5) a GCS that is incorrectly defined, (6) a GCS that is undefined, and (7) a non-GCS. Recently created automated troubleshooting tools to determine a missing map projection file are discussed.     

地理遥感信息模型与地理数学

地理图像信息模型是在地形模型、物理模型、数学模型的基础上提出的一种新型模型。概述了地理图像信息模型的基本概念、技术与应用。提出了符合地理科学自身规律的非线性数学方法 ,解决了确定性问题与不确定问题的结合 ,从形式逻辑计算发展到辩证逻辑的计算 ,从抽象公式的计算发展到抽象思维与形象思维结合的公式与图像合为一体的计算 ,从而解决了地理数学问题 ,为发展地理数学奠定了基础。     

A new differential code bias (C1–P1) estimation method and its performance evaluation

The current satellite clock products are computed using the ionosphere-free phase (L1/L2) and code (P1/P2) observations. Thus, if users conduct undifferenced positioning using these clock products together with C1 and P2 observations, the differential code bias (DCB) (C1–P1) should be properly compensated. The influence of DCB (C1–P1) on the undifferenced ambiguity solutions is investigated. Based on the investigation, we propose a new DCB (C1–P1) estimation method. Using it, the satellite DCB (C1–P1) can be computed. A 30-day (DOY 205–234, 2012) dual-frequency GPS data set is processed to estimate the DCB (C1–P1). Comparing the estimated results with that of IGS DCB products, the accuracy is better than 0.13 m. The performances of DCB (C1–P1) in the code-based single-point positioning, precise point positioning (PPP) convergence and wide-lane uncalibrated phase delay (UPD) estimation are investigated using the estimated DCB (C1–P1). The results of the code-based single-point positioning show that the influence of DCB (C1–P1) on the up direction is more evident than on the horizontal directions. The accuracy is improved by 50 % and reaches to decimeter level with DCB (C1–P1) application. The performance of DCB (C1–P1) in PPP shows that it can accelerate PPP convergence through improving the accuracy of the code observation. The computed UPD values show that influence of DCB (C1–P1) on UPD of each satellite is different, and some values are larger than 0.3 cycles.     

北斗三号全球卫星导航系统空间信号精度评估

针对北斗三号 (BDS-3)正式开通后的空间信号精度情况,选取2020-08-01—2021-07-31共 1 a的混合广播星历数据,以德国波茨坦地学研究中心(GFZ)和武汉大学国际GNSS服务(IGS)数据中心(WHU)提供的精密星历为参考分别从轨道精度、钟差精度和空间信号测距误差(SISRE)来进行BDS-3的空间信号精度评估. 结果表明:BDS-3的轨道精度在径向(R)、切向(A)、法向(C)三个方向上分别优于0.100 m、0.405 m、0.547 m,钟差精度优于1.926 ns,仅受轨道影响的SISRE (orb)为0.134 m,SISRE为0.612 m. 地球静止轨道(GEO)卫星的SISRE为1.137 m,倾斜地球同步轨道(IGSO)卫星和中圆地球轨道(MEO)卫星的SISRE相比GEO卫星分别减少36.3%、51.3%.      

北斗三号全球导航卫星系统服务性能评估:定位导航授时、星基增强、精密单点定位、短报文通信与国际搜救

本文给出了北斗三号全球导航卫星系统定位导航授时、星基增强、精密单点定位、区域短报文通信、全球短报文通信和国际搜救共6类服务的测试评估方法,并利用实测数据对各类服务的核心指标进行了评估.结果表明,定位导航授时服务方面,空间信号测距误差0.23 m(RMS),空间信号可用性99.44％,空间信号连续性99.99％,PDOP...     

Surveying co-located space-geodetic instruments for ITRF computation

A new and comprehensive method is presented that can be used for estimating eccentricity vectors between global positioning system (GPS) antennas, doppler orbitography and radiopositioning integrated by satellites (DORIS) antennas, azimuth-elevation (AZ-EL) very long baseline interferometry (VLBI) telescopes, and satellite laser ranging (SLR) and lunar laser ranging (LLR) telescopes. The problem of reference point (RP) definition for these space-geodetic instruments is addressed and computed using terrestrial triangulation and electronic distance measurement (EDM) trilateration. The practical ground operations, the surveying approach and the terrestrial data processing are briefly illustrated, and the post-processing procedure is discussed. It is a geometrically based analytical approach that allows computation of RPs along with a rigorous statistical treatment of measurements. The tight connection between the geometrical model and the surveying procedure is emphasized. The computation of the eccentricity vector and the associated variance–covariance matrix between an AZ-EL VLBI telescope (with or without intersecting axes) and a GPS choke ring antenna is concentrated upon, since these are fundamental for computing the International Terrestrial Reference Frame (ITRF). An extension to RP computation and eccentricity vectors involving DORIS, SLR and LLR techniques is also presented. Numerical examples of the quality that can be reached using the authors approach are given. Working data sets were acquired in the years 2001 and 2002 at the radioastronomical observatory of Medicina (Italy), and have been used to estimate two VLBI-GPS eccentricity vectors and the corresponding SINEX files.     

最优Tikhonov正则化矩阵及其在卫星导航定位模糊度解算中的应用

首先,用贝叶斯（Bayes）统计理论的观点,把未知参数看作随机变量,引入未知参数的无信息先验分布函数,从数学上推导了均方误差最小意义下的正则化矩阵;然后,结合最优正则化矩阵和快速截断奇异值算法,提出了一种新的正则化方法;最后,探讨了新方法在全球卫星导航系统（Global Navigation Satellite System,GNSS）模糊度解算中的应用。通过一组GNSS模糊度解算实验,比较了最小二乘（least squares,LS）方法、L曲线岭估计和新方法的性能。结果表明,新方法解算成功率略高于L曲线岭估计,远高于LS方法;计算耗时略大于LS方法,远小于L曲线岭估计。     

一种顾及电离层延迟信息的长基线北斗三频模糊度解算方法

北斗卫星导航系统播发3个频点的导航信号,有利于载波相位模糊度解算。鉴于传统的三频模糊度解算方法由于受基线距离的限制难以在中长基线情形下可靠地固定模糊度,本文提出一种适用于北斗卫星系统中长基线模糊度固定的新方法。实验结果表明,改进的新算法不受基线长度的约束,在保证超宽巷、宽巷模糊度正确固定的同时,宽巷模糊度估值误差在0.3周以内;窄巷模糊度估值误差在3周以内。相比于传统算法,新方法的改进效果较好。     

Variance reduction of GNSS ambiguity in (inverse) paired Cholesky decorrelation transformation

It has been discovered that (a) the variance of all entries of the ambiguity vector transformed by a (inverse) paired Cholesky integer transformation is reduced relative to that of the corresponding entries of the original ambiguity vector; (b) the higher the dimension of the ambiguity vector, the more significantly the transformed variance will be decreased. The property of variance reduction is explained theoretically in detail. In order to better measure the property of variance reduction, an efficiency factor on variance reduction of ambiguities is defined. Since the (inverse) paired Cholesky integer transformation is generally performed many times for the GNSS high-dimensional ambiguity vector, the computation formula of the efficiency factor on the multi-time (inverse) paired Cholesky integer transformation is deduced. The computation results in the example show that (a) the (inverse) paired Cholesky integer transformation has a very good property of variance reduction, especially for the GNSS high-dimensional ambiguity vector; (b) this property of variance reduction can obviously improve the success rate of the transformed ambiguity vector.     

基于等式的等间隔GM(1,1)模型比较研究

本文归纳了基于等式的2种等间隔GM(1,1)模型,比较了这2种模型与常规模型的精度,算例显示:当发展系数a较小时,3种模型的后验差比值C和小误差概率P的精度一致;当发展系数较大时,基于等式的模型比常规模型的后验差比值C和小误差概率P的精度高,且基于等式的这2种模型的后验差比值C和小误差概率P精度基本相当.     

遥感地表温度降尺度方法比较————性能对比及适应性评价

在归纳现有遥感地表温度降尺度方法的基础上, 选取3种代表性方法:Normalized Difference Vegetation Index (NDVI)、Pixel Block Intensity Modulation (PBIM)和Linear Spectral Mixture Model (LSMM)方法进行实验比较, 并建立了一种纹理相似性度量指标CO-RMSE (Co-Occurrence Root Mean Square Error)。结果表明:(1)NDVI方法受季节影响最严重, 不适于春、冬季, 其次为PBIM方法;(2)LSMM方法受分辨率限制最大, 低分辨率时丢失大量纹理信息, NDVI方法在较高分辨率时优于PBIM方法, 较低分辨率时则相反;(3)3种方法的适用区域分别为植被与裸土像元并存区域, 山区和反照率变化较大区域, 以及类别间温差较大区域;(4)NDVI方法操作最简单, LSMM方法最复杂。分析认为, 尺度因子是决定方法性能的关键, 应根据季节、分辨率、地表覆盖、应用目的和操作性等综合选择。     

DEM Generation for Lunar Surface using Chandrayaan-1 TMC Triplet Data

Digital Elevation Model (DEM) is an important prerequisite for understanding the lunar surface. However, making accurate DEM is a very challenging task due to (a) lack of support of projection parameters in COTS packages (eg. PCI Geomatica), which are to be used in generation of Lunar DEM and (b) unavailability of Ground Control Points (GCPs). In the present study, DEM generation of lunar surface was attempted without GCPs using Rational Function (RF) model from Chandrayaan-1 TMC triplet images. In the study, a good correlation (of almost same order) is observed between Nadir-Fore (NF), Nadir - Aft (NA), Fore - Aft (FA) and Fore - Nadir - Aft (FNA) image pairs. The results suggest that DEM for lunar surface can be created without GCPs using RF model.