An improved regularization method to resolve integer ambiguity in rapid positioning using single frequency GPS receivers

A new approach is employed in GPS rapid positioning using several-epoch single frequency phase data.Firstly, the structure characteristic of the normal matrix in GPS rapid positioning is analyzed. Then, in the light of the characteristic, based on TIKHONOV regularization theorem,a new regularizer is designed to mitigate the ill-condition of the normal matrix. The accurate float ambiguity solutions and their MSEM (Mean Squared Error Matrix) are obtained using several-epoch single frequency phase data. Combined with LAMBDA method, the new approach was used to fix the integer ambiguities correctly and quickly using MSEM instead of the cofactor matrix of the ambiguities. Finally, a baseline over 3 km is taken as an example. The fixed integer ambiguities by the new approach using five epoch single frequency phase data are the same as those fixed by Bernese software using long time data. The success rate of fixing the integer ambiguities is 100 percent using 197 group data.Compared with the traditional methods, the new approach provides better accuracy and efficiency in GPS rapid positioning. So, the new approach has an extensive application outlook in deformation monitoring, pseudokinematic relative positioning, and attitude determination, etc.     

北斗二号/三号融合的分米级星基增强算法与性能分析

北斗卫星导航系统星基增强服务通过地球静止卫星向用户播发等效钟差、轨道改正数、电离层格网改正数和分区综合改正数等四重广域差分改正数,用户在此基础上利用载波相位观测值实现实时分米级的定位性能.本文介绍了分米级星基增强服务的参数匹配算法以及单频、双频用户精密定位模型.将系统播发的四重差分改正数应用于北斗二号与三号融合的精密单点定位,分析了不同频点及定位模型的系统精密定位服务性能.18个测站7 d的结果表明:北斗二号/三号融合的星基增强服务双频组合动态精密单点定位平均12.42 min收敛至0.5 m以内,收敛后的平均定位精度为平面0.15 m,高程0.2 m;相比仅使用北斗二号系统,不同定位模型收敛时间平均缩短了56.7%;而基于非差非组合的分区定位收敛速度更快,并且能达到与无电离层组合模型相同的精度水平.使用北斗电离层格网信息改正的单频动态定位PPP平均11.74 min收敛至0.8 m以内,收敛后的平均定位精度为平面0.2 m,高程0.3 m;相比使用广播星历电离层模型改正的结果,静态和动态定位平均收敛时间分别缩减了21.4%和25.2%.     

Using quasi ionosphere-free post-processing algorithm on the medium-range kinematic high accuracy GPS relative positioning

We utilize Quasi Ionosphere-Free (QIF) post-processing algorithm to account for ionosphere delay and use addition parameters to solve for tropospheric bias. Then the estimated integer ambiguities and troposphere parameters are fixed to acquire kinematic relative positions at every epoch.Using kinematic relative positioning, data from the Taiwan continuous GPS network (TCGN) are utilized to analyze the co-seismic displacements associated with the 21 September 1999 Chi-Chi earthquake (ML=7.3). The station near the highest peak of Taiwan, Yushan (YUSN) and a station ineastem Taiwan, Fenglin (FLNM) show significant co-seismic displacements of 18 and 12 cm in the north direction as well as 16 and 24 cm in the west direction, respectively. Comparing the co-seismic displacements estimated from daily solutions with those from kinematic results, the differences are less than 2 cm in the horizontal components. The impact of the major aftershocks occurred immediately after the mainshock can be identified from the kinematic positioning. The same algorithm is also applied to study the 1 Hz sampling rate data related to 31 March 2002 off Hualien earthquake (ML=6.8), seven stations of the TCGN are analyzed to study the co-seismic deformation. With the higher sampling rate data, the instantaneous ground motion caused by the propagation of seismic waves can be observed.     

An analysis of single point positioning with real-time internet-based precise GPS data

Single Point Positioning (SPP) is currently capable of providing position accuracy of several meters. To obtain a better accuracy, the Differential GPS (DGPS) method must be applied. For large-scale applications such as aerial survey and mapping, however,the requirement of a base station(s) in conventional DGPS often become problematic in practice due to the increased operational cost and complexity. Recently a concept of Global Differential GPS (GDGPS) has attracted increasing interests among the GPS communities. GDGPS has the same user's implementation as SPP,but its accuracy is augmented by the globally or regionally distributed precise GPS data currently including precise satellite orbit and clock corrections. The major advantage of GDGPS lies in two aspects: system simplicity at the user's end, and globally consistent positioning accuracy. This paper presents GDGPS positioning results using the precise GPS data generated by the Natural Resources Canada (NRCan). NRCan's precise data can be retrieved real-time from Internet base on Virtual Private Network (VPN) and Multicast technology. The packet delay and Packet Loss Rate (PLR) of multicasting over Intemet will first be investigated.The total latency of precise GPS data as well as the position accuracyof GDGPS will then be analyzed. The numerical results have shown that a meter to half-meter level accuracy is obtainable based on epoch-by-epoch data processing. With phase-smoothed code observations, the positioning accuracy can be further improved.     

一种有效的单频GPS相位模糊度解算方法

针对快速定位中GPS单频相位模糊度较难归整的问题，采用理论分析和实验验证的方法，推导了实时动态下相位平滑伪距的递推公式，给出了一些提高观测方程线性化初始值精度的思路。在分析了短时间段双差方程结构特性的基础上，提出采用迭代选权拟合法提高相位模糊度实数解精度的新方法。算例表明，该方法提高了模糊度实数解的精度和可靠性，缩小了模糊度的搜索空间，促进了模糊度解算效率和成功率，从而能促进单频GPS接收机在高精度快速定位中的应用。     

Yaw attitude of eclipsing GPS satellites and its impact on solutions from precise point positioning

During the period when a GPS satellite, the Earth and the Sun are approximately collinear, the phenomenon of eclipsing the satellite occurs, when the satellite yaw attitude deviates from its nominal case, i.e. the body X-axis cannot point towards the Sun for Block II&IIA or away from it for Block IIR satellites. The yaw attitude of the eclipsing satellites has a significant influence on both the satellite clock estimation at each International GNSS Service (IGS) Analysis Center (AC) and for users of the precise point positioning (PPP) implementations. It is known that, during the eclipsing periods, inconsistent yaw attitude models among the ACs will contribute to the errors of the IGS combined clock products. As for the PPP user, the influence of the eclipsing satellite is two-fold. First, as the satellite clocks are always kept fixed during PPP implementation, the above-mentioned problematic IGS clocks will inevitably be passed on to the PPP estimates. Second, the improper yaw attitude modeling of the eclipsing satellite will cause a correction bias exceeding 1 dm for the two kinds of attitude-related systematic errors, namely the phase wind-up and satellite antenna phase center offset, which will further deteriorate the accuracy of the PPP solutions. A yaw attitude model is introduced in this paper with the aim of improving the reliability of PPP solutions during the satellite eclipsing period.     

全球参考站网窄巷非校准相位延迟

窄巷非校准相位延迟（UPD）产品的质量和可用性是影响精密单点定位模糊度固定（PPPAR）效率的重要因素.采用全球108个国际GPS服务（International GPS Service,IGS）测站观测数据,计算了基于全球参考站网的窄巷UPD产品,分析了窄巷UPD产品的变化特性,其单日变化量最大可达0.6周.通过分析UPD改正后的模糊度残差,论证了UPD产品和用户端模糊度均受到因未被恰当模型化而造成的残余误差的影响,且UPD的时变特性与各参考站残余系统误差有关.最后,采用4个用户站进行PPPAR实验分析UPD产品的可用性,以模糊度固定失败率、固定错误率和首次固定时间为评估指标,结果表明,全球参考站网窄巷UPD产品的最佳使用时限不大于30 min.     

一种GPS接收机的完整自检测和故障分离技术

载波相位测量是目前GPS测量中精度最高的观测量,利用载波相位求解的DGPS(RTK)的精度很高,是目前高精度要求的主要产品,利用载波相位的主要问题就是容易出现周跳.更好地解决周跳问题就可以大幅度地提高GPS接收机的性能.运用最小二乘法解出敏感残差距阵,利用相关系数检测并确定发生周跳的卫星,然后进行排除.得出的这种快捷的自检测和故障分离技术,经过试验验证准确高效,可以大幅度的提高RTK接收机的性能.     

单频GPS载波相位整周模糊度解算研究

介绍了一种求解单频GPS载波相位整周模糊度的改进算法.通过Tikhonov正则化,减弱GPS快速定位中少数历元情形下法矩阵的病态性,得到更接近整周模糊度准确值的浮点解.然后对整周模糊度的方差协方差阵白化滤波,减弱短时间内双差整周模糊度之间的相关性,取整后得到整周模糊度的固定解.并结合一个实例与白化滤波、Lambda方法和白化滤波 Lambda方法进行对比,验证改进方法的效果.     

基于天牛须种群算法的整周模糊度解算算法

如何快速、准确的固定整周模糊度是载波相位测量中的一个关键问题。为了提高整周模糊度搜索速率,本文提出了一种基于天牛须种群算法(Beetle Antennae Colony Search, BACS)的整周模糊度解算算法。通过与BAS算法、BAS-Nadam算法、LAMBDA算法以及MLAMBDA算法进行解算速率、稳定性的对比实验,在三维模糊度解算时,BACS算法在与LAMBDA和MLAMBDA算法解算成功率相当的情况下,能利用更少的时间搜索到模糊度最优解。为了验证BACS算法在高维模糊度解算以及工程解算情况下是否适用,进行了高维模糊度解算的实验以及单频单GPS系统下BACS算法的应用实验。分析及实验表明,BACS算法能很好保证高维模糊度解算的实时性和鲁棒性,对于12维模糊度解算,平均解算时间0.068秒,解算成功率为92%,对于低维模糊度解算,解算速率更快,解算成功率更高。在单频单GPS系统工程解算中,x,y,z方向定位精度分别为±0.008米,±0.01米,±0.01米,能达到厘米级精度定位。     

基于空间分集和轨迹连续的实时Fingerprint定位算法

在室外复杂环境下,接收信号强度的浮动是制约Fingerprint定位精度的一个主要问题。传统的方法利用时间分集和平均滤波器来减小信号的浮动,这增加了定位的延迟,无法满足室外实时定位的需求。为了解决信号浮动和定位延迟问题,在分析接收信号强度空间相关性的基础上,提出了一种实时的Fingerprint定位算法,利用空间分集减小信号的浮动和定位延迟,同时根据运动物体轨迹的连续性提高定位精度。室外环境下的实验结果表明了所提算法能显著提高Fingerprint定位系统的性能。     

附加约束法在单频GPS快速静态定位中的应用

针对在短时间内GPS观测方程的法方程容易形成病态的实际,探讨用附加约束条件来消除其病态性的方法,然后用LAMBDA方法确定其整周模糊度,实验证明,对于单频GPS接收机,利用5个历元数据,使用该技术即可正确确定整周模糊度,从而实现厘米级定位.     

北斗高精度相对定位选星方法研究

针对北斗系统中高轨卫星会带来较全球定位系统（global positioning system ,GPS）更为严重的法方程病态性这一问题,分析了双差载波相位观测方程系数矩阵对整周模糊度浮点解解算的影响,结合北斗系统三轨道星座混合的特点,研究了区域北斗高精度相对定位选星方法,以仰角最高的地球同步轨道（geostationary earth orbit, GEO）卫星作为参考星,优先选取仰角高于10°的中地球轨道（medium earth orbit,MEO）卫星,然后按照均匀分布的原则选取倾斜地球同步轨道（inclined geosynchronous satellite orbit,IGSO）卫星。通过对实测数据进行试验和分析,证明了该方法的正确性和合理性,在进行区域北斗高精度相对定位时,能在一定程度上改善法方程的病态性,使模糊度浮点解较快收敛至真值附近,有利于模糊度的快速正确固定。     

一种动对动相对定位中平滑惯导辅助模糊度解算策略

针对基于单频载波相位的动对动相对定位中实时模糊度固定可靠性不高的问题,本文提出了一种基于DGNSS/INS紧组合的平滑惯导辅助模糊度解算策略,以提高低成本接收机高精度定位的普适性。首先,基于伪距和载波相位观测量构建动对动相对定位模型;其次,对惯性导航数据进行卡尔曼滤波处理,并利用滤波平滑后的惯导位置预测卫地距重构双差观测方程并构造惯导位置约束方程,继而获得较高精度浮点解及其协方差阵,采用LAMBDA算法进行整周模糊度固定及Ratio检验;最后,由DGNSS/INS紧组合算法对惯性误差进行反馈校正,以维持惯性高精度导航。实测数据实验结果表明,对比没有惯导辅助、有惯导辅助和经滤波平滑后的惯导辅助结果,本文采用的方法可以有效地提高模糊度浮点解精度,减小模糊度搜索空间,提升整周模糊度固定成功率,三种方法下模糊度固定成功率分别为92.3%,99.1%和99.6%,并最终实现厘米级动态相对定位。     

DCB对精密单点定位中的精度影响分析

在精密单点定位中,通常假定接收机差分码偏差(Differential Code Bias,DCB)被钟差吸收,而不去单独进行考虑,从而可能影响最终的定位精度。为了验证DCB对定位精度的影响,针对2019年1月1日BJFS站一天的观测数据,用Bernese软件进行数据解算,并分是否考虑DCB影响的两种情况进行实验。结果表明,在考虑DCB影响后精密单点定位的收敛速度及定位精度得到明显提高,定位精度达厘米级。     

基于改进的遗传算法解算GPS双差模糊度的研究

将遗传算法(GA)应用于GPS双差模糊度解算过程,针对双差模糊度的整数特性,进行了实数编码的改进、遗传算法的改进等算法设计,实现了双差模糊度直接在大范围、高精度、整数域上的优化搜索,提高了解算的稳定性与高效性。试验结果表明,经过改进的实数编码GA可以取得比二进制编码GA更高的效率和成功率,更适于双差模糊度搜索。     

Research on the estimation of GPS phase ambiguities by triple frequency observations

As a part of modernization of GPS, a new signal with a frequency of 1 176.45 MHz will be made available to the civilian community and can provide more measurements for positioning in combination with the well known L1 and L2 signals. Applying the law of variance-covariance propagation, the correlation of triple-frequency ambiguity is discussed, the L1 ambiguity is week correlate with wide lane and long wide lane ambiguity. Under a comprehensive analysis of linear combination, no matter how long the baseline is, the ambiguities of long wide lane carrier phase combination can be determined using code measurements directly, ambiguity of short baseline can be fixed fast because of very small standard error of ambiguities of many linear combinations, the main efforts of TCAR are ambiguity resolution of long baseline. The ionosphere-free combinations used widely are not suitable for ambiguity resolution because of very short wavelength with high noise and very large standard error of ambiguity. The smoothing procedure reduces the standard errors of code and also can improve ambiguity estimation, the ambiguity of wide-lane, in long baseline case, can be rounded to the nearest integer within six epochs.     

多参考站网络的虚拟观测值生成算法

讨论了GPS观测值误差改正方法,提出了一种基于多参考站的GPS观测值向流动站用户发布虚拟观测值的算法.该算法通过参考站的已知精确坐标和已经解算的模糊度计算参考站间双差空间相关误差,然后内插局域网内任意一点空间相关误差作为改正数.当只使用3个参考站时使用线性内插法,多于3个参考站时使用曲面拟合或最小二乘平差方法等内插方法.用内插获得的改正数改正离流动站最近的参考站(主参考站)的观测值,形成虚拟观测值,然后发送给流动站用户,流动站用户仍然应用已有的单参考站GPS定位算法进行定位.通过对江苏局域参考站网络收集的实测数据计算分析证明了本文算法的有效性,达到厘米级定位精度.     

Precise GPS/GNSS positioning solution for airborne data acquisition systems

The precise positioning of aircrafts during flights belongs to the great challenges with respect to the development of airborne data acquisition systems. Satellite positioning systems like GPS offers a unique capability for precise positioning but requires in depth knowledge of GPS in airborne applications, e.g.GPS for high dynamic application, integration of GPS with other sensors, dynamic behaviour of aircrafts or antenna location. For its positioning reference system of Flight Inspection systems Aerodata AG has developed a robust GPS carrier phase ambiguity solution P-DGPS, Precise Differential GPS combined with complementary sensors like INS, barometers, radio altimeters or laser altimeters as well as laser trackers. Using recorded data during the flight the algorithm offers also the capability to calculate more accurate positions in post-processing. The presented sensor fusion algorithm using GPS without differential corrections (SGPS, standalone GPS) offers a precise height reference solution for approach calibration based only on aircraft-based sensors. SGPS data are combined in post-processing with inertial, pressure, radio and laser altimeter data. Flight trials with a Bombardier "Global Express" at Braunschweig Airport on May 2002 shows the achieved accuracies of the height reference solution calculated by SGPS in comparison to P-DGPS. The SGPS solution for precise height calculation of special mission aircrafts provides accuracies in the order of 5 m and at the runway's threshold in the order of 30 cm.     

精密单点定位技术发展及应用

综述了精密单点定位(precise point positioning,PPP)技术的发展及其应用现状。主要从PPP模糊度解、实时PPP和多系统组合PPP等3个方面进行了总结。根据PPP技术的优点,阐述了该技术在测绘、监测、气象和水汽遥感等方面的实际应用。针对最新发展起来的多频多模块多系统联合定位,展望了PPP技术未来的发展趋势,最后指出随着PPP技术的成熟及模型的精细化和改进,PPP快速初始化的问题有望得到突破,PPP技术的应用会更广泛。