BDS网络RTK中距离参考站整周模糊度单历元解算方法

提出了一种BDS网络RTK中距离(50~100 km)参考站间的双频载波相位整周模糊度单历元解算方法。该方法首先利用B1、B2载波相位整周模糊度间的线性关系选取B1、B2载波相位整周模糊度备选值。利用双频载波相位整周模糊度备选值计算双差电离层延迟误差,根据参考站各卫星电离层延迟误差间的空间关系,使用双差电离层延迟误差构建双差电离层延迟误差的线性计算模型。通过双差电离层延迟误差线性计算模型的建立搜索和确定B1、B2载波相位的整周模糊度。经CORS网实测数据试验算例的验证,该方法只需一个历元的观测数据即可确定参考站间双差B1、B2载波相位整周模糊度,且不受周跳影响。     

BDS网络RTK参考站三频整周模糊度解算方法

北斗卫星导航系统是目前唯一一个全星座提供三频观测数据的卫星导航定位系统,三频观测值有助于载波相位整周模糊度的快速、准确固定。本文提出了一种BDS网络RTK参考站三频整周模糊度解算方法。首先利用B2、B3频率的观测值及严格的模糊度固定标准确定超宽巷整周模糊度,将固定的超宽巷整周模糊度与其他宽巷整周模糊度的线性关系作为约束条件,然后估计宽巷整周模糊度、相对天顶对流层延迟误差和电离层延迟误差,并搜索确定宽巷整周模糊度。利用固定的宽巷整周模糊度与三频载波相位整周模糊度的整数线性关系,将线性关系加入载波相位整周模糊度参数估计观测模型中,然后确定载波相位整周模糊度。使用实测的CORS网BDS三频观测数据进行算法验证,结果表明,该方法可正确有效地实现参考站间三频载波相位整周模糊度的快速解算。     

BDS参考站三频整周模糊度单历元确定方法

参考站载波相位整周模糊度的准确确定是实现BDS网络RTK定位的关键。本文研究了BDS参考站三频载波相位整周模糊度单历元确定方法。首先推导了参考站三频载波相位整周模糊度之间的多个整数线性关系,根据双频载波相位整周模糊度的整数线性关系,以及B1载波相位整周模糊度备选值,确定B1/B2和B1/B3载波相位整周模糊度的备选组合。然后利用不受误差影响的三频载波相位整周模糊度间整数线性关系,对整周模糊度备选值进行约束和确定。根据大气误差的空间相关性,采用以卫星高度角和方位角为依据的基准卫星选择方法,降低了对流层延迟误差残差对多频载波相位整周模糊度之间线性关系约束能力的影响。试验结果表明,本文方法能够实现参考站三频载波相位整周模糊度的单历元准确确定,且计算效率高,算法简单。     

长距离GPS/BDS参考站网多频载波相位整周模糊度解算方法

长距离网络RTK是实现GPS/BDS高精度实时定位的主要手段之一,其核心是长距离参考站网GPS/BDS整周模糊度的快速准确确定。本文提出了一种长距离GPS/BDS参考站网载波相位整周模糊度解算方法,首先利用GPS双频观测数据计算和确定宽巷整周模糊度,同时利用BDS的B2、B3频率观测值确定超宽巷整周模糊度。然后建立GPS载波相位整周模糊度和大气延迟误差的参数估计模型,附加双差宽巷整周模糊度的约束,解算双差载波相位整周模糊度,并建立参考站网大气延迟误差的空间相关模型。根据B2、B3频率的超宽巷整周模糊度建立包含大气误差参数的载波相位整周模糊度解算模型,利用大气延迟误差空间相关模型约束BDS双差载波相位整周模糊度的解算。克服了传统的使用无电离层组合值解算整周模糊度的不利影响。采用实测长距离CORS网GPS、BDS多频观测数据进行算法验证,试验结果证明该方法可实现长距离参考站网GPS/BDS载波相位整周模糊度的准确固定。     

一种北斗非差非组合长距离基准站模糊度解算方法

为了充分利用各频率观测值信息,提出了一种非差非组合的北斗卫星导航系统长距离基准站间整周模糊度解算方法。首先,直接利用不同频率的观测值建立误差观测方程,并采用随机游走策略估计相对天顶对流层湿延迟误差和电离层延迟误差,增加历元间的约束;然后,采用一种非差整周模糊度实时线性计算方法,依次得到基准站网当前历元所有卫星的非差整周模糊度,解决了在基准星变换时,模糊度需要承接或者重新进行法方程叠加的问题;最后,使用实测数据进行方法验证,结果表明,各基准站模糊度平均固定速度为20个历元（采样间隔1 s）,可快速实现基准站载波相位整周模糊度解算。由于所提方法充分利用了各频率观测值信息,避免了线性组合放大噪声对整周模糊度固定的影响,其模糊度固定成功率与无电离层组合法相比有较大的提高。     

大范围网络RTK基准站间整周模糊度实时快速解算

网络RTK是目前实现高精度实时动态定位的重要手段之一,而网络RTK高精度定位的关键问题是基准站间整周模糊度的实时快速准确固定。对于大范围网络RTK,由于基准站间距离的增加,电离层延迟误差、对流层延迟误差和卫星轨道误差相关性降低,导致基准站间整周模糊度不能快速准确地固定,因此本文提出了一种大范围网络RTK基准站间整周模糊度固定算法。该算法首先利用L1、L2载波相位观测值和P1、P2伪距观测值解算基准站间的双差宽巷模糊度;然后采用Saastamoinen模型和Chao映射函数模型相结合解算双差对流层延迟误差,并将双差宽巷模糊度作为L1、L2双差载波相位整周模糊度的约束关系来确定L1、L2双差载波相位整周模糊度;最后采用CORS站的实测数据进行试验,并将本文的试验结果同GAMIT软件的解算结果进行比对,结果表明该算法可以快速准确地实现单历元双差载波相位整周模糊度的固定。     

BDS中长距离基线高精度静态定位方法与实验

针对BDS高精度相对定位中,大气延迟误差的空间相关性随基线长度的增加而降低,影响整周模糊度解算效率和测站定位精度的问题,该文研究了一种BDS中长距离基线高精度静态定位方法。在解算出宽巷整周模糊度的基础上,通过载波相位无电离层组合观测值对相对天顶对流层延迟误差进行参数估计,处理对流层延迟误差的影响。同时进行载波相位整周模糊度解算和定位计算。采用两组基线7 d实测观测数据,进行中长距离基线高精度静态定位实验,实验结果表明本文的方法可以实现BDS中长距离基线毫米级静态定位。     

长距离网络RTK基准站间整周模糊度单历元确定方法

提出一种长距离(100～200km)网络RTK基准站间的整周模糊度单历元确定方法。该方法首先利用载波相位模糊度间的线性约束关系对双差宽巷模糊度进行搜索。为了减小非弥散误差残差对载波相位模糊度解算的影响,采用了一种新的根据高度角重新选择基准卫星的方法。然后根据双差宽巷模糊度选取双频载波相位模糊度的备选组合,利用基准站间非弥散误差残差的计算值对双差载波相位模糊度进行搜索和确定。经试验算例的验证,该方法快速、稳定,不受周跳影响,只需一个历元的观测数据即可确定长距离基准站间的双差整周模糊度。     

长距离GPS/BDS双系统网络RTK方法

基于区域参考站网的网络实时动态定位(real-time kinematic,RTK)方法是实现全球定位系统(global positioning system,GPS)、北斗卫星导航系统(BeiDou satellite navigation system,BDS)高精度定位的主要手段。研究了一种长距离GPS/BDS双系统网络RTK方法,首先采用长距离参考站网GPS/BDS多频观测数据确定宽巷整周模糊度,利用引入大气误差参数的参数估计模型解算GPS/BDS双差载波相位整周模糊度;然后按照长距离参考站网观测误差特性的不同,分类处理参考站观测误差,利用误差内插法计算流动站观测误差,以改正流动站GPS/BDS双系统载波相位观测值的观测误差;最后使用流动站多频载波相位整周模糊度解算方法确定GPS/BDS载波相位整周模糊度并解算位置参数。使用长距离连续运行参考站(continuously operating reference stations,CORS)网的实测数据进行实验,结果表明,该方法能够利用长距离GPS/BDS参考站网实现流动站的厘米级定位。     

基于模糊度相关法的北斗三频载波单历元基线解算

单历元基线解算一直是卫星导航定位中的热点和难点,随着北斗导航定位系统的全面组网,三频载波可以形成更多优良的组合观测值,有效地提高了单历元基线解算的精度和可靠性。本文在传统TCAR的基础上引入电离层延迟先验信息,将电离层延迟与位置参数和模糊度作为未知参数,采用最小二乘配置原理一并求解。同时,采用考虑电离层延迟影响的模糊度相关法约束模糊度搜索空间。结果表明,加入电离层延迟先验信息可以较大提高单历元模糊度固定的成功率;而采用考虑电离层延迟的模糊度相关法可以缩小模糊度搜索空间,有效地提高单历元模糊度解算的成功率和可靠性。     

Three-frequency BDS precise point positioning ambiguity resolution based on raw observables

All BeiDou navigation satellite system (BDS) satellites are transmitting signals on three frequencies, which brings new opportunity and challenges for high-accuracy precise point positioning (PPP) with ambiguity resolution (AR). This paper proposes an effective uncalibrated phase delay (UPD) estimation and AR strategy which is based on a raw PPP model. First, triple-frequency raw PPP models are developed. The observation model and stochastic model are designed and extended to accommodate the third frequency. Then, the UPD is parameterized in raw frequency form while estimating with the high-precision and low-noise integer linear combination of float ambiguity which are derived by ambiguity decorrelation. Third, with UPD corrected, the LAMBDA method is used for resolving full or partial ambiguities which can be fixed. This method can be easily and flexibly extended for dual-, triple- or even more frequency. To verify the effectiveness and performance of triple-frequency PPP AR, tests with real BDS data from 90 stations lasting for 21 days were performed in static mode. Data were processed with three strategies: BDS triple-frequency ambiguity-float PPP, BDS triple-frequency PPP with dual-frequency (B1/B2) and three-frequency AR, respectively. Numerous experiment results showed that compared with the ambiguity-float solution, the performance in terms of convergence time and positioning biases can be significantly improved by AR. Among three groups of solutions, the triple-frequency PPP AR achieved the best performance. Compared with dual-frequency AR, additional the third frequency could apparently improve the position estimations during the initialization phase and under constraint environments when the dual-frequency PPP AR is limited by few satellite numbers.     

Performance analysis of triple-frequency ambiguity resolution with BeiDou observations

We investigate triple-frequency ambiguity resolution performance using real BeiDou data. We test four ambiguity resolution (AR) methods which are applicable to triple-frequency observations. These are least squares ambiguity decorrelation adjustment (LAMBDA), GF-TCAR (geometry-free three-carrier ambiguity resolution), GB-TCAR (geometry-based three-carrier ambiguity resolution) and GIF-TCAR (three-carrier ambiguity resolution based on the geometry-free and ionospheric-free combination). A comparison between LAMBDA, GF-TCAR and GB-TCAR was conducted over three short baselines and two medium baselines. The results indicated that LAMBDA is optimal in both short baseline and medium baseline cases. However, the performances of GB-TCAR and LAMBDA differ slightly for short baselines. Compared with GF-TCAR, which uses the geometry-free model, the GB-TCAR using the geometry-based model improves the AR performance significantly. Compared with dual-frequency observations, the LAMBDA AR results show a significant improvement when using triple-frequency observations over short baselines. The performance of GIF-TCAR is evaluated using multi-epoch observations. The results indicated that multi-path errors on carrier phases will have a significant influence on GIF-TCAR AR results, which leads to different GIF-TCAR AR performance for different type of satellites. For GEO (Geostationary Orbit) satellites, the ambiguities can barely be correctly fixed because the multi-path errors on carrier phases are very systematic. For IGSO (Inclined Geosynchronous Orbit) and MEO (Medium Earth Orbit) satellites, when the elevation cutoff angle is set as 30°, several tens to several hundreds of epochs are needed for correctly fixing the narrow lane ambiguities. The comparison of positioning performance between dual-frequency observations and triple-frequency observations was also conducted. The results indicated that a minor improvement can be achieved by using triple-frequency observations compared with using dual-frequency observations.     

联合GEO/IGSO/MEO的北斗PPP模糊度固定方法与试验分析

由于北斗地球静止轨道（geostationary earth orbiting,GEO）卫星轨道精度较低且其观测值受多路径误差和伪距偏差影响严重,目前各分析中心尚未针对北斗GEO卫星提供长期稳定的相位小数偏差（uncalibrated phase delay,UPD）产品,北斗精密单点定位（precise point positioning,PPP）模糊度固定技术研究主要针对倾斜轨道（inclined geosynchronous orbiting,IGSO）和中地球轨道（medium earth orbiting,MEO）卫星。本文采用Wanninger和Beer的高度角模型消除了IGSO/MEO观测值伪距偏差,并通过小波变换提取低频分量修正伪距观测值的方法削弱了GEO卫星多路径和伪距偏差的影响。由于窄巷UPD估值受未模型化误差影响较大,本文改进了窄巷UPD估计的策略,该策略利用上一历元成功估计的窄巷UPD对当前历元的浮点模糊度进行改正,剔除了残差较大的浮点模糊度,修正固定错误的整周模糊度,从而提高了窄巷UPD的精度和稳定性。利用估计得到的UPD产品,本文实现了联合GEO、IGSO和MEO卫星的北斗非差PPP模糊度固定,并对其定位性能进行分析。结果表明：联合GEO、IGSO和MEO卫星的PPP固定解的首次固定时间和收敛时间均可以缩短到30 min以内;6 h后的E、N、U方向的定位误差由（1.35、0.35、2.75）cm减少到（1.07、0.26、2.24）cm,分别减少了20%、27%和18%。     

北斗三频电离层延迟及码硬件延迟解算方法

准确固定非差模糊度是利用相位观测量获取高精度电离层延迟的关键。三频观测条件下常规的处理策略需依次固定超宽巷、宽巷以及窄巷模糊度,通常利用MW（melbourne-wubbena）组合解算宽巷模糊度时易受到码硬件延迟和观测噪声的影响而固定错误。利用北斗三频数据和GIM（grid ionosphenimap）产品,通过固定的超宽巷模糊度以及构造相位无几何组合解算宽巷模糊度,进而重构得到高精度电离层延迟,并且分离了码硬件延迟总量。结果表明,GIM模型辅助条件下宽巷模糊度固定成功率能达到100%,且消除了系统性偏差;电离层重构值与GIM模型改正值存在约1 m的差异,等效精度约6TECU;分离的码硬件延迟变化平稳,标准偏差不超过0.3 m。     

Network-based triple-frequency carrier phase ambiguity resolution between reference stations using BDS data for long baselines

Network-based ambiguity resolution (AR) between reference stations is the prerequisite to realize a precise real-time kinematic positioning service. With the help of BDS triple-frequency signals, we can efficiently deal with the ionospheric delay and tropospheric delay, and achieve rapid and reliable AR. To overcome the inaccurate ionospheric delay estimated by the geometry-free three carrier ambiguity resolution (GF TCAR) technique, which leads to failure in the original ambiguity resolution, we propose an ionospheric-free (IF) TCAR method to resolve the ambiguity between the reference stations over long baselines. Taking full advantage of the known positions of the reference stations, the easily resolved extra-wide-lane (EWL) ambiguity, and the IF phase combinations, we can reliably fix the wide-lane (WL) ambiguity. A Kalman filter is applied to estimate precise IF ambiguities and the original ambiguity is resolved with the fixed WL ambiguity. A numerical analysis with triple-frequency BDS data from three long baselines of a CORS network is provided to compare the AR performance of GF TCAR with that of IF TCAR. The results show that both methods can reliably resolve the WL ambiguity with a remarkable correctly-fixed rate of higher than 99%, and the reliably-fixed rates of the IF TCAR slightly increase from 92.19, 94.67 and 94.61–98.26, 99.54 and 97.51% for the three baselines. Herein “correctly-fixed” and “reliably-fixed” mean the difference between the float ambiguity and the true one are less than ± 0.5 and ± 0.25 cycles, respectively. On the other hand, the AR performance of the original signals with the IF TCAR method is much better than that with the GF TCAR method attaining a 100% correctly-fixed rate, while the GF TCAR method can hardly fix the original ambiguity with the largest bias being as much as 4 cycles because of the amplified systematic bias.