抗差自适应卡尔曼滤波在GPS精密单点定位中的应用

卡尔曼滤波是GPS精密单点定位中最常用的参数估计方法.理论上讲,随着观测数据的增多,通过卡尔曼滤波可以得到更精确的状态估值,但有时由于状态异常或发生大的周跳等原因,使得状态估值与实际状态之间的误差较大,滤波会发生发散现象,为此,本文提出了将抗差自适应滤波模型运用到精密单点定位中,通过算例分析显示,该方法将显著提高定位结...     

Single-frequency precise point positioning with optimal filtering

The accuracy of standalone GPS positioning improved significantly when Selective Availability was turned off in May 2000. With the availability of various public GPS related products including precise satellite orbits and clocks, and ionosphere maps, a single-frequency standalone user can experience even a further improvement of the position accuracy. Next, using carrier phase measurements becomes crucial to smoothen the pseudorange noise. In this contribution, the most critical sources of error in single-frequency standalone positioning will be reviewed and different approaches to mitigate the errors will be considered. An optimal filter (using also carrier phase measurements) will be deployed. The final approach will then be evaluated in a decently long static test with receivers located in different regions of the world. Kinematic experiments have also been performed in various scenarios including a highly dynamic flight trial. The accuracy, in general, can be confirmed at 0.5 m horizontal and 1 m vertical, with static tests. Ultimate results demonstrate an accuracy close to 2 dm (95%) for the horizontal position components and 5 dm (95%) for the vertical in the flight experiment.

GPS sidereal filtering: coordinate- and carrier-phase-level strategies

Multipath error is considered one of the major errors affecting GPS observations. One can benefit from the repetition of satellite geometry approximately every sidereal day, and apply filtering to help minimize this error. For GPS data at 1 s interval processed using a double-difference strategy, using the day-to-day coordinate or carrier-phase residual autocorrelation determined with a 10-h window leads to the steadiest estimates of the error-repeat lag, although a window as short as 2 h can produce an acceptable value with > 97% of the optimal lag’s correlation. We conclude that although the lag may vary with time, such variation is marginal and there is little advantage in using a satellite-specific or other time-varying lag in double-difference processing. We filter the GPS data either by stacking a number of days of processed coordinate residuals using the optimum “sidereal” lag (23 h 55 m 54 s), and removing these stacked residuals from the day in question (coordinate space), or by a similar method using double-difference carrier-phase residuals (observational space). Either method results in more consistent and homogeneous set of coordinates throughout the dataset compared with unfiltered processing. Coordinate stacking reduces geometry-related repeating errors (mainly multipath) better than carrier-phase residual stacking, although the latter takes less processing time to achieve final filtered coordinates. Thus, the optimal stacking method will depend on whether coordinate precision or computational time is the over-riding criterion.     

GPS星历精度对精密单点定位的影响

精密单点定位的实质就是利用精密星历和精密卫星钟改正来实现单机精密定位。本文简要地介绍了精密单点定位的原理及技术关键,在此基础上,分析了IGS目前提供的3种精密星历(IGF、IGR、IGU)的精度和时延性。根据实验数据进一步分析了3种精密星历对精密单点定位精度的影响。通过精度分析,得出利用IGS的超快星历也可以达到厘米级定位精度,为全球厘米级单站RTK提供了有益的参考。     

GPS静态精密单点定位算法精度分析

采用精密轨道和钟差,利用Bernese软件解算得到亚洲地区13个IGS跟踪站的站坐标、对流层ZTD和接收机钟差,将解算的结果与CODE发布的结果对比发现：静态PPP算法解算的N方向收敛精度明显优于E方向和U方向,4~6 h后,坐标偏差在1 cm左右;NEU RMS均值分别为0.45、0.29、0.69 cm,ZTD RMS均值为0.85 cm,接收机钟差RMS均值为0.14 ns。试验表明：精密单点定位算法具有较高的精度和可靠性,可为实际工程测量及相关地球物理信号研究提供理论依据。     

基于GPS单频接收机的精密单点定位研究

介绍了利用单频GPS接收机进行精密单点定位的数学模型及解算方案,并采用选权拟合法得到比较准确的状态参数初值及其方差-协方差,加快了卡尔曼滤波的收敛。算例结果表明,利用精密卫星星历及卫星钟改正数并采用单频观测值,半个小时后的定位精度可达1~2分米的水平。     

Triple-frequency GPS precise point positioning with rapid ambiguity resolution

At present, reliable ambiguity resolution in real-time GPS precise point positioning (PPP) can only be achieved after an initial observation period of a few tens of minutes. In this study, we propose a method where the incoming triple-frequency GPS signals are exploited to enable rapid convergences to ambiguity-fixed solutions in real-time PPP. Specifically, extra-wide-lane ambiguity resolution can be first achieved almost instantaneously with the Melbourne-Wübbena combination observable on L2 and L5. Then the resultant unambiguous extra-wide-lane carrier-phase is combined with the wide-lane carrier-phase on L1 and L2 to form an ionosphere-free observable with a wavelength of about 3.4 m. Although the noise of this observable is around 100 times the raw carrier-phase noise, its wide-lane ambiguity can still be resolved very efficiently, and the resultant ambiguity-fixed observable can assist much better than pseudorange in speeding up succeeding narrow-lane ambiguity resolution. To validate this method, we use an advanced hardware simulator to generate triple-frequency signals and a high-grade receiver to collect 1-Hz data. When the carrier-phase precisions on L1, L2 and L5 are as poor as 1.5, 6.3 and 1.5 mm, respectively, wide-lane ambiguity resolution can still reach a correctness rate of over 99 % within 20 s. As a result, the correctness rate of narrow-lane ambiguity resolution achieves 99 % within 65 s, in contrast to only 64 % within 150 s in dual-frequency PPP. In addition, we also simulate a multipath-contaminated data set and introduce new ambiguities for all satellites every 120 s. We find that when multipath effects are strong, ambiguity-fixed solutions are achieved at 78 % of all epochs in triple-frequency PPP whilst almost no ambiguities are resolved in dual-frequency PPP. Therefore, we demonstrate that triple-frequency PPP has the potential to achieve ambiguity-fixed solutions within a few minutes, or even shorter if raw carrier-phase precisions are around 1 mm. In either case, we conclude that the efficiency of ambiguity resolution in triple-frequency PPP is much higher than that in dual-frequency PPP.     

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.     

Real-time precise point positioning regional augmentation for large GPS reference networks

An increasing number of GNSS reference stations are installed around the world to provide real-time precise positioning services. In most of the current services, a full network solution is required for the precise determination of biases. Such a network solution is time consuming and difficult to achieve for very large regions such as Europe or China. Therefore, we developed a multi-layer processing scheme for precise point positioning (PPP) regional augmentation to avoid processing large networks. Furthermore, we use L1 and L2 raw observations and estimate atmospheric delays, which were properly constrained to the atmospheric corrections derived from the reference stations. Therefore, inaccurate representation of atmospheric delays due to temporal and/or spatial atmospheric fluctuations in the processing can be compensated. The proposed scheme of PPP regional augmentation was implemented into the operational real-time PPP service system at GFZ for validation. The real-time orbit and clock corrections, the uncalibrated phase delays, and regional augmentation corrections are generated by this system. The augmentation corrections from the regional network are investigated and the positioning performance in terms of positioning accuracy and time for fixed solution is demonstrated in real-time. Our results indicate that a reliable fixing is possible after 5 s on average. The positioning accuracy is about 12, 10, and 25 mm in east, north, and vertical direction, respectively.     

Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning

With the development of precise point positioning (PPP), the School of Geodesy and Geomatics (SGG) at Wuhan University is now routinely producing GPS satellite fractional cycle bias (FCB) products with open access for worldwide PPP users to conduct ambiguity-fixed PPP solution. We provide a brief theoretical background of PPP and present the strategies and models to compute the FCB products. The practical realization of the two-step (wide-lane and narrow-lane) FCB estimation scheme is described in detail. With GPS measurements taken in various situations, i.e., static, dynamic, and on low earth orbit (LEO) satellites, the quality of FCB estimation and the effectiveness of PPP ambiguity resolution (AR) are evaluated. The comparison with CNES FCBs indicated that our FCBs had a good consistency with the CNES ones. For wide-lane FCB, almost all the differences of the two products were within ±0.05 cycles. For narrow-lane FCB, 87.8 % of the differences were located between ±0.05 cycles, and 97.4 % of them were located between ±0.075 cycles. The experimental results showed that, compared with conventional ambiguity-float PPP, the averaged position RMS of static PPP can be improved from (3.6, 1.4, 3.6) to (2.0, 1.0, 2.7) centimeters for ambiguity-fixed PPP. The average accuracy improvement in the east, north, and up components reached 44.4, 28.6, and 25.0 %, respectively. A kinematic, ambiguity-fixed PPP test with observation of 80 min achieved a position accuracy of better than 5 cm at the one-sigma level in all three coordinate components. Compared with the results of ambiguity-float, kinematic PPP, the positioning biases of ambiguity-fixed PPP were improved by about 78.2, 20.8, and 65.1 % in east, north, and up. The RMS of LEO PPP test was improved by about 23.0, 37.0, and 43.0 % for GRACE-A and GRACE-B in radial, tangential, and normal directions when AR was applied to the same data set. These results demonstrated that the SGG FCB products can be produced with high quality for users anywhere around the world to carry out ambiguity-fixed PPP solutions.     

GPS/GLONASS组合精密单点定位性能分析

本文利用IGS 5个站的观测数据分7个时段进行了GPS/GLONASS组合精密单点定位计算,与单独GPS精密单点定位的结果在精度和收敛时间方面进行了性能比较。结果表明,在当前GPS卫星数量充足的情况下,增加少量的GLONASS卫星对定位精度的提高帮助不大,但能显著改善滤波收敛的时间。     

GPS、BDS、GPS+BDS精密单点定位精度评估

由于北斗系统卫星正式完成组网,因此有必要对BDS系统性能进行精度评估与分析.本文选取了MGEX网所采集的31 d观测数据,对比分析了GPS、BDS、GPS+BDS不同情况下静态与动态精密单点定位精度.试验结果表明,GPS和BDS单系统静态PPP在N、E、U方向上的精度分别优于4、4、7 cm;GPS+BDS组合系统静态...     

GPS inter-frequency clock bias modeling and prediction for real-time precise point positioning

To ensure the consistent use of the current GPS precise satellite clock products, the inter-frequency clock bias (IFCB) should be carefully considered for triple-frequency precise point positioning (PPP). It is beneficial to investigate the modeling of the IFCB for multi-frequency PPP, especially for real-time users suffering from difficulties in real-time IFCB estimations. Our analysis is based on datasets from 129 stations spanning a whole year. A harmonic analysis is performed for all single-day IFCB time series, and periodic IFCB variations with periods of 12, 8, 6, 4.8, 4 and 3 h are identified. An empirical model composed of a sixth-order harmonic function and a linear function is presented to describe daily variations in the IFCB, and the modeling accuracy is 4 mm. A least squares fit is adopted to estimate the single-day harmonic coefficients phase and amplitude. The prediction accuracy of the IFCB models degrades from 7.2 to 12.3 mm when the time span of prediction is increased from a day to a week. When using IFCB models of the previous day to obtain the IFCB correction values, the positioning accuracy of triple-frequency PPP is improved by 21, 11 and 16% over the triple-frequency PPP neglecting the IFCB in the post-processing mode in the east, north and up directions, respectively. As to the real-time triple-frequency PPP, the corresponding accuracy improvement is 24, 9 and 10% in the three directions, respectively.     

不同星历和钟差产品对车载PPP定位的影响分析

星历误差和星钟误差是GPS动态精密单点定位的主要误差源,不同的星历和钟差产品会对结果产生影响。利用IGS网站给出的不同星历和钟差数据及广播星历数据进行计算,采用Waypoint软件进行不同的组合计算,对不同星历和钟差组合对机载GPS数据定位结果进行分析。     

基于单频GPS精密单点定位算法研究

研究单频GPS精密单点定位的算法,包括单频精密单点定位的回归方程及卡尔曼滤波用于单频精密单点定位.探讨卡尔曼滤波的观测方程和状态方程,给出状态转移矩阵及系统噪声矩阵.通过算例验证在1 s采样率的情况下,定位达到了分米级的精度.     

GPS精密单点定位中对流层延迟处理方法研究

本文首先介绍了GPS精密单点定位技术,采用宽巷组合的方法得到观测方程。然后对精密定位中的误差改正作了简述,主要讨论了处理对流层延迟的Saastamoinen模型和Niell映射函数。提出用扩展卡尔曼滤波参数估计方法来处理对流层延迟,通过实例用Saastamoinen模型、Saastamoinen模型加Niell映射函数和扩展卡尔曼滤波参数估计三种方法对对流层延迟进行改正,结果表明该方法优于Saastamoinen模型。     

The application of GPS precise point positioning technology in aerial triangulation

In traditional GPS-supported aerotriangulation, differential GPS (DGPS) positioning technology is used to determine the 3-dimensional coordinates of the perspective centers at exposure time with an accuracy of centimeter to decimeter level. This method can significantly reduce the number of ground control points (GCPs). However, the establishment of GPS reference stations for DGPS positioning is not only labor-intensive and costly, but also increases the implementation difficulty of aerial photography. This paper proposes aerial triangulation supported with GPS precise point positioning (PPP) as a way to avoid the use of the GPS reference stations and simplify the work of aerial photography.Firstly, we present the algorithm for GPS PPP in aerial triangulation applications. Secondly, the error law of the coordinate of perspective centers determined using GPS PPP is analyzed. Thirdly, based on GPS PPP and aerial triangulation software self-developed by the authors, four sets of actual aerial images taken from surveying and mapping projects, different in both terrain and photographic scale, are given as experimental models. The four sets of actual data were taken over a flat region at a scale of 1:2500, a mountainous region at a scale of 1:3000, a high mountainous region at a scale of 1:32000 and an upland region at a scale of 1:60000 respectively. In these experiments, the GPS PPP results were compared with results obtained through DGPS positioning and traditional bundle block adjustment. In this way, the empirical positioning accuracy of GPS PPP in aerial triangulation can be estimated. Finally, the results of bundle block adjustment with airborne GPS controls from GPS PPP are analyzed in detail.The empirical results show that GPS PPP applied in aerial triangulation has a systematic error of half-meter level and a stochastic error within a few decimeters. However, if a suitable adjustment solution is adopted, the systematic error can be eliminated in GPS-supported bundle block adjustment. When four full GCPs are emplaced in the corners of the adjustment block, then the systematic error is compensated using a set of independent unknown parameters for each strip, the final result of the bundle block adjustment with airborne GPS controls from PPP is the same as that of bundle block adjustment with airborne GPS controls from DGPS. Although the accuracy of the former is a little lower than that of traditional bundle block adjustment with dense GCPs, it can still satisfy the accuracy requirement of photogrammetric point determination for topographic mapping at many scales.     

Modeling and assessment of combined GPS/GLONASS precise point positioning

A combination of GPS and GLONASS observations can offer improved reliability, availability and accuracy for precise point positioning (PPP). We present and analyze a combined GPS/GLONASS PPP model, including both functional and stochastic components. Numerical comparison and analysis are conducted with respect to PPP based on only GPS or GLONASS observations to demonstrate the benefits of the combined GPS/GLONASS PPP. The observation residuals are analyzed for more appropriate stochastic modeling for observations from different navigation systems. An analysis is also made using different precise orbit and clock products. The performance of the combined GPS/GLONASS PPP is assessed using both static and kinematic data. The results indicate that the convergence time can be significantly reduced with the addition of GLONASS data. The positioning accuracy, however, is not significantly improved by adding GLONASS data if there is a sufficient number of GPS satellites with good geometry.