基于GPS基准网的GPS快速静态定位及动态定位方法

介绍基于GPS基准网进行GSP快速静态定位和动态定位的原理和方法。通过计算基准网改正数及其空间分布，利用内插方法求出用户站的模型误差改正数，不仅可以提高GPS整周模糊度的可靠性，而且能够大大改善GPS测量的精度。利用香港GPS基准网2001年3月的实测数据进行了解算，发现地区在该时间段内受强电离层活动的影响，采用常规GPS测量方法很难确定整周模糊度。利用传统的快速静态定位方法对香港GPS基准网其中一条边（9.2km）24h的观测数据按每15min计算，模糊度确定的准确率仅为45％。采用基准网内插改正数后，仅利用L1的观测数据模糊度确定的准确率提高到100％。点位精度平面位置由2cm提高到5mm，高程精度由4cm提高到3cm。     

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。     

BDS/GPS非差误差改正数的实时动态定位方法

针对我国地区观测数据的实验定位结果精度问题,该文提出BDS/GPS非差误差改正数的实时动态定位方法,研究了BDS/GPS单参考站非差实时动态定位算法模型,流动站使用非差误差改正数,不需要进行双差观测值的组合。参考站将非差误差改正数传递给流动站,对流动站的观测值进行误差改正,可以直接固定流动站的模糊度。实验表明:在我国南方地区BDS精度要优于GPS,而在北方地区,BDS/GPS定位精度和GPS定位精度明显优于BDS。并且与单系统相比,组合系统的可视卫星数明显增加,改善了卫星空间几何分布结构,从而提高了导航定位的可用性和精度。     

Quality assessment of GPS rapid static positioning with weighted ionospheric parameters in generalized least squares

Precise GPS positioning requires the processing of carrier-phase observations and fixing integer ambiguities. With increasing distance between receivers, ambiguity fixing becomes more difficult because ionospheric and tropospheric effects do not cancel sufficiently in double differencing. A popular procedure in static positioning is to increase the length of the observing session and/or to apply atmospheric (ionospheric) models and corrections. We investigate the methodology for GPS rapid static positioning that requires just a few minutes of dual-frequency GPS observations for medium-length baselines. Ionospheric corrections are not required, but the ionospheric delays are treated as pseudo-observations having a priori values and respective weights. The tropospheric delays are reduced by using well-established troposphere models, and satellite orbital and clock errors are eliminated by using IGS rapid products. Several numerical tests based on actual GPS data are presented. It is shown that the proposed methodology is suitable for rapid static positioning within 50–70 km from the closest reference network station and that centimeter-level precision in positioning is feasible when using just 1 min of dual-frequency GPS data.     

Comparing DGPS corrections prediction using neural network, fuzzy neural network, and Kalman filter

Position information obtained from standard global positioning system (GPS) receivers has time variant errors. For effective use of GPS information in a navigation system, it is essential to model these errors. A new approach is presented for improving positioning accuracy using neural network (NN), fuzzy neural network (FNN), and Kalman filter (KF). These methods predict the position components’ errors that are used as differential GPS (DGPS) corrections in real-time positioning. Method validity is verified with experimental data from an actual data collection, before and after selective availability (SA) error. The result is a highly effective estimation technique for accurate positioning, so that positioning accuracy is drastically improved to less than 0.40 m, independent of SA error. The experimental test results with real data emphasize that the total performance of NN is better than FNN and KF considering the trade-off between accuracy and speed for DGPS corrections prediction.     

Generation of differential GPS corrections along with performance of quality control

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Generation of differential GPS corrections along with performance of quality control

The DGPS technique can provide considerably better relative positioning accuracy than the stand-alone GPS positioning, but the improvement depends on the distance between the user and the reference station (spatial correlation), the latency of differential corrections (temporal correlation), and the quality of differential corrections. Therefore, how to correctly generate differential corrections as well as their pricision is very important to the DGPS positioning technique. This paper presents a new algorithm for generating differential GPS corrections. This algorithm directly uses code and carrier observations in the measurement model of a Kalman filter, so that it is possible to use a simple stochastic model and to use the standard algorithm of the Kalman filter. The algorithm accounts for biases like multipath errors and instrumental delays in code observations and it shows how differential corrections are differently affected by code biases when dual or single frequency data is used. In addition, the algorithm can be integrated with a real time quality control procedure. As a result, the quality of differential corrections can be guaranteed with a certain probability.     

Analysis of GPS RTK performance using external NOAA tropospheric corrections integrated with a multiple reference station approach

For high-accuracy geodetic applications, time-variable tropospheric propagation delay errors limit global positioning system real-time kinematic positioning accuracy. Potential improvements in positioning accuracy are evaluated by using the National Oceanic and Atmospheric Administration (NOAA) real-time tropospheric corrections (herein called NOAA model) within a multiple reference station network approach. The results are compared with those for modified Hopfield tropospheric model corrections, for six scenarios in three geographical regions in the U.S. National Geodetic Survey network of Continuously Operating Reference Stations, for baseline lengths of 60~150 km. Analyses are conducted at rover locations for relatively humid days, and misclosures for various double difference observations are computed; these observations include each frequency (L1 and L2) and three linear combinations [wide lane, ionosphere free (IF), and geometry free]. The effectiveness of the network approach is demonstrated, with overall performance improvements of 15 and 19%, using the modified Hopfield and the NOAA model, respectively. The IF linear combination, a measure of tropospheric and orbital errors, shows a 3% improvement for the NOAA model compared with the modified Hopfield model.     

BDS/GPS网络差分定位试验分析

针对在传统网络差分定位中,单GPS系统在观测条件不好情况下会出现可用卫星数量偏少甚至不够、观测值存在粗差而影响定位等问题,该文提出BDS/GPS双系统组合网络伪距差分定位的数学模型,并加入基于最小二乘残差法探测粗差观测数据的质量控制算法。基于省CORS网实时BDS/GPS双系统数据,以国产的手持机终端作为流动端,利用BDS/GPS伪距差分平台进行了车载动态试验,根据试验对比和分析,动态定位平面精度优于1m,在加入质量控制算法模式下,定位精度和可靠性都有一定提高。     

考虑随机模型精化的精密GPS动态定位新方法

GPS动态定位要求建立函数模型和随机模型。函数模型描述的是观测值和待估参数之间的物理和几何关系，随机模型描述了GPS观测值的统计特征，并通过观测值的方差协方差给定了每个观测值对最后的定位结果的贡献。正确给定函数模型和随机模型对于GPS定位结果的估计和观测值的粗差探测均至关重要。由于有各种误差存在于伪距和载波相位观测值中，一般GPS动态定位模型均采用双差观测值来构建函数模型。有时候，仔细地使用单差观测值，较之双差观测值有更多的优点，给出了选用单差观测值的理由。但是单差观测值给函数模型带来了接收机钟差，如果直接使用单差观测方程，设计矩阵是奇异的。为了解决这个问题，将伪距观测值中接收机钟差项和接收机延迟项合并为一个新的未知参数。至于载波相位观测值，首先选定一个参考卫星，然后在观测方程的右端同时增加一正一负的参考卫星单差整周模糊度，将正项与接收机钟差项和接收机延迟项合并为一个新的未知参数，将负项和原观测方程中的单差整周模糊度项合并为双差整周模糊度，而参考卫星观测方程的模糊度项则为零，这样无须组建双差观测值，软件实现较容易，也可以直接使用LAMBDA法求整周模糊度，最终也解决了观测方程奇异的问题。准确理解观测值的统计特征是建立GPS随机模型的基础，长期以来GPS商业软件均采用简化模型。关于GPS随机模型的研究远没有函数模型那样受到广泛关注，静态GPS定位可以采用方差协方差分量估计等严密的方法，而动态定位无法承担方差协方差分量估计的计算负担。GPS观测值的信噪比(SNR)是GPS接收机观测过程中的副产品，影响SNR值的因素，如大气层、多路径、接收机内部电路等，也正好是GPS观测值的误差源，因此GPS观测值的方差与SNR存在一定的对应关系。利用这个对应关系来精化GPS随机模型。为了验证本文采用的函数模型的正确性和随机模型的有效性，我们对1999年的一次实测数据(包括零基线和短基线)进行了试算。与零基线的真值和GPSurvey 2．35处理的短基线静态结果比较，表明使用的函数模型是正确的。简化随机模型和精化随机模型处理的结果比较说明精化模型提高了基线处理的精度，同时说明了研究GPS随机模型精化的必要性。     

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。     

Precise GPS Positioning by Applying Ionospheric Corrections from an Active Control Network

In this article, initial results are presented of a method to improve fast carrier phase ambiguity resolution over longer baselines (with lengths up to about 200 km). The ionospheric delays in the global positioning system (GPS) data of these long baselines mainly hamper successful integer ambiguity resolution, a prerequisite to obtain precise positions within very short observation time spans. A way to correct the data for significant ionospheric effects is to have a GPS user operate within an active or permanently operating network use ionospheric estimates from this network. A simple way to do so is to interpolate these ionospheric estimates based on the expected spatial behaviour of the ionospheric delays. In this article such a technique is demonstrated for the Dutch Active Control Network (AGRS.NL). One hour of data is used from 4 of the 5 reference stations to obtain very precise ionospheric corrections after fixing of the integer ambiguities within this network. This is no problem because of the relatively long observation time span and known positions of the stations of the AGRS.NL. Next these interpolated corrections are used to correct the GPS data from the fifth station for its ionospheric effects. Initial conclusions about the performance of this technique are drawn in terms of improvement of integer ambiguity resolution for this baseline. ? 1999 John Wiley & Sons, Inc.     

基于BP神经网络的GPS导航算法

GPS导航解算中常用最小二乘算法。随着高动态用户需求精度的不断提高，且由于线性化忽略高次项，初始值精度低以及差分后剩余或放大误差的存在。导航解精度很难满足高动态用户的需求。为此，本文基于BP神经网络的非线性逼近性能。给出了基于BP神经网络的GPS导航算法。实测数据计算结果表明该算法能够真实地反映载体运动轨迹，其导航解的精度和可靠性有明显的提高。     

粗差检测与抗差估计相结合的方法在动态相对定位中的应用

分析了粗差对GPS动态相对定位的影响,给出了相应的影响函数和抗差估计方法。建议采用粗差探测与抗差估计相结合的方法来处理GPS动态定位中的粗差问题。抗差估计中的等价权分别采用了IGG3方案和双因子等价权函数,对两种方案的效果进行比较和分析,并利用实测数据对所提方法的实际效果进行了检验。结果表明,基于粗差探测和抗差估计相结合的粗差处理方法可有效控制和抵御粗差的影响;分别采用IGG3方案和双因子等价权函数的定位结果差异较小。     

Accurate absolute GPS positioning through satellite clock error estimation

 An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore, the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them. Received: 16 May 2000 / Accepted: 23 October 2000     

局域差分GPS的数学模型

局域差分GPS中,用户到基准站的距离对定位精度有着决定性影响。利用基准站生成用户误差改正数,其算法很多。文中针对局域差分GPS的数学模型空间相关性,介绍几种常用的内插方法,如加权平均法、线性内插法、低次曲面模型法及三角形内插法,并分析各种方法的内插系数和内插质量因子。利用局域差分GPS进行定位时,只有当用户站位于基准站构成的多边形网内时,才可能得到较高的精度。     

Affine distortion of small GPS networks with large height differences

GPS is a promising tool for real-time monitoring of deformations of slopes or large structures. However, remaining systematic effects in GPS phase observations after double differencing and application of a priori models affect the resulting coordinates. They complicate the proper separation of the actual deformations from pseudo-deformations induced by the systematic effects. This paper shows that for small monitoring networks (baseline lengths <5 km) only affine distortions of the network geometry are generated by the remaining distance dependent systematic effects, e.g. unmodelled tropospheric and ionospheric propagation effects, or satellite orbit errors. Hence, a generic correction model is given by a three-dimensional affine transformation involving a maximum of 12 transformation parameters. For the determination of these parameters, four high quality GPS stations are necessary which are not affected by the actual deformations to be monitored. Based on the analysis of network geometries of synthetic GPS networks with large height differences and considering the physics of the GPS observations it is shown, however, that less than 12 parameters are sufficient for the computation of the corrections. The proposed 8 parameter model was applied to the GPS monitoring network of the Gradenbach landslide. For this small network with large height differences, it was shown that the distortions can be reduced by about 75%.     

GPS参考站网络的多路径误差建模技术研究

通过研究多路径误差的周日重复性特征,将参考站网络多路径历史数据用于减弱参考站网络基线解算中的多路径效应影响,以提高网络解算(尤其指低高度角卫星和新升卫星)的初始化进程及可靠性。通过分析多路径误差的产生机理,研究多路径误差与信噪比信息的强相关关系,建立信噪比相关网络内插模型(SNRIM),用于流动用户位置高精度多路径改正数的实时计算。最后通过四川GPS观测网络实验,验证上述方法在网络高精度实时定位领域应用的有效性及可靠性。     

On accuracy and reliability of instantaneous network RTK as a function of network geometry, station separation, and data processing strategy

The network-based approach to kinematic GPS positioning significantly increases the distance, over which carrier-phase ambiguity resolution can be performed. This can be achieved either by introducing geometric conditions based on the fixed reference locations, and/or through the use of reference network data to estimate the corrections to GPS observations that can be broadcast to the users. The Multi Purpose GPS Processing Software (MPGPS) developed at The Ohio State University uses the multiple reference station approach for wide area and regional differential kinematic GPS positioning. The primary processing algorithm uses the weighted free-net (WFN) approach with the distance-dependent weighting scheme to derive optimal estimates of the user coordinates and realistic accuracy measures. The WFN approach, combined with the single epoch (instantaneous) ambiguity resolution algorithm is presented here as one approach to real-time kinematic (RTK) GPS. Since for baselines exceeding ~100 km, the instantaneous ambiguity resolution may not always be possible due to the increasing observation noise and insufficient number of observations to verify the integer selection, an alternative approach, based on a single- (or multiple-) baseline solution, supported by a double-difference (DD) ionospheric delay propagated from the previous epoch is also presented. In this approach, some data accumulation, supported by the network-derived atmospheric corrections, is required at the beginning of the rover data processing to obtain the integer ambiguities; after this initialization period, the processing switches to the instantaneous RTK positioning mode. This paper presents a discussion on the effects of the network geometry, station separation and the data reduction technique on the final quality and reliability of the rover positioning solution. A 24-h data set of August 31, 2003, collected by the Ohio Continuously Operating Reference Station (CORS) network was processed by both techniques under different network geometry and reference station separation. Various solutions, such as (1) single-baseline solution for varying base-rover separation, (2) multi-baseline solution with medium-range base separation (over 100 km), and (3) multi-baseline solution with long-range base separation (up to 377 km), were obtained and compared for accuracy and consistency. The horizontal positioning accuracy achieved in these tests, expressed as the difference between the estimated coordinates and the known rover coordinates, is at the sub-decimeter level for the first approach, and at the centimeter-level for the second method, for baselines over 100 km. In the vertical coordinate, decimeter- and sub-decimeter levels were achieved for the two approaches, respectively. Even though all the results presented here were obtained in post-processing, both algorithms are suitable for real-time applications.     

SBAS星历改正数及UDRE参数生成算法分析

星基增强系统(satellite based augmentation system,SBAS)通过地球同步轨道卫星实时播发导航卫星星历改正数和完好性参数,以提升用户定位精度和完好性。采用最小方差法解算GPS星历改正数,利用卡方统计进行改正数完好性检核,并依据星历改正数方差-协方差信息计算SBAS用户差分距离误差(user differential range error,UDRE)和信息类型28(message type 28, MT28)等完好性参数。利用中国区域27个监测站的实测数据,首先以国际GNSS服务组织的精密轨道和钟差产品为参考解算星历改正数,结果表明,钟差改正精度优于0.1 m,轨道改正精度优于0.4 m;然后解算广播星历改正数,并生成UDRE和MT28参数,广播星历残余误差卡方检验值均小于告警门限,保证了改正数的完好性;最后利用生成的改正数进行SBAS定位解算,得到定位结果的水平精度优于0.7 m,垂直精度优于1.0 m,对比GPS单点定位,所提算法的水平和垂直方向精度分别提升了30%和40%。