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.     

A new algorithm for generating carrier adjusted differential GPS corrections

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 observation 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 are used.     

Algorithm for carrier-adjusted DGPS positioning and some numerical results

This paper derives a DGPS positioning algorithm, referred to as the algorithm for carrier-adjusted DGPS positioning. This algorithm can be applied by a DGPS user when code and carrier observations are available and when the dynamic behaviours of both mobile positions and receiver-clock biases can and cannot be modelled. Since the algorithm directly uses code and carrier observations, the stochastic model of observations has a simple structure and can be easily specified. When the dynamic behaviour of mobile positions can be modelled, the algorithm can provide recursive solutions of the positions, on the other hand, when the behaviour cannot be modelled, it can provide their instantaneous solutions. Furthermore, the algorithm can integrate with a real-time quality-control procedure so that the quality of the position estimates can be guaranteed with a certain probability. Since in the use of the algorithm there always exist redundant observations unless the position parameters are inestimable, the quality control can even be performed when only four satellites are tracked. Using the algorithm and real GPS data collected at a 100-km baseline, this contribution investigates how DGPS positioning accuracies vary with the type of observables used at reference and mobile stations, and how important it is to choose an elevation-dependent standard deviation for code observations in DGPS data reduction. It was found that using carrier observations along with code observations is more important at the reference station than at the mobile station. Choosing an elevation-dependent standard deviation for code observations can result in better positioning accuracy than choosing a constant standard deviation for code observations. For the 100-km baseline, half-metre single-epoch positioning accuracy was achieved when dual-frequency data was used at both reference and mobile stations. The positioning accuracy became better than 0.75m when the types of observable used at the mobile station were replaced by L1 code and carrier. Received: 9 April 1996 / Accepted: 6 February 1997     

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.     

GPS手机的差分定位系统研究

提高GPS手机的定位精度具有很广阔的应用前景,本文研究GPS手机的实时定位差分系统的设计和实现方法。该系统采用基准站广播位置差分值、移动站实时处理的差分GPS方案,其主要优点是定位精度高、改正速度快、设备简单、操作方便;分析了位置差分GPS的定位误差,给出了测量结果。理论分析和测试结果都表明,该系统的差分定位精度比手机GPS直接定位相对提高31m左右,定位误差达4m左右,能够满足相关领域测量精度要求。     

Group delay variations of GPS transmitting and receiving antennas

GPS code pseudorange measurements exhibit group delay variations at the transmitting and the receiving antenna. We calibrated C1 and P2 delay variations with respect to dual-frequency carrier phase observations and obtained nadir-dependent corrections for 32 satellites of the GPS constellation in early 2015 as well as elevation-dependent corrections for 13 receiving antenna models. The combined delay variations reach up to 1.0 m (3.3 ns) in the ionosphere-free linear combination for specific pairs of satellite and receiving antennas. Applying these corrections to the code measurements improves code/carrier single-frequency precise point positioning, ambiguity fixing based on the Melbourne–Wübbena linear combination, and determination of ionospheric total electron content. It also affects fractional cycle biases and differential code biases.     

基于GPS双频原始观测值的精密单点定位算法及应用

本文提出一种基于GPS双频原始观测值的PPP算法,与基于消电离层组合观测值的传统PPP算法不同,新算法通过参数化站星视线方向的电离层延迟以消除其对PPP估值的不利影响;该新算法可以有效避免观测值组合过程所引起的观测数据噪声以及多路径效应被放大的不利影响;同时在利用扩展卡尔曼滤波模型进行未知参数的递归估计过程中,通过对大气延迟参数引入符合实际的约束,可以加快滤波收敛,提高参数估值的可靠性;视线方向电离层延迟可与其他未知参数同时估计得到,进而便于利用PPP技术进行精密电离层研究;此外,对于可能的模型误差（如码观测值粗差、相位观测值周跳等）,基于DIA的质量控制策略以消除或削弱其对参数估值的不利影响。利用实测数据对新算法在静态、低动态以及高动态定位应用方面的精度进行检验,结果表明,静、动态定位结果的外符合精度可分别达到1~2 cm和7~8 cm,验证了新算法的可行性和有效性。     

基于方差分量估计原理的自适应卡尔曼滤波及其应用

简单介绍了GPS伪距动态定位的卡尔曼滤波模型的建立，针对传统卡尔曼滤波中动态噪声不准或不容易确定以及因动态目标机动而导致滤波发散的现象，提出了一种根据方差分量估计原理，利用预报残差计算模型的动态噪声方差分量的自适应滤波算法，当利用预报残差进行计算时，这一方面增加的计算量不大，能有效地克服由上述原因而导致的滤波不稳定现象，适用于GPS动态定位数据的实时处理。     

An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK

A user of heterogeneous GPS and GLONASS receiver pairs in differential positioning mode will experience ambiguity fixing challenges due to the presence of inter-channel biases. These biases cannot be canceled by differencing GLONASS observations, whether pseudorange or carrier phase. Fortunately, pre-calibration of GLONASS pseudorange and carrier phase observations can make ambiguity fixing for GPS/GLONASS positioning much easier. We propose an effective algorithm that transforms an RTK (real-time kinematic) solution in a mixed receiver baseline from a float to a fixed ambiguity solution. Carrier phase and code inter-channel biases are estimated from a zero baseline. Then, GLONASS both carrier phase and code observations are corrected accordingly. The results show that a mixed baseline can be transformed from a float (~100 %) to a fixed (more than 92 %) solution.     

广域差分GPS中用户定位算法的研究

广域差分GPS中用户接收机多为较廉价的单频接收机，可以接收差分播发站发播的差分改正信号进行DGPS计算，由于WADGPS的算法和常规算法不一致，差分改正信号难以是标准的RTCM格式，因此必须研制专用的差分信号接收机和DSP运算平台，并在平台上集成用户定位的算法，用户定位软件可以实时对观测数据、差分改正信号进行解码，计算用户的三维位置和速度。     

Impact of GLONASS pseudorange inter-channel biases on satellite clock corrections

GLONASS carrier phase and pseudorange observations suffer from inter-channel biases (ICBs) because of frequency division multiple access (FDMA). Therefore, we analyze the effect of GLONASS pseudorange inter-channel biases on the GLONASS clock corrections. Different Analysis Centers (AC) eliminate the impact of GLONASS pseudorange ICBs in different ways. This leads to significant differences in the satellite and AC-specific offsets in the GLONASS clock corrections. Satellite and AC-specific offset differences are strongly correlated with frequency. Furthermore, the GLONASS pseudorange ICBs also leads to day-boundary jumps in the GLONASS clock corrections for the same analysis center between adjacent days. This in turn will influence the accuracy of the combined GPS/GLONASS precise point positioning (PPP) at the day-boundary. To solve these problems, a GNSS clock correction combination method based on the Kalman filter is proposed. During the combination, the AC-specific offsets and the satellite and AC-specific offsets can be estimated. The test results show the feasibility and effectiveness of the proposed clock combination method. The combined clock corrections can effectively weaken the influence of clock day-boundary jumps on combined GPS/GLONASS kinematic PPP. Furthermore, these combined clock corrections can improve the accuracy of the combined GPS/GLONASS static PPP single-day solutions when compared to the accuracy of each analysis center alone.     

Avoiding numerical stability problems of long duration DGPS/INS Kalman filters

A current pursuit of the geodetic community is the optimal integration of differential GPS (DGPS) and inertial navigation system (INS) data streams for precise and efficient position and gravity vector surveying. Therein a complete INS and multiple-antenna GPS receiver payload, mounted on a moving platform, is used in conjunction with a network of ground-fixed single antenna GPS receivers. This paper presents a complete, GPS-based, external updating measurement model for the applicable Kalman filter. The model utilizes four external observation types for every GPS satellite in-view: DGPS range differences, single phase differences, and single phase-rate differences; as well as the mobile, multipleantenna GPS receiver's measurement of theerrors in the INS's estimate of the phase difference between any two vehicle-borne GPS antennae. Although not widely conveyed in the geodetic world, the inertial navigation community has long known that traditional Kalman filter covariance propagation recurrences are inherently unstable when such highly accurate external updates are repeatedly applied (every 1 second) over long time durations. A hybrid square root covariance/U — D covariance factorization approach is a numerically stable alternative and is reviewed herein. The hybrid makeup of the algorithm is necessitated by the correlated nature of the fourth type of GPS external measurement listed above (each vehicle-borne GPS antenna formstwo baselines). Such measurement correlations require a functional transformation of the overall external updating model to permit the multiple updates (simultaneously available at each updating epoch) to be sequentially (and efficiently) processed. An appropriate transformation is given. Stable covariance propagation relationships are presented and the transformed Kalman gain is also furnished and its use in the determination of the externally updated error states is discussed. Specific DGPS/INS instabilities produced by the traditional recurrences are displayed. The stable alternative method requires about 25% more CPU time than the traditional Kalman recurrences. With the ever-increasing computational speeds of microprocessors, this added CPU time is of no real concern.     

估计接收机差分码偏差的GPS/BDS非组合精密单点定位模型

在传统多系统非差非组合精密单点定位（precise point positioning,PPP）模型中,电离层延迟会吸收部分接收机码硬件延迟,其估计值可能为负数。提出了一种估计接收机差分码偏差（differential code bias,DCB）参数的GPS（Global Positioning System）/BDS（BeiDou Navigation Satellite System）非组合PPP模型,将每个系统第1个频率上的接收机码硬件延迟约束为零,对接收机DCB进行参数估计,达到了分离电离层延迟和接收机码硬件延迟的目的,降低了接收机钟差和电离层延迟的相关程度。利用4个多星座实验（multi-GNSS experiment,MGEX）跟踪站的GPS/BDS数据进行了静态和动态PPP试验,结果表明,与不估计DCB参数的PPP模型相比,采用估计DCB参数PPP模型后,静态模式下定位精度和收敛速度平均提高了29.3%和29.8%,动态模式下定位精度和收敛速度平均提高了15.7%和21.6%。     

Triple Differencing with Kalman Filtering: Making It Work

Since global positioning system (GPS) measurements are ranges (code) and biased ranges (carrier), it seems natural to model them as ranges and determine the biases. This is particularly compelling since the double-difference range biases turn out to be integers. At some level there is also an elegance, perhaps therefore a naturalness, to modeling the carrier measurements as time differences of double differences. While something is lost something else is gained. Here we apply the proven delayed-state Kalman filter to processing carrier phase measurements as triple differences. In practice we process these triple differences along with double-difference code measurements. We also treat the measurement error as, mostly, Gauss-Markov states to be determined. Many of the details are discussed and experimental results are included. These demonstrate that excellent performance can be obtained if the Kalman filter modeling is done carefully. ? 2000 John Wiley & Sons, Inc.     

确定卫星与接收机信号延迟偏差的新方法及其应用

单频ＧＰＳ接收机用户通常需要进行电离层延迟改正,电离层延迟改正量通常来源于电离层延迟改正模型或双频ＧＰＳ基准站信息,后者即是利用双频ＧＰＳ观测值估计电子含量总数,求解电离层延迟改正量。利用双频ＧＰＳ观测值估计电子含量总数,一个关键总是是去掉卫星与接收信号延迟偏差。     

Assessment of the LandStar Real-Time DGPS Service under Several Operational Conditions

LandStar is a differential global positioning service (DGPS) that provides 24-h real-time positioning for various applications on land, water, and air in North America, Australia, New Zealand, Europe, and Africa. Its focus is on real-time applications requiring a submeter positioning capability such as agriculture, forestry, Geospatial Information Systems (GIS), survey/mapping, and land/vehicular navigation. LandStar uses a Wide Area Network of reference stations to derive DGPS corrections to model the variation of GPS error sources over a large area. These model parameters are used by the Virtual Reference Station processors to calculate standard corrections that are available for all predefined locations in the network. The corrections are transmitted to the user by L-band satellite communication in the standard RTCM SC104 DGPS correction format. This article investigates the performance of the LandStar Mk III system under various operational conditions and assesses its performance in both static and kinematic modes. Four field tests were conducted during 12 months that tested the sysem in clear static and kinematic conditions as well as suboptimal environments associated with low and heavy foliage conditions. Both the accuracy and availability of the system under these conditions is investigated, with an emphasis on whether the above variables are caused by the LandStar system differential corrections, the GPS measurements, or a combination of both. ? 1999 John Wiley & Sons, Inc.     

动态定位的模型偏差检测与校正

动态定位的数据处理中广泛应用卡尔曼滤波,而卡尔曼滤波的应用要求动态模型(函数模型)和随机模型可靠和切合实际,但实际测量定位中难以保证观测对象的规则运动,因而容易出现模型误差.探讨在实际应用中存在模型误差时的卡尔曼滤波,研究动态定位时卡尔曼滤波的模型检测与校正,给出一种偏差分离估计方法.由于不存在状态增广,因而该方法计算效率高.最后以一数字仿真(模拟)实验论证方法的可行性.     

Precise Real-Time Positioning in WADGPS Networks

In recent years the importance of real-time positioning and navigation with the Global Positioning System (GPS) has grown rapidly. Starting from the establishment of differential GPS (DGPS) reference stations for marine and land navigation, new users and applications have emerged that resulted in a high demand for the establishment of a high-density network of reference stations around the world. Many countries have established their own DGPS service, which is either governmentally or commercially owned. These services are referred to as Local Area DGPS Systems (LADGPS). However, the costs for the establishment and maintenance of a dense network of reference stations are very high. Therefore Wide Area DGPS Systems (WADGPS) are being developed to overcome the main drawbacks of LADGPS. In this case, only a few reference stations are used to cover a large area, such s a continent like Europe. To achieve high positioning accuracies, real-time modeling of the main error sources for long-range baselines is required as errors in the satellite orbit and ionospheric refraction do not cancel entirely in double differencing. In this article, a real-time correction model based on the Kalman filter for WADGPS and networked LADGPS services is discussed and results of field tests in a WADGPS network in Europe are presented. ? 2000 John Wiley & Sons, Inc.     

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。