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.     

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.     

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。     

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.     

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     

Double-filter model with modified Kalman filter for baseband signal pre-processing with application to ultra-tight GPS/INS integration

In federated design of ultra-tight GPS/INS integrated system, the baseband signal pre-processing is completed in a single pre-filter assigned for each channel. As the state space model of this single pre-filter includes the code tracking errors coupled with carrier tracking errors, ionospheric errors and normalized signal amplitude, the carrier tracking process may be destroyed. Also, the measurement noises are not independent any longer after passing through the code and carrier discriminators. Therefore, we propose a double-filter-based pre-filter model that distributes the carrier and code tracking into two independent filters: a conventional pre-filter, where the normalized signal amplitude is excluded from the state space and tracks only the code signal, and a 3-dimension state filter, tracking the carrier signal. The measurement information from both filters is a scalar quantity, which removes most of the noise correlation. To further improve the performance of the double-filter-based pre-filter model, we propose a modified Kalman filter algorithm. Simulation and field tests have been conducted, and the performance analysis has been done for the following configurations in a vector-tracking mode: double-filter model with modified Kalman filter, double-filter model with conventional Kalman filter and traditional single-filter model. The preliminary analysis indicates that the double-filter model with modified Kalman filter shows the best performance in tracking and navigation domains, while the traditional single-filter model shows a sub-optimal performance.     

扩展卡尔曼滤波的虚拟格网伪距差分算法研究

针对传统伪距差分服务端压力大,以及在复杂环境下进行导航定位,某些历元卫星信号弱、卫星数不足、无法连续定位的问题,该文提出了基于扩展卡尔曼滤波算法的虚拟格网伪距差分方法。该方法充分利用先验信息和动力学模型,解决了复杂环境中动态定位结果不连续、定位精度低等问题。为验证算法的有效性,该文分别进行了动态、静态实验,并与最小二乘结果进行对比,实验结果表明:静态模式下,卡尔曼滤波算法比最小二乘算法的定位精度,在N、E、U方向分别提高48.3%、47.1%、52.5%;动态模式下,卡尔曼滤波算法比最小二乘算法更加稳定,更适合复杂环境定位。     

北斗卫星伪距多路径系统偏差的修正方法及其对单频PPP的影响分析

北斗伪距观测值存在特有的多路径系统性偏差,偏差的数量级达到几个分米到米。该系统偏差可分为两类:一类是IGSO/MEO卫星随高度角变化的伪距系统性偏差;另一类是GEO卫星(高度角仅微小变化)明显的伪距系统性偏差。系统性的伪距偏差导致GEO卫星MP序列的标准偏差较大,本文针对GEO卫星伪距偏差问题提出了一种基于卡尔曼滤波的修正方法,修正后的GEO卫星MP序列的标准偏差下降了10%~16%。基于伪距相位组合的单频PPP技术的伪距权重较大,会受到北斗伪距偏差的影响,分析表明该系统性偏差将导致单频PPP定位结果高程方向产生约1m的偏差。对GEO伪距偏差采用提出的卡尔曼滤波修正方法进行修正,并应用Wanninger和Beer的高度角模型消除IGSO/MEO观测值伪距偏差,本文对修正后的单频精密单点定位精度进行了分析。4个multi-GNSS experiment(MGEX)站10d观测数据的分析结果表明:仅改正和卫星多路径误差,高程方向定位结果精度可改善65%左右;采用本文方法对GEO卫星的多路径修正后,该方向定位结果精度改善比例将进一步提高至75%左右。     

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.     

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.     

北斗三号卫星导航信号接收机端伪距偏差建模与验证

接收机端伪距偏差是指非理想的卫星导航信号在接收机前端带宽和相关器间隔不同时产生的伪距测量系统性偏差.研究表明,北斗二号、GPS和Galileo系统均存在与接收机类型相关的伪距偏差,影响基于混合类型接收机站网的精密数据处理.本文基于iGMAS网和MGEX网观测数据,采用MW组合、伪距残差和伪距无几何距离无电离层组合3种方...     

Calibration errors on experimental slant total electron content (TEC) determined with GPS

The Global Positioning System (GPS) has become a powerful tool for ionospheric studies. In addition, ionospheric corrections are necessary for the augmentation systems required for Global Navigation Satellite Systems (GNSS) use. Dual-frequency carrier-phase and code-delay GPS observations are combined to obtain ionospheric observables related to the slant total electron content (sTEC) along the satellite-receiver line-of-sight (LoS). This observable is affected by inter-frequency biases [IFB; often called differential code biases (DCB)] due to the transmitting and the receiving hardware. These biases must be estimated and eliminated from the data in order to calibrate the experimental sTEC obtained from GPS observations. Based on the analysis of single differences of the ionospheric observations obtained from pairs of co-located dual-frequency GPS receivers, this research addresses two major issues: (1) assessing the errors translated from the code-delay to the carrier-phase ionospheric observable by the so-called levelling process, applied to reduce carrier-phase ambiguities from the data; and (2) assessing the short-term stability of receiver IFB. The conclusions achieved are: (1) the levelled carrier-phase ionospheric observable is affected by a systematic error, produced by code-delay multi-path through the levelling procedure; and (2) receiver IFB may experience significant changes during 1 day. The magnitude of both effects depends on the receiver/antenna configuration. Levelling errors found in this research vary from 1.4 total electron content units (TECU) to 5.3 TECU. In addition, intra-day vaiations of code-delay receiver IFB ranging from 1.4 to 8.8 TECU were detected.     

基于渐消因子的改进Kalman滤波时间尺度估计算法

Kalman滤波时间尺度算法是一种实时的原子钟状态估计方法,在守时实验室具有重要实用价值。由于原子钟状态模型误差估计存在偏差,Kalman滤波时间尺度算法中状态估计可能出现相应异常扰动,应当对状态模型误差进行实时控制。对此,引入基于渐消因子的改进Kalman滤波时间尺度算法。对状态预测协方差矩阵引入渐消因子,利用统计量实时计算渐消因子的量值,控制状态预测协方差阵的增长,降低了原子钟状态估计的扰动。实验结果表明,相比于标准Kalman滤波时间尺度算法和基于预测残差构造自适应因子的Kalman滤波算法,基于渐消因子的改进Kalman滤波时间尺度算法能够提高原子钟状态估计的准确度,改进时间尺度的稳定度。     

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%。     

Consideration of time-correlated errors in a Kalman filter applicable to GNSS

An algorithm for considering time-correlated errors in a Kalman filter is presented. The algorithm differs from previous implementations in that it does not suffer from numerical problems; does not contain inherent time latency or require reinterpretation of Kalman filter parameters, and gives full consideration to additive white noise that is often still present but ignored in previous implementations. Simulation results indicate that the application of the new algorithm yields more realistic and therefore useful state and covariance information than the standard implementation. Results from a field test of the algorithm applied to the problem of kinematic differential GPS demonstrate that the algorithm provides slightly pessimistic covariance estimates whereas the standard Kalman filter provides optimistic covariance estimates.     

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.     

基于AR（p）的卡尔曼滤波在GPS变形监测中的应用

由于AR（p）模型结构比较简单且计算比较方便,在变形分析中,目前常采用此模型建立变形模型。然而单纯的AR模型把模型参数作为定值,变形数据拟合误差及变形预测误差可能会比较大。介绍了将卡尔曼滤波引入AR模型,利用观测数据建立AR模型,即建立观测方程;以AR模型的参数为状态向量建立状态方程。从而形成动态系统的卡尔曼滤波函数模型,动态计算出AR模型的参数以便预测。此方法快速、实时,且占有较少内存,充分利用了AR模型和卡尔曼滤波二者的优点。     

精密单点定位不等精度观测值的RKF研究

推导了精密单点定位含有粗差观测数据的M-LS滤波原理,对等价权阵采用三段降权函数实现抗差。从新息和残差的协方差关系出发,利用对粗差敏感的残差标准差作为抗差因子。通过迭代减弱卫星间载波残差及其抗差因子的相关性。针对载波和伪距观测值不等观测精度和不相关性,采用双抗差因子实现静态抗差卡尔曼滤波（robust Kalman filtering,RKF）。采用标准卡尔曼滤波、基于新息RKF、基于残差的增益矩阵双抗差因子RKF、基于残差的等价权阵双抗差因子RKF等4种模型,分别对一组实测数据解算分析。结果表明,基于新息RKF对精度较高的载波粗差不敏感;基于残差的增益矩阵RKF对载波较小的粗差抗差效果较差,且发生粗差历元时刻的状态参数与真值偏差较大;而基于残差构造的等价权阵双抗差因子RKF可以非常精确和高效地实现抗差,单个卫星粗差对测站位置参数影响小于1 mm。