R-T-S平滑算法在POS数据后处理中的应用

高精度的定位定姿系统（POS,Position and Orientation System）在测绘领域发挥着重要的作用,为了提高数据的精度,将平滑技术应用于POS数据的后处理中.文中介绍POS数据后处理算法的流程,对平滑技术尤其是应用最为广泛的R-T-S平滑进行详细分析,并对该算法进行数值仿真.结果表明,与传统的卡尔曼滤波相比,R-T-S平滑不仅可以提高位置姿态精度,而且在卫星信号失锁的情况下精度也能得到大幅改善,是一种有效的数据处理算法.     

On-line detection of abrupt changes in the carrier-phase measurements of GPS

The detection of cycle slips in carrier-phase data, outliers in phase rate or in code ranges, or any other type of disorder in the measurements of the GPS system, is one of the major quality-control problems that needs to be addressed, especially where GPS is used for real-time applications or for those applications that require continuous and reliable positioning results. This study is concerned with designing algorithms to detect failures or changes of small magnitude, in order to monitor and control the quality of GPS measurements for critical real-time and/or deformation applications. In this regard, the statistical technique known as the cumulative-sum test is described for the detection of abrupt changes in the GPS carrier-phase measurements. Real GPS data have been used to test and evaluate the algorithm. Received: 27 August 1996 / Accepted: 26 February 1997     

不同采样率对GPS原始相位观测值周跳探测方法的影响及其效果比较

在GPS精密定位中，载波相位观测值周跳探测和修复的好坏程度将直接影响定位结果的精度，特别是实时动态定位（RTK）。当接收机采用不同采样率时，由于相位观测值所组成的序列函数收敛性将发生变化，各种周跳探测方法的能力也将发生改变。综述了几种常规的周跳探测方法，并对其特点与局限性进行了分析，然后对构造出的周跳检验量进行了比较，在此基础上通过大量算例探讨了在不同采样率下其探测周跳的能力和适用度，最后得出了一些有益的结论。     

A cycle slip fixing method with GPS + GLONASS observations in real-time kinematic PPP

A key limitation of precise point positioning (PPP) is the long convergence time, which requires about 30 min under normal conditions. Frequent cycle slips or data gaps in real-time operation force repeated re-convergence. Repairing cycle slips with GPS data alone in severely blocked environments is difficult. Adding GLONASS data can supply redundant observations, but adds the difficulty of having to deal with differing wavelengths. We propose a single-difference between epoch (SDBE) method to integrate GPS and GLONASS for cycle slip fixing. The inter-system bias can be eliminated by SDBE, thus only one receiver clock parameter is needed for both systems. The inter-frequency bias of GLONASS satellites also cancels in the SDBE, so cycle slips are preserved as integers, and the LAMBDA method is adopted to search for cycle slips. Data from 7 days of 20 globally distributed IGS sites were selected to test the proposed cycle slip fixing procedure with artificial blocking of the signal; cycle slips were introduced for all un-blocked satellites at each epoch. For a 30-s sampling interval, the average success rate of fixing can be improved from 73 to 98 % by adding GLONASS. Even for a 180-s sampling interval, GPS + GLONASS can achieve a success rate of 81 %. A real-time kinematic PPP experiment was also performed, and the results show that using GPS + GLONASS can achieve continuous high-accuracy real-time PPP without re-convergence.     

Attenuation effect on seasonal basin-scale water storage changes from GRACE time-variable gravity

In order to effectively recover surface mass or geoid height changes from the gravity recovery and climate experiment (GRACE) time-variable gravity models, spatial smoothing is required to minimize errors from noise. Spatial smoothing, such as Gaussian smoothing, not only reduces the noise but also attenuates the real signals. Here we investigate possible amplitude attenuations and phase changes of seasonal water storage variations in four drainage basins (Amazon, Mississippi, Ganges and Zambezi) using an advanced global land data assimilation system. It appears that Gaussian smoothing significantly affects GRACE-estimated basin-scale seasonal water storage changes, e.g., in the case of 800 km smoothing, annual amplitudes are reduced by about 25–40%, while annual phases are shifted by up to 10°. With these effects restored, GRACE-estimated water storage changes are consistently larger than model estimates, indicating that the land surface model appears to underestimate terrestrial water storage change. Our analysis based on simulation suggests that normalized attenuation effects (from Gaussian smoothing) on seasonal water storage change are relatively insensitive to the magnitude of the true signal. This study provides a numerical approach that can be used to restore seasonal water storage change in the basins from spatially smoothed GRACE data.     

A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver

This paper develops a new automated cycle slip detection and repair method that is based on only one single dual-frequency GPS receiver. This method jointly uses the ionospheric total electron contents (TEC) rate (TECR) and Melbourne–Wübbena wide lane (MWWL) linear combination to uniquely determine the cycle slip on both L1 and L2 frequencies. The cycle slips are inferred from the information of ionospheric physical TECR and MWWL ambiguity at the current epoch and that at the previous epoch. The principle of this method is that when there are cycle slips, the MWWL ambiguity will change and the ionospheric TECR will usually be significantly amplified, the part of artificial TECR (caused by cycle slips) being significantly larger than the normal physical TECR. The TECR is calculated based on the dual-frequency carrier phase measurements, and it is highly accurate. We calculate the ionospheric change information (including TECR and TEC acceleration) using the previous epochs (30 epochs in this study) and use the previous data to predict the TECR for the epoch needing cycle slip detection. If the discrepancy is larger than our defined threshold 0.15 TECU/s, cycle slips are regarded to exist at that epoch. The key rational of method is that during a short period (1.0 s in this study) the TECR of physical ionospheric phenomenon will not exceed the threshold. This new algorithm is tested with eight different datasets (including one spaceborne GPS dataset), and the results show that the method can detect and correctly repair almost any cycle slips even under very high level of ionospheric activities (with an average Kp index 7.6 on 31 March 2001). The only exception of a few detected but incorrectly repaired cycle slip is due to a sudden increased pseudorange error on a single satellite (PRN7) under very active ionosphere on 31 March 2001. This method requires dual-frequency carrier phase and pseudorange data from only one single GPS receiver. The other requirement is that the GPS data rate ideally is 1 Hz or higher in order to detect small cycle slips. It is suitable for many applications where one single receiver is used, e.g. real-time kinematic rover station and precise point positioning. An important feature of this method is that it performs cycle slip detection and repair on a satellite-by-satellite basis; thus, the cycle slip detection and repair for each satellite are completely independent and not affected by the data of other satellites.     

Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing

The network-based real-time kinematic (RTK) positioning has been widely used for high-accuracy applications. However, the precise point positioning (PPP) technique can also achieve centimeter to decimeter kinematic positioning accuracy without restriction of inter-station distances but is not as popular as network RTK for real-time engineering applications. Typically, PPP requires a long initialization time and continuous satellite signals to maintain the high accuracy. In case of phase breaks or loss of signals, re-initialization is usually required. An approach of instantaneous cycle slips fixing using undifferenced carrier phase measurements is proposed, which leads to instantaneous re-initialization for real-time PPP. In the proposed approach, various errors such as real-time orbit and clock errors, atmosphere delay and wind-up effects are first refined and isolated from integer cycle slips. The integer values of cycle slips can then be estimated and fixed with the LAMBDA technique by applying a cascade cycle slip resolution strategy. Numerical experiments with different user dynamics are carried out to allow a comprehensive evaluation of efficiency and robustness of the cycle slip fixing algorithm. The results show that the cycle slips can be fixed correctly in all cases considered and that data gaps of up to 300?s can be connected with high confidence. As a result, instantaneous re-initialization is achieved in the real-time PPP processing.     

A harmonic spline model for local estimation of planetary gravity fields from line-of-sight acceleration data

The spline interpolation technique is applied to estimate locally the radial component of a planetary gravity field from residual acceleration data along a special direction, the direction of observation from the Earth. After the presentation of the theoretical framework, the method is tested on synthetic and real data in the case of Venus. It is shown that this spline technique can be used succesfully to build local models of radial gravity fields at the planet surface. Received: 13 March 1997 / Accepted: 17 November 1998     

用低通滤波器探测和修复单频GPS载波相位的周跳

使用一种在时间序列分析中常用的异常值的检测方法双低通滤波器奇异值检定法来检测GPS载波相位观测值中的周跳，给出了数据窗的宽度Vmax以及门槛系数女，提出了利用低通滤波器进行周跳定值的迭代计算方法。试验表明，该方法计算简单，能够探测1周甚至0．5周的周跳。     

Integrity Monitoring of IGEX-98 Data,Part I: Availability

The International GLONASS Experiment 1998 (IGEX-98) was the first international tracking campaign of the Russian counterpart to the Global Positioning System (GPS), GLONASS. Started in October 1998, the campaign was originally scheduled to last for three months. However, the launch of additional GLONASS satellites and a widespread enthusiasm among the participants led to an indefinite continuation of the campaign on a “best effort” basis. At the Delft University of Technology, the data of six IGEX-98 stations have been analyzed in detail with integrity monitoring software, developed at the Department of Mathematical Geodesy and Positioning of the University. The software aims to detect outliers and slips in code and phase observations in real time. In addition, the software also allows the validation of the information contained in the broadcast navigation messages. The results of the IGEX-98 data analyses will be presented in a three-part series. In the second part, GLONASS outlier and slips statistics will be discussed, while in the third part the anomaly detection results of the GLONASS and GPS messages will be shown. In this first part of the series, however, the most basic of all statistics will be considered: a simple day-to-day count of the number of GLONASS and GPS observations. Although simple, this statistic yields a surprising amount of information both on the availability of the GLONASS satellites and on the peculiarities of some of the receiver makes participating in the IGEX-98 campaign. ? 2000 John Wiley & Sons, Inc.     

Ionospheric super-bubble effects on the GPS positioning relative to the orientation of signal path and geomagnetic field direction

Using GPS data of the Japanese network GEONET, we analyze occurrence of GPS-phase slips and positioning errors during the geomagnetic storm of February 12, 2000. Although the storm was not intensive, registering a minimum Dst excursion of −133 nT and a maximum Kp = 6.7 value, it attracted the attention of researchers because of the appearance of a super-bubble at mid-latitudes. We identified numerous GPS-phase slips in the area of the super-bubble. By the time of the bubble’s appearance, a total of 33% of GPS receivers experienced positioning errors of more than 500 m. Around 13:00 UT, the positioning quality was worse than 100 m almost all of Japan. We also found that the occurrence of phase slips of the satellite signals depends on the angle γ between the receiver-satellite line of sight and geomagnetic field lines. The maximum value of GPS-phase slips corresponds to γ = 0° and 90°. For the satellites positioned close to the magnetic zenith region, the density of phase slips reached 32%. In addition to carrier-phase slips, the super-bubble caused sharp increases in positioning errors of several hundred meters at receiver locations below 38°N latitude. As a result, precise positioning was not possible for about 2 h.     

A double-differenced cycle slip detection and repair method for GNSS CORS network

The difficulty to detect and repair cycle slip of carrier phase measurements is a key limit for continuously high accuracy of GNSS positioning and navigation services. We propose an automated cycle slip detection and repair method for data preprocessing of a CORS network. The method jointly uses double-differenced (DD) geometry-free (GF) combination and ionospheric-free observation corrected for the computed geometrical distance (IF-OMC) to estimate the cycle slips in dual-frequency observations. The DD GF combination, which is only affected by the ionospheric residual, can be used to detect cycle slips with high reliability except for special pairs such as (77, 60) on GPS L1/L2 frequencies. The detection principle of the IF-OMC observable is such that there is a large discontinuity related to the previous epoch when cycle slips occur at the present epoch. The disadvantages of these two combinations can be overcome employing the proposed detection method. The cycle slip pair (77, 60) has no effect on the GF combination, while a change of 14.65 m is derived from GPS L1/L2 observations using the IF-OMC algorithm. Using pre-determined station coordinates as precise values, we found that the accuracy of the DD IF-OMC combination was 18 mm for a 200-km CORS baseline. Therefore, cycle slips in dual-frequency observations can be correctly and uniquely determined using DD GF and IF-OMC equations. The proposed method was verified by adding simulated cycle slips in observations collected from the CORS network under a quiet ionosphere and shown to be effective. Moreover, the method was assessed with observations made during intense ionospheric activity, which generated extensive cycle slips. The results show that the algorithm can detect and repair all cycle slips apart from two exceptions relating to long data gaps.     

Rapid GPS ambiguity resolution for short and long baselines

 A method of quick initial carrier cycle ambiguity resolution is described. The method applies to high-quality dual-band global positioning system observations. Code measurements on both frequencies must be available. The rapidity of the method is achieved through smoothing pseudoranges by phase observables and forming linear combinations between the phase observables. Two cases are investigated. Case 1: ionospheric bias is neglected (short distances); and case 2: the bias is taken into account (longer distances, more than, say, 10 km). The method was tested on six baselines, from 1 to 31 km long. In most cases, single-epoch ambiguity resolution was achieved. Received: 6 October 1999 / Accepted: 4 March 2002     

GPS signal diffraction modelling: the stochastic SIGMA-δ model

The SIGMA-Δ model has been developed for stochastic modelling of global positioning system (GPS) signal diffraction errors in high precision GPS surveys. The basic information used in the SIGMA-Δ model is the measured carrier-to-noise power-density ratio (C/N0). Using the C/N0 data and a template technique, the proper variances are derived for all phase observations. Thus the quality of the measured phase is automatically assessed and if phase observations are suspected to be contaminated by diffraction effects they are weighted down in the least-squares adjustment. The ability of the SIGMA-Δ model to reduce signal diffraction effects is demonstrated on two static GPS surveys as well as on a kinematic high-precision GPS railway survey. In cases of severe signal diffraction the accuracy of the GPS positions is improved by more than 50% compared to standard GPS processing techniques. Received: 27 July 1998 / Accepted: 1 March 1999     

图像平滑算法比较研究及改进策略

图像平滑作为去除图像中含有噪声的图像增强处理技术，是各种与图像有关软件中必不可少的功能模块。文中在分析噪声模型的基础上，对均值平滑、中值平滑、边缘保持平滑等技术从图像处理空间域中的算法原理、实现方法及效率等方面进行了详细比较。针对图像中含有的不同噪声模型，通过多次试验，得出了值得从事图像处理研究者参考的结论。这将有助于提高图像处理软件开发的效率。     

Combination procedure for length-of-day time series according to the noise frequency behavior

 Length-of-day (LOD) estimates from seven Global Positioning System (GPS) and three satellite laser ranging (SLR) analysis centers were combined into an even-spaced time series for a 27-month period (1996–1998). This time series was compared to the multi-technique Earth-orientation-parameter (EOP) combined solution (C04) derived at the Central Bureau of the International Earth Rotation Service (IERS/CB). Due to inhomogeneities in the different series derived from the various techniques (time, length, quality, and spatial resolution), the concept of a combined solution is justified. The noise behavior in LOD for different techniques varies with frequency; the data series were divided into frequency windows after removing both biases and trends. Different weight factors were assigned in each window, discriminating by technique, and produced one-technique combined solutions. Finally, these one-technique combined solutions were combined to obtain the final multi-technique solution. The LOD combined time series obtained by the present method based on the frequency windows combined series (FWCS) is very close to the IERS C04 solution. It could be useful to generate a new LOD reference time series to be used in the study of high-frequency variations of Earth rotation. Received: 28 March 2000 / Accepted: 15 February 2001     

LEO GPS attitude determination algorithm for a micro-satellite using boom-arm deployed antennas

This paper describes a low earth orbiter micro-satellite attitude determination algorithm using GPS phase and pseudorange data as the only observables. It is designed to run in real-time, at a rate of 10 Hz, on-board the spacecraft, using minimal chip and memory resources. The spacecraft design includes four GPS antennas deployed on boom arms to improve the antenna separations. The boom arms feature smart sensors, from which time-varying deformation data are used to calculate changes in the body-fixed system (BFS) co-ordinates of the attitude antennas. These data are used as input to the attitude algorithm to improve the accuracy of the output. The conventional double-difference phase observation equations have been re-arranged so that the only unknown parameters in the functions (once the ambiguities have been determined) are the spacecraft Euler angles. This greatly increases the redundancy in the mathematical model, and is exploited to enhance the algorithm's ability to trap observations contaminated by unmodelled multipath. This approach has been shown to be successful in identifying phase outliers at the 5–10 mm level. Speed of execution of the program is improved by utilising numerical differentiation of the model equations in the linearisation process. Furthermore, as the number of solve-for parameters is reduced to three by the chosen mathematical model, matrix inversion requirements are minimised. A novel approach to ambiguity resolution and determination of initial estimates of the attitude parameters has been developed utilising a heuristic technique and the known, and time varying, BFS co-ordinates of the antenna array. Algorithm testing is based on a simulation of the micro-satellite trajectory combined with variations in attitude derived from spin-stabilisation and periodic roll and pitch parameters. The trajectory of the spacecraft centre of mass was calculated by numerical integration of a force model using Earth gravity field parameters, third body effects due to the Sun and the Moon, dynamic Earth tide effects (solar and lunar), and a solar radiation pressure model. Frame transformations between J2000 and ITRF97 used the IERS conventions. A similar approach was used to calculate the trajectories of all available GPS satellites during the same period, using initial conditions of position and velocity from IGS precise orbits. RMS differences between the published precise orbit and the integrated satellite positions were at the 5-mm level. Phase observables are derived from these trajectories, biased by simulation of receiver and satellite clock errors, cycle slips, random or systematic noise and initial integer ambiguities. In the actual simulation of the attitude determination process in orbit, GPS satellite positions are calculated using broadcast ephemerides. The results show that the aim of 0.05° (two sigma) attitude precision can be met provided that the phase noise can be reduced to the level of 1–2 mm. Attitude precision was found to vary strongly with constellation geometry, which can change quite rapidly depending on the variations in spacecraft attitude. The redundancy in the mathematical model was found to be very effective in trapping and isolating cycle slips to the double difference observations that are contaminated. This allows for the possibility of correcting for cycle slips without full recourse to the ambiguity resolution algorithm. Electronic Publication     

Cycle slip detection and repair of undifferenced single-frequency GPS carrier phase observations

Cycle slip detection and repair is an important issue in the GPS data processing. Different methods have been developed to detect and repair cycle slips on undifferenced , single- or double-differenced observations. The issue is still crucial for high-precision GPS positioning, especially for the undifferenced GPS observations. A method is proposed to fix cycle slips based on the generalized likelihood ratio (GLR) test. The method has a good performance on cycle slip fixing of undifferenced carrier phase observations on individual frequencies, either on L1 or on L2, without making a linear combination among the observables. The functional model is a piecewise cubic curve fitted to a number of consecutive data using the least squares cubic spline approximation (LS-CSA). For fixing the cycle slips, an integer estimation technique is employed to determine the integer values from the float solution. The performance of the proposed method is then compared with the existing two methods using simulated data. The results on a few GPS data sets with sampling rate of 1 Hz or higher confirm that this method can detect and correct all simulated cycle slips regardless of the size of the cycle slip or the satellite elevation angle. The efficacy of the method is then investigated on the GPS data sets with lower sampling rates of 5, 10, and 30 s. The results indicate that the proposed method always performs the best for the data sets considered. This is thus an appropriate method for cycle slip detection and repair of single-frequency GPS observations.     

星载双频GPS二次周跳探测方法研究

在利用W-M宽巷组合进行周跳初步探测的基础上,加入了新方法进行二次周跳探测。该方法通过利用来自同颗GPS卫星的无电离层影响L3组合相位观测值在相邻历元间的变化量与dm级精度的先验轨道坐标,计算得出星载GPS接收机历元间的钟差变化值。对于存在周跳的载波相位观测值,其计算结果会与同历元其他无周跳观测值解算的钟差变化量存在较大差异。实验结果表明,二次探测可以发现新的周跳并对初步探测结果进行检核。     

模糊度直接求解算法用于GPS周跳的探测与修复

探测与修复周跳是GPS数据处理中的一个关键问题.针对CPS载波相位定位中出现的周跳问题,本文提出了一种新的周跳探测与修复的方法:首先组成双差相位观测方程,并根据观测文件中的近似坐标求得基线约束条件;随后利用基线约束条件直接求解各个历元的模糊度值,并依据历元间的模糊度变化来探测与修复周跳.通过编写应用程序和实例验证表明这...