面向绕月交会对接的同波束VLBI研究

针对"嫦娥5号"(CE-5)探测器间高精度相对测量需求,设计了我国深空干涉测量处理中心框架下的同波束VLBI处理算法,分析了X波段同波束VLBI相位解模糊条件和结果;通过引入群时延辅助的相位干涉技术,大幅抑制了干涉时延随机误差,为同波束VLBI中相位解模糊提供了先验条件;利用CE-5对接实测数据验证了本文工作的有效性,为CE-5任务同波束VLBI的实施奠定了基础。     

Predicting atmospheric delays for rapid ambiguity resolution in precise point positioning

Integer ambiguity resolution in precise point positioning (PPP) can shorten the initialization and re-initialization time, and ambiguity-fixed PPP solutions are also more reliable and accurate than ambiguity-float PPP solutions. However, signal interruptions are unavoidable in practical applications, particularly while operating in urban areas. Such signal interruptions can cause discontinuity of carrier phase arc, which introduces new integer ambiguities. Usually it will take approximately 15 min of continuous tracking to a reasonable number of satellites to fix new integer ambiguities. In many applications, it is impractical for a PPP user to wait for such a long time for the re-initialization. In this paper, a method for rapid ambiguity fixing in PPP is developed to avoid such a long re-initialization time. Firstly, the atmospheric delays were estimated epoch by epoch from ambiguity-fixed PPP solutions before the data gap or cycle slip occurs. A random walk procedure is then applied to predict the atmospheric delays accurately over a short time span. The predicted atmospheric delays then can be used to correct the observations which suffer from signal interruptions. Finally, the new ambiguities can be fixed with a distinct WL-LX-L3 (here LX denotes either of L1, L2) cascade ambiguity resolution strategy. Comprehensive experiments have demonstrated that the proposed method and strategy can fix zero-difference integer ambiguities successfully with only a single-epoch observation immediately after a short data gap. This technique works even when all satellites are interrupted at the same time. The duration of data gap bridged by this technique could be possibly extended if a more precise atmospheric delay prediction is found or on-the-fly (OTF) technology is applied. Based on the proposed method, real-time PPP with integer ambiguity fixing becomes more feasible in practice.     

Fringe fitting and group delay determination for geodetic VLBI observations of DOR tones

Extracting the group and phase delays of interferometric observations produced in the Very Long Baseline Interferometry (VLBI) measurement concept requires a special fringe fitting and delay search algorithm for the recorded bandwidth. While fringe fitting is in use routinely for several megahertz wide channels in geodetic and astrometric VLBI with quasar observations, fringe fitting for artificial tones of very small bandwidth of artificial signals for Differential One-way Ranging (DOR) requires a different way of handling. In a project called Observing the Chang’E-3 Lander with VLBI (OCEL), the DOR tones emitted by the Chang’E-3 lander were observed in a standard geodetic VLBI mode with 8 or 4?MHz wide channels to maintain compatibility with the corresponding quasar observations. For these observations, we modified the existing fringe fitting program of the Haystack Observatory Processing Software (HOPS), fourfit, to properly handle narrow band DOR tones. The main motivations are that through this modification, the data of quasars and artificial radio sources can be processed in the existing geodetic analysis pipeline, and that the algorithm can be used for similar projects as well. In this paper, we describe the algorithm and show that the new algorithm produces much more reliable group delay results than using the standard fourfit algorithm. This is done by a simulation test and in particular by processing of real observations. It is shown that in many cases, systematic deviations of several nanoseconds, which are seen with the standard fourfit algorithm, can be avoided. The ultimate benefit of the new procedure is demonstrated by reducing the errors in delay triangle closures by at least a factor of 3, which, in the OCEL case, is from ～300 to ～100?ps.     

The effect of neglecting VLBI reference station clock offsets on UT1 estimates

Very Long Baseline Interferometry (VLBI) allows to monitor universal time (UT1) by conducting regular international experiments. Such dedicated observation networks are equipped with different hardware components, which require different processing strategies when the data are correlated. As the timing units at each stations are usually offset with respect to universal time (UTC) this effect should be considered during correlation processing. Thus, it is investigated how neglecting of these offsets theoretically impacts the estimation of UT1. Three different strategies for the proper handling of the timing offset will be discussed and their advantages/drawbacks will be pointed out. Moreover, it is studied how neglecting of these timing offsets affects UT1 time-series and how such a missing correction can be applied a posteriori. Although the discussed effect is for most of the UT1 experiments smaller than the formal error of the estimates, it is important to consider station clock offsets properly in next-generation VLBI systems, which are expected to improve accuracy of results by about one order of magnitude.     

用于太阳系天体VLBI观测的时延模型

VLBI观测技术可以用于对深空航天器的跟踪定位以及测速观测．这类近距离天体发出的射电信号波前是球面波．为此，本文提出了一个1ps精度下近距离射电天体地面VLBI观测时间延迟模型．     

Using only observation station data for PPP ambiguity resolution by UPD estimation

This article proposes a new method for uncalibrated phase delay (UPD) estimation to improve the accuracy of precise point positioning (PPP), which uses only observation station data. This means that the station used to generate the UPDs is the same station to which they are applied. First, dual-frequency observation equations based on a raw PPP model are developed. Then, the UPDs are calculated from integer linear combinations of float ambiguities. Third, with the UPD corrections, the least-squares ambiguity decorrelation adjustment (LAMBDA) method is utilized to obtain the integer ambiguities. Since only observation station data are used for UPD estimation, the partial ambiguity resolution (PAR) method is adopted to increase the possibility of finding a subset of integer ambiguities. The UPD estimation and ambiguity resolution are performed in each epoch. To obtain the correct integer ambiguity, the ratio test and success rate (bootstrapping) are used to evaluate the estimated integer ambiguity. Finally, by treating the integer ambiguities as constants, fixed solutions can be obtained. Quality control is also applied throughout the entire data processing procedure to obtain high quality float and fixed solutions. Data from 22 stations of the International Global Navigation Satellite System (GNSS) Service (IGS) in East Asia on day of year (DOY) 206, 2017, are used to verify the feasibility of this method. The experimental results show that compared with the float solution, the proposed method can significantly improve the accuracy in the east, north and up directions by 24%, 21% and 18% for static PPP and 36%, 18% and 34% for dynamic PPP, respectively. However, the accuracy of the proposed method is still lower than that of the fixed solutions obtained by the PRIDE-PPPAR software, in which the fractional cycle bias is computed based on reference network data. These findings sufficiently show that the proposed method can offer better solution accuracy than the float solution. However, the quality of the UPDs estimated only from observation station data is not as good as that of the estimates obtained based on reference network data.     

Testing a new multivariate GNSS carrier phase attitude determination method for remote sensing platforms

GNSS (Global Navigation Satellite Systems)-based attitude determination is an important field of study, since it is a valuable technique for the orientation estimation of remote sensing platforms. To achieve highly accurate angular estimates, the precise GNSS carrier phase observables must be employed. However, in order to take full advantage of the high precision, the unknown integer ambiguities of the carrier phase observables need to be resolved. This contribution presents a GNSS carrier phase-based attitude determination method that determines the integer ambiguities and attitude in an integral manner, thereby fully exploiting the known body geometry of the multi-antennae configuration. It is shown that this integral approach aids the ambiguity resolution process tremendously and strongly improves the capacity of fixing the correct set of integer ambiguities. In this contribution, the challenging scenario of single-epoch, single-frequency attitude determination is addressed. This guarantees a total independence from carrier phase slips and losses of lock, and it also does not require any a priori motion model for the platform. The method presented is a multivariate constrained version of the popular LAMBDA method and it is tested on data collected during an airborne remote sensing campaign.     

Inertial aided BDS triple-frequency integer ambiguity rounding method

The integer ambiguity resolution (AR) of carrier phase is significant for Global Navigation Satellite System (GNSS) precise positioning. However, in kinematic case, single-epoch AR methods based on alone GNSS are usually not reliable due to the instable pseudorange accuracy. Moreover, the computation of classical AR method Least Squares Ambiguity Decorrelation Adjustment (LAMBDA) is large. Thus, the inertial measurement unit (IMU) is introduced, a new inertial-aided AR method that directly rounds the float ambiguity of BeiDou triple-frequency combined observations, which is characterized by long wavelength, low carrier-phase noise and ionospheric delay, is proposed. The mathematical model of the new method is derived first. Then the impacts of the carrier-phase noise, ionospheric delay and inertial navigation system (INS) position error on the AR success ratio of combined observation are analyzed through probabilistic approach. Based on above investigation, the combinations (0, ?1, 1), (1, 4, ?5) and (4, ?2, ?3) are selected to resolve the original ambiguity. A vehicular integrated navigation test is performed to demonstrate the proposed method. The results show that the average AR success ratios of the three selected combinations, whose float ambiguity errors are 0.041, 0.146, 0.279 cycle respectively, are above 97.25% without regard to low-elevation C05. With respect to positioning accuracy based on our AR method when compared with IE software, the east, north, up error RMS of position are 0.042, 0.024, 0.069 m, respectively. In terms of the AR recover after the BeiDou signals outage, as long as 62 s BeiDou signal complete outage, all the ambiguities of all satellites could be re-fixed immediately. Besides, during the 90 s signals partial outage, the AR is not influenced by the position error, since the float ambiguity errors are all below half-cycle. The research of this contribution demonstrates the effectiveness of the proposed new method, which indicates it is applicable to kinematic positioning, even in BDS degraded and denied environments.     

Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (real-time kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used 7 days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 min of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 min to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology.     

RTK model and positioning performance analysis using Galileo four-frequency observations

This paper proposes a real-time kinematic (RTK) model that uses one common reference satellite for the Galileo system with four frequency observations. In the proposed model, the double-differenced (DD) pseudorange and carrier phase biases among the different frequencies are estimated as unknown parameters to recover the integer features of the DD ambiguities among the different frequencies for ambiguity resolution and precise positioning. Analysis results show that the E5a, E5b, and E5 frequencies have virtually the same performance in terms of the positioning accuracy, observation residuals, and ratio values of ambiguity resolution. However, the E1 frequency performs worse than the E5a, E5b, and E5 frequencies. The RTK results for the combination of multiple frequencies are much better than those for a single-frequency observation, the coordinates’ standard deviation is improved about 20–30%, and the ambiguity fix time is improved about 10%.     

Chang’E-1 precision orbit determination and lunar gravity field solution

In this paper we present results assessing the role of Very Long Baseline Interferometry (VLBI) tracking data through precision orbit determination (POD) during the check-out phase for Chang’E-1, and the lunar gravity field solution CEGM-01 based on the orbital tracking data acquired during the nominal phase of the mission. The POD of Chang’E-1 is performed using S-band two-way Range and Range Rate (R&RR) data, together with VLBI delay and delay rate observations. The role of the VLBI data in the POD of Chang’E-1 is analyzed, and the resulting orbital accuracies are estimated for different solution strategies. The final orbital accuracies proved that the VLBI tracking data can improve the Chang’E-1 POD significantly. Consequently, CEGM-01 based on six-month tracking data during Chang’E-1 nominal mission phase is presented, and the accuracy of the model is assessed by means of the gravity field power spectrum, admittance and coherence between gravity and topography, lunar surface gravity anomaly and POD for both Chang’E-1 and Lunar Prospector (LP). Our analysis indicates that CEGM-01 has significant improvements over a prior model (i.e. GLGM-2), and shows the potential of Chang’E-1 tracking data in high resolution lunar gravity field model solution by combining with SELENE and LP tracking data.     

Proposal of application of same beam VLBI measurements in precision orbit determination of lunar orbiter and return capsule and lunar gravity field simulation in Chang’E-3 mission

High accuracy differenced phase delay can be obtained by observing multiple point frequencies of two spacecraft using the same beam Very Long Baseline Interferometry (VLBI) technology. Its contribution in lunar spacecraft precision orbit determination has been performed during the Japanese lunar exploration mission SELENE. In consideration that there will be an orbiter and a return capsule flying around the moon during the Chinese lunar exploration future mission Chang’E-3, the contributions of the same beam VLBI in spacecraft precision orbit determination and lunar gravity field solution have been investigated. Our results show that the accuracy of precision orbit determination can be improved more than one order of magnitude after including the same beam VLBI measurements. There are significant improvements in accuracy of low and medium degree coefficients of lunar gravity field model obtained from combination of two way range and Doppler and the same beam VLBI measurements than the one that only uses two way range and Doppler data, and the accuracy of precision orbit determination can reach meter level.     

一种用于深空导航定位的新型DOR信标

甚长基线干涉测量(VLBI)是深空探测器导航定位的重要手段之一,深空探测器的VLBI观测通常采用差分单程测距(DOR)信标和双差单程测距(Delta-DOR)测量体制,精确地测量深空探测器相对于河外射电源的角距.相位杂散是影响Delta-DOR测量精度的主要误差源之一,针对这项误差研究了一种基于伪随机噪声调制方式的新型...     

GPS/Galileo组合导航的模糊度搜索空间

为了组合导航的载波相位模糊度固定,将目前在GPS中常用的模糊度固定方法--最小二乘降相关平差（LAMBDA）法直接应用于GPS/Galileo组合模糊度固定,发现其搜索空间的确定方法并不能很好地适应GPS/Galileo组合中模糊度维数较高的情况。通过对常规LAMBDA搜索空间确定方法的分析比较,在传统方法的基础上提出了一种专门针对高维模糊度固定的搜索空间确定方法--修正法确定模糊度搜索空间。通过对修正法进行仿真试验,证明该方法能保证在GPS/Galileo组合定位模式下实际备选模糊度个数基本与预先设定的备选模糊度个数一致,进而能在不降低模糊度固定成功率的基础上有效提高LAMBDA模糊度固定的搜索效率,其性能优于传统的模糊度搜索空间确定方法。     

A priori zenith wet delays in the analysis of VLBI CONT sessions

Tropospheric delay is one of the major sources of error in VLBI (Very Long Baseline Interferometry) analysis. The principal component of this error can be accurately computed through reliable surface pressure data —hydrostatic delay— yet there is also a small but volatile component —wet delay— which is difficult to be modelled a priori. In VLBI analysis, troposphere delay is typically modelled in the theoretical delays using Zenith Hydrostatic Delays (ZHD) and a dry mapping function. Zenith Wet Delay (ZWD) is not modelled but estimated in the analysis process. This work studies inter alia the impact of including external GNSS estimates to model a priori ZWD in VLBI analysis, as well as other models of a priori ZWD.In a first stage, two different sources of GNSS troposphere products are compared to VLBI troposphere estimates in a period of 5 years. The solution with the best agreement to VLBI results is injected in the VLBI analysis as a priori ZWD value and is compared to other options to model a priori ZWD. The dataset used for this empirical analysis consists of the six CONT campaigns.It has been found that modelling a priori ZWD has no significant impact either on baseline length and coordinates repeatabilities. Nevertheless, modelling a priori ZWD can change the magnitude of the estimated coordinates a few millimeters in the up component with respect to the non-modelling approach. In addition, the influence of a priori ZWD on Earth Orientation Parameters (EOP) and troposphere estimates —Zenith Total Delays (ZTD) and gradients—has also been analysed, resulting in a small but significant impact on both geodetic products.     

Polarization VLBI observations of AGN jets now and into the future

The history of Very Long Baseline Interferometry (VLBI) observations has been characterized predominantly by an ongoing quest for increasingly high resolution and sensitivity. VLBI monitoring of relatively large samples of Active Galactic Nuclei (AGNs) with uniform quality and linear polarization sensitivity are now available at the moderately high frequencies of 15 and 43 GHz. This has enabled considerable advances in our understanding of the relativistic jets of AGNs, but gaps in the available observational material remain, which must be addressed in future VLBI polarization observations. Linear polarization observations at frequencies above 43 GHz remain non-routine, and the availability of multi-frequency and circular polarization measurements is still limited. It is of interest both to push inward toward the jet base and to study details of the jets themselves on parsec scales, such as magnetic field structures along and across the jets, which are intrinsically related to their formation, launching and propagation. Requirements for future VLBI polarization observations are considered, highlighting the key role that can be played by space VLBI observations. Unique opportunities are offered by relatively low-frequency space VLBI observations that are sensitive to effects such as Faraday rotation, opacity, and low-frequency absorption.     

Near real-time PPP-based monitoring of the ionosphere using dual-frequency GPS/BDS/Galileo data

Ionosphere delay is very important to GNSS observations, since it is one of the main error sources which have to be mitigated even eliminated in order to determine reliable and precise positions. The ionosphere is a dispersive medium to radio signal, so the value of the group delay or phase advance of GNSS radio signal depends on the signal frequency. Ground-based GNSS stations have been used for ionosphere monitoring and modeling for a long time. In this paper we will introduce a novel approach suitable for single-receiver operation based on the precise point positioning (PPP) technique. One of the main characteristic is that only carrier-phase observations are used to avoid particular effects of pseudorange observations. The technique consists of introducing ionosphere ambiguity parameters obtained from PPP filter into the geometry-free combination of observations to estimate ionospheric delays. Observational data from stations that are capable of tracking the GPS/BDS/GALILEO from the International GNSS Service (IGS) Multi-GNSS Experiments (MGEX) network are processed. For the purpose of performance validation, ionospheric delays series derived from the novel approach are compared with the global ionospheric map (GIM) from Ionospheric Associate Analysis Centers (IAACs). The results are encouraging and offer potential solutions to the near real-time ionosphere monitoring.     

Mechanism of error propagation from the subdaily Universal Time model into the celestial pole offsets estimated by VLBI

Within the analysis of space geodetic observations, errors of the applied subdaily Earth rotation model can induce systematic effects in different estimated parameters. In this paper, we focus on the impact of the subdaily Universal Time (UT1) model on the celestial pole offsets (CPO) estimated from very long baseline interferometry (VLBI) observations. We provide a mechanism that describes the error propagation from the subdaily UT1 into the daily CPO.In typical 24-h VLBI sessions the observed quasars are well distributed over the sky. But the observations, if looked at from the Earth-fixed frame, are not homogeneously distributed. The amount of observations performed in different terrestrial directions shows an irregularity which can be roughly compared to the case where the observations are collected in only one Earth-fixed direction. This peculiarity leads to artefacts in VLBI solutions, producing a correlation between the subdaily variations in UT1 and the position of the celestial pole. As a result errors in diurnal terms of the subdaily UT1 model are partly compensated by the estimated CPO. We compute for each 24-h VLBI session from 1990 until 2011 the theoretical response of the CPO to an error in the subdaily UT1 by setting up a least-squares adjustment model and using as input the coordinates of the observed quasars and observation epochs. Then real observed response of the estimated CPO derived from the VLBI session solutions is compared to the predicted one. A very good agreement between the CPO values estimated from VLBI and the predicted values was achieved. The presented model of error propagation from the subdaily UT1 into the daily CPO allows to predict and explain the behaviour of CPO estimates of VLBI solutions computed with different subdaily Earth rotation models, what can be helpful for testing the accuracy of different subdaily tidal models.     

Ambiguity resolution performance with GPS and BeiDou for LEO formation flying

The evolving BeiDou Navigation Satellite System constellation brings new opportunities for high-precision applications. In this contribution the focus will be on one such application, namely precise and instantaneous relative navigation of a formation of LEO satellites. The aim is to assess the ambiguity resolution performance with the future GPS and BeiDou constellations depending on system choice (GPS, BeiDou, or GPS+BeiDou), single- or dual-frequency observations, receiver noise, and uncertainties in ionosphere modelling. In addition, for the GPS+BeiDou constellation it will be shown how the growing BeiDou constellation in the years to come can already bring an important performance improvement compared to the GPS-only case. The performance will be assessed based on the percentage of time that the required precision can be obtained with a partial ambiguity resolution strategy.     

Precise line-of-sight vector estimation based on an inter-satellite radio frequency system

This paper proposes a precise line-of-sight (LOS) vector estimation using an inter-satellite radio frequency system. GNSS-like technology is inherited such that the ranging signals are locally generated inside the formation. However, the approach differs from the standard GNSS model usage in that the LOS vector to be of a unit length is fully explored as a priori constraint for the carrier phase integer ambiguity resolution. The constraint is lumped to the mapping process from the real-valued ambiguities to the integers by what is called validation or subset ambiguity bounding. These two approaches have the same rules of regarding the constraint as a gateway to accept or reject the ambiguity candidates, but differ by using “all-ambiguity-set” and “subset-ambiguity”. Both show remarkable improvement with up to 80% lower integer fixing failure rates than without treating the constraint. Validation provides a slightly better performance than the subset ambiguity bounding in terms of the integer fixing failure rates and the computational efficiency. The predefined tolerance regions that are critical for these two methods are analytically determined as function of the carrier noise. The paper also introduces a LOS dependent ambiguity dilution of precision (ADOP_LOS) measure that can serve as a metric to characterize the expectation of being able to successfully resolve the ambiguities. The region of ADOP_LOS lower than 0.21 is empirically summarized as the safe region where the integer fixing failure rates are less than 1%. A closed form of the ADOP_LOS is derived which is able to capture the impact of the various factors. Antenna baseline geometries and multiple frequencies in the form of an ultra-BOC signal structure are demonstrated as the most important influencing factors. With multiple properly arrayed antennas and using ultra-BOC structure, instantaneous ambiguity resolution can be achieved and the LOS accuracy can reach millimeter level.