Connected-element Interferometry Research Articles

A CEI-Based Method for Precise Tracking and Measurement of LEO Satellites in Future Mega-Constellation Missions

With the development of low-orbit mega-constellations, low-orbit navigation augmentation systems, and other emerging LEO projects, the tracking accuracy requirement for low-orbit satellites is constantly increasing. However, existing methods have obvious shortcomings, and a new tracking and measurement method for LEO satellites is thus urgently needed. Given this, in this paper, a Connected Element Interferometry (CEI)-based “near-field” measurement model for low-orbit satellites is proposed. On this basis, the goniometric error formula of the model is derived, and the factors included in each error source are briefly discussed, followed by the simplification of the error formula. Furthermore, for the feasibility analysis of the proposed method, the common view time of CEI array on LEO satellites is analyzed in different regions and different baseline lengths. Finally, this paper simulates the effects of satellite–station distance, baseline length, and goniometric angle on the error coefficients in the goniometric error formula, and provides the theoretical goniometric accuracy of this model for different baseline lengths and goniometric angles. Under a baseline length of 240 km, the accuracy can reach 10 nrad. The research results of this paper could play the role of theoretical a priori in accuracy prediction in future low-orbit satellite tracking measurements.

A Measurement Method for Cislunar Spacecraft Based on Connected Element Interferometry and BeiDou-3 Interplanetary Link in Future Lunar Exploration

To meet the urgent need for high-precision tracking and reliable cataloging of non-cooperative targets in the Earth–Moon space, this paper proposes a GNSS Inter-Satellite Link and Connected Element Interferometry (CEI)-based measurement method for high-value cislunar space targets. Firstly, the general flow and basic scenario of the proposed method are given, followed by the mathematical model which, mainly includes four parts: (i) dynamical constraint equations for targets; (ii) GNSS-based interplanetary link for irradiation of targets; (iii) transmission loss equation of GNSS inter-satellite link signal in Earth–Moon space; (iv) CEI-based precision measurements of targets. On this basis, the full process link budget analysis is carried out, followed by the performance evaluation, which includes the reception performance of CEI receiving arrays and the measurement accuracy of targets. The feasibility of the proposed method is evaluated and verified in experiments, and it is illustrated that (i) for inter-satellite link visibility analysis, at least 20 satellites can simultaneously provide inter-satellite link signals to the Earth–Moon space targets, with a single GEO satellite up to 8.5 h continuously, while the chain access can be available at up to 73,000 km, with the angle ranging from −80∘ to 360∘; (ii) the Max Duration of Chain Access for BD3-lunarprobe-CEI (from 24 March 2023 04:00:00.000 to 31 March 2023 10:00:00.000) is 50,998.804 s/day, with a Total Duration of 358,408.797 s in 7 days; (iii) for link budget and measurement accuracy analysis, even beyond the farthest Earth–Moon Lagrangian point, the C/N0 will be above 56.1 dBHZ, while even approaching the distances of 4.5×105km, the σDLL and σFLL will be below 5.345 m and 3.475×10−4 m/s, respectively, and the final measurement error will remain at 62.5 m with the proposed method. The findings of this paper could play a key role in future increasingly serious space missions, such as Earth–Moon space situational awareness, and will have a broad application prospect, if put into actual testing and operations.

Investigation on GEO satellite orbit determination based on CEI measurements of short baselines

Connected-Element Interferometry (CEI) is a technique for measuring the phase delay of difference of Time Of Arrival (TOA) of a downlink radio signal to two antennae on a short baseline. This technique can use an atomic clock for time-frequency transmission and achieve intermediate accuracy angular tracking. Owing to the relatively short length of the baseline, the passive reception mode, and near real-time operation, CEI can be used to continuously monitor the orbit variations of both cooperative and non-cooperative satellites. In this paper, a small-scale CEI system of two orthogonal baselines (75 m × 35 m) is investigated to track a Geostationary Earth Orbit (GEO) Television (TV) satellite at 110·5°E. The phases are extracted from correlation results. The results show that the Root Mean Square (RMS) of the phase fitting residuals, if not calibrated, is within 2° at night and up to 10° in the daytime. After applying the calibration signal, the RMS of the phase fitting residuals in the daytime decreases to the same level at night. Comparing the phase delay with the a priori phase delay using Two-Line-Element (TLE) data, the integer ambiguity is successfully resolved. Finally, a batch algorithm is used to estimate the orbit of the GEO satellite, and the orbit determination accuracy is evaluated using the precise orbits provided by the China National Time Service Centre (NTSC). The results show that the accuracies in the radial direction and the cross-track direction are less than 1 km, and the Three-Dimensional (3D) position accuracy reaches the 2 km order of magnitude.

An approved frequency tracking method in connected element interferometry

Carrier tracking loop is a basic method of frequency tracking in CEI (connected element interferometry), but the tracking error is very large or even worse at high dynamic. To solve this problem, a frequency tracking method assisted by open loop frequency estimation is proposed in this paper. First, an open-loop frequency estimation algorithm is used to estimate the frequency of signals at different moments, then, the least squares fitting method is used to estimate the corresponding dynamic parameters of different orders. Next, a local signal is generated to compensate the received signal. After eliminating most of the dynamic characteristics, the signal is fed into PLL (Frequency locked loop) and high-precision frequency tracking results can be obtained. Simulation results show that, in the condition of low SNR, the new method has higher accuracy than the method assisted by FLL (Frequency locked loop), and the processing time is shorter. When there is a two order Doppler frequency change, the open-loop assisted method can overcome the steady phase error of the PLL, and is of great significance in the applications of connected elements interferometry.

Research of Ambiguity Solution in CEI-based Orbit Determination

相位干涉测量是一种被动测角跟踪方法, 其中的中短基线相位干涉测量(CEI)具有测角精度高、基线短、布网灵活、实时性好等特点. 分析采用CEI对GEO卫星定轨时初始整周模糊度解算的可行性, 由于中继卫星的初始轨道精度较低, 对其定轨时必须首先解决模糊度问题. 主控站具有测距功能时, 利用精度较高的距离观测量来计算整周模糊度; 主控站没有测距功能时, 提出了固定模糊度参数的参数估计方法. 仿真计算表明, 系统误差小于1.0 m时该方法效果较好. 给出了该方法对星下点在中国上空一定经度带上的GEO卫星网的整体定轨能力, 当系统误差为0.1 m时, 110°E卫星的迹向精度达到25 m, 对于80°E, 140°E卫星, 迹向精度分别达82 m, 34 m.

DETECTING CHANGING POLARIZATION STRUCTURES IN SAGITTARIUS A* WITH HIGH FREQUENCY VLBI

Sagittarius A* is the source of near infrared, X-ray, radio, and (sub)millimeter emission associated with the supermassive black hole at the Galactic Center. In the submillimeter regime, Sgr A* exhibits time-variable linear polarization on timescales corresponding to <10 Schwarzschild radii of the presumed 4 million solar mass black hole. In previous work, we demonstrated the potential for total-intensity (sub)millimeter-wavelength VLBI to detect time-variable -- and periodic -- source structure changes in the Sgr A* black hole system using nonimaging analyses. Here we extend this work to include full polarimetric VLBI observations. We simulate full-polarization (sub)millimeter VLBI data of Sgr A* using a hot-spot model that is embedded within an accretion disk, with emphasis on nonimaging polarimetric data products that are robust against calibration errors. Although the source-integrated linear polarization fraction in the models is typically only a few percent, the linear polarization fraction on small angular scales can be much higher, enabling the detection of changes in the polarimetric structure of Sgr A* on a wide variety of baselines. The shortest baselines track the source-integrated linear polarization fraction, while longer baselines are sensitive to polarization substructures that are beam-diluted by connected-element interferometry. The detection of periodic variability in source polarization should not be significantly affected even if instrumental polarization terms cannot be calibrated out. As more antennas are included in the (sub)mm-VLBI array, observations with full polarization will provide important new diagnostics to help disentangle intrinsic source polarization from Faraday rotation effects in the accretion and outflow region close to the black hole event horizon.

Ionospheric scintillation observations with radio interferometry

Radio astronomical interferometric observations are affected by atmospheric refraction, being particularly sensitive to inhomogeneities in the atmosphere. At frequencies below 2 GHz the influences of the ionosphere are significant in radio astronomy, especially for single dish observations and for connected element interferometry. Analytical expressions for the manifestations of weak ionospheric scintillation in radio interferometric observations, are derived. We indicate which ionospheric scintillation parameters can be derived from radio interferometric measurements. It is shown that the baseline dependence of the observed amplitude scintillation index implies a direct determination of the height of the region of random irregular electron distribution. Furthermore, the linear scale of the irregularities causing scintillation can be determined directly from the baseline dependence of the scintillation index S 4. From the mean square phase fluctuations as a function of interferometer baseline, the spatial scale of the irregularities responsible for this effect can also be determined. From a comparison with observational mid-latitude data we find indications that scintillation irregularities occur in the lower parts of the F2-layer. The spatial scale of irregularities causing amplitude scintillation is of the order of about 25 to about 500 metres. Phase scintillations are caused by irregularities with dimensions which are an order of magnitude larger.