In recent years, space VLBI observation technology has made great breakthroughs. The development of this technology has enabled telescopes from different stations on Earth to simultaneously observe distant radio-powered objects and synthesize their signals to obtain more accurate data. However, to achieve this magnificent synthesis, complex and precise steps are required.
First, we need to understand that radio signals from the universe are often considered plane waves, but due to differences in position between different observatories, the timing of these signals to reach the telescope at each station varies. Therefore, when processing these signals, they must be delayed compensated and phase aligned to ensure that they are perfectly aligned to the same wavefront. Only after accurate compensation of delay and phase can the signal data of each station be weighted in the full spectrum.
To better understand this process, we can consider the signals received by a telescope. This signal can be expressed as Ri(t), where i represents the telescope number. After mixing mediation, we get A(t) as the baseband signal at the center of the earth, Ni(t) as the noise signal, and f0 as the sky frequency. In order to synchronize the signals of all telescopes to the same moment, the relevant processors need to perform delay compensation and phase adjustment of the baseband signals recorded by each telescope to achieve signal synchronization.
In the Earth-Moon Space VLBI, we use a weighted full-spectrum signal synthesis technique, which is as follows. First, after the signals of ground-based telescopes X and Y are compensated by a priori delay model, there may still be some residual delay and residual delay rate. Therefore, we perform the calculation of the mutual power spectrum and use the mutual power spectrum for fringe fitting, so as to obtain the residual delay and residual delay rate information. To maximize the baseline signal-to-noise ratio after synthesis, we need to adjust the phases between the different telescopes so that their signals are perfectly aligned. In this process, we search for phase φ to achieve the highest signal-to-noise ratio of the synthesized signal-to-noise ratio. This optimal phase will be used to compensate for the signals from station X to ensure that the signals from station X and station Y can be synthesized efficiently.
To achieve this process, we need to refer to the center of the earth as a reference point. First, the signals of ground-based telescopes X and Y are integer bit compensated and fringed rotated in the time domain, and then converted to the frequency domain by a fast Fourier transform. In the frequency domain, we perform fractional bit compensation, then reverse FFT back to the time domain, and then phase align for weighted full-spectrum synthesis. This synthesized signal can be VLBI interfered with space telescopes or other telescopes.
In our study, we used VLBI observations from the Chinese lunar exploration project mission Chang'e-4 for verification. These observations come from the Kunming 40-meter telescope, the Urumqi Nanshan 26-meter telescope and the Shanghai Tianma 65-meter telescope. By analyzing this data, we can determine the optimal weighting factor to achieve the highest baseline signal-to-noise ratio. The experimental results show that when the signal proportions of Km station and Ur station are 47% and 53%, respectively, the signal-to-noise ratio of the baseline processing results of Km+Ur synthesis station and Tm station reaches the highest value. This result shows that our weighted full-spectrum synthesis algorithm can significantly improve the baseline signal-to-noise ratio, thereby improving the sensitivity of the baseline.
We also verify the stability of the optimal weighting coefficient. First, we check whether the optimal weighting coefficient of the same observation source is stable at different observation times and different observation codes. The experimental results show that the optimal weighting coefficient of different observation times and observation sources is stable under the same observation code, which indicates that the parameter stability of the telescope also has an impact on the optimal weighting coefficient. In addition, we verify the stability of the optimal weighting coefficients of different radio sources under different observation codes. The experimental results show that the optimal weighting coefficient of different radio sources is stable under the same observation code, but the optimal weighting coefficient of the radio source may change under different observation codes, which is related to the change of the telescope state. In general, the stability of the optimal weighting coefficient depends on the nature of the observation source and the state of the telescope.
In summary, we design a weighted full-spectrum synthesis algorithm based on VLBI raw signal, which can greatly improve the baseline signal-to-noise ratio by meshing to search for the optimal weighting coefficient, thereby improving the sensitivity of the baseline. The key to this algorithm is the determination of the optimal weighting coefficient, which is only related to the performance parameters of the telescope
Related, independent of the characteristics of the observation source itself. This means that we can use the same optimal weighting coefficient under different observation conditions, which improves the versatility of the algorithm and the convenience of practical application.
By verifying the optimal weighting coefficients under different observation codes and observation times, we confirm the stability and reliability of the algorithm. Whether the same observation source is under different observation times, or different observation sources are in the same observation code, the optimal weighting coefficient can remain stable, which provides a feasible scheme for long-term and continuous VLBI observation.
In addition, our study shows that the optimal weighting coefficient remains stable when the baseline signal-to-noise ratio remains stable. This means that once we have determined the optimal weighting coefficient for a particular observation, it can be reused under similar observational conditions without recalculation, improving the efficiency of data processing.
In conclusion, the weighted full-spectrum synthesis algorithm based on VLBI raw signal provides an effective data processing method for spatial VLBI observation. Through the determination of the optimal weighting coefficient and the stability verification, we can obtain a higher baseline signal-to-noise ratio under different observation conditions, which improves the quality of the observation data and the sensitivity of the baseline. The successful application of this algorithm has provided strong support for radio astronomy research and the development of cosmic science, allowing us to explore the mysteries of the universe in greater depth. The future development of the space VLBI will benefit from the continuous optimization and improvement of this algorithm, bringing us more wonderful discoveries about the universe.
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