Reconstruction method of quadratic time delay model of radio sources for space VLBI
By adopting data segmentation processing and fitting segmented data under reasonable constraints in space VLBI, a quadratic time delay model of radio sources is constructed, which solves the problem of increased computational complexity in existing technologies, realizes high-precision reconstruction of radio source delay models, and improves the accuracy and reliability of space VLBI data processing.
Patent Information
- Application Number
- CN202210687084.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-16
- Publication Date
- 2025-09-16
- Estimated Expiration
- 2042-06-16
AI Technical Summary
The existing multi-grid fringe search algorithm cannot guarantee the delay accuracy of the correlation processor model over a long time range when constructing the radio source prediction delay model for space VLBI. Moreover, adding a quadratic term to the delay model will increase the computational complexity and affect the algorithm usability.
Without increasing the computational complexity, a quadratic time delay model of radio sources is constructed by segmenting the data and fitting the segmented data under reasonable constraints, including steps S1 to S6. Grid division and Fourier transform in the two-dimensional time delay-delay rate space are used to reconstruct a high-precision quadratic time delay model of radio sources.
While keeping the computational complexity unchanged, a high-precision quadratic delay model of the radio source was obtained, which improved the accuracy and reliability of space VLBI data processing.
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Figure CN115097532B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of radio interference technology, and more particularly to a method for reconstructing a quadratic term time delay model of a radio source for space VLBI. Background Art
[0002] Very Long Baseline Interferometry (VLBI) is a radio interferometry technique characterized by high resolution and high precision. It uses a highly stable independent local oscillator system and data acquisition device controlled by an atomic clock to simultaneously receive target source signals through multiple telescopes, record the data, and send it to a remote VLBI data processing center for processing to obtain the observation results. Two radio telescopes on the same baseline receive detector or radio source signals, and the signal delay is obtained through correlation, which is further processed to obtain the spatial position of the signal source. In VLBI observations, the distance between the two radio telescopes is called the baseline, which is one of the important factors determining VLBI resolution. The theoretical maximum baseline length of a ground-to-ground baseline is the diameter of the Earth. However, if a space telescope and a ground-based telescope form an air-to-ground baseline, the baseline length can exceed the diameter of the Earth, achieving higher resolution.
[0003] The Chinese VLBI Network (CVN) consists of five stations and one center: Sheshan, Tianma, Miyun, Nanshan, and Kunming, along with a VLBI data processing center in Shanghai. Observational data from the five stations are transmitted via a network to the VLBI data processing center, where VLBI measurements are obtained through a series of operations, including correlation processing, post-processing, and orbit determination and positioning. The correlation processor is the core of VLBI data processing and relies on a high-precision predicted delay model. This model reflects the time difference between the arrival of the same signal wavefront at the station and a reference point (usually the center of the Earth). It is calculated based on information such as the target source ephemeris, Earth orientation parameter (EOP), and station coordinates. The radio telescopes used in all the successfully completed lunar exploration missions and Mars missions were all on Earth. Extensive pre-mission calibrations have yielded extremely accurate station coordinates and instrument delays. The high-precision radio source predicted delay model calculated based on this model meets the requirements of the correlation processor.
[0004] In recent years, my country has been advancing space-based VLBI projects, launching radio telescopes into space and integrating them with ground-based telescopes to form space-based VLBI systems. For example, my country's upcoming fourth lunar exploration mission will utilize the 4.1-meter parabolic antenna on the Chang'e-7 relay satellite to conduct lunar-terrestrial VLBI experiments. Unlike ground-based VLBI, the radio source prediction delay models used for space-based VLBI can produce significant errors due to the influence of the relay satellite's orbital perturbations and equipment delays, making them incapable of guiding the relevant processors to function properly. Furthermore, inaccurate radio source prediction delay models can lead to observation failures.
[0005] Most current methods for constructing forecast delay models use a multi-grid fringe search algorithm. The basic idea behind this algorithm is to divide the two-dimensional delay-delay rate plane into multiple layers based on different search step sizes. The initial layer has a low resolution and a large search step. After determining the coarse search results, the search step size is reduced and the resolution is increased within the coarse search range to continue the refined search. This process is repeated multiple times to achieve a result that meets the required accuracy.
[0006] The existing multi-grid fringe search algorithm searches in the two-dimensional space of time delay and time delay rate, obtaining a linear delay model with time as the independent variable. This algorithm is suitable for application scenarios where the radio source signal is strong and fringes can be obtained by integrating for a short time. Due to technical limitations, the aperture of space antennas is usually much smaller than that of ground antennas, so the received radio source signal is weak. In order to improve the signal-to-noise ratio during data processing to obtain interference fringes, a longer integration time is required. However, the linear delay model cannot guarantee the delay accuracy of the correlation processor model over a longer time range, and it is necessary to try to construct a more accurate quadratic delay model. However, if the quadratic delay term is directly added to the conventional multi-grid, the search space will expand from two dimensions to three dimensions, and the computational complexity will increase by an order of magnitude, which will greatly affect the usability of the algorithm. Summary of the Invention
[0007] To solve the above problems in the prior art, the present invention provides a method for reconstructing a quadratic time delay model of a radio source for space VLBI, which can obtain a high-precision quadratic time delay model of a radio source without increasing the complexity to process space VLBI data.
[0008] The present invention provides a method for reconstructing a quadratic delay model of a radio source for space VLBI, comprising:
[0009] Step S1, according to a preset observation plan, determining parameter information for space VLBI, and obtaining a radio source baseband signal sequence of a first station and a radio source baseband signal sequence of a second station;
[0010] Step S2: determining a search range in the two-dimensional delay-delay rate space, determining a search step size based on parameter information for spatial VLBI, and dividing the two-dimensional delay-delay rate space into a grid based on the search range and the search step size, where the search step size includes a delay step size and a delay rate step size.
[0011] Step S3: for each divided grid point, performing segmented processing on the radio source baseband signal sequence of the first station and the radio source baseband signal sequence of the second station to obtain the maximum correlation amplitude mean corresponding to each grid point;
[0012] Step S4, finding the grid point with the largest maximum correlation amplitude mean;
[0013] Step S5: reconstructing a quadratic delay model of a radio source for space VLBI based on the grid point with the largest mean value of the maximum correlation amplitude.
[0014] Furthermore, the method for grid division in step S2 is: with the delay as the x-axis, the delay rate as the y-axis, the delay A0 and the delay rate B0 as the coordinate origin, a two-dimensional coordinate system is established, and the two-dimensional space is divided into I*J grids according to the delay step Δa and the delay rate step Δb in the search step; wherein, the delay A0 and the delay rate B0 are the starting points of the search range.
[0015] Furthermore, step S3 includes:
[0016] Step S31: for any grid point (i, j), construct its initial time delay model τ(t);
[0017] Step S32: The baseband signal sequence of the second radio source of the second station with a length of 2BT is converted to Evenly divide into K data segments, the length of each data segment is N, where K = 2BT / N, B represents the channel bandwidth, T represents the data duration, and N is one of the spectral channels of the two-dimensional Fourier transform, 0≤n<2BT;
[0018] Step S33: Based on the radio source baseband signal sequence of the second station The segmented data and the initial time delay model τ(t) of any grid point (i, j) are used to calculate the baseband signal sequence {s n} to segment;
[0019] Step S34, according to the radio source baseband signal sequence {s n} and the second station's radio source baseband signal sequence Segmented data, get K segments of length N / 2 sequence Among them, the superscript k represents the kth segment of data, and the subscript n represents the sequence number within the segment;
[0020] Step S35: K segments of sequence with length N / 2 Divide into P = K / M groups, each group has M segments, and perform Fourier transform on each group to obtain the residual delay Δa p and residual delay rate Δb p The correlation amplitude function F(Δa p ,Δb p ); where M is one of the spectral channels of the two-dimensional Fourier transform;
[0021] Step S36, obtaining the maximum correlation amplitude of each group in the P groups according to the two-dimensional Fourier transform residual delay-delay rate search graph;
[0022] Step S37: Calculate the mean of the maximum correlation amplitudes of the P groups according to the maximum correlation amplitude of each group.
[0023] Furthermore, the step S34 includes:
[0024] Step S341: perform fringe rotation on the kth segment of data from the first station, and perform fast Fourier transform on the fringe-rotated data with a spectral channel number of N to obtain the sequence kN+m≤n<(k+ 1)N+m;
[0025] Step S342, the sequence obtained in step S341 Perform fractional delay compensation and obtain the sequence after fractional compensation
[0026] Step S343: Perform a fast Fourier transform with N spectral channels on the kth segment of data from the second station to obtain the sequence
[0027] Step S344: the sequence obtained in step S342 and the sequence obtained in step S343 Conjugate and multiply the first N / 2 terms of to get a sequence of length N / 2
[0028] Step S345, repeat steps S341 to S344 until all K segments of data are processed.
[0029] Furthermore, the step S5 includes:
[0030] Step S51: for the grid point (I max ,J max ), and construct its initial delay model as follows:
[0031]
[0032] in, Represents the grid point (I max ,J max ) initial delay, Represents the grid point (I max ,J max )’s initial delay rate;
[0033] Step S52, obtain the grid point (I max ,J max ) corresponding to the residual delay and residual delay rate of group P {(Δa p ,Δb p ),0≤p<P}, the initial delay and delay rate and the residual delay and residual delay rate of group P (Δa p ,Δb p ) are added together to obtain the delay and delay rate of each group of P data at the start time {(a p ,b p ),0≤p<P};
[0034] Step S53: Correct the delay of each set of data according to the continuity requirement and obtain the corrected delay item
[0035] Step S54, fitting the quadratic delay coefficient according to the corrected delay term;
[0036] Step S56: Obtain the final radio source quadratic delay model based on the fitted quadratic delay coefficient.
[0037] The present invention maintains the search space of the two-dimensional space of time delay and time delay rate unchanged, constructs a quadratic time delay model through data segmentation processing and fitting the segmented data under reasonable constraints, and can obtain a high-precision radio source delay model while the computational complexity does not increase by orders of magnitude. BRIEF DESCRIPTION OF THE DRAWINGS
[0038] Figure 1 The present invention is a flow chart of a method for reconstructing a quadratic time delay model of a radio source for space VLBI.
[0039] Figure 2 is the two-dimensional Fourier transform residual delay-delay rate search graph.
[0040] Figure 3 is the correlation magnitude map obtained using the existing multi-grid search algorithm.
[0041] Figure 4 is used Figure 3 The peak point of the correlation amplitude corresponds to the correlation processing result diagram of the time delay model.
[0042] Figure 5 This is a correlation amplitude diagram obtained by using the radio source quadratic term time delay model reconstruction method for space VLBI of the present invention.
[0043] Figure 6 is used Figure 5 The correlation processing result diagram of the time delay model corresponding to the correlation amplitude peak point. DETAILED DESCRIPTION
[0044] The preferred embodiments of the present invention are given below in conjunction with the accompanying drawings and described in detail.
[0045] like Figure 1 As shown, the method for reconstructing the quadratic term delay model of a radio source for space VLBI provided by the present invention includes the following steps:
[0046] Step S1: According to a preset observation plan, parameter information for space VLBI is determined, and a radio source baseband signal sequence of a first station and a radio source baseband signal sequence of a second station are obtained.
[0047] The parameter information used for spatial VLBI includes: channel bandwidth B, sampling rate 2B, data duration T, sky frequency f0, and the number of spectrum channels N and M of the two-dimensional Fourier transform. The baseband signal sequence of the radio source of the first station is denoted as {s n}, the baseband signal sequence of the radio source of the second station is recorded as Moreover, the length of the baseband signal sequence of the radio sources of the two stations is 2BT, 0≤n<2BT.
[0048] Step S2: determining a search range in the two-dimensional delay-delay rate space, determining a search step size according to parameter information for spatial VLBI, and dividing the two-dimensional delay-delay rate space into grids according to the search range and the search step size.
[0049] The search range is determined by the known prediction delay model and the design parameters of the hydrogen oscillator. For example, assuming the delay and delay rate distributions in the prediction delay model are a0 and b0, and the delay and delay rate accuracy ranges of the hydrogen oscillator are a1 and b1, respectively, then the delay search range is (a0-a1) to (a0+a1), denoted as A0~A1; the delay rate search range is (b0-b1) to (b0+b1), denoted as B0~B1.
[0050] The delay step Δa and the delay rate step Δb are determined according to the following formula:
[0051]
[0052]
[0053] The method of grid division is as follows: taking the time delay as the x-axis, the time delay rate as the y-axis, and the time delay A0 and the time delay rate B0 as the coordinate origin, a two-dimensional coordinate system is established, and the two-dimensional space is divided into an I*J grid according to the time delay step Δa and the time delay rate step Δb. I and J satisfy:
[0054]
[0055]
[0056] Step S3: For each grid point divided, segment the radio source baseband signal sequence of the first station and the radio source baseband signal sequence of the second station, and obtain the average value of the maximum correlation amplitude corresponding to each grid point. Step S3 includes:
[0057] Step S31: For any grid point (i, j), construct its initial time delay model τ(t) as follows:
[0058] τ(t) = a i + b j t (5)
[0059] a i = A0 + i*Δa, 0 ≤ i < I (6)
[0060] b j = B0 + j*Δb, 0 ≤ j < J (7)
[0061] The initial time delay model reflects the time difference of the same wavefront signal of the radio source arriving at the two stations. Since the relative positions between the radio source and the stations change at all times, τ(t) is a function of time. Next, taking the signal of B station as the reference, using the FX-type correlation processing algorithm, the signal sequence {s n} of the first station is model-corrected and correlated with the signal sequence of the second station, and then the residual time delay and the time delay rate are obtained using the two-dimensional Fourier transform. correlation processing, and then use the two-dimensional Fourier transform to find the residual time delay and the time delay rate.
[0062] Therefore, in step S32, since one of the spectral channels of the two-dimensional Fourier transform is N, the signal sequence of the second station with a length of 2BT is evenly divided into K data segments, and the length of each data segment is N, where K = 2BT / N, and the kth (0 < k < K) segment of the second station's data starts from beginning.
[0063] Step S33: According to the segmented data of the signal sequence of the second station and the initial time delay model τ(t) of any grid point (i, j), segment the signal sequence {s n} of the first station.
[0064] Specifically, the starting time of the kth segment of data at the second station is The signal lags at this moment Arriving at the first station, make integer delay compensation for the first station, and take [] is the rounding symbol, so the kth segment of data at the first station is from s kN+m Initially, the fractional delay is
[0065] The data of the second station is directly segmented, and the data of the first station is compensated for integer delay according to the initial delay model, so that the data of the same segment number of the two stations are on the same wave front of the radio source signal.
[0066] Step S34: Obtain K segments of sequence with a length of N / 2 based on the segmented data of the first station and the second station. The superscript k represents the kth segment of data, and the subscript n represents the sequence number within the segment.
[0067] The specific steps include:
[0068] Step S341, perform stripe rotation on the kth segment of data of the first station, and perform stripe rotation on the data after stripe rotation. Perform fast Fourier transform with N spectral channels to obtain the sequence kN+m≤n< (k+1)N+m. The formula for fringe rotation is as follows:
[0069]
[0070] Step S342, the sequence obtained in step S341 Perform fractional delay compensation and obtain the sequence after fractional compensation Sequence after decimal compensation Calculate according to the following formula:
[0071]
[0072] in, It should be noted that, due to the conjugate symmetry of the spectrum of a real signal, only the sequences numbered 0≤i<N / 2 need to be considered.
[0073] Step S343: Perform a fast Fourier transform with N spectral channels on the kth segment of data from the second station to obtain the sequence
[0074] Step S344: The sequence of length N / 2 obtained in step S342 is and the sequence obtained in step S343 Conjugate and multiply the first N / 2 terms of to get a sequence of length N / 2 Right now:
[0075]
[0076] Wherein, * indicates conjugation.
[0077] Step S345, repeat steps S341-S344 until all K segments of data are processed. In this way, K segments of sequences with a length of N / 2 can be obtained.
[0078] Step S35: Since one of the spectral channels of the two-dimensional Fourier transform is M, K segments of the sequence with a length of N / 2 are converted into Divide into P = K / M groups, each group has M segments, and perform Fourier transform on each group to obtain the residual delay Δa p and residual delay rate Δb p The correlation amplitude function F(Δa p ,Δb p ):
[0079]
[0080] like Figure 2 As shown, select the appropriate residual delay and residual delay rate, the correlation amplitude F(Δa p ,Δb p ) has a maximum value. Therefore, in step S36, according to the two-dimensional Fourier transform residual delay-delay rate search map, the maximum correlation amplitude of each group in the P group is obtained, and the residual delay and delay rate corresponding to the maximum correlation amplitude are recorded as {(Δa p ,Δb p ),0≤p<P}.
[0081] Step S37: Calculate the mean of the maximum correlation amplitudes of the P groups based on the maximum correlation amplitude of each group.
[0082]
[0083] Step S4, find the grid point with the largest maximum correlation amplitude mean. For each grid point, perform the above steps S31 to S37 to obtain the maximum correlation amplitude mean. The two-dimensional grid size is I*J, so there are a total of I*J maximum correlation amplitude means. The coordinates of the grid point with the largest maximum correlation amplitude mean are recorded as (I max ,J max ).
[0084] Step S5: Reconstructing the quadratic delay model of the radio source for space VLBI based on the grid point with the largest maximum correlation amplitude mean. This includes:
[0085] Step S51: for the grid point (I max ,J max ), and construct its initial delay model as follows:
[0086]
[0087] in, Represents the grid point (I max ,J max ) initial delay, Represents the grid point (I max ,J max )’s initial delay rate.
[0088] Step S52, obtain the grid point (I max ,J max ) corresponding to the residual delay and residual delay rate of group P {(Δa p ,Δb p ),0≤p<P}, the initial delay and delay rate and the residual delay and residual delay rate of group P (Δa p ,Δb p ) are added together to obtain the delay and delay rate of each group of P data at the start time {(a p ,b p ),0≤p<P}:
[0089]
[0090]
[0091] VLBI observations require a continuous time delay model. However, in the process of solving the residual time delay and delay rate, data grouping results in discontinuities at the junction of two groups of data.
[0092] Therefore, in step S53, the delay of each group of data is corrected according to the continuity requirement to obtain the corrected delay item
[0093]
[0094]
[0095] Step S54: Fit the quadratic delay coefficient based on the corrected delay term. Assume that the unknown quadratic delay coefficient is [x0, x1, x2], and solve the polynomial of delay and delay rate as:
[0096]
[0097]
[0098] Step S56: Obtain the final radio source quadratic delay model based on the fitted quadratic delay coefficient. Specifically, the overdetermined system of equations (18) and (19) is established by combining them, and the unknowns [x0, x1, x2] are solved using QR decomposition. Finally, the delay model for radio source fringe search is obtained as:
[0099] τ(t)=x0+x1t+x2t 2 (20)
[0100] The following uses a specific example to illustrate that the existing heavy grid search algorithm cannot obtain a time delay model, but the present invention can obtain a time delay model.
[0101] 1) RadioAstro Project and Data Description
[0102] The RadioAstron project is a space-based very long baseline interferometry (VLBI) initiative proposed in the mid-1980s. In 2011, Russia launched the 10-meter-diameter RadioAstron space radio telescope (Spektr-R, Ra) satellite. Ra, along with several large ground-based radio telescopes, forms a space-based VLBI system with an orbital altitude of 600 km at perigee and 330,000 km at apogee.
[0103] The algorithm was validated using data from a joint observation of radio source 0823+033 in 2014 using the Ra, Arecibo Radio Telescope (Ar), and Westerbork Synthesis Radio Telescope (Wb). The observations started at 23:07:00 on April 11, 2014, and ended at 23:07:59 on April 11, 2014. The sky frequency was 4836 MHz, the bandwidth was 16 MHz, and the integration time was 8.192 e. -3 The data size after correlation processing is 60×120×8192, and the two-dimensional Fourier transform is performed using the data of each 120×8192 points as a group.
[0104] The search step size for delay and delay rate is:
[0105]
[0106]
[0107] The priori delay model is used as the center point of the search. The grid size of the delay and delay rate search is 20×200, and the search range of the delay is 6.33600e. -3 ~8.28160e-3 s, the search range of the delay rate is 1.62700e -6 ~4.13858e -6 s / s.
[0108] 2) Use the multi-grid search algorithm to process the results
[0109] Figure 3 This is the correlation amplitude graph using the multi-grid search algorithm. The grid coordinates corresponding to the peak point are (15,158), and the correlation amplitude value is 2.8690e -4 . Figure 4 The phase results of the peak point delay model are used for correlation processing, and there are no obvious interference fringes in the figure.
[0110] 3) Processing results using the method of the present invention
[0111] Figure 5 The correlation amplitude value obtained by the present invention is the grid coordinate (11,101) corresponding to the peak point, and the correlation amplitude value is 1.96700e -3 After fitting, the quadratic delay coefficient [7.36875e -3 ,2.88784e -6 ,-4.29989e -11 ]. Figure 6 Obvious fringes can be seen in the figure due to the phase results of the correlation processing using this quadratic time delay model.
[0112] Compared with the multi-grid grid search algorithm currently used for ground-based VLBI, the advantage of the present invention is that while maintaining the search space unchanged—the two-dimensional space of delay and delay rate, that is, the computational complexity does not increase by orders of magnitude—it solves the problem of constructing a quadratic delay model for searching for radio source signal stripes in space-based VLBI by processing data in segments and fitting segmented data under reasonably designed constraints.
[0113] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the present invention. Various modifications are possible. In other words, any simple, equivalent changes and modifications made in accordance with the claims and description of the present invention are within the scope of protection of the patent claims. Anything not fully described in this invention constitutes conventional technology.
Claims
1. A method for reconstructing a quadratic delay model of a radio source for space VLBI, characterized in that: include: Step S1, according to a preset observation plan, determining parameter information for space VLBI, and obtaining a radio source baseband signal sequence of a first station and a radio source baseband signal sequence of a second station; Step S2: determining a search range in the two-dimensional delay-delay rate space, determining a search step size based on parameter information for spatial VLBI, and dividing the two-dimensional delay-delay rate space into a grid based on the search range and the search step size, where the search step size includes a delay step size and a delay rate step size. Step S3: for each divided grid point, performing segmented processing on the radio source baseband signal sequence of the first station and the radio source baseband signal sequence of the second station to obtain the maximum correlation amplitude mean corresponding to each grid point; Step S4, finding the grid point with the largest maximum correlation amplitude mean; Step S5, reconstructing a quadratic delay model of a radio source for space VLBI based on the grid point with the largest mean value of the maximum correlation amplitude, comprising: Step S51: for the grid point with the largest maximum correlation amplitude mean , construct its initial delay model as follows: t， in, Represents grid points The initial delay, Represents grid points The initial delay rate of Step S52: Get grid points Corresponding residual delay and residual delay rate of group P }, the initial delay and delay rate and residual delay and residual delay rate of group P Add them up separately to get the delay and delay rate of each group of P data at the start time }; where P = K / M, K = 2BT / N, represents the channel bandwidth, represents the data duration, N is one of the spectral channels of the two-dimensional Fourier transform, and M is one of the spectral channels of the two-dimensional Fourier transform; Step S53: Correct the delay of each set of data according to the continuity requirement and obtain the corrected delay item }; Step S54, fitting the quadratic delay coefficient according to the corrected delay term; Step S56: Obtain the final radio source quadratic delay model based on the fitted quadratic delay coefficient.
2. The method for reconstructing a quadratic delay model of a radio source for space VLBI according to claim 1, wherein: The method of grid division in step S2 is: taking the delay as the x-axis, the delay rate as the y-axis, and the delay as the and latency As the coordinate origin, establish a two-dimensional coordinate system, according to the delay step in the search step and delay rate step size Divide the two-dimensional space into I*J grids; among them, the delay and latency is the starting point of the search range.
3. The method for reconstructing a quadratic delay model of a radio source for space VLBI according to claim 1, wherein: The step S3 comprises: Step S31: For any grid point (i, j), construct its initial delay model ; Step S32: The baseband signal sequence of the second radio source of the second station with a length of 2BT is converted to Evenly divided into K data segments, the length of each data segment is N, where K=2BT / N, represents the channel bandwidth, Indicates the data duration, N is one of the spectral channels of the two-dimensional Fourier transform, ; Step S33: Based on the radio source baseband signal sequence of the second station The segmented data and the initial delay model of any grid point (i, j) , for the baseband signal sequence of the radio source of the first station Segmentation; Step S34, according to the radio source baseband signal sequence of the first station The baseband signal sequence of the radio source of the second station Segmented data, get K segments of length N / 2 sequence ; Wherein, the superscript k represents the kth segment of data, and the subscript n represents the sequence number within the segment; Step S35: K segments of sequence with length N / 2 Divide into P = K / M groups, each group has M segments, and perform Fourier transform on each group to obtain the residual delay and residual delay rate The correlation amplitude function ; Wherein, M is one of the spectral channels of the two-dimensional Fourier transform; Step S36, obtaining the maximum correlation amplitude of each group in the P groups according to the two-dimensional Fourier transform residual delay-delay rate search graph; Step S37: Calculate the mean of the maximum correlation amplitudes of the P groups according to the maximum correlation amplitude of each group.
4. The method for reconstructing a quadratic delay model of a radio source for space VLBI according to claim 3, wherein: The step S34 includes: Step S341: perform fringe rotation on the kth segment of data from the first station, and perform fast Fourier transform on the fringe-rotated data with a spectral channel number of N to obtain the sequence , ; Step S342, the sequence obtained in step S341 Perform fractional delay compensation and obtain the sequence after fractional compensation { }; Step S343: Perform a fast Fourier transform with N spectral channels on the kth segment of data from the second station to obtain the sequence ; Step S344, the sequence { } and the sequence obtained in step S343 Conjugate and multiply the first N / 2 terms of to get a sequence of length N / 2 ; Step S345, repeat steps S341 to S344 until all K segments of data are processed.