A Method for Estimating Time-Frequency Difference of Cross-Ambiguity Function Based on Data Segmentation

Abstract

The present invention belongs to the technical field of electronic countermeasures, and particularly relates to a method for calculating the time-frequency difference of the cross ambiguity function based on data segmentation. The present invention realizes the calculation of the cross ambiguity function by segmenting the data. Since data segmentation reduces the number of FFT calculation samples, but also reduces the resolution of frequency difference extraction, high-precision frequency difference can be obtained through local frequency domain interpolation, so as to realize the calculation of the cross ambiguity function with high processing gain on the FPGA. The method of the present invention can reduce the number of FFT points in the calculation of the cross ambiguity function, can adapt to the FPGA hardware resources to realize the calculation of the cross ambiguity function, and has a fast speed and no loss of accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of electronic countermeasures, and particularly relates to a method for estimating time-frequency difference of cross ambiguity function based on data segmentation. Background Technique

[0002] The basis for the realization of a time-frequency difference positioning system is to obtain time difference / frequency difference (TDOA / FDOA) parameters. These two parameters are generated due to different paths and radial velocities during signal propagation, and generally, time-frequency analysis methods are used to jointly estimate the parameters. Currently, there are many methods for time-frequency analysis. Generally speaking, they can be classified into the following three categories: TDOA / FDOA joint estimation algorithms based on second-order statistics, TDOA / FDOA joint estimation algorithms based on higher-order statistics, and TDOA / FDOA joint estimation algorithms based on the cyclostationary characteristics of signals. In the application of satellite signal radiation source positioning, since the noise of the radiation source signals received by satellites is often independent, the cross-correlation function based on second-order statistics is effective and is a method with relatively small computational complexity, and has been widely used.

[0003] In satellite signal radiation source positioning, since radiation sources often use directional antennas for communication, when using multiple stations for time difference positioning, the secondary stations all receive the sidelobe signals of the radiation source, resulting in a very low signal-to-noise ratio, generally below -40 dB. In order to locate this type of radiation source, it is necessary to increase the processing gain (time-bandwidth product) to extract the time-frequency difference between the radiation source signals of different stations.

[0004] Increasing the time-bandwidth product leads to a significant increase in the number of sampling points participating in the calculation of the cross ambiguity function. When extracting the time-frequency difference of a -40 dB signal, 1M to 100M sample points are required for cyclic FFT calculation, while the existing FFT calculation cores of hardware resources generally only support 64K-point FFT, making it difficult to implement the cross ambiguity function processing with high processing gain on an FPGA. Summary of the Invention

[0005] In view of the above problems, the present invention realizes the calculation of the cross ambiguity function by segmenting data. Although data segmentation reduces the number of FFT calculation sample points, it also reduces the resolution of frequency difference extraction. High-precision frequency difference can be obtained through local frequency domain interpolation, so as to realize the calculation of the cross ambiguity function with high processing gain on an FPGA.

[0006] The technical solution of the present invention is as follows:

[0007] A method for calculating the time-frequency difference of the cross ambiguity function based on data segmentation, comprising the following steps:

[0008] S1. After segmenting the signal data and performing conjugate multiplication, the corresponding spectrum is obtained. Specifically, define two-channel signal data as , the length of each data path is L, each data path is divided into M segments, each segment has a length of N, and the data after conjugate multiplication is , and the corresponding spectrum is:

[0009]

[0010] Among them, is the discrete expression of , is the discrete conjugate expression of

[0011] S2. Fix , and perform a circular shift on . For each shift of one sampling point, perform a segmented spectrum calculation according to the formula in S1, so as to obtain the cross ambiguity function calculation result after data segmentation:

[0012]

[0013] Among them, , respectively represent the time difference and frequency difference, represents the time for the signal to be used for correlation accumulation, represents the calculation of the cross ambiguity function for two signals with noise; represents the calculation of the cross ambiguity function for two signals without noise, represents the time difference between the two signals, represents the frequency difference between the two signals;

[0014] S3. Find the maximum value of the modulus of the cross ambiguity function calculation result, and use the corresponding result as the rough estimation result of the time difference and frequency difference:

[0015]

[0016] Among them, , are the estimated values of the time difference and frequency difference respectively;

[0017] S4. Compensate the second signal according to the obtained rough estimation result of the time difference, and then conjugate multiply the first signal with the compensated second signal. The corresponding spectrum is:

[0018]

[0019] Determine the CZT range according to the obtained rough estimation result of the frequency difference, and use CZT to quickly calculate the refined spectrum of the conjugate multiplication result:

[0020]

[0021] Among them, Indicates the number of spectrum points after CZT refinement, which belongs to the rough estimate spectrum range, and represents the equivalent number of segmented sections corresponding to the refined spectrum;

[0022] Based on the frequency corresponding to the maximum modulus value, the refined frequency difference estimation result is obtained;

[0023] S5. Compensate the second signal according to the obtained refined frequency difference estimation result to obtain , and use the fast Fourier transform to find and the correlation value of to obtain the rough time difference estimation sequence:

[0024]

[0025] where, , are the spectrum and conjugate spectrum of the two signals respectively;

[0026] S6. According to the rough time difference estimation result, calculate the local time domain interpolation to obtain the high-precision time difference estimation result, specifically:

[0027] Let , and zero-pad the spectrum so that the data length is , then:

[0028]

[0029] Since only the time domain values in a certain interval are required, , where , it can be obtained that:

[0030]

[0031]

[0032] Let , ,

[0033] The expression of the interpolated correlation function is as follows:

[0034]

[0035] Perform a convolution operation on and , and find the n corresponding to the maximum value, which is the high-precision time difference estimation value.

[0036] The beneficial effects of the present invention are as follows. The method of the present invention can reduce the number of FFT points in the calculation of the cross ambiguity function, can adapt to the FPGA hardware resources to implement the cross ambiguity function calculation, has a fast speed and does not lose accuracy. Description of the Drawings

[0037] Figure 1 It is a schematic flow chart of the method of the present invention.

[0038] Figure 2 It is a cross ambiguity function graph for segment 2.

[0039] Figure 3 It is a cross ambiguity function graph for segment 8. Detailed Embodiment

[0040] The present invention will be described in detail below with reference to the drawings and simulations.

[0041] As Figure 1 shown, it is a schematic flow chart of the present invention, which specifically includes the following processes:

[0042] 1) According to the time difference search center and the time difference search range, calculate the signal time domain point index corresponding to the time difference search range;

[0043] 2) According to the frequency difference search center and the frequency difference search range, calculate the signal time domain point index corresponding to the frequency difference search range;

[0044] 3) Obtain the segment length, and define the two-way data as , the length of each path of data is L, each path of data is divided into M segments, and the length of each segment is N. Due to data segmentation, the number of frequency points is reduced from points to points, and the corresponding resolution is also reduced by times.

[0045] 4) Perform a rough estimation, which specifically includes: conjugate multiplying the main adjacent star signals, that is, conjugate multiplying the two-way signals. Let the data after conjugate multiplication be , then the spectrum corresponding to the conjugate multiplication result is:

[0046] (1)

[0047] Perform a segmented FFT on the conjugate multiplication result of the main adjacent star conjugate signals, that is, fix , perform circular shifting on , and perform a segmented spectrum calculation according to the above formula for each shifted sampling point, and the cross ambiguity function calculation result after data segmentation can be obtained;

[0048]

[0049] Find the maximum value of the modulus of the cross ambiguity function calculation result, and the corresponding result is the rough estimation result of time difference and frequency difference.

[0050]

[0051] 5) Fine frequency difference estimation. Select the cross ambiguity function slice with the time difference filled, and with the rough frequency difference estimation result as the center, within a small range, interpolate the frequency domain to obtain the fine frequency difference estimation result, which specifically includes:

[0052] Compensate the second path signal (adjacent satellite signal) according to the obtained rough time difference estimation result, and then conjugate multiply the first path signal (main satellite signal) with the compensated second path signal. In order to improve the resolution, after modifying (1), we get

[0053] (2)

[0054] As can be seen from the above formula, the spectrum with improved spectral resolution is periodic with L, that is, the number of spectral points at this time is L, and the corresponding frequency resolution is fs / L.

[0055] Calculate the CZT range according to the obtained rough frequency difference estimation result, and the range is a total of 1 frequency resolution; directly use CZT to quickly calculate the refined spectrum of the conjugate multiplication result:

[0056] (3)

[0057] Among them, represents the number of spectral points after CZT refinement, represents the equivalent number of segments corresponding to the refined spectrum.

[0058]

[0059] In order to reduce the computational complexity, the value range of

[0060]

[0061] After obtaining the value ranges of M' and k', the spectrum of each segment of data can be refined using CZT, then multiplied by the corresponding phase information respectively, and finally summed to obtain the refined spectrum of the conjugate multiplication result of the two path signals.

[0062] Then find the index corresponding to the maximum value of CZT, that is, find The frequency corresponding to the maximum modulus value is the fine frequency difference estimation result.

[0063] 6) Fine time difference estimation, which specifically includes:

[0064] Compensate the adjacent satellite signal with the frequency difference estimation result , obtain , and use the fast Fourier transform to calculate the correlation value of the two signals to obtain the rough time difference estimation result. Among them 、 are the spectra and conjugate spectra of the two signals respectively.

[0065]

[0066] According to the rough time difference estimation result, calculate the local time domain interpolation to obtain the high-precision time difference estimation result.

[0067] Let , and zero-pad the spectrum so that the data length is , then:

[0068]

[0069] Since only the time domain values in a certain interval need to be obtained, , where , it can be obtained that:

[0070]

[0071]

[0072] Let ,

[0073] The expression of the correlated function after interpolation is as follows,

[0074]

[0075] For and perform a convolution operation, and this convolution operation can be implemented by the FFT and IFFT algorithms. Find the n corresponding to the maximum value, which is the high-precision time difference estimation value.

[0076] Simulation example:

[0077] Generate two signals, with the modulation mode being QPSK signal, the sampling rate being 10M, the time difference being 0.054820144102s, the frequency difference being 12.325Hz, and the total data length being 524K samples.

[0078] By segmenting the data into 32K samples and 8K samples for cross ambiguity function calculation as Figure 2 and Figure 3As shown, the time difference error obtained by calculating 32K samples in segments is 2e-12 s, and the frequency difference error is 5.14e-4 Hz; the time difference error obtained by calculating 8K samples in segments is 2e-12 s, and the frequency difference error is 1.055e-3 Hz. From the results, since data segmentation does not change the sampling rate (time resolution), the time difference errors are the same in both segmentation cases, which is a ps-level error; data segmentation changes the frequency resolution. The shorter the data, the worse the frequency resolution. Higher-precision frequency differences need to be obtained through interpolation. In both cases of data segmentation, the frequency difference errors are at the levels of 0.1 mHz and 1 mHz, and the precision is much higher than the measurement error caused by noise in the actual system. Therefore, this data segmentation cross-ambiguity function calculation method has good practical value.

Claims

1. A method for estimating the time-frequency difference of the cross ambiguity function based on data segmentation, characterized in that Including the following steps: S1. After segmenting the signal data and performing conjugate multiplication, the corresponding spectrum is obtained, specifically: Define two channels of signal data as , the length of each channel of data is L, each channel of data is divided into M segments, the length of each segment is N, and the data after conjugate multiplication is , and the corresponding spectrum is: ， Among them, is the discrete expression of, , is the discrete conjugate expression of; S2. Fixation , perform circular shift. For each shifted sampling point, perform a segmented spectrum calculation according to the formula in S1, so as to obtain the calculation result of the cross-ambiguity function after data segmentation: ， Among them, , respectively represent the time difference and the frequency difference, represents the time for the signal to perform correlation accumulation, represents the calculation of the cross ambiguity function for two signals with noise; represents the calculation of the cross ambiguity function for two signals without noise, represents the time difference between two signals, represents the frequency difference between two signals; S3. Search for the maximum value of the modulus of the cross ambiguity function calculation result, and the corresponding result is used as the rough estimation result of time difference and frequency difference: ， Among them, , are the rough estimated values of the time difference and the frequency difference, respectively; S4. Compensate the second signal according to the obtained rough estimation result of time difference, and then conjugate multiply the first signal with the compensated second signal. The corresponding spectrum is: ， Determine the CZT range according to the obtained rough estimation result of frequency difference, and use CZT to quickly calculate the refined spectrum of the conjugate multiplication result: ， Among them, represents the number of spectral points after CZT refinement, belongs to the rough estimation spectral range, represents the equivalent number of segmented sections corresponding to the refined spectrum; Based on Obtain the fine estimation result of the frequency difference according to the frequency corresponding to the largest modulus value; S5. Compensate the second path signal according to the obtained fine frequency difference estimation result to obtain , and use the fast Fourier transform to calculate and to obtain a rough time difference estimation sequence by obtaining the correlation value: ， Among them, and are the spectra and conjugate spectra of two signals respectively; S6. According to the rough estimation result of time difference, calculate the local time domain interpolation to obtain the high-precision time difference estimation result, specifically: Let , and zero-pad the spectrum so that the data length is , then: ， Since only the time-domain values in a certain interval are required, , where , it can be obtained that: ， ， Let , , The expression of the correlation function after interpolation is as follows: ， For and perform a convolution operation, and find the n corresponding to the maximum value, which is the high-precision time difference estimation value.

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