Cross-ambiguity function time-frequency difference estimation method based on data segmentation

Abstract

The invention belongs to the technical field of electronic countermeasures, and particularly relates to a cross-ambiguity function time-frequency difference calculation method based on data segmentation. According to the method, the calculation of the cross-ambiguity function is realized by segmenting the data, the number of FFT calculation sample points is reduced by the data segmentation, but the resolution of frequency difference extraction is also reduced, and a high-precision frequency difference can be obtained through local frequency domain interpolation, so that the calculation of the cross-ambiguity function with high processing gain is realized on an FPGA (Field Programmable Gate Array). According to the method, the FFT point number in the calculation of the cross-ambiguity function can be reduced, the method can adapt to FPGA hardware resources to realize the calculation of the cross-ambiguity function, the speed is high, and the precision is not lost.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic countermeasures, and in particular relates to a method for calculating time-frequency difference of mutual fuzzy functions based on data segmentation. Background Art

[0002] The basis for the implementation of the time-frequency difference positioning system is to obtain the time difference / frequency difference (TDOA / FDOA) parameters. The two parameters are generated due to the different paths and radial velocities during signal propagation. Time-frequency analysis methods are usually used to achieve joint estimation of the parameters. There are many methods currently used for time-frequency analysis. Generally speaking, they can be summarized into the following three categories: TDOA / FDOA joint estimation algorithm based on second-order statistics, TDOA / FDOA joint estimation algorithm based on high-order statistics, and TDOA / FDOA joint estimation algorithm based on signal cyclostationary characteristics. In the application of satellite signal radiation source positioning, because the radiation source signal noise received by the satellite is often independent, the cross-correlation function based on the second-order statistics is effective. It is a method with relatively small computational complexity and has been widely used.

[0003] In satellite signal radiation source positioning, since the radiation source often uses directional antennas for communication, when multiple stations are used for time difference positioning, the secondary stations all receive the radiation source sidelobe signals, so the signal-to-noise ratio is very low, generally below -40dB. 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 signal stations.

[0004] Increasing the time-bandwidth product leads to a significant increase in the sampling points involved in the calculation of the mutual ambiguity function. When extracting the -40dB signal time-frequency difference, 1M to 100M sample points are required for cyclic FFT calculation. However, the existing hardware resource FFT calculation core can generally only support 64K point FFT, making it difficult to achieve high processing gain mutual ambiguity function processing on FPGA. Summary of the invention

[0005] In view of the above problems, the present invention realizes the calculation of the mutual ambiguity function by segmenting the data. Since data segmentation reduces the number of FFT calculation samples, it also reduces the resolution of frequency difference extraction. High-precision frequency difference can be obtained by local frequency domain interpolation, thereby realizing the calculation of mutual ambiguity function with high processing gain on FPGA.

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

[0007] A method for calculating time-frequency difference of mutual fuzzy function based on data segmentation comprises the following steps:

[0008] S1, segment the signal data and perform conjugate multiplication to obtain the corresponding spectrum. Specifically, define two signal data as s1 s2, the length of each data is L, divide each data into M segments, the length of each segment is N, and the data after conjugate multiplication is s m , the corresponding spectrum is:

[0009]

[0010] Among them, s1(n) is the discrete expression of s1, n = 0, 1, ... N-1, is the discrete conjugate expression of s2;

[0011] S2, fix s1, perform cyclic shift on s2, and perform a segmented spectrum calculation according to the formula in S1 for each shift of one sampling point, so as to obtain the calculation result of the mutual ambiguity function after data segmentation:

[0012]

[0013] Among them, t and f represent the time difference and frequency difference respectively, T represents the time for the signal to be used for correlation accumulation, and A xy Indicates the calculation of mutual fuzzy function of two signals with noise; A ss represents the calculation of the mutual ambiguity function of the two signals without noise, D0 represents the time difference between the two signals, and f d Indicates the frequency difference between two signals;

[0014] S3, find the maximum value of the modulus of the result of the mutual fuzzy function calculation, and use the corresponding result as the rough estimation result of the time difference and frequency difference:

[0015]

[0016] in, are the estimated values ​​of time difference and frequency difference respectively;

[0017] S4. Compensate the second signal according to the 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] The CZT range is determined based on the rough estimation result of the frequency difference, and the refined spectrum of the conjugate multiplication result is obtained by fast calculation using CZT:

[0020]

[0021] Among them, L' represents the number of spectrum points after CZT refinement, k' belongs to the rough estimate spectrum range, and M' represents the equivalent number of segments corresponding to the refined spectrum;

[0022] Based on the frequency corresponding to the maximum modulus value of S(k'), the frequency difference accurate estimation result is obtained;

[0023] S5. Compensate the second signal according to the obtained frequency difference precise estimation result to obtain s2', and use fast Fourier transform to calculate the correlation value between s1 and s2' to obtain the rough time difference estimation result:

[0024]

[0025] Among them, S1(k), S2 * (k) 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, which is specifically:

[0027] Letnk=[n 2 +k 2 -(kn) 2 ] / 2, and fill the spectrum with zeros so that the data length is L, then:

[0028]

[0029] Since we only need to get the time domain value of a certain interval, Where 0≤P,P+M≤L-1, we can get:

[0030]

[0031] P=L / N×R0-M / 2

[0032] make The related function expression after interpolation is as follows:

[0033]

[0034] Perform a convolution operation on Z(k) and H(k) and find n corresponding to the maximum value, which is the high-precision time difference estimate.

[0035] The beneficial effect of the present invention is that the method of the present invention can reduce the number of FFT points in the calculation of the mutual ambiguity function, can adapt to FPGA hardware resources to realize the calculation of the mutual ambiguity function, and has a high speed and no loss of accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0037] Figure 2 It is the diagram of the piecewise 2 mutual fuzzy function.

[0038] Figure 3It is the diagram of the segmented 8 mutual fuzzy function. DETAILED DESCRIPTION

[0039] The present invention is described in detail below with reference to the accompanying drawings and simulations.

[0040] like Figure 1 As shown, it is a schematic diagram of the process of the present invention, which specifically includes the following processes:

[0041] 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;

[0042] 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;

[0043] 3) Obtain the segment length, define the two data channels as s1 s2, the length of each channel is L, and divide each channel into M segments, each segment length is N. Due to data segmentation, the number of frequency points is reduced from L points to N points, and the corresponding resolution is also reduced by M times.

[0044] 4) Perform a rough estimate, specifically including: conjugate multiplication of the primary and neighboring satellite signals, that is, conjugate multiplication of the two signals, assuming that the data after conjugate multiplication is s m , then the spectrum corresponding to the conjugate multiplication result is:

[0045]

[0046] The multiplication result of the primary and neighboring satellite conjugate signals is subjected to segmented FFT, that is, s1 is fixed, s2 is cyclically shifted, and a segmented spectrum calculation is performed once for each shift of a sampling point according to the above formula, and the calculation result of the mutual ambiguity function after data segmentation can be obtained;

[0047]

[0048] Find the maximum value of the modulus of the result of the mutual fuzzy function calculation, and the corresponding result is the rough estimation result of the time difference and frequency difference

[0049]

[0050] 5) Frequency difference precise estimation: select the time difference filled mutual ambiguity function slice, take the frequency difference rough estimation result as the center, and interpolate the frequency domain within a small range to obtain the frequency difference precise estimation result, which includes:

[0051] The second signal (neighboring satellite signal) is compensated according to the rough estimation result of the time difference, and then the first signal (primary satellite signal) is conjugate-multiplied with the compensated second signal. In order to improve the resolution, (1) is modified to obtain

[0052]

[0053] It can be seen from the above formula that the spectrum with improved spectral resolution is based on L as a period, that is, the number of spectrum points at this time is L, and the corresponding frequency resolution is fs / L.

[0054] The CZT range is calculated based on the rough estimate of the frequency difference, with a total frequency resolution of 1. The refined spectrum of the conjugate multiplication result is obtained by direct use of CZT for fast calculation:

[0055]

[0056] Among them, L' represents the number of spectrum points after CZT refinement, and M' represents the number of equivalent segments corresponding to the refined spectrum.

[0057]

[0058] In order to reduce the amount of calculation, the value range of k' can be searched only near the rough estimation result of the frequency difference, and the value range is as follows:

[0059]

[0060] After obtaining the value range of M', k', CZT can be used to refine the spectrum of each segment of data, and then multiply it with the corresponding phase information respectively, and finally sum them to obtain the refined spectrum of the conjugate multiplication result of the two signals.

[0061] Then find the index corresponding to the maximum value of CZT, that is, find the frequency corresponding to the maximum modulus value of S(k'), which is the precise estimation result of the frequency difference.

[0062] 6) Time difference precise estimation, including:

[0063] The frequency difference estimation result is used to compensate the neighboring satellite signal s2 to obtain s2', and the correlation value of the two signals is calculated by fast Fourier transform to obtain the rough estimation result of the time difference. * (k) are the spectrum and conjugate spectrum of the two signals respectively.

[0064]

[0065] According to the rough estimation result of the time difference, the local time domain interpolation is calculated to obtain the high-precision time difference estimation result.

[0066] Letnk=[n 2 +k 2 -(kn) 2 ] / 2, and fill the spectrum with zeros so that the data length is L, then:

[0067]

[0068] Since we only need to get the time domain value of a certain interval, Where 0≤P,P+M≤L-1, we can get:

[0069]

[0070] P=L / N×R0-M / 2

[0071] make The related function expression after interpolation is as follows:

[0072]

[0073] Perform a convolution operation on Z(k) and H(k). This convolution operation can be implemented through FFT and IFFT algorithms. The n corresponding to the maximum value is obtained, which is the high-precision time difference estimation value.

[0074] Simulation example:

[0075] Generate two signals, the modulation mode is QPSK signal, the sampling rate is 10M, the time difference is 0.054820144102s, the frequency difference is 12.325Hz, and the total data length is 524K samples.

[0076] By segmenting the data into 32K samples and 8K samples, the mutual ambiguity function is calculated as follows: Figure 2 and Figure 3 As shown in the figure, the time difference error obtained by calculating the segmented 32K samples is 2e-12s, and the frequency difference error is 5.14e-4Hz; the time difference error obtained by calculating the segmented 8K samples is 2e-12s, and the frequency difference error is 1.055e-3Hz. From the results, since the data segmentation does not change the sampling rate (time resolution), the time difference error in the two segmentation cases is the same, which is a ps-level error; the data segmentation changes the frequency resolution, and the shorter the data, the worse the frequency resolution, and it is necessary to obtain a higher-precision frequency difference through interpolation. In the two data segmentation cases, the frequency difference error is at the level of 0.1mHz and 1mHz, which is much more accurate than the measurement error caused by noise in the actual system. Therefore, the data segmentation mutual ambiguity function calculation method has good practical value.

Claims

1. A method for calculating time-frequency difference of mutual fuzzy function based on data segmentation, characterized in that: The following steps are involved: S1, segment the signal data and perform conjugate multiplication to obtain the corresponding spectrum. Specifically, define two signal data as s1 s2, the length of each data is L, divide each data into M segments, the length of each segment is N, and the data after conjugate multiplication is s m , the corresponding spectrum is: Among them, s1(n) is the discrete expression of s1, n = 0, 1, ... N-1, is the discrete conjugate expression of s2; S2, fix s1, perform cyclic shift on s2, and perform a segmented spectrum calculation according to the formula in S1 for each shift of one sampling point, so as to obtain the calculation result of the mutual ambiguity function after data segmentation: Among them, t and f represent the time difference and frequency difference respectively, T represents the time for the signal to be used for correlation accumulation, and A xy Indicates the calculation of mutual fuzzy function of two signals with noise; A ss represents the calculation of the mutual ambiguity function of the two signals without noise, D0 represents the time difference between the two signals, and f d Indicates the frequency difference between two signals; S3, find the maximum value of the modulus of the result of the mutual fuzzy function calculation, and use the corresponding result as the rough estimation result of the time difference and frequency difference: in, are the rough estimates of time difference and frequency difference respectively; S4. Compensate the second signal according to the rough estimation result of the time difference, and then conjugate-multiply the first signal with the compensated second signal. The corresponding spectrum is: The CZT range is determined based on the rough estimation result of the frequency difference, and the refined spectrum of the conjugate multiplication result is obtained by fast calculation using CZT: Among them, L' represents the number of spectrum points after CZT refinement, k' belongs to the rough estimate spectrum range, and M' represents the equivalent number of segments corresponding to the refined spectrum; Based on the frequency corresponding to the maximum modulus value of S(k'), the frequency difference accurate estimation result is obtained; S5. Compensate the second signal according to the obtained frequency difference precise estimation result to obtain s2', and use fast Fourier transform to calculate the correlation value between s1 and s2' to obtain the rough time difference estimation result: Among them, S1(k), S2 * (k) are the spectrum and conjugate spectrum of the two signals respectively; S6. According to the rough time difference estimation result, calculate the local time domain interpolation to obtain the high-precision time difference estimation result, which is specifically: Letnk=[n 2 +k 2 -(kn) 2 ] / 2, and fill the spectrum with zeros so that the data length is L, then: Since we only need to get the time domain value of a certain interval, Where 0≤P,P+M≤L-1, we can get: P=L / N×R0-M / 2 make The related function expression after interpolation is as follows: Perform a convolution operation on Z(k) and H(k) and find n corresponding to the maximum value, which is the high-precision time difference estimate.

Images