A Beidou anti-interference method for transmission line monitoring based on energy residual search

Abstract

The present invention discloses a Beidou monitoring anti-interference method for power transmission lines based on energy residual search, including: 1. By Hilbert transform, the discrete Beidou satellite original signal is changed into the form of analytical signal and dimension normalization is performed; 2. Ozaktas sampling method is adopted to perform fractional Fourier transform on the analytical signal to obtain the transform domain signal; 3. N-Sigma method is adopted to perform spectrum excision on the transform domain signal; 4. An energy residual function construction method is proposed, and the energy residual is obtained by using the analytical signal and the transform domain signal after spectrum excision; 5. The optimal order interval is contracted to obtain the maximum value of the one-dimensional energy residual function, and the optimal order transform domain signal corresponding to the maximum value is inversely transformed to obtain the signal after filtering out interference. The present invention has the characteristics of high detection accuracy and low algorithm complexity for multi-period swept frequency interference, and has important application value.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation and positioning technology, and in particular to a Beidou monitoring anti-interference method for power transmission lines based on energy residual search. Background Art

[0002] In today's power transmission field, navigation and positioning technology plays an extremely important role. Navigation and positioning technology is not only the key to the exploration of topography and geological conditions of transmission lines, but also an effective power asset monitoring tool. Its existence ensures that workers can stay away from dangerous areas when performing tasks, and can also help power companies identify potential risk points in transmission lines. It significantly improves the speed and accuracy of the team's maintenance of fault points, thereby improving the operating efficiency and reliability of the entire power grid. In today's application of various complex interference environments, the characteristics of this technology that are susceptible to interference have also been exposed. Therefore, it is very important to study the anti-interference technology of satellite navigation system receivers.

[0003] The main sources of receiver interference are: first, natural environment interference, mainly referring to transmission path interference (tropospheric interference, ionospheric interference and multipath attenuation), adjacent frequency band interference (mobile communication system, radar system, etc.); second, artificial malicious interference, mainly referring to suppression interference and deception interference. Suppression interference includes continuous wave (CW), pulse wave (PCW), linear frequency modulation interference (LFM) and Gaussian white noise (AWGN), which can directly prevent the receiving device from obtaining effective positioning and timing results. Third, deception interference is a broadband interference with good concealment and complete signal structure. It controls the signal tracking loop by forging or forwarding signals, misleading the receiving device to obtain incorrect positioning or timing solutions. Among them, linear frequency modulation interference (LFM), also known as chrip signal interference, has the characteristics of low power and easy generation among broadband interference signals with the same power. At present, most commercial jammers can generate this kind of interference, which poses a huge threat to the entire GNSS system.

[0004] The existing anti-interference methods for linear frequency modulation interference are mainly divided into two methods, one is to use array antennas, and the other is to use digital signal processing methods for time-frequency domain analysis to target linear frequency modulation interference. Common time-frequency analysis methods include short-time Fourier transform, Winger-Ville distribution, wavelet transform and fractional Fourier transform, but these methods have defects such as low resolution, poor high-dimensional characteristics, cross terms and complex calculations, so there is room for improvement. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings of the prior art and propose a Beidou monitoring anti-interference method for power transmission lines based on energy residual search. Its advantages are that the energy residual function is used as the optimal order search function, avoiding the search for the cycle, reducing the calculation dimension, and using the interval contraction method in the one-dimensional search to quickly approximate the optimal order, thereby improving the detection and suppression efficiency of linear frequency modulation signals.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A Beidou monitoring anti-interference method for power transmission lines based on energy residual search comprises the following steps:

[0008] Step 1: The time width obtained by the Beidou receiver is T obs The discrete original satellite signal s[n] is subjected to discrete Hilbert transform to obtain the phase delay signal The above two signals are synthesized into an analytical signal z[n];

[0009] The sampling rate of the signal is f s Substitute the unknown signal bandwidth B, determine the signal scale factor S and normalized width Δx; use the above scale factor S and normalized width Δx to scale the discrete analytical signal, and convert the original time width T obs The signal z[n] is transformed into the interval [-Δx / 2, Δx / 2], forming a signal with the same length of N but with an interval of The discrete signal after scaling At this time, the value range of n is

[0010] Step 2: Use the Ozaktas sampling method and use the Shannon interpolation formula to Double interpolation is performed to obtain At this time, the value range of n is:

[0011] According to the following formula, perform P-order FRFT on the interpolated discrete signal, and double the transformed signal to obtain the transform domain signal

[0012] β=cscα,α∈[0,π]

[0013] γ=cotα

[0014]

[0015] Where F is the Fourier transform operator, P is the fractional Fourier transform order, j is the imaginary unit, m is the discrete sampling point variable in the transform domain, and its range is the same as n after interpolation. αis the transformation coefficient, α is the transformation angle, which is proportional to P, β is the cosecant function of α, γ is the cotangent function of α, and the range of m is the same as n before interpolation.

[0016] Step 3: Use the N-sigma method to select the noise ratio coefficient and calculate the removal threshold, then transform the domain signal Perform spectrum excision;

[0017]

[0018] Th=ψ·δ+μ

[0019] In the formula, ψ t is the preset proportional coefficient corresponding to the variance interval, the subscript t is the interval mark, u and l are the upper and lower limit marks of the interval; Th is the set excision threshold, and ψ is the currently selected noise proportional coefficient.

[0020] Using the given removal threshold Th, the spectrum line of the transformed signal is removed;

[0021]

[0022] Step 4: Calculate the transform domain signal energy and analytical signal energy after removing the spectrum line, and construct the residual function;

[0023] Step 5: Use the non-interpolation RMS method to perform peak search on the one-dimensional energy residual function; first, specify the initial step size T0, error tolerance ε and starting point a=0; then, determine the search sequence u0,u1,...,u v , and construct the initial search interval [u0, u v ];

[0024]

[0025] In the formula, F i is the i-th Fibonacci number, u i is the i-th search variable (whose maximum value does not exceed the maximum value of P 2), g i is the i-th search function (obtained by negating the energy residual function calculated in the previous step), v is the number of search points; the starting point u0 of the search interval is equal to the starting point a, and the end point u v is the first search function value g(u v ) is greater than the search variable u of the initial search function value g(u0) i , if v≤2, reduce the initial step length T0 to the original Repeat the above steps until a reasonable search sequence and search interval are obtained;

[0026] Calculate the mean square value u of the above point v rms,q, insert it into the search sequence in ascending order of the search variable, and determine the minimum point B and its adjacent points A and C in the search interval. The above three points constitute a new search sequence and search interval, and then calculate the mean square value of the above three points;

[0027]

[0028] In the formula, the subscript rms is the symbol of the mean square value, q is the number of mean square value iterations, s is the subscript of the search variable with the smallest search function value in the search sequence, min is the symbol for finding the minimum value, A, B, and C are the endpoints of the new interval and the minimum point;

[0029] According to the above mean square value calculation results, if it is established, stop the iteration and select the mean square value point u rms,q is the peak point of the energy residual function. Otherwise, add the mean square value point calculated by A, B, and C to the search sequence of A, B, and C, reconstruct a new search interval, calculate the mean square value again, and then return to this step:

[0030] |u rms,q -u rms,q-1 |<ε|u rms,q |

[0031] The peak point u of the energy residual function obtained by searching rms,q The corresponding transform domain signal after spectral line removal is in order -u rms,q According to step 3, the FRFT inverse transform is calculated to obtain the original discrete Beidou satellite signal after filtering out interference.

[0032] The present invention is further configured that the delay signal in step 1 The calculation formula is: In the formula, To obtain the discrete Hilbert transform result of the original satellite signal s[n], the total length of the s[n] sequence is N, n is the discrete sampling point variable in the time domain, and its value range is 1 to N, where K is the signal period extension number, s K [nk] is s[n] after period extension, k is the Shannon interpolation point variable, and its value range is (k is not 0).

[0033] The present invention is further configured such that the calculation formula of the analytical signal z[n] in step 1 is: Where j is the imaginary unit.

[0034] The present invention is further configured such that the scale factor S of the signal in step 1 is expressed as: The expression of normalized width Δx is:

[0035] The present invention is further configured that in step 3, μ is the calculated transform domain signal mean, and its expression is:

[0036] The present invention is further configured that, in step 3, δ is the calculated transform domain signal variance, and its expression is:

[0037]

[0038] The present invention is further configured such that the residual function expression in step 4 is:

[0039]

[0040] res(P)=|E1-E2(P)| 2

[0041] Where res is the energy residual function, E1 is the calculated analytical signal energy, and E2 is the calculated transform domain signal energy after spectral line removal corresponding to the P-order transform.

[0042] The beneficial effects of the present invention are:

[0043] 1. The present invention analyzes the shortcomings of the existing multi-cycle search algorithm and the multi-peak characteristics of multi-cycle signal transformation, combines the monotonicity of the signal energy difference, constructs an energy residual function, and converts the multi-peak function that is difficult to search into a low-dimensional single-peak function. At the same time, it breaks through the limitation of sequence length and can suppress interference for signals of any length, making up for the shortcomings of the existing method that the search cycle and transformation length are limited by cycles, greatly improving the efficiency of interference detection.

[0044] 2. The present invention makes full use of the Parseval characteristic of FRFT to calculate the signal energy while cutting the spectrum line in the transform domain, avoiding the need to perform inverse transformation on the spectrum line cutting sequence when calculating the energy residual function, which greatly reduces the required amount of calculation.

[0045] 3. When performing one-dimensional search, the present invention adopts a non-interpolation root mean square method to shrink the interval. When constructing the initial search range, the search interval where the optimal transformation order is located is reduced at a high speed. By calculating the mean square value, the calculation of the interpolation points of the function is avoided, thereby improving the calculation efficiency while enhancing the peak search accuracy and interference suppression performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic diagram of a transmission line Beidou measurement anti-multi-period LFM interference process of a transmission line Beidou monitoring anti-interference method based on energy residual search proposed by the present invention;

[0047] Figure 2A schematic diagram of FRFT transformation of a single-cycle frequency sweep interference of a Beidou monitoring anti-interference method for power transmission lines based on energy residual search proposed by the present invention;

[0048] Figure 3 A schematic diagram of FRFT transformation of multi-period frequency sweep interference of a Beidou monitoring anti-interference method for power transmission lines based on energy residual search proposed by the present invention;

[0049] Figure 4 A schematic diagram of the hardware experimental scheme architecture of a Beidou anti-interference method for power transmission line monitoring based on energy residual search proposed by the present invention;

[0050] Figure 5 A schematic diagram of the effect before suppression of multi-period LFM interference signals of a Beidou anti-interference method for power transmission line monitoring based on energy residual search proposed by the present invention;

[0051] Figure 6 This is a schematic diagram of the effect of suppressing the energy residual function of a multi-period LFM interference signal constructed in a Beidou monitoring anti-interference method for power transmission lines based on energy residual search proposed by the present invention. DETAILED DESCRIPTION

[0052] The technical solution of this patent is further described in detail below in conjunction with specific implementation methods.

[0053] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0054] Reference Figure 1-6 , a Beidou monitoring anti-interference method for power transmission lines based on energy residual search, comprising the following steps:

[0055] Step 1: The time width obtained by the Beidou receiver through formula (1) is T obs The discrete original satellite signal s[n] is subjected to discrete Hilbert transform to obtain the phase delay signal Then, the above two signals are synthesized into an analytical signal z[n] using equation (2), which can effectively concentrate the signal energy and improve the spectral line resolution:

[0056]

[0057] In formula (2), is the discrete Hilbert transform result of the original satellite signal s[n] obtained by formula (1), j is the imaginary unit, the total length of the s[n] sequence is N, n is the discrete sampling point variable in the time domain, and its value range is 1 to N. In formula (1), K is the signal period extension number, s K [nk] is s[n] after period extension, k is the Shannon interpolation point variable, and its value range is (k is not 0).

[0058] The sampling rate of the signal is f s Replace the unknown signal bandwidth B with a sampling frequency at least twice the bandwidth, which can contain all the signal energy. Use equations (3) and (4) to determine the signal scale factor S and normalized width Δx:

[0059]

[0060] The discrete analytical signal is scaled using the above scale factor S and normalized width Δx, and the original time width is T obs The signal z[n] is transformed into the interval [-Δx / 2, Δx / 2], forming a signal with the same length of N but with an interval of The discrete signal after scaling At this time, the value range of n is

[0061] Step 2: Use the Ozaktas sampling method and use the Shannon interpolation formula to Double interpolation is performed to obtain At this time, the value range of n is According to formula (9), the interpolated discrete signal is subjected to P-order FRFT, and the transformed signal is doubled according to formula (10) to obtain the transform domain signal

[0062]

[0063] β=cscα,α∈[0,π] (7)

[0064] γ=cotα (8)

[0065]

[0066] In formula (9), F is the Fourier transform operator, P is the fractional Fourier transform order, j is the imaginary unit, m is the discrete sampling point variable in the transform domain, and its range is the same as n after interpolation. αis the transformation coefficient shown in formula (6), α is the transformation angle, which is proportional to p according to formula (5), β is the cosecant function of α shown in formula (7), γ is the cotangent function of α shown in formula (8), and the range of m in formula (10) is the same as n before interpolation. The summation part of the above formula is discrete convolution, which can be calculated by FFT, and its complexity is NlogN.

[0067] Step 3: Use the N-sigma method to select the noise ratio coefficient according to formula (13) and calculate the removal threshold using formula (14), then transform the domain signal To perform line excision:

[0068]

[0069] Th=ψ·δ+μ (14)

[0070] In formula (13), ψ t is the preset proportional coefficient corresponding to the variance interval, the subscript t is the interval mark, and u and l are the upper and lower limit marks of the interval. In formula (14), Th is the set excision threshold, μ is the transform domain signal mean calculated by formula (11), δ is the transform domain signal variance calculated by formula (12), and ψ is the currently selected noise proportional coefficient.

[0071] Using the above given removal threshold Th, the spectrum line of the transformed signal is removed according to formula (15):

[0072]

[0073] Step 4: Calculate the transform domain signal energy and analytical signal energy after removing the spectrum line, and construct the residual function according to formula (18):

[0074]

[0075] res(P)=|E1-E2(P)| 2 (18)

[0076] In formula (18), res is the energy residual function. The energy residual function corrects the multi-peak multi-period spectrum line into a one-dimensional single-maximum function, changes the structure of the interference suppression algorithm, reduces the search dimension, and greatly improves the efficiency of solving the optimal transformation order P. E1 is the analytical signal energy calculated by formula (16), and E2 is the transform domain signal energy after the spectrum line is cut off corresponding to the P-order transformation calculated by formula (17).

[0077] Step 5: Use the non-interpolation RMS method to perform peak search on the one-dimensional energy residual function. First, specify the initial step size T0, error tolerance ε, and starting point a = 0. Then, use equations (19) and (20) to determine the search sequence u0, u1, ..., u v, and construct the initial search interval [u0, u v ]:

[0078]

[0079] In formula (19) and formula (20), F i is the i-th Fibonacci number, u i is the i-th search variable (whose maximum value does not exceed the maximum value of P 2), g i is the i-th search function (obtained by negating the energy residual function calculated in the previous step), and v is the number of search points. The starting point u0 of the search interval is equal to the starting point a, and the end point u v is the first search function value g(u v ) is greater than the search variable u of the initial search function value g(u0) i , if v≤2, reduce the initial step length T0 to the original Repeat the above steps until a reasonable search sequence and search interval are obtained.

[0080] Use formula (21) to calculate the mean square value u of the above point v rms,q , insert it into the search sequence in ascending order of the search variable, and determine the minimum point B and its adjacent points A and C in the search interval by formula (22). The above three points constitute a new search sequence and search interval, and then calculate the mean square value of the above three points by formula (23):

[0081]

[0082] In formula (21), the subscript rms is the mean square value sign, q is the number of mean square value iterations, in formula (22), s is the subscript of the search variable with the smallest search function value in the search sequence, min is the symbol for finding the minimum value, and in formula (23), A, B, and C are the endpoints of the new interval and the minimum point.

[0083] According to the above mean square value calculation results, if equation (24) holds, stop the iteration and select the mean square value point u rms,q is the peak point of the energy residual function. Otherwise, add the mean square value point calculated by A, B, and C to the search sequence of A, B, and C, re-construct a new search interval according to formula (22), calculate the mean square value again according to formula (23), and then return to this step:

[0084] |u rms,q -u rms,q-1 |<ε|u rms,q | (24)

[0085] The peak point u of the energy residual function obtained by searching rms,q The corresponding transform domain signal after spectral line removal is in order -u rms,qAccording to step 3, the FRFT inverse transform is calculated to obtain the original discrete Beidou satellite signal after filtering out interference.

[0086] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A Beidou monitoring anti-interference method for power transmission lines based on energy residual search, characterized in that: The following steps are involved: Step 1: The time width obtained by the Beidou receiver is T obs The discrete original satellite signal s[n] is subjected to discrete Hilbert transform to obtain the phase delay signal The above two signals are synthesized into an analytical signal z[n]; The sampling rate of the signal is f s Substitute the unknown signal bandwidth B, determine the signal scale factor S and normalized width Δx; use the above scale factor S and normalized width Δx to scale the discrete analytical signal, and convert the original time width T obs The signal z[n] is transformed into the interval [-Δx / 2, Δx / 2], forming a signal with the same length of N but with an interval of The discrete signal after scaling At this time, the value range of n is Step 2: Use the Ozaktas sampling method and use the Shannon interpolation formula to Double interpolation is performed to obtain At this time, the value range of n is: According to the following formula, perform P-order FRFT on the interpolated discrete signal, and double the transformed signal to obtain the transform domain signal β=cscα,α∈[0,π] γ=cotα Where F is the Fourier transform operator, P is the fractional Fourier transform order, j is the imaginary unit, m is the discrete sampling point variable in the transform domain, and its range is the same as n after interpolation. α is the transformation coefficient, α is the transformation angle, which is proportional to P, β is the cosecant function of α, γ is the cotangent function of α, and the range of m is the same as that of n before interpolation; Step 3: Use the N-sigma method to select the noise ratio coefficient and calculate the removal threshold, then transform the domain signal Perform spectrum excision; Th=ψ·δ+μ In the formula, ψ t is the preset proportional coefficient corresponding to the variance interval, the subscript t is the interval mark, and u and l are the upper and lower limit marks of the interval; Th is the set excision threshold, δ is the calculated transform domain signal variance; ψ is the currently selected noise proportional coefficient; Using the given cutting threshold Th, the spectrum line of the transformed signal is cut off; Step 4: Calculate the transform domain signal energy and analytical signal energy after removing the spectrum line, and construct the residual function; Step 5: Use the non-interpolation RMS method to perform peak search on the one-dimensional energy residual function; first, specify the initial step size T0, error tolerance ε and starting point a=0; then, determine the search sequence u0,u1,...,u v , and construct the initial search interval [u0, u v ]; In the formula, F i is the i-th Fibonacci number, u i is the i-th search variable, g i is the i-th search function, v is the number of search points; the starting point u0 of the search interval is equal to the starting point a, and the end point u of the search interval is equal to the starting point a. v is the first search function value g(u v ) is greater than the search variable u of the initial search function value g(u0) i , if v≤2, reduce the initial step length T0 to the original Repeat the above steps until a reasonable search sequence and search interval are obtained; Calculate the mean square value u of the above point v rms,q , insert it into the search sequence in ascending order of the search variable, and determine the minimum point B and its adjacent points A and C in the search interval. The above three points constitute a new search sequence and search interval, and then calculate the mean square value of the above three points; In the formula, the subscript rms is the symbol of the mean square value, q is the number of mean square value iterations, s is the subscript of the search variable with the smallest search function value in the search sequence, and min is the symbol for finding the minimum value. A, B, and C are the endpoints and minimum points of the new interval; According to the above mean square value calculation results, if it is established, stop the iteration and select the mean square value point u rms,q is the peak point of the energy residual function. Otherwise, add the mean square value point calculated by A, B, and C to the search sequence of A, B, and C, reconstruct a new search interval, calculate the mean square value again, and then return to this step: |in rms,q -in rms,q-1 |<ε|u rms,q | The peak point u of the energy residual function obtained by searching rms,q The corresponding transform domain signal after spectral line removal is in order -u rms,q According to step 3, the FRFT inverse transform is calculated to obtain the original discrete Beidou satellite signal after filtering out interference.

2. According to claim 1, a Beidou monitoring anti-interference method for power transmission lines based on energy residual search is characterized in that: The delay signal in step 1 The calculation formula is: In the formula, To obtain the discrete Hilbert transform result of the original satellite signal s[n], the total length of the s[n] sequence is N, n is the discrete sampling point variable in the time domain, and its value range is 1 to N. In the formula, K is the signal period extension number, s K [nk] is s[n] after period extension, k is the Shannon interpolation point variable, and its value range is 3. According to claim 2, a Beidou monitoring anti-interference method for power transmission lines based on energy residual search is characterized in that: The calculation formula of the analytical signal z[n] in step 1 is: Where j is the imaginary unit.

4. According to the energy residual search-based Beidou monitoring anti-interference method for power transmission lines according to claim 3, it is characterized in that: The expression of the scale factor S of the signal in step 1 is: The expression of normalized width Δx is:

5. According to claim 1, a Beidou monitoring anti-interference method for power transmission lines based on energy residual search is characterized in that: In step 3, μ is the calculated transform domain signal mean, and its expression is:

6. The method for Beidou monitoring and anti-interference of power transmission lines based on energy residual search according to claim 5 is characterized in that: In step 3, δ is the calculated transform domain signal variance, and its expression is:

7. The method for Beidou monitoring and anti-interference of power transmission lines based on energy residual search according to claim 1 is characterized in that: The residual function expression in step 4 is: res(P)=|E1-E2(P)| 2 Where res is the energy residual function, E1 is the calculated analytical signal energy, and E2 is the calculated transform domain signal energy after spectral line removal corresponding to the P-order transform.

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