A wind power Beidou anti-interference method based on learning automaton optimization FrFT

Abstract

The invention discloses a wind power Beidou anti-interference method of learning automaton optimization FrFT, comprising the following steps: 1. Analyze and represent Beidou signals containing frequency sweep interference; 2. Set the initial order p, perform fractional Fourier transform (FrFT) on the analytical signal to form an energy peak; 3. Convert the detection problem of the frequency sweep interference signal into the optimal order solution problem by comparing the size of the energy peak; 4. Use the learning automaton algorithm to narrow the search space, further solve the optimal order p, and then calculate the p-order FrFT of the analytical signal; 5. Use the N‑sigma algorithm to design a filter with an adaptive threshold; 6. Perform p-order fractional Fourier inverse transform on the processed signal to obtain the Beidou positioning signal after interference suppression. The present invention can effectively detect and suppress the influence of frequency sweep interference on Beidou signals, ensure the accuracy and stability of Beidou technology application in wind power environment, and has broad application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of high-precision satellite navigation, and in particular to a wind power Beidou anti-interference method of learning automaton optimization FrFT. Background Art

[0002] Under the trend of low-carbon development, wind power generation, as one of the fastest-growing green energy technologies, has broad prospects and relatively mature technology. In terms of foundation settlement monitoring of wind farm facilities, Beidou satellite navigation technology has become the most effective automated high-precision monitoring method. However, the application environment of wind turbine towers will produce strong electromagnetic interference, and the defects of Beidou positioning signals being affected by electromagnetic interference are gradually emerging. Therefore, it is very important to study the anti-interference technology of wind power Beidou receivers.

[0003] The commonly used methods for interference detection of existing wind power Beidou receivers include automatic gain control method, time domain method, frequency domain method and wavelet transform method. In an environment with weak interference, the detection performance of the AGC method will be greatly reduced. Regarding the use of time domain method or frequency domain method for navigation reception interference detection, they cannot fully describe the nature and characteristics of time-varying interference in the received navigation signal. Time-frequency analysis can observe the changing characteristics of the signal from two dimensions: time domain and frequency domain, and has become a powerful tool for processing non-stationary signals, especially swept frequency interference.

[0004] Among the many time-frequency analysis methods, the wavelet transform method has the disadvantages of being difficult to construct the wavelet basis and having time shift defects and frequency aliasing. The Wigner-Ville distribution has multiple signal terms that produce cross-term interference due to interaction, which will lead to the failure of original signal recognition. The fractional Fourier transform has advantages in processing swept frequency interference in non-stationary signals, but the performance of the fractional Fourier transform is affected by the optimal fractional order and the filter threshold. Therefore, a wind power Beidou anti-interference method based on learning automaton optimized FrFT is urgently needed to change this situation. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings of the prior art and propose a wind power Beidou anti-interference method of learning automaton optimization FrFT. Its advantages are that it can effectively suppress the influence of sweep frequency interference and noise, and retain good time-frequency positioning characteristics, thereby solving the problems of time-frequency compromise, cross-term interference, and energy non-aggregation of navigation reception signals in sweep frequency interference detection.

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

[0007] A wind power Beidou anti-interference method based on learning automaton optimization FrFT includes the following steps:

[0008] Step 1: Perform analytical transformation on the original continuous-time signal received by the Beidou receiver to obtain the analytical signal y s (t);

[0009] Step 2: Analyze the signal y s (t) Perform a p-order fractional Fourier transform (FrFT), and map the analytical signal to the u domain after Fourier transformation;

[0010] Step 3: Observe the analytical signal y s (t) The amplitude value after the p-order fractional Fourier transform. When the amplitude value reaches the maximum value, the analytical signal y s (t) Energy aggregation is formed in the fractional order domain, at which time the corresponding parameters p and u obtain the optimal values; therefore, the problem of the maximum amplitude value of the swept frequency interference signal in the fractional order domain can be transformed into the problem of solving the optimal order;

[0011] Step 4: Use the learning automaton algorithm to solve the optimal order p. To reduce the complexity of solving the optimal order, first roughly estimate the search interval of the optimal order p. Multiply the swept frequency interference signal s(t) with the conjugate signal delayed by τ time units to obtain the expression of the signal M(t):

[0012] M(t)=s(t)·s * (t-τ)

[0013] In the formula, s * (t-τ) is the conjugate of the signal s(t) delayed by τ time units; the expression of the swept frequency interference signal s(t) is:

[0014]

[0015] In the formula, represents the amplitude value A of the swept frequency interference; Substituting the expression of the swept frequency interference signal s(t) into the formula, we get

[0016]

[0017] The above formula is approximately a single-frequency complex sine signal. Perform a fast Fourier transform on the signal to obtain the frequency f M , then the frequency within the delay τ time unit can be estimated, and then the estimated order can be obtained

[0018]

[0019] In the formula, is the estimated rotation angle;

[0020] Initialize the action set of the learning automaton [p L ,p R ], obtained To roughly estimate the interval [p - ,p + ], then the action set [p L ,p R ] is initialized to [p - ,p + ]; Set the initial iteration number q to 1; the maximum amplitude is A max ;

[0021] Create an action according to the following formula:

[0022]

[0023] In the formula, represents the action selected when the number of iterations is q, that is, the order selected when the number of iterations is q; r q is a uniformly distributed random number between 0 and 1. The initial value of q is 1, and the corresponding p L and p R They are p - and p + ;

[0024] For the analytical signal y s (t) The transformed amplitude value A is q With the maximum amplitude A max Make comparison and feed back the reinforcement signal β(q);

[0025]

[0026] In the formula, the feedback reinforcement signal 0 represents success, 1 represents failure;

[0027] Update the action interval according to the feedback reinforcement signal β(q), p L and p R To update:

[0028]

[0029] Set the number of iterations q = q + 1, and continue the above steps until the action interval [p L ,p R ] is reduced to a point p'; this point is the optimal action, that is, the optimal order value p';

[0030] Step 5: After determining the optimal order value p' in step 4 above, calculate the analytical signal y s p'-order fractional Fourier transform of (t);

[0031] Step 6: Get F p'(u) Then, the N-sigma algorithm is used to set the adaptive threshold filter, and the spectrum lines exceeding the threshold are set to zero to suppress the interference signal;

[0032] The amplitude obtained in FrFT is converted into dB form, as shown in the following formula:

[0033] E u =10log 10 |F p′ [y s (t)](u)|

[0034] In the formula, E u is the amplitude in dB;

[0035] Calculate the mean μ of the fractional-order spectrum line of the x-th iteration signal respectively x and variance σ x ;

[0036] Calculate the xth weighting factor M by the standard deviation of the two iterations. x ; Calculate the xth iteration threshold value T x and will exceed the threshold T x The spectrum line is set to zero;

[0037] Step 7: Perform p'-order fractional Fourier inverse transform on the filtered signal to capture the normal Beidou positioning signal:

[0038]

[0039] Where y(t) is the captured analytical signal after filtering out the interference signal, F -p' (·) represents the fractional Fourier inverse transform operation, is the kernel function K p' Conjugate operation of (u,t).

[0040] The present invention is further configured that in step 1, the parsing signal y s The expression of (t) is: Where j is the imaginary root unit, y(t) represents the original continuous-time signal; Represents the signal of y(t) after Hilbert transform.

[0041] The present invention is further configured such that the calculation formula of the u domain in step 2 is: In the formula, F p (u) is the signal after p-order FrFT; F p (·) represents the FrFT operation; u is the time axis in the fractional domain.

[0042] The present invention is further configured that the K p(u, t) is the kernel function of FrFT, and its expression is:

[0043]

[0044] In the formula, p is the order, the rotation angle of the time-frequency surface n is an integer. When α=2nπ or α=(2n±1)π, K p (u,t) is the impulse response.

[0045] The present invention is further configured such that the formulas for the parameters p and u in step 3 are:

[0046] In the formula, |F p [y s (t)](u)| represents the analytical signal y s (t) The amplitude value in the fractional order domain; {p,u} represents the optimal order p and optimal u threshold corresponding to the maximum amplitude value.

[0047] The present invention is further configured that the analysis signal y in step 5 s The p'-order fractional Fourier transform formula of (t) is:

[0048] In the formula, F p' (u) is the signal after p'-order FrFT; F p' (·) represents FrFT operation; u is the time axis in the fractional domain; K p' (u,t) is the kernel function of FrFT.

[0049] The present invention is further configured such that the mean value μ in step 6 is x and variance σ x The calculation formula is:

[0050]

[0051] The present invention is further configured such that the weighting factor M in step 6 is x The calculation formula is:

[0052]

[0053] Where γ is the update factor, σ x-1 and σ x are the standard deviations of the x-1th and xth iterations respectively.

[0054] The present invention is further configured such that the xth iteration threshold value T in step 6 is x count

[0055] The calculation formula is:

[0056] T x =μ x +M x σ x

[0057]

[0058] Where M x F is an adaptive weighting factor. A high threshold weighting is selected for a high-power interference signal, and a low threshold weighting is selected for a low-power interference signal. p ” (u) is the analytical signal y containing swept frequency interference after FrFT s (t) Adaptive filter passed; |F p' [y s (t)](u)| is the amplitude value after FrFT, and H(u) is the filter function.

[0059] The beneficial effects of the present invention are:

[0060] 1. The method proposed in the present invention is more accurate in frequency estimation of interference. Interference detection is more accurate. The present invention adopts fractional-order Fourier transform optimized by learning automaton to overcome the limitation of short-time Fourier transform window function, and designs a filter with adaptive threshold of N-sigma algorithm. The method of the present invention is more accurate in frequency estimation of interference, greatly retains the power of useful signals, and enables high-precision positioning value of wind turbine tower to be obtained in interference environment.

[0061] 2. The method proposed in the present invention has high efficiency, good real-time performance, and realizes dynamic application. The present invention converts the detection domain separation problem of the swept frequency interference signal based on the fractional Fourier transform into the problem of solving the optimal order, and adopts the learning automaton method to optimize the optimal order of the fractional Fourier transform, thereby improving the search accuracy while reducing the computational complexity, having high real-time performance, and being able to be dynamically applied. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A schematic diagram of the working process of a wind power Beidou anti-interference method of optimizing FrFT by a learning automaton proposed by the present invention;

[0063] Figure 2 It is a WVD scale diagram of the GPS L1-C / A signal subjected to frequency sweep interference in the prior art;

[0064] Figure 3 A schematic diagram of the FrFT results of a swept frequency signal containing Gaussian white noise at the optimal order of a wind power Beidou anti-interference method of optimizing FrFT by a learning automaton proposed in the present invention;

[0065] Figure 4A schematic diagram of the FrFT amplitude of a Beidou signal with swept frequency interference in the presence of an interference-to-noise ratio of -2dB in a wind power Beidou anti-interference method of optimizing FrFT using a learning automaton proposed by the present invention;

[0066] Figure 5 This is a schematic diagram of signal capture after adaptive filtering is used to suppress frequency sweep interference in a wind power Beidou anti-interference method based on a learning automaton optimized FrFT proposed by the present invention. DETAILED DESCRIPTION

[0067] The technical solution of this patent is further described in detail below in conjunction with specific implementation methods.

[0068] 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.

[0069] Reference Figure 1 , a wind turbine tower Beidou positioning anti-interference method based on joint learning automaton optimization FrFT, comprising the following steps:

[0070] Step 1: Use equation (1) to perform analytical transformation on the original continuous-time signal received by the Beidou receiver to obtain the analytical signal y s (t):

[0071]

[0072] In formula (1), j is the imaginary root unit, y(t) represents the original continuous time signal; Represents the signal of y(t) after Hilbert transform;

[0073] Step 2: Within a certain fractional domain, FrFT has the best aggregation performance for swept frequency interference. Sweep frequency interference can only concentrate the energy of the signal after appropriate coordinate rotation and show the form of impulse function. Therefore, FrFT is most suitable for processing swept frequency interference signals. s (t) Perform a p-order fractional Fourier transform (FrFT). The analytical signal is mapped to the u domain after Fourier transformation. The calculation formula is:

[0074]

[0075] In formula (2), F p (u) is the signal after p-order FrFT; F p (·) represents FrFT operation; u is the time axis in the fractional domain; K p(u, t) is the kernel function of FrFT, and its expression is:

[0076]

[0077] In formula (3), p is the order, the rotation angle of the time-frequency surface n is an integer. When α=2nπ or α=(2n±1)π, K p (u, t) is the impulse response. The kernel function is not only a function of (u, t), but also related to the order p.

[0078] Step 3: Observe the analytical signal y s (t) The amplitude value after the p-order fractional Fourier transform. When the amplitude value reaches the maximum value, the analytical signal y s (t) forms energy aggregation in the fractional order domain, at which time the corresponding parameters p and u obtain the optimal values. Therefore, the problem of the maximum amplitude value of the swept frequency interference signal in the fractional order domain can be transformed into the problem of solving the optimal order, that is, satisfying the following formula:

[0079]

[0080] In formula (4), |F p [y s (t)](u)| represents the analytical signal y s (t) The amplitude value in the fractional order domain; {p,u} represents the optimal order p and optimal u threshold corresponding to the maximum amplitude value.

[0081] Step 4: Use the learning automaton algorithm to solve the optimal order p.

[0082] In order to reduce the complexity of solving the optimal order, we first roughly estimate the search interval of the optimal order p. Multiply the swept frequency interference signal s(t) with the conjugate signal delayed by τ time units, and the expression of the signal M(t) is:

[0083] M(t)=s(t)·s * (t-τ) (5)

[0085] In formula (5), s * (t-τ) is the conjugate of the signal s(t) delayed by τ time units. The expression of the swept frequency interference signal s(t) is

[0086]

[0087] In formula (6), represents the amplitude value A of the swept frequency interference. Substituting the expression of the swept frequency interference signal s(t) into formula (5), we get

[0088]

[0089] Formula (7) is approximately a single-frequency complex sinusoidal signal. The signal is subjected to a fast Fourier transform to obtain the frequency f M , then the frequency within the delay τ time unit can be estimated, and then the estimated order can be obtained

[0090]

[0091] In formula (8), is the estimated rotation angle.

[0092] Initialize the action set of the learning automaton [p L ,p R ], obtained according to step 4.1 To roughly estimate the interval [p - ,p + ], then the action set [p L ,p R ] is initialized to [p - ,p + ]; Set the initial iteration number q to 1; the maximum amplitude is A max .

[0093] Create an action according to the following formula:

[0094]

[0095] In formula (9), represents the action selected when the number of iterations is q, that is, the order selected when the number of iterations is q; r q is a uniformly distributed random number between 0 and 1. The initial value of q is 1, and the corresponding p L and p R They are p - and p + .

[0096] For the analytical signal y s (t) The transformed amplitude value A is q With the maximum amplitude A max Compare and feed back the enhanced signal β(q).

[0097]

[0098] In formula (10), the feedback reinforcement signal 0 represents success and 1 represents failure.

[0099] Update the action interval according to the feedback reinforcement signal β(q), p L and pR Update according to formula (11):

[0100]

[0101] Set the number of iterations q = q + 1, and continue the above steps until the action interval [p L ,p R ] is reduced to a point p'. This point is the optimal action, which is also the optimal order value p'.

[0102] Step 5: After determining the optimal order value p' in step 4 above, calculate the analytical signal y s The p'-order fractional Fourier transform of (t) is as follows:

[0103]

[0104] In formula (12), F p' (u) is the signal after p'-order FrFT; F p' (·) represents FrFT operation; u is the time axis in the fractional domain; K p' (u,t) is the kernel function of FrFT.

[0105] Step 6: Get F p' (u) Then, the N-sigma algorithm is used to set the adaptive threshold filter, and the spectrum lines exceeding the threshold are set to zero to suppress the interference signal.

[0106] The amplitude obtained in FrFT is converted into dB form, as shown in formula (13):

[0107] E u =10log 10 |F p′ [y s (t)](u)| (13)

[0109] In formula (13), E u It is the amplitude in dB.

[0110] Calculate the mean μ of the fractional-order spectrum line of the x-th iteration signal respectively x and variance σ x :

[0111]

[0112]

[0113] Calculate the xth weighting factor M by the standard deviation of the two iterations. x :

[0114]

[0115] In formula (16), γ is the update factor, σ x-1 and σ x are the standard deviations of the x-1th and xth iterations respectively.

[0116] Calculate the xth iteration threshold value T x and will exceed the threshold T x The spectrum line is set to zero.

[0117] T x =μ x +M x σ x (17)

[0119]

[0120] In formula (17), M x It is an adaptive weighting factor. A high threshold weighting is selected for a high-power interference signal, and a low threshold weighting is selected for a low-power interference signal.

[0121] In formula (18), F′ p′ (u) is the analytical signal y containing swept frequency interference after FrFT s (t) Adaptive filter passed; |F p' [y s (t)](u)| is the amplitude value after FrFT, and H(u) is the filter function.

[0122] Step 7: Perform p'-order fractional Fourier inverse transform on the filtered signal to capture the normal Beidou positioning signal.

[0123]

[0124] In formula (19), y(t) is the captured analytical signal after filtering out the interference signal, F -p' (·) represents the fractional Fourier inverse transform operation, is the kernel function K in formula (3) p' Conjugate operation of (u,t).

[0125] The present invention adopts a software jammer to generate a swept frequency interference signal for a GNSS application. The generated swept frequency interference is added to the GPS samples collected by the front end of the GNSS receiver, thereby generating a GPS signal interfered by the swept frequency interference.

[0126] To verify the effectiveness of this method, it is compared with the existing classic method WVD. Figure 2The WVD of the GPS L1-C / A signal in the presence of scanning interference is depicted. Although a straight line can be seen on the TF plane to represent the frequency modulation law of the scanning interference, severe cross terms can also be observed due to the bilinear nature of the WVD, which inevitably leads to errors in the instantaneous frequency estimation. The scanning interference signal makes it difficult to detect the interference, so the GNSS interference characteristic parameters cannot be correctly extracted using the WVD.

[0127] Figure 3 This is the processing result of the FrFT of the satellite navigation signal containing frequency sweep interference at the optimal order p = 0.9231 after the learning automaton method is used to solve the optimal stage p. In the figure, there is a pulse-shaped peak that is significantly larger than other components. This peak represents the signal component of the frequency sweep interference. Other peaks represent the satellite navigation signal itself and Gaussian white noise interference.

[0128] Figure 4 The amplitude of the GPS L1-C / A signal with C / N0=40dB and JNR=-2dB subjected to frequency sweep interference after the learning automaton optimizes FrFT. According to the rotation characteristics of FrFT, it can be clearly seen that there is an energy peak in the parameter domain, and the largest energy peak is the contribution of the corresponding frequency sweep interference. The corresponding frequency sweep interference interference parameter information can be calculated by locating the corresponding peak in the parameter domain.

[0129] Figure 5 The signal capture diagram after adaptive filtering is used to suppress the swept frequency interference. It can be seen from the figure that the signal component representing the swept frequency interference (the section perpendicular to the u-axis) is effectively removed in the transform domain, and the remaining irregular signal component represents the original Beidou positioning signal.

[0130] 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 wind power Beidou anti-interference method based on learning automaton optimization FrFT, characterized in that: The following steps are involved: Step 1: Perform analytical transformation on the original continuous-time signal received by the Beidou receiver to obtain the analytical signal y s (t); Step 2: Analyze the signal y s (t) Perform a p-order fractional Fourier transform (FrFT), and map the analytical signal to the u domain after Fourier transformation; Step 3: Observe the analytical signal y s (t) The amplitude value after the p-order fractional Fourier transform. When the amplitude value reaches the maximum value, the analytical signal y s (t) Energy aggregation is formed in the fractional order domain, at which time the corresponding parameters p and u obtain the optimal values; therefore, the problem of the maximum amplitude value of the swept frequency interference signal in the fractional order domain can be transformed into the problem of solving the optimal order; Step 4: Use the learning automaton algorithm to solve the optimal order p. To reduce the complexity of solving the optimal order, first roughly estimate the search interval of the optimal order p. Multiply the swept frequency interference signal s(t) with the conjugate signal delayed by τ time units to obtain the expression of the signal M(t): M(t)=s(t)·s * (t-τ) In the formula, s * (t-τ) is the conjugate of the signal s(t) delayed by τ time units; the expression of the swept frequency interference signal s(t) is: In the formula, represents the amplitude value A of the swept frequency interference; Substituting the expression of the swept frequency interference signal s(t) into the formula, we get The above formula is approximately a single-frequency complex sine signal. Perform a fast Fourier transform on the signal to obtain the frequency f M , then the frequency within the delay τ time unit can be estimated, and then the estimated order can be obtained In the formula, is the estimated rotation angle; Initialize the action set of the learning automaton [p L ,p R ], obtained To roughly estimate the interval [p - ,p + ], then the action set [p L ,p R ] is initialized to [p - ,p + ]; Set the initial iteration number q to 1; the maximum amplitude is A max ; Create an action according to the following formula: In the formula, represents the action selected when the number of iterations is q, that is, the order selected when the number of iterations is q; r q is a uniformly distributed random number between 0 and 1; the initial value of q is 1, and the corresponding p L and p R They are p - and p + ; For the analytical signal y s (t) The transformed amplitude value A is q With the maximum amplitude A max Make comparison and feed back the reinforcement signal β(q); In the formula, the feedback reinforcement signal 0 represents success, 1 represents failure; Update the action interval according to the feedback reinforcement signal β(q), p L and p R To update: Set the number of iterations q = q + 1, and continue the above steps until the action interval [p L ,p R ] is reduced to a point p'; this point is the optimal action, that is, the optimal order value p'; Step 5: After determining the optimal order value p' in step 4 above, calculate the analytical signal y s p'-order fractional Fourier transform of (t); Step 6: Get F p' (u) Then, the N-sigma algorithm is used to set the adaptive threshold filter, and the spectrum lines exceeding the threshold are set to zero to suppress the interference signal; The amplitude obtained in FrFT is converted into dB form, as shown in the following formula: E u D10log 10 |F p’ [y s (t)](u)| In the formula, E u is the dB form of amplitude; F p (·) indicates FrFT operation; Calculate the mean μ of the fractional-order spectrum line of the x-th iteration signal respectively x and variance σ x ; Calculate the xth weighting factor M by the standard deviation of the two iterations. x ; Calculate the xth iteration threshold value T x and will exceed the threshold T x The spectrum line is set to zero; Step 7: Perform p'-order fractional Fourier inverse transform on the filtered signal to capture the normal Beidou positioning signal: Where y(t) is the captured analytical signal after filtering out the interference signal, F -p' (·) represents the inverse fractional Fourier transform operation, is the kernel function K p' Conjugate operation of (u,t).

2. According to claim 1, a wind power Beidou anti-interference method of learning automaton optimization FrFT is characterized in that: In step 1, the signal y is analyzed s The expression of (t) is: Where j is the imaginary root unit, y(t) represents the original continuous-time signal; Represents the signal of y(t) after Hilbert transform.

3. The wind power Beidou anti-interference method of learning automaton optimization FrFT according to claim 1 is characterized in that: The calculation formula of the u domain in step 2 is: In the formula, F p (u) is the signal after p-order FrFT; F p (·) represents FrFT operation; u is the time axis in the fractional domain; K p' (u,t) is the kernel function of FrFT.

4. The wind power Beidou anti-interference method of learning automaton optimization FrFT according to claim 3 is characterized in that: The K p (u, t) is the kernel function of FrFT, and its expression is: In the formula, p is the order, the rotation angle of the time-frequency surface n is an integer; when α=2nπ or α=(2n±1)π, K p (u,t) is the impulse response.

5. The wind power Beidou anti-interference method of learning automaton optimization FrFT according to claim 1 is characterized in that: The formulas for the parameters p and u in step 3 are: In the formula, |F p [y s (t)](u)| represents the analytical signal y s (t) The amplitude value in the fractional order domain; {p,u} represents the optimal order p and optimal u threshold corresponding to the maximum amplitude value.

6. The wind power Beidou anti-interference method of learning automaton optimization FrFT according to claim 1 is characterized in that: In step 5, the signal y is analyzed s The p'-order fractional Fourier transform formula of (t) is: In the formula, F p' (u) is the signal after p'-order FrFT; F p' (·) represents FrFT operation; u is the time axis in the fractional domain; K p' (u,t) is the kernel function of FrFT.

7. The wind power Beidou anti-interference method of learning automaton optimization FrFT according to claim 1 is characterized in that: The mean value μ in step 6 x and variance σ x The calculation formula is:

8. The wind power Beidou anti-interference method of learning automaton optimization FrFT according to claim 7 is characterized in that: The weighting factor M in step 6 x The calculation formula is: Where γ is the update factor, σ x-1 and σ x are the standard deviations of the x-1th and xth iterations respectively.

9. The wind power Beidou anti-interference method of learning automaton optimization FrFT according to claim 8 is characterized in that: The xth iteration threshold value T in step 6 x The calculation formula is: T x =μ x +M x s x Where M x is an adaptive weighting factor. A high threshold weighting is selected for a high-power interference signal, and a low threshold weighting is selected for a low-power interference signal. F p ” (u) is the analytical signal y containing swept frequency interference after FrFT s (t) Adaptive filter passed; |F p' [y s (t)](u)| is the amplitude value after FrFT, and H(u) is the filter function.

Images