Short-time adaptive time-varying filtering method based on grid search

Abstract

The invention discloses a short-time adaptive time-varying filtering method based on grid search, and the method comprises the steps: obtaining input interference, and segmenting the input interference into a plurality of short-time interferences; determining the total number of segments, and initializing a current segment serial number and a segment serial number counter; judging whether the segment serial number is equal to the total segment number; extracting short-time interference from the obtained input interference, and for each section of short-time interference, carrying out the following processing: calculating an instantaneous frequency parameter vector by using discrete Fourier transform of the short-time interference; based on the short-time interference and the instantaneous frequency parameter vector, filtering the short-time interference by using a grid search and orthogonal subspace projection method; and extracting a short-time interference final filtering result from the current filtering result. According to the method, the estimation accuracy of the interference instantaneous frequency is remarkably improved, so that the filtering effect is effectively enhanced. Particularly, when the interference and the target signal are in the same frequency band, the method can automatically identify the instantaneous frequency of the interference and filter the instantaneous frequency without causing loss to useful signals.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal and information processing, and particularly relates to a short-time adaptive time-varying filtering method based on grid search. Background Art

[0002] In the fields of modern technology and engineering, signal processing is a very important field. Whether in communication, radar, biomedical imaging or other fields, signal processing is indispensable. However, signals in the actual environment are often affected by various interferences, which will seriously affect the quality and reliability of the signals. Therefore, an efficient filter is needed to remove these interferences to ensure the accuracy and stability of the signals.

[0003] In the prior art, according to the working principles and methods of filters, common ones include adaptive filters and convolutional filters; adaptive filters can adaptively adjust filter parameters and are applicable to non-linear systems, but a reference signal needs to be introduced in advance and they cannot handle unknown interferences; convolutional filters are simple and easy to understand, but they show high sensitivity when facing noise and sudden interferences and cannot handle short signals; according to the frequency response characteristics of filters, common ones include low-pass filters, high-pass filters, band-pass filters and band-stop filters, which can effectively suppress interferences in a specified frequency band, but the range of interference frequencies needs to be known in advance. If the interference and the useful signal are in the same frequency band, while suppressing the interference, the useful signal will also be lost and the useful signal cannot be correctly identified. Moreover, traditional filters have certain limitations in dealing with time-varying interferences and cannot effectively adaptively identify and remove interferences. Therefore, there is a need for a filter that can overcome the above disadvantages. Summary of the Invention

[0004] The object of the present invention is to provide a short-time adaptive time-varying filtering method based on grid search, which can automatically identify the instantaneous frequency of the interference and perform filtering to remove the interference.

[0005] To achieve the above task, the present invention adopts the following technical solutions:

[0006] A short-time adaptive time-varying filtering method based on grid search, comprising:

[0007] S1. Obtain the input interference s(n), segment the input interference s(n) into several short-time interferences; determine the total number of segments L and initialize the current segment number l s and the counter Count s of l ls ;

[0008] S2. Judge whether the segment number l s is equal to the total number of segments L; if l sIf it is equal to the total number of segments \(L\), then the final instantaneous frequency estimation of all short-time interferences has been completed; otherwise, update \(l\). s = Count ls + 1, Count ls = \(l\) s , and jump to step S3 to extract the \(l\)-th s segment of short-time interference;

[0009] S3. Extract the \(l\)-th s segment of short-time interference \(s\) s (n 1 ) from the obtained input interference \(s(n)\);

[0010] S4. Calculate the instantaneous frequency parameter vector \(\theta\) using the discrete Fourier transform of the \(l\)-th s segment of short-time interference \(s\) s (n 1 );

[0011] S5. Based on the \(l\)-th s segment of short-time interference and the instantaneous frequency parameter vector \(\theta\), filter the \(l\)-th s segment of short-time interference using the grid search and orthogonal subspace projection method;

[0012] S6. Extract the final filtering result \(s\) fBest of the \(l\)-th s segment of short-time interference from the current filtering result \(S\) f (n 2 ), and then return to step S2.

[0013] Furthermore, the initial values of the total number of segments \(L\), segment number \(l\) s and Count ls are respectively: l s = 0; Count ls = 0; \(N\) represents the total length of the input interference \(s(n)\), \(N\) w represents the length of each segment of short-time interference; represents rounding down.

[0014] Furthermore, the extraction of the \(l\)-th s segment of short-time interference \(s\) s (n 1 ) from the obtained input interference \(s(n)\) is expressed as:

[0015] s s (n 1 ) = s(n 1 + \(l\) s \(N\) w - \(N\) w ), \(n\) 1 = 1, 2,..., \(N\)w

[0016] Among them, n 1 represents the nth 1 sampling point.

[0017] Furthermore, the calculation of the instantaneous frequency parameter vector θ by using the discrete Fourier transform of the lth s segment of short-time interference s s (n 1 ) includes:

[0018] S4.1, according to the extracted lth s segment of short-time interference s s (n 1 ), calculate the discrete Fourier transform S stft (F):

[0019]

[0020] Among them, e is the natural constant, represents the imaginary symbol, m represents the mth sampling point, F represents the normalized frequency, and N fft represents the total number of discrete Fourier transform frequency points;

[0021] S4.2, calculate the instantaneous frequency parameter vector θ according to the discrete Fourier transform S stft (F):

[0022] θ = [F max , 0 1×Q-1 T

[0023] Among them, 0 1×Q-1 represents a 1×Q - 1 dimensional zero vector, Q represents the maximum order of the basis function space, and [] T represents the transpose.

[0024] Furthermore, based on the lth s segment of short-time interference and the instantaneous frequency parameter vector θ, use the grid search and orthogonal subspace projection method to filter the lth s segment of short-time interference, including:

[0025] S5.1, initialize the grid search iteration round number l l = 0, the counter Count l of l ll = 1; initialize the global minimum residual power ε min = +∞;

[0026] S5.2, judge whether the search iteration round number l l is equal to the total number of search iterations L l ​; If l is equal to the total number of search iterations L l , the filtering of the short-term interference for the l s th time is completed, the loop ends, and it jumps to step S6; If l is not equal to the total number of search iterations L l , then execute the update of l l = Count ll + 1, Count ll = l l , and jump to step S5.3;

[0027] S5.3, Initialize the search point index k = 0 and the counter Count k of k to 0; Uniformly distribute N up values between the upper limit θ down and the lower limit θ s of the instantaneous frequency parameter vector θ for each dimension as search points, and establish a search point set θ s ;

[0028] S5.4, Determine whether the search point index k is equal to the total number of search points N k ; If the search point index k is equal to the total number of search points N k , the calculation of all search points is completed, and it jumps to step S5.2; If the search point index k is not equal to the total number of search points N k , then execute k = Count k + 1, Count k = k, and jump to step S5.5;

[0029] S5.5, Through the current search point θ k , use the basis function space expansion to obtain the estimated instantaneous frequency f s (n 1 ) of this short-term interference;

[0030] S5.6, Accumulate and sum the estimated instantaneous frequency f s (n 1 ) to obtain the estimated instantaneous phase

[0031] S5.7, Calculate the projected residual power ε using orthogonal subspace projection;

[0032] S5.8, Determine whether the residual power ε corresponding to the search point is less than the global minimum residual power ε min ;

[0033] If the residual power ε is not less than the global minimum residual power ε min , then jump to step S5.4;

[0034] If the residual power ε is less than the global minimum residual power εmin , then update the instantaneous frequency parameter vector θ = θ k , the global minimum residual power ε min = ε and save the result S after short-time interference filtering f as the current filtering result S fBest = S f ; Jump to step S5.4 to calculate the residual power of the next search point.

[0035] Further, the upper limit θ up and the lower limit θ down of the instantaneous frequency parameter vector θ are expressed as:

[0036] θ up = θ + 0.1×1 Q×1

[0037] θ down = θ - 0.1×1 Q×1

[0038] where, 1 Q×1 represents a Q×1 all-ones matrix, and the number of sampling points N s = 100, the total number of search points

[0039] Further, the estimated instantaneous frequency f s (n 1 ) of the short-time interference obtained by expanding in the basis function space is expressed as:

[0040]

[0041] where, the parameter superscript T represents the transpose operation, and the search point θ k is the k-th search point in the search point set θ s , and the formula for the basis function space U(n 1 ) is as follows:

[0042]

[0043] Further, the projection residual power ε is calculated by using orthogonal subspace projection, and the specific formula is:

[0044] S s = [s s (1), …, s s (N w )] T

[0045]

[0046] P ⊥ = I - S P(S P H S P ) -1 S P

[0047] S f = P ⊥ S s

[0048] ε = ||S f || 2

[0049] where S s is the matrix representation of the l-th s short-time interference, e is the natural constant, j is the imaginary unit, S P is the matrix representation of the estimated short-time interference, P ⊥ is the orthogonal projection matrix of the estimated short-time interference matrix S P , the superscript H represents the conjugate transpose, I represents the identity matrix, S f represents the result after short-time interference filtering, || || 2 represents the 2-norm.

[0050] Furthermore, the extraction of the final filtering result s fBest of the l-th s short-time interference from the current filtering result S f (n 2 ):

[0051]

[0052] N ls = l s * N w - N w + 1

[0053] where N ls is the starting serial number of the l-th s short-time interference, represents the (n fBest - N 2 + 1)-th element in the optimal filtering result S ls , n 2 represents the n-th 2 sampling point.

[0054] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, the short-time adaptive time-varying filtering method based on grid search is implemented.

[0055] A computer-readable storage medium stores a computer program therein; when the computer program is executed by a processor, the short-time adaptive time-varying filtering method based on grid search is implemented.

[0056] Compared with the prior art, the present invention has the following technical features:

[0057] 1. The present invention iteratively updates the instantaneous frequency parameter vector through a grid search algorithm, thereby accurately estimating the instantaneous frequency and performing filtering. The entire process does not rely on a reference signal and is completely data-driven.

[0058] 2. The present invention adopts an orthogonal subspace projection method to reduce the influence of noise on the instantaneous frequency estimation, and has excellent anti-noise performance.

[0059] 3. The present invention uses an orthogonal subspace projection method for filtering processing, and can effectively and accurately process short-time interference.

[0060] 4. Compared with the prior art, the short-time adaptive time-varying filtering method based on grid search of the present invention has a significant improvement in the accuracy of interference instantaneous frequency estimation, thereby effectively enhancing the filtering effect. In particular, when the interference and the target signal are in the same frequency band, the present invention can automatically identify the instantaneous frequency of the interference and filter it out to ensure that there is no loss to the useful signal. Description of the Drawings

[0061] Figure 1 It is a flowchart of the short-time adaptive time-varying filtering method based on grid search;

[0062] Figure 2 It is a flowchart of short-time interference filtering using grid search and orthogonal subspace projection methods;

[0063] Figure 3 It is a time-frequency distribution diagram of the short-time Fourier transform of the simulated linear frequency modulation interference in Embodiment 1;

[0064] Figure 4 It is a comparison diagram of the true instantaneous frequency curve and the filtered instantaneous frequency curve of the simulated linear frequency modulation interference in Embodiment 1;

[0065] Figure 5 It is a comparison diagram of the real part of the simulated linear frequency modulation interference and the real part of the filtering result in Embodiment 1;

[0066] Figure 6 It is a comparison diagram of the imaginary part of the simulated linear frequency modulation interference and the imaginary part of the filtering result in Embodiment 1;

[0067] Figure 7 It is a time-frequency distribution diagram of the short-time Fourier transform of the simulated sawtooth wave frequency modulation interference in Embodiment 2;

[0068] Figure 8 It is a comparison graph of the true instantaneous frequency curve and the filtered instantaneous frequency curve of the simulated sawtooth frequency modulation interference in Embodiment 2;

[0069] Figure 9 It is a comparison graph of the real part of the simulated sawtooth frequency modulation interference and the real part of the filtering result in Embodiment 2;

[0070] Figure 10 It is a comparison graph of the imaginary part of the simulated sawtooth frequency modulation interference and the imaginary part of the filtering result in Embodiment 2.

[0071] Figure 11 It is a comparison graph of the root mean square error of the instantaneous frequencies of the simulated linear frequency modulation interference and the simulated sawtooth frequency modulation interference varying with the signal-to-noise ratio in Embodiment 3;

[0072] Figure 12 It is a comparison graph of the interference residual rate of the simulated linear frequency modulation interference and the simulated sawtooth frequency modulation interference varying with the signal-to-noise ratio in Embodiment 3. Specific implementation manner

[0073] As Figure 1 and Figure 2 shown, a short-time adaptive time-varying filtering method based on grid search provided by the present invention includes:

[0074] S1. Obtain the input interference s(n), and segment the input interference s(n) into several short-time interferences; determine the total number of segments L, and initialize the current segment number l s and s counter Count ls .

[0075] Among them, the initial values of the total number of segments L, the segment number l s and Count ls are respectively: l s =0; Count ls =0; N represents the total length of the input interference s(n), N w represents the length of each short-time interference; represents rounding down. In this scheme, the length N w of each short-time interference takes the value of 8.

[0076] S2. Judge whether the segment number l s is equal to the total number of segments L; if l s is equal to the total number of segments L, the final instantaneous frequency estimation of all short-time interferences has been completed, the loop ends, and the overall filtering is completed; if l s is not equal to the total number of segments L, then execute to update l s =Count ls +1, Count ls =ls , and jump to step S3 to extract the l-th s short-time interference segment.

[0077] S3. Extract the l-th s short-time interference segment s s (n 1 ) from the obtained input interference s(n), where:

[0078] s s (n 1 ) = s(n 1 + l s N w - N w ), n 1 = 1, 2,..., N w

[0079] where n 1 represents the n-th 1 sampling point.

[0080] S4. Calculate the instantaneous frequency parameter vector θ using the discrete Fourier transform of the l-th s short-time interference segment s s (n 1 ).

[0081] S4.1. Calculate the discrete Fourier transform S s (F) according to the extracted l-th s short-time interference segment s 1 (n stft ). The specific formula is:

[0082]

[0083] where e is the natural constant, represents the imaginary unit, m represents the m-th sampling point, F represents the normalized frequency, and N fft represents the total number of discrete Fourier transform frequency points, which is 100 in this scheme.

[0084] S4.2. Calculate the instantaneous frequency parameter vector θ according to the discrete Fourier transform S stft (F). The specific formula is:

[0085] θ = [F max , 0 1×Q-1 T

[0086] where 0 1×Q-1 represents a 1×Q - 1 dimensional zero vector, Q represents the maximum order of the basis function space, and [] T represents the transpose. In this scheme, Q is taken as 2.​

[0087] S5. Based on the short-term interference and instantaneous frequency parameter vector θ in the l-th segment, use the grid search and orthogonal subspace projection method to filter the short-term interference in the l-th segment. s For the short-term interference and instantaneous frequency parameter vector θ in the l-th segment, use the grid search and orthogonal subspace projection method to filter the short-term interference in the l-th segment. s

[0088] S5.1. Initialize the grid search iteration count l l = 0, the counter Count of l l = 1; Initialize the global minimum residual power ε ll = +∞; min

[0089] S5.2. Determine whether the search iteration count l l is equal to the total number of search iterations L l ; If l is equal to the total number of search iterations L l , the filtering of the short-term interference in the l-th segment has been completed, end the loop, and jump to step S6; if l is not equal to the total number of search iterations L s , then execute to update l l = Count l + 1, Count ll = l ll , and jump to step S5.3 for more accurate filtering; among them, the total number of iterations L in this scheme l = 10. l

[0090] S5.3. Initialize the search point index k = 0, the counter Count of k k = 0; Each dimension is uniformly distributed with N up values between the upper limit θ down and the lower limit θ s of the instantaneous frequency parameter vector θ as search points, and establish a search point set θ s , and the specific formula is:

[0091] θ up = θ + 0.1×1 Q×1

[0092] θ down = θ - 0.1×1 Q×1

[0093] where 1 Q×1 represents a Q×1 all-ones matrix, and the number of value points N in the present invention s = 100, the total number of search points

[0094] S5.4. Determine whether the search point index k is equal to the total number of search points N k ; If the search point index k is equal to the total number of search points N​​​k , all the search point calculations are completed, the loop ends, and it jumps to step S5.2; if the search point index k is not equal to the total number of search points N k , then execute k = Count k + 1, Count k = k, and jump to step S5.5 to calculate the residual power of the next search point.

[0095] S5.5, through the current search point θ k , use the basis function space expansion to obtain the estimated instantaneous frequency f s (n 1 ):

[0096]

[0097] Among them, the parameter superscript T represents the transpose operation, and the search point θ k is the k-th search point in the search point set θ s , and the formula for the basis function space U(n 1 ) is as follows:

[0098]

[0099] S5.6, perform cumulative summation on the estimated instantaneous frequency f s (n 1 ) to obtain the estimated instantaneous phase The specific formula is:

[0100]

[0101] S5.7, use orthogonal subspace projection to calculate the projected residual power ε, and the specific formula is:

[0102] S s = [s s (1), …, s s (N w )] T

[0103]

[0104] P ⊥ = I - S P (S P H S P ) -1 S P

[0105] S f = P ⊥ S s

[0106] ε = ||S f || 2

[0107] where S s is the matrix representation of the l s -th short-time interference, S P is the matrix representation of the estimated short-time interference, P ⊥ is the orthogonal projection matrix of the estimated short-time interference matrix S P , the superscript H represents the conjugate transpose, I represents the identity matrix, S f represents the result after filtering, || || 2 represents the 2-norm;

[0108] S5.8. Judge whether the residual power ε corresponding to the search point is less than the global minimum residual power ε min ;

[0109] If the residual power ε is not less than the global minimum residual power ε min , then jump to step S5.4;

[0110] If the residual power ε is less than the global minimum residual power ε min , then update the instantaneous frequency parameter vector θ = θ k , the global minimum residual power ε min = ε and save the result S f after filtering the short-time interference as the current filtering result S fBest = S f , and jump to step S5.4 to calculate the residual power of the next search point;

[0111] S6. Extract the final filtering result s fBest of the l s -th short-time interference from the current filtering result S f (n 2 ), and then return to step S2; The specific extraction formula is:

[0112]

[0113] N ls = l s * N w - N w + 1

[0114] where N ls is the starting serial number of the l s -th short-time interference, represents the n fBest -th 2 - N ls + 1 element in the optimal filtering result S

[0115] Embodiment:

[0116] In an embodiment of the present invention, the model of the simulated linear frequency modulation interference s(n) is:

[0117]

[0118] where A is the interference amplitude, F s is the sampling rate, f 1 is the starting frequency of the interference, f 2 is the ending frequency of the interference, is the initial phase of the interference, and N is the total length of the interference. w(n) is additive white Gaussian noise with a mean of 0 and a variance of σ 2 The magnitude is determined by the jamming-to-noise ratio JNR, and the specific formula is:

[0119]

[0120] To accurately evaluate the filter effect, the root mean square error RMSE of the instantaneous frequency and the interference power residue rate R p are used as evaluation indicators, and the specific formula is:

[0121]

[0122] where f r (n) is the true instantaneous frequency of the interference, and f(n) is the filtered instantaneous frequency.

[0123] Embodiment 1:

[0124] In this embodiment, linear frequency modulation interference is used, and the parameter settings are: interference amplitude A = 10, sampling rate F s = 1000Hz, starting frequency of the interference f 1 = 100, ending frequency of the interference f 2 = 400, initial phase The total length of the interference N = 1000, signal-to-noise ratio SNR = 20dB, Figure 3 The time-frequency distribution diagram of the short-time Fourier transform of the linear frequency modulation interference is given.

[0125] According to step 1, input the interference s(n), segment the input interference s(n) into several short-time interferences, calculate the total number of segments L = 125, and initialize the current segment number l s = 0, Count ls is l s counter.

[0126] According to step 2, determine whether the segment number l s is equal to the total number of segments L;

[0127] If l s is equal to the total number of segments L, the final instantaneous frequency estimation of all short-time interferences is completed, the loop is ended, and the overall filtering is completed;

[0128] If l s is not equal to the total number of segments L, then execute l s = Count ls + 1, Count ls = l s , and jump to step S3 to extract the l s -th segment of short-time interference.

[0129] According to step 3, extract the l s -th segment of short-time interference s s (n 1 ).

[0130] According to step 4, use the discrete Fourier transform to calculate the instantaneous frequency parameter vector θ = [0.1, 0] T .

[0131] According to step 5, through the l s -th segment of short-time interference and the instantaneous frequency parameter vector θ, use the grid search and orthogonal subspace projection method to filter the l s -th segment of short-time interference.

[0132] According to step 6, extract the final filtering result s s of the l f (n 2 ), execute step S2 to determine whether all short-time interferences have been processed.

[0133] The comparison graph of the true instantaneous frequency curve and the filtered instantaneous frequency curve of the simulated linear frequency modulation interference is as Figure 4 shown. The root mean square error of the instantaneous frequency is 0.5160. The filtered instantaneous frequency curve basically fits the true instantaneous frequency curve, and the error is small. Such a result also confirms that the algorithm of the present invention can effectively use the grid search to iteratively update the instantaneous frequency parameter vector, thereby obtaining accurate instantaneous frequency and accurately filtering out interference. The comparison graph of the real part and the imaginary part of the simulated linear frequency modulation interference and the filtering result is as Figure 5 and Figure 6 shown, and the interference has been basically filtered out.

[0134] Example 2:

[0135] In this example, a sawtooth wave frequency modulation interference is used, which is composed of two segments of linear frequency modulation interference. The parameters of the first segment of linear frequency modulation interference are set as follows: interference amplitude A = 10, sampling rate F s = 1000Hz, the starting frequency f 1 of the interference = -100, the ending frequency f2 = 500, initial phase The total length of the interference N = 500, the jamming-to-noise ratio JNR = 20 dB, and the parameters of the second chirp interference are set as follows: the interference amplitude A = 10, the sampling rate F s = 1000 Hz, the starting frequency f of the interference 1 = 0, the ending frequency f of the interference 2 = -300, initial phase The total length of the interference N = 500, the jamming-to-noise ratio JNR = 20 dB, Figure 7 The time-frequency distribution diagram of the short-time Fourier transform of the sawtooth frequency modulation interference is given.

[0136] According to step 1, input the interference s(n), segment the input interference s(n) into several short-time interferences, calculate the total number of segments L = 125, and initialize the current segment number l s = 0, Count ls is l s counter.

[0137] According to step 2, judge whether the segment number l s is equal to the total number of segments L;

[0138] If l s is equal to the total number of segments L, the final instantaneous frequency estimation of all short-time interferences has been completed, the loop ends, and the overall filtering is completed;

[0139] If l s is not equal to the total number of segments L, then execute l s = Count ls + 1, Count ls = l s , and jump to step S3 to extract the l s th short-time interference.

[0140] According to step 3, extract the l s th short-time interference s s (n 1 ).

[0141] According to step 4, use the discrete Fourier transform to calculate the instantaneous frequency parameter vector θ = [-0.1, 0] T .

[0142] According to step 5, through the l s th short-time interference and the instantaneous frequency parameter vector θ, use the grid search and orthogonal subspace projection method to filter the l s th short-time interference.

[0143] According to step 6, extract the final filtering result s of the l s th short-time interferencef (n 2 ),perform step S2 to determine whether all short-term interferences have been processed.

[0144] The comparison diagram of the true instantaneous frequency curve of the simulated sawtooth frequency modulation interference and the filtered instantaneous frequency curve is as Figure 8 shown. Excluding 8 sampling points of the intermediate frequency transition, the root mean square error of the instantaneous frequency is 0.5321. The filtered instantaneous frequency curve basically fits the true instantaneous frequency curve, and the error is small. Such a result also confirms that the algorithm of the present invention can effectively use grid search to iteratively update the instantaneous frequency parameter vector, thereby obtaining accurate instantaneous frequency and accurately filtering out interference. The comparison diagram of the real part and the imaginary part of the simulated linear frequency modulation interference and the filtering result is as Figure 9 and Figure 10 shown, and the interference has been basically filtered out.

[0145] Example 3:

[0146] In this example, 2100 Monte Carlo experiments are carried out. The dry signal-to-noise ratio ranges from 0 dB to 20 dB, with an interval of 1 dB. The interference patterns are linear frequency modulation interference and sawtooth frequency modulation interference respectively.

[0147] Among them, the parameters of the linear frequency modulation interference are: interference amplitude A = 10, sampling rate F s = 1000 Hz, the starting frequency f 1 of the interference is a random number within [-500, 500], the ending frequency f 2 of the interference is a random number within [-500, 500], the initial phase is a random number within [0, π], and the total length N of the interference is 1000.

[0148] The sawtooth frequency modulation interference is composed of two segments of linear frequency modulation interference. The parameter settings of the two segments of linear frequency modulation interference are: interference amplitude A = 10, sampling rate F s = 1000 Hz, the starting frequency f 1 of the interference is a random number within [-500, 500], the ending frequency f 2 of the interference is a random number within [-500, 500], the initial phase is a random number within [0, π], and the total length N of each segment of interference is 500.

[0149] The results of the root mean square error are as Figure 11 shown. From Figure 11It can be seen that whether it is linear frequency modulation interference or sawtooth wave frequency modulation interference, when the SNR increases, the RMSE value gradually decreases and tends to be stable, and the RMSE value is relatively small at high SNR. This indicates that the short-time adaptive time-varying filtering method based on grid search proposed by the present invention can more accurately estimate the instantaneous frequency of interference. In addition, since this method filters by segmenting short-time interference, the filtering effect is not affected by the frequency change trend. Even if there are breakpoints in the frequency change, it will not have an adverse impact on the filtering effect.

[0150] The results of the interference residual power are as Figure 12 shown. It can be seen from Figure 12 that whether it is linear frequency modulation interference or sawtooth wave frequency modulation interference, the residual interference rate is less than 0.2%. Among them, the filtering effect is relatively poor at the turning point of the sawtooth interference frequency. However, since each short-time interference only has eight sampling points, it has little impact on the overall filtering effect. This indicates that the short-time adaptive time-varying filtering method based on grid search proposed by the present invention, on the basis of accurately estimating the interference frequency, uses the orthogonal subspace projection method for filtering processing, can accurately eliminate short-time interference, and thus ensure the accuracy of the overall filtering effect.

[0151] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A short-term adaptive time-varying filtering method based on grid search, characterized in that: include: S1, obtain the input interference s(n), and segment the input interference s(n) into several short-term interferences; Determine the total number of segments L and initialize the current segment number l s , l s Counter Count ls ; S2, determine the segment number l s Is it equal to the total number of segments L? s If L is equal to the total number of segments, the final instantaneous frequency estimation of all short-term interferences has been completed; otherwise, update l s =Count ls +1, Count ls = l s , and jump to step S3 to extract the first s Short-term interference; S3, extract the lth s Short-term interference s (n1); S4, using the first s Short-term interference s The discrete Fourier transform of (n1) calculates the instantaneous frequency parameter vector θ; S5, based on the first s The short-term interference and instantaneous frequency parameter vector θ are used to perform the lth s Filtering of short-term interference; S6, from the current filtering result S fBest Extract the first s The final filtering result of the short-term interference f (n2), and then return to step S2.

2. The short-term adaptive time-varying filtering method based on grid search according to claim 1 is characterized in that: The total number of segments L, segment number l s and Count ls The initialization values ​​are: l s =0;Count ls =0; N represents the total length of the input interference s(n), N w Indicates the length of each short-term interference; Indicates rounding down.

3. The short-term adaptive time-varying filtering method based on grid search according to claim 1 is characterized in that: The method extracts the first s Short-term interference s (n1), expressed as: S s (n1)=s(n1+l s N w -N w ),n1=1,2,...,N w Among them, n1 represents the n1th sampling point.

4. The short-term adaptive time-varying filtering method based on grid search according to claim 1 is characterized in that: The utilization of s Short-term interference s The discrete Fourier transform of (n1) calculates the instantaneous frequency parameter vector θ, including: S4.1, according to the extracted first s Short-term interference s (n1), calculate the discrete Fourier transform S stft (F): Among them, e is a natural constant, represents the imaginary number symbol, m represents the mth sampling point, F represents the normalized frequency, N fft Indicates the total number of discrete Fourier transform frequency points; S4.2, according to the discrete Fourier transform S stft (F) Calculate the instantaneous frequency parameter vector θ: θ=[F max ,0 1×Q-1 ] T in, 0 1×Q-1 represents a 1×Q-1 dimensional zero vector, Q represents the maximum order of the basis function space, [] T Indicates transpose.

5. The short-term adaptive time-varying filtering method based on grid search according to claim 1 is characterized in that: The first s The short-term interference and instantaneous frequency parameter vector θ are used to perform the lth s The filtering of short-term interference includes: S5.1, initialize the grid search iteration number l l =0, l l Counter Count ll =1; Initialize the global minimum residual power ε min =+∞; S5.2, determine the number of search iterations l l Is it equal to the total number of search iterations L? l ; If l is equal to the total number of search iterations L l , then the first s Filter the short-term interference, end the loop, and jump to step S6; if l is not equal to the total number of search iterations L l , then update l l =Count ll +1, Count ll = l l , and jump to step S5.3; S5.3, initialize the search point index k = 0, k's counter Count k = 0; the upper limit θ of each dimension in the instantaneous frequency parameter vector θ up With the lower limit θ down Evenly distributed N s Take the values ​​as search points and establish a search point set θ s ; S5.4, determine whether the search point index k is equal to the total number of search points N k ; If the search point index k is equal to the total number of search points N k , the calculation of all search points has been completed, and jump to step S5.2; if the search point index k is not equal to the total number of search points N k , then execute k = Count k +1, Count k = k, and jump to step S5.5; S5.5, through the current search point θ k , using the basis function space expansion to obtain the estimated instantaneous frequency f of this short-term interference s (n1); S5.6, to estimate the instantaneous frequency f s (n1) Accumulate and sum to obtain the estimated instantaneous phase S5.7, calculate the projected residual power ε using orthogonal subspace projection; S5.8, determine whether the residual power ε corresponding to the search point is less than the global minimum residual power ε min ; If the residual power ε is not less than the global minimum residual power ε min , then jump to step S5.4; If the residual power ε is less than the global minimum residual power ε min , then update the instantaneous frequency parameter vector θ = θ k , the global minimum residual power ε min =ε and save the result S after short-time interference filtering f As the current filtering result S fBest =S f ; Jump to step S5.4 to calculate the residual power of the next search point.

6. The short-term adaptive time-varying filtering method based on grid search according to claim 5 is characterized in that: The upper limit θ of the instantaneous frequency parameter vector θ up With the lower limit θ down It is expressed as: i up =θ+0.1×1 Q×1 i down =θ-0.1×1 Q×1 Among them, 1 Q×1 Represents a Q×1-dimensional all-1 matrix, the number of value points in the present invention is N s =100, total number of search points 7. The short-term adaptive time-varying filtering method based on grid search according to claim 5 is characterized in that: The estimated instantaneous frequency f of the short-term interference is obtained by expanding the basis function space. s (n1), expressed as: The parameter superscript T represents the transposition operation, and the search point θ k is the search point set θ s For the k-th search point in , the formula of the basis function space U(n1) is as follows:

8. The short-term adaptive time-varying filtering method based on grid search according to claim 1, characterized in that: The specific formula for calculating the residual power ε after projection by using orthogonal subspace projection is: S s =[s s (1),…,s s (N w )] T P ⊥ =I-S P (S P H S P ) -1 S P S f =P ⊥ S s ε=||S f ||2 Among them, S s It is the first s The matrix representation of the short-term interference is: e is a natural constant, j is an imaginary unit, S P is the matrix representation of the estimated short-term interference, P ⊥ To estimate the short-term interference matrix S P The orthogonal projection matrix, the superscript H represents the conjugate transpose, I represents the identity matrix, S f represents the result after short-time interference filtering, and || ||2 represents the 2-norm.

9. The short-term adaptive time-varying filtering method based on grid search according to claim 1, characterized in that: The current filtering result S fBest Extract the first s The final filtering result of the short-term interference f (n2): N ls l s *N w -N w +1 Among them, N ls For the first s The starting sequence number of the short-term interference segment, Represents the optimal filtering result S fBest The n2-Nth ls +1 element.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the short-term adaptive time-varying filtering method based on grid search according to any one of claims 1 to 9 is implemented.

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