A short-time adaptive time-varying filtering method based on gauss-newton algorithm

Abstract

The application provides a short-time self-adaptive time-varying filtering method based on Gauss Newton algorithm, mainly solves the problems that the prior art adaptive filter needs to introduce a reference signal in advance and cannot process unknown interference and the problem that interference and useful signal are in the same frequency band and the useful signal cannot be correctly identified; the scheme adopted by the application can automatically identify the instantaneous angular frequency of interference and perform filtering, so as to remove the interference, without a reference signal, while improving the accuracy of the estimation of the instantaneous angular frequency of interference, thereby enhancing the filtering effect, and when the interference and the signal are in the same frequency band, the application can automatically identify the instantaneous angular frequency of interference and perform designated filtering, without causing loss to the useful signal.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal and information processing, and particularly relates to a self-adaptive time-varying filtering method. BACKGROUND

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

[0003] In the prior art, according to the working principle and method of the filter, the common ones are convolution type filter and adaptive filter; the convolution type filter is simple and easy to understand, but it shows high sensitivity when facing noise and burst interference; the adaptive filter can adaptively adjust the filter parameters, which is suitable for nonlinear systems, but needs to introduce a reference signal in advance, and cannot process unknown interference; according to the frequency response characteristics of the filter, the common ones are low-pass filter, high-pass filter, band-pass filter and band-stop filter, which can effectively suppress the interference in the specified frequency band, but need to know the range of interference frequency in advance. If the interference and the useful signal are in the same frequency band, the useful signal will also be lost while the interference is suppressed, the useful signal cannot be correctly identified, and the traditional filter has certain limitations when dealing with time-varying interference, and cannot effectively adaptively identify and remove the interference, therefore, a filter which can overcome the above shortcomings is needed. SUMMARY

[0004] In order to overcome the shortcomings of the prior art, the application provides a short-time self-adaptive time-varying filtering method based on Gauss-Newton algorithm, which can automatically identify the instantaneous angular frequency of the interference and filter to remove the interference.

[0005] A short-time self-adaptive time-varying filtering method based on Gauss-Newton algorithm, comprising the following steps:

[0006] S1: according to the input interference s(n) and the sampling rate F s , set the instantaneous angular frequency parameter vector θ U , and initialize it;

[0007] The method for setting the instantaneous angular frequency parameter vector θ U is fixed value method or obtained through time-frequency analysis method; the time-frequency analysis method includes short-time Fourier transform time-frequency analysis method and Wigner-Ville time-frequency analysis method;

[0008] S2: divide the input interference s(n) into several short-time interferences, the total number of division is L, and ls is the current segment number;

[0009] S3: traverse all short-term interferences, judge whether the current segment number l s is equal to the total number of segments L;

[0010] If l s is equal to the total number of segments L, the final instantaneous angular frequency estimation of all short-term interferences is completed, the loop is ended, and the step S5 is jumped to;

[0011] If l s is not equal to the total number of segments L, the step S4 is executed, l s = Count ls +1, Count ls =l s , and the step S4 is jumped to to extract the final instantaneous angular frequency of the l s th segment short-term interference;

[0012] S4: through the l s th segment short-term interference and the instantaneous angular frequency parameter vector θ U , the final instantaneous angular frequency ω(n) of the l s th segment short-term interference is extracted by using the basis function space expansion and the Gauss-Newton algorithm, and then the step S3 is turned to;

[0013] S5: according to the interference final instantaneous angular frequency ω(n) and the time-varying filter transfer function, the filtering result y(n) is calculated.

[0014] Further, the step of setting the instantaneous angular frequency parameter vector by the Wigner-Ville time-frequency analysis method is:

[0015] S1-1.1: according to the input interference s(n) and the sampling rate F s , the Wigner-Ville distribution WVD(n1,ω s1 ) is calculated;

[0016] The specific formula of the Wigner-Ville distribution WVD(n1,ω s1 ) is:

[0017]

[0018] Wherein, the sampling point number n1 takes the value range of [1, 2,..., N w ], N w represents the length of the short-term interference, and the angular frequency ω s1 takes the value of z(n1) represents the analytic signal, and the specific formula is:

[0019]

[0020] Wherein, j represents the imaginary number symbol;

[0021] S1-1.2: Calculate the Wigner-Wiley distribution WVD(n1,ω s1 ) moment vector t w1 The angular frequency vector ω with the maximum energy corresponding to each moment w1 , the specific formula is

[0022]

[0023] S1-1.3: Using the time vector t w1 The angular frequency vector ω with the maximum energy corresponding to each moment w1 Calculate the estimated instantaneous angular frequency parameter vector θ U , the specific formula is:

[0024]

[0025] in, Represents the time vector t w1 The i-th power of each element in, Q represents the maximum order of the basis function space, U w1 is the time vector t w1 The corresponding basis function space is represents the Moore-Penrose pseudoinverse.

[0026] Furthermore, the steps of the short-time Fourier transform time-frequency analysis method are:

[0027] S1-2.1: Input disturbance s(n) and sampling rate F s , calculate the short-time Fourier transform S(n2,ω s2 );

[0028]

[0029] Among them, the sampling point number Angular frequency represents the window function; N w2 Indicates the length of the window function, the window function w(m w2 ) is expressed as:

[0030]

[0031] S1-2.2: Calculate the short-time Fourier transform S(n2,ω s2 ) moment vector t w2 The angular frequency vector ω with the maximum energy corresponding to each moment w2 , the specific formula is:

[0032]

[0033] S1-2.3: using time vector t w2 and the angular frequency vector ω with the maximum energy corresponding to each time w2 calculating the estimated instantaneous angular frequency parameter vector θ U The specific formula is:

[0034]

[0035] wherein, denotes the time vector t w2 The i-th power of each element in the vector, Q represents the maximum order of the basis function space, U w2 is the time vector t w2 corresponding to the basis function space, denotes Moore-Penrose pseudo-inverse.

[0036] Further, in step S2, the specific steps of segmenting the input interference s(n) into a plurality of short-time interferences are:

[0037] Segmenting the input interference s(n) into a plurality of short-time interferences, the total number of segments is L, the starting sequence number of each short-time interference is N s (l s ), the ending sequence number of each short-time interference is N e (l s ), l s is the current segment number, Count ls is the l s counter;

[0038] wherein, the total number of segments L, the starting sequence number N s (l s ), the ending sequence number N e (l s ), the initial value of the segment number l s , and the initial value of Count ls are respectively:

[0039]

[0040] N s (l s ) = (l s -1)N m +1;

[0041]

[0042] l s =0;

[0043] Count ls =0;

[0044] where N denotes the total length of the input interference s(n), N m denotes the length of the moving when extracting each segment of short-time interference; denotes rounding down.

[0045] Further, in the step S4, the lth s segment of short-time interference and the instantaneous angular frequency parameter vector θ U , the final instantaneous angular frequency ω(n) of the lth s segment of short-time interference is extracted by using the basis function space expansion and Gauss-Newton algorithm, and the specific steps are as follows:

[0046] S4.1: Extract the lth s segment of short-time interference, establish the basis function space U, the pole contraction coefficient ρ(l) and the regularization matrix Γ (l) , and initialize the iteration round number l of the Newton-Gauss algorithm, the initial value of l is l = 1; Count l is the counter for l; Count l = 1

[0047] s s (n3) = s(n3 + l s N w -N w ), n3 = 1, 2,..., N e (l s )-N s (l s ), s s (n3) is the lth s segment of short-time interference;

[0048]

[0049] Γ (l) = 10 -Q (10-l)I Q

[0050]

[0051] where I Q denotes the Q-order unit matrix;

[0052] S4.2: Multiply the instantaneous angular frequency parameter vector θ U by the basis function space U to obtain the estimated instantaneous angular frequency ω s (n4) of the segment of short-time interference:

[0053] ω s (n4) = θ U U(n4), n4 = 1, 2,..., N w

[0054] S4.3: estimating the instantaneous angular frequency ω s (n4) to obtain the time-varying filter coefficient a(n4);

[0055] a(n4) = -2 cos [ω s (n4)], n4 = 1, 2,..., N w

[0056] S4.4: calculating the prediction error ε(n4) and the instantaneous angular frequency parameter vector gradient ψ(n4) by the time-varying filter transfer function;

[0057] The calculation of the prediction error ε(n4) and the instantaneous angular frequency parameter vector gradient ψ(n4) by the time-varying filter transfer function in step S4.4 is specifically as follows:

[0058] ε(n4) = s s (n4) + a(n4)s s (n4-1) + s s (n4-2) - p(n4)a(n4)ε(n4-1) - p 2 (n4)ε(n4-2), n4 = 1, 2,..., N w

[0059]

[0060] wherein is the gradient of the time-varying filter coefficient a(n4) relative to the prediction error ε(n4), and the specific formula is as follows:

[0061] s F (n4) = s s (n4) - p 2 (n4)s F (n4-2) - p(n4)s F (n4-1)a(n4), n4 = 1, 2,..., N w

[0062] ε F (n4) = ε(n4) - p 2 (n4)ε F (n4-2) - p(n4)ε F (n4-1)a(n4), n4 = 1, 2,..., N w

[0063]

[0064] wherein s F (n4) and ε F (n4) are intermediate variables;

[0065] S4.5: Determine the cost β of the first cycle (l) and the cost value β of the l-1th cycle (l-1) Is the absolute error less than the threshold δ?

[0066] If the cost of the first cycle is β (l) and the cost value β of the l-1th cycle (l-1) If the absolute error is less than the threshold δ, then the current instantaneous angular frequency ω s (n4) is the final instantaneous angular frequency, go to step S3;

[0067] If the cost of the first cycle is β (l) and the cost value β of the l-1th cycle (l-1) If the absolute error is greater than or equal to the threshold δ, then execute step S4.6;

[0068] Cost value β (l) The specific formula is:

[0069]

[0070] The threshold value δ is 1×10 -6 ;

[0071] The formula for extracting the final instantaneous angular frequency ω(n) is:

[0072]

[0073]

[0074] ω(n)=ω s (nl s *N m +N m ),n=N ss ,N ss +1,...,N se

[0075] where N ss Indicates extracting the first s The starting number of the final instantaneous angular frequency of the short-term interference, N se Indicates extracting the first s The ending sequence number of the final instantaneous angular frequency of the short-term interference segment;

[0076] S4.6: Update the instantaneous angular frequency parameter vector θ using the Gauss-Newton algorithm U As the instantaneous angular frequency parameter vector of the l+1th cycle, execute step S4.2;

[0077] Update the instantaneous angular frequency parameter vector θ UThe specific formula is:

[0078]

[0079] l = Count l + 1

[0080] Count l = l

[0081] Wherein R (l) is the cost function pseudo-Hessian matrix of the lth cycle, is the cost function gradient of the lth cycle.

[0082] Further, the specific steps for calculating the filtering result y(n) according to the interference final instantaneous angular frequency ω(n) and the time-varying filter transfer function in the step S5 are as follows:

[0083] y(n) = s(n) - 2cos[ω(n)]s(n-1) + s(n-2) + 2ρ e cos[ω(n)]y(n-1) - ρ e 2 y(n-2), n = 1, 2,..., N

[0084] Wherein ρ e is a filter coefficient; the filter coefficient ρ e is 0.995.

[0085] The beneficial effects of the present application are:

[0086] 1. The present application uses Gauss-Newton algorithm to iteratively update the instantaneous angular frequency parameter vector, so as to obtain accurate instantaneous angular frequency and perform filtering, without reference signal, and is completely data-driven;

[0087] 2. Compared with the prior art, the short-time adaptive time-varying filtering method based on fixed initial value Gauss-Newton algorithm improves the accuracy of the estimation of the instantaneous angular frequency of the interference, thereby enhancing the filtering effect, and when the interference and the signal are in the same frequency band, the present application can automatically identify the instantaneous angular frequency of the interference for specified filtering, without causing loss to the useful signal; when setting the instantaneous angular frequency parameter vector to estimate the first short-time interference instantaneous angular frequency by using the short-time Fourier transform time-frequency analysis method or the Wigner-Ville time-frequency analysis method, the number of iteration rounds is further reduced on the basis of the fixed value method, thereby reducing the calculation amount;

[0088] 3. The present application uses a time-varying filter to reduce the influence of noise on the estimation of the instantaneous angular frequency, and has strong anti-noise performance;

[0089] 4. For multi-component signals, the present application obtains the instantaneous angular frequency of the highest angular frequency component, so that further processing of multi-component interference can be achieved by filtering the filtered signal again. BRIEF DESCRIPTION OF DRAWINGS

[0090] Figure 1 Flow chart for short-time adaptive time-varying filter based on Gauss-Newton algorithm

[0091] Figure 2 Flow chart for setting instantaneous angular frequency parameter vector for short-time Fourier transform time-frequency analysis method

[0092] Figure 3 Flow chart for setting instantaneous angular frequency parameter vector for Wigner-Ville time-frequency analysis method

[0093] Figure 4 Short-time Fourier transform time-frequency distribution diagram for simulating real true-chord FM interference in embodiment 1 of the present application

[0094] Figure 5 Comparison diagram of real instantaneous frequency curve and filtered instantaneous frequency curve for simulating real true-chord FM interference in embodiment 1 of the present application

[0095] Figure 6 Comparison diagram of real true-chord FM interference and filtering result in embodiment 1 of the present application

[0096] Figure 7 Wigner-Ville time-frequency distribution diagram for simulating quadratic FM interference in embodiment 2 of the present application

[0097] Figure 8 Comparison diagram of real instantaneous frequency curve and filtered instantaneous frequency curve for simulating quadratic FM interference in embodiment 2 of the present application

[0098] Figure 9 Comparison diagram of real quadratic FM interference and filtering result in embodiment 2 of the present application DETAILED DESCRIPTION

[0099] The present application is further described below in combination with the drawings and embodiments.

[0100] A short-time adaptive time-varying filtering method based on Gauss-Newton algorithm comprises the following steps:

[0101] S1: inputting interference s(n) and sampling rate F s , setting instantaneous angular frequency parameter vector θ U , and initializing;

[0102] Instantaneous angular frequency parameter vector θ U is:

[0103] θU =[ω1,ω2,.ω i ..,ω Q ]

[0104] where ω i is the i-th fitting parameter for estimating the instantaneous angular frequency, and Q represents the maximum order of the basis function space;

[0105] θ U The initial value of is fixed or obtained through time-frequency analysis method;

[0106] θ U When the initial value of is fixed, where 0 Q-1 is a 1×(Q-1) vector;

[0107] In order to take into account the computational complexity of the present invention and the fitting effect of the final instantaneous angular frequency, the preferred Q value is 4, and the instantaneous angular frequency parameter vector is initialized

[0108] Time-frequency analysis methods include short-time Fourier transform and Wigner-Wiley distribution method;

[0109] The instantaneous angular frequency parameter vector θ is set using the Wigner-Wiley time-frequency analysis method. U The initial value of , the specific steps are as follows:

[0110] S1-1.1: According to the input interference s(n) and sampling rate F s , calculate the Wigner-Wiley distribution WVD(n1,ω s1 );

[0111] Wigner-Wiley distribution WVD(n1,ω s1 )The specific formula is:

[0112]

[0113] Among them, the sampling point number n1 ranges from [1,2,...,N w ],N w Indicates the length of short-term interference, the value is 256, the angular frequency ω s1 The value is z(n1) represents the analytical signal, and the specific formula is:

[0114]

[0115] Wherein, j represents the imaginary number symbol;

[0116] S1-1.2: Calculate the Wigner-Wiley distribution WVD(n1,ω s1 ) moment vector t w1The angular frequency vector ω with the maximum energy corresponding to each moment w1 , the specific formula is

[0117]

[0118] S1-1.3: Using the time vector t w1 The angular frequency vector ω with the maximum energy corresponding to each moment w1 Calculate the estimated instantaneous angular frequency parameter vector θ U , the specific formula is:

[0119]

[0120] in, Represents the time vector t w1 The i-th power of each element in, Q represents the maximum order of the basis function space, U w1 is the time vector t w1 The corresponding basis function space is represents Moore-Penrose pseudoinverse;

[0121] The instantaneous angular frequency parameter vector θ is set using the short-time Fourier transform time-frequency analysis method. U The initial value of , the specific steps are as follows:

[0122] S1-2.1: Input disturbance s(n) and sampling rate F s , calculate the short-time Fourier transform S(n2,ω s2 );

[0123]

[0124] Among them, the sampling point number Angular frequency represents the window function; N w2 Indicates the length of the window function, the value is 32, the window function w(m w2 ) is expressed as:

[0125]

[0126] S1-2.2: Calculate the short-time Fourier transform S(n2,ω s2 ) moment vector t w2 The angular frequency vector ω with the maximum energy corresponding to each moment w2 , the specific formula is:

[0127]

[0128] S1-2.3: Using the time vector t w2 The angular frequency vector ω with the maximum energy corresponding to each momentw2 The estimated instantaneous angular frequency parameter vector θ is calculated U , and the specific formula is:

[0129]

[0130] Wherein, The time vector t w2 is raised to the power of i, Q represents the maximum order of the basis function space, and U w2 is the time vector t w2 corresponding to the basis function space, Moore-Penrose pseudo-inverse is represented;

[0131] S2: segment the input interference s(n) into a plurality of short-time interferences, the total number of segments is L, the starting sequence number of each segment of the short-time interference is N s (l s ), the ending sequence number of each segment of the short-time interference is N e (l s ), l s is the current segment number, Count ls is the l s counter;

[0132] Wherein, the total number of segments L, the starting sequence number N s (l s ), the ending sequence number N e (l s ), the initial value of the segment number l s , and the initial value of Count ls are respectively:

[0133]

[0134] N s (l s ) = (l s -1)N m +1;

[0135]

[0136] l s =0;

[0137] Count ls =0;

[0138] Wherein N represents the total length of the input interference s(n), and N m represents the length of the movement when each segment of the short-time interference is extracted; represents the floor function;

[0139] In the present application, the length of the movement when each segment of the short-time interference is extracted is 32.

[0140] S3: judge segment number l s whether equal to the total number of segments L;

[0141] If l s equal to the total number of segments L, the final instantaneous angular frequency estimation of all short-term interference has been completed, end the loop, jump to step S5;

[0142] If l s not equal to the total number of segments L, execute l s = Count ls +1, Count ls = l s , and jump to step S4 to extract the final instantaneous angular frequency of the l s th segment short-term interference;

[0143] S4: extract the final instantaneous angular frequency of the l s th segment short-term interference by using the basis function space expansion and Gauss-Newton algorithm with the l U th segment short-term interference and θ s :

[0144] S4.1: extract the l s th segment short-term interference, establish the basis function space U, pole contraction coefficient ρ(l) and regularization matrix Γ (l) , and initialize the iteration number of Newton-Gauss algorithm l, the initial value of l is l=1; Count l is the l counter; Count l =1

[0145] s s (n3) = s(n3+l s N w -N w ), n3=1,2,...,N e (l s )-N s (l s ), s s (n3) is the l s th segment short-term interference;

[0146]

[0147] Γ (l) =10 -Q (10-l)I Q

[0148]

[0149] where I Q represents a Q-order unit matrix;

[0150] S4.2: Calculate the instantaneous angular frequency parameter vector θ U (n4) of the segment short-time interference by multiplying the basis function space U s (n4) with the estimated instantaneous angular frequency ω

[0151] (n4) = θ s (n4) = θ U U(n4), n4 = 1, 2,..., N w

[0152] S4.3: Perform cosine and multiplication operations on the estimated instantaneous angular frequency ω s (n4) to obtain the time-varying filter coefficient a(n4);

[0153] a(n4) = -2cos[ω s (n4)], n4 = 1, 2,..., N w

[0154] S4.4: Calculate the prediction error ε(n4) and the instantaneous angular frequency parameter vector gradient ψ(n4) through the time-varying filter transfer function;

[0155] The calculation of the prediction error ε(n4) and the instantaneous angular frequency parameter vector gradient ψ(n4) through the time-varying filter transfer function in step S4.4 is specifically as follows:

[0156] ε(n4) = s s (n4) + a(n4)s s (n4-1) + s s (n4-2) - p(n4)a(n4)ε(n4-1) - p 2 (n4)ε(n4-2), n4 = 1, 2,..., N w

[0157]

[0158] wherein is the gradient of the time-varying filter coefficient a(n4) relative to the prediction error ε(n4), and the specific formula is as follows:

[0159] s F (n4) = s s (n4) - p 2 (n4)s F (n4-2) - p(n4)s F (n4-1)a(n4), n4 = 1, 2,..., N w

[0160] ε F (n4) = ε(n4) - p2 (n4)ε F (n4-2)-ρ(n4)ε F (n4-1)a(n4),n4=1,2,...,N w

[0161]

[0162] where s F (n4) and ε F (n4) are intermediate variables;

[0163] S4.5: judge whether the absolute error between the value β (l) of the lth iteration and the value β (l-1) of the (l-1)th iteration is less than a threshold value δ:

[0164] If the absolute error between the value β (l) of the lth iteration and the value β (l-1) of the (l-1)th iteration is less than the threshold value δ, the current instantaneous angular frequency ω s (n4) is considered as the final instantaneous angular frequency, and the process goes to step S3;

[0165] If the absolute error between the value β (l) of the lth iteration and the value β (l-1) of the (l-1)th iteration is greater than or equal to the threshold value δ, step S4.6 is executed;

[0166] The specific formula of the value β (l) is:

[0167]

[0168] where the threshold value δ is 1x10 -6 , and the value β (0) =0;

[0169] The formula for extracting the final instantaneous angular frequency ω(n) is:

[0170]

[0171] ω(n) = ω s (n-1 s *N m +N m ), n = N ss , N ss +1,..., N se

[0172] where N ss represents the starting sequence number for extracting the final instantaneous angular frequency of the l s th segment of short-time interference.se representing the extracted lth s the end sequence number of the segment short-time interference final instantaneous angular frequency;

[0173] S4.6: updating the instantaneous angular frequency parameter vector θ using the Gauss-Newton algorithm U the instantaneous angular frequency parameter vector of the (l+1)th cycle, performing step S4.2;

[0174] updating the instantaneous angular frequency parameter vector θ U The specific formula is:

[0175]

[0176] l=Count l +1

[0177] Count l =l

[0178] where R (l) is the cost function pseudo-Hessian matrix of the lth cycle, is the cost function gradient of the lth cycle;

[0179] S5: calculating the filtering result y(n) according to the signal final instantaneous angular frequency ω(n) and the time-varying filter transfer function;

[0180] y(n)=s(n)-2cos[ω(n)]s(n-1)+s(n-2)+2ρ e cos[ω(n)]y(n-1)-ρ e 2 y(n-2), n=1, 2,..., N

[0181] where ρ e is the filter coefficient; the filter coefficient ρ e takes a value of 0.995.

[0182] In the embodiment of the application, the models of the real sine frequency modulation interference s1(n) and the quadratic frequency modulation interference s2(n) are:

[0183]

[0184] where A is the interference amplitude, f c is the carrier frequency, A f is the amplitude of the instantaneous frequency change of the sine frequency modulation interference, f f is the frequency of the instantaneous frequency change of the sine frequency modulation interference, is the initial phase of the instantaneous frequency change of the sine frequency modulation interference, F s is the sampling rate of the interference, f1 is the starting frequency of the quadratic frequency modulation interference, and f2 is the termination frequency of the quadratic frequency modulation interference, N is the total length of the jammer. w(n) is the additive white Gaussian noise with mean 0 and variance σ 2 , and the size is determined by the jam-to-noise ratio JNR, and the specific formula is:

[0185]

[0186] In order to accurately evaluate the filter effect, the instantaneous frequency mean square error is used as the evaluation index, and the specific formula is:

[0187]

[0188] Where f r (n) is the real instantaneous frequency of the jammer, and f(n) is the filtered instantaneous frequency, and the specific formula is:

[0189]

[0190] Example 1:

[0191] In this embodiment, the sinusoidal frequency modulation jamming is used, and the parameters are set as follows: jamming amplitude A = 1, sampling rate F s = 1000 Hz, carrier frequency f c = 320, jamming instantaneous frequency change amplitude A f = 40, jamming instantaneous frequency change frequency f f = 2, jamming instantaneous frequency change initial phase Jamming initial phase The total length of the jammer N = 4000, the jam-to-noise ratio JNR = 30 dB, Figure 4 The short-time Fourier transform time-frequency distribution diagram of the sinusoidal frequency modulation jamming is given.

[0192] According to step 1, input the jamming s(n) and the sampling rate F s , set the instantaneous angular frequency parameter vector θ U , and initialize the instantaneous angular frequency parameter vector

[0193] According to step 2, the input jamming s(n) is segmented into a plurality of short-time jammers, the total number of segments L = 117, the starting sequence number N s (l s ) of each short-time jammer and the ending sequence number N e (l s ) of each short-time jammer are calculated, and the segment number l s = 0, and the counter Count ls = 0.

[0194] According to step 3, judge the current segment number l swhether equal to the total number of segments L:

[0195] if l s = Total number of segments L, the final instantaneous angular frequency estimation of all short-time interference has been completed, the loop is ended, and the step 5 is jumped to.

[0196] if l s ≠ Total number of segments L, the l s = Count ls +1, Count ls = l s is executed, and the step S4 is jumped to, to extract the final instantaneous angular frequency of the l s th segment short-time interference.

[0197] According to the step 4, the final instantaneous angular frequency of the l s th segment short-time interference is extracted by using the basis function space expansion and the Gauss-Newton algorithm with the l U th segment short-time interference and the instantaneous angular frequency parameter vector θ s , and the step 3 is turned to.

[0198] According to the step 5, the filtering result y(n) is calculated according to the final instantaneous angular frequency ω(n) and the time-varying filter transfer function.

[0199] The comparison chart of the real instantaneous frequency curve of the simulated real string frequency modulation interference and the filtered instantaneous frequency curve is shown in Figure 5 , the instantaneous frequency mean square error is 0.328, the filtered instantaneous frequency curve basically fits the real instantaneous frequency curve, the error is small, and such result also proves that the algorithm of the present application can effectively use the Gauss-Newton algorithm to iteratively update the instantaneous angular frequency parameter vector, so as to obtain the accurate instantaneous angular frequency and accurately filter the interference, the comparison chart of the simulated real string frequency modulation interference and the filtering result is shown in Figure 6 , and the interference has been basically filtered.

[0200] Embodiment 2:

[0201] In this embodiment, the quadratic frequency modulation interference is adopted, and the parameters are respectively set as: interference amplitude A = 1, sampling rate F s = 1000 Hz, starting frequency of interference f1 = 200, termination frequency of interference f2 = 410, initial phase total length of interference N = 4000, and jam-to-noise ratio JNR = 30 dB. Figure 7 The Wigner-Ville time-frequency distribution chart of the quadratic frequency modulation interference is given.

[0202] According to the step 1, the interference s(n) and the sampling rate F s are input, and the instantaneous angular frequency parameter vector θ Uand the initial instantaneous angular frequency parameter vector θ is obtained by using the short-time Fourier transform time-frequency analysis method U = [1.26, 0.16, -1.89, 5.91].

[0203] According to step 2, the input interference s(n) is segmented into a plurality of short-time interferences, the total number of segments L = 117, the starting sequence number N s (l s ) of each short-time interference and the ending sequence number N e (l s ) of each short-time interference are calculated, and the segment number l s = 0, and the counter Count ls = 0 are initialized.

[0204] According to step 3, it is judged whether the current segment number l s is equal to the total number of segments L:

[0205] If l s is equal to the total number of segments L, the final instantaneous angular frequency estimation of all short-time interferences has been completed, the loop is ended, and the process jumps to step 5.

[0206] If l s is not equal to the total number of segments L, l s = Count ls + 1, Count ls = l s are executed, and the process jumps to step S4 to extract the final instantaneous angular frequency of the l s th segment short-time interference.

[0207] According to step 4, the final instantaneous angular frequency of the l s th segment short-time interference is extracted by using the basis function space expansion and Gauss-Newton algorithm based on the l U th segment short-time interference and the instantaneous angular frequency parameter vector θ s , and the process jumps to step 3.

[0208] According to step 5, the filtering result y(n) is calculated based on the final instantaneous angular frequency ω(n) and the time-varying filter transfer function.

[0209] The comparison chart of the real instantaneous frequency curve of the simulated frequency modulation interference and the filtered instantaneous frequency curve is as shown in Figure 8As shown, the filtering starting instantaneous frequency is 199.63 Hz, the real starting frequency is 200 Hz, the filtering ending instantaneous frequency is 409.80 Hz, the real ending frequency is 410 Hz, the instantaneous frequency mean square error is 0.295, the filtered instantaneous frequency curve basically fits the real instantaneous frequency curve, and the error is small. Such results also confirm that the algorithm of the present application can effectively use the Gauss-Newton algorithm to iteratively update the instantaneous angular frequency parameter vector, thereby obtaining accurate instantaneous angular frequency and accurately filtering the interference. The simulation secondary frequency modulation interference and filtering result comparison graph is as shown in Figure 9 As shown, the interference has been basically filtered out.

[0210] Embodiment 3:

[0211] In this embodiment, 100 independent experiments were carried out under the conditions of signal-to-noise ratios of 30 dB, 40 dB and 50 dB, respectively.

[0212] Among them, the secondary frequency modulation interference parameters are set as follows: interference amplitude A = 1, sampling rate F s = 1000 Hz, starting frequency f1 of interference is a random number in [200, 300], ending frequency f2 of interference is a random number in [350, 450], initial phase is a random number in [0, π], and the total length N of interference is 4000.

[0213] The sinusoidal frequency modulation interference parameters are set as follows: interference amplitude A = 1, sampling rate F s = 1000 Hz, carrier frequency f c is a random number in [250, 350], amplitude A f of interference instantaneous frequency change is 40, frequency f f of interference instantaneous frequency change is a random number in [0, 2], initial phase of interference instantaneous frequency change is a random number in [0, π], initial phase of interference is a random number in [0, 2π], and the total length N of interference is 4000.

[0214] Under different signal-to-noise ratios, the short-time Fourier transform and the Wigner-Vill time-frequency analysis method are used to estimate the interference instantaneous angular frequency, a time-varying filter is designed according to the interference instantaneous angular frequency, and the interference suppression amount is calculated based on the short-time adaptive time-varying filter of the Gauss-Newton algorithm. At the same time, when the signal-to-noise ratio JNR = 30 dB, the fixed value method, the short-time Fourier transform time-frequency analysis method and the Wigner-Vill time-frequency analysis method are used to set the instantaneous angular frequency parameter vector θ U The influence of the number of iterations on the estimation of the first segment of short-time interference instantaneous angular frequency.

[0215] Among them, the interference suppression amount is calculated as follows:

[0216] △J = JNR1 - JNR2

[0217] where JNR1 represents the dry noise ratio before filtering, and JNR2 represents the dry noise ratio after filtering.

[0218] The result summary table is as follows:

[0219] Table 1 Average interference suppression amount of different methods

[0220]

[0221]

[0222] Table 2 Average iteration round number when estimating the first segment short-time interference instantaneous angular frequency by different initial methods

[0223]

[0224] As can be seen from Table 1, the short-time adaptive time-varying filter based on the Gauss-Newton algorithm has the best effect. In the case of a dry noise ratio of 20 dB and 30 dB, this method can almost completely filter out the interference; in the case of a dry noise ratio of 40 dB, it can also effectively filter out most of the interference. In contrast, the two methods of estimating the instantaneous angular frequency of the interference using the short-time Fourier transform and the Wigner-Ville time-frequency analysis method, and designing a time-varying filter according to the frequency for filtering, have more residual interference after filtering due to the large error in estimating the instantaneous angular frequency of the interference. In the case of sinusoidal frequency modulation interference, the Wigner-Ville time-frequency analysis method is easily affected by the cross term, thus incorrectly estimating the instantaneous angular frequency of the interference, resulting in the failure of this method. However, in the case of quadratic frequency modulation interference, the Wigner-Ville time-frequency analysis method is more accurate in estimating the instantaneous angular frequency of the interference, and its filtering effect is better than that of the time-varying filter based on the short-time Fourier transform.

[0225] As can be seen from Table 2, the use of the short-time Fourier transform time-frequency analysis method or the Wigner-Ville time-frequency analysis method to set the instantaneous angular frequency parameter vector θ U In estimating the instantaneous angular frequency of the first segment short-time interference, compared with the fixed value method, the iteration round number can be reduced, the accuracy can be improved, and the incorrect estimation of the instantaneous angular frequency of the interference can be prevented.

[0226] The above description is merely a specific implementation of the present application, enabling a person skilled in the art to understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A short-time adaptive time-varying filtering method based on Gauss-Newton algorithm, characterized in that: The steps include: S1: According to input interference and sampling rate , set the instantaneous angular frequency parameter vector , and initialize; Set the instantaneous angular frequency parameter vector The method is a fixed value method or a time-frequency analysis method; the time-frequency analysis method includes a short-time Fourier transform time-frequency analysis method and a Wigner-Wiley time-frequency analysis method; S2: Input interference The segments are divided into several short-term interferences, and the total number of segments is , is the current segment number; S3: Traverse all short-term interferences and determine the current segment number Is it equal to the total number of segments? ; like Equal to the total number of segments , the final instantaneous angular frequency estimation of all short-term interferences has been completed, the loop ends, and jumps to step S5; like Not equal to the total number of segments , then execute , , and jump to step S4 to extract the The final instantaneous angular frequency of the short-term interference; S4: Through Segment short-term interference and instantaneous angular frequency parameter vector , using the basis function space expansion and Gauss-Newton algorithm to extract the The final instantaneous angular frequency of the short-term interference , then go to step S3; Through the Segment short-term interference and instantaneous angular frequency parameter vector , using the basis function space expansion and Gauss-Newton algorithm to extract the The final instantaneous angular frequency of the short-term interference The specific steps are: S4.1: Extract Segment short-time interference, establish basis function space , extreme contraction coefficient and the regularization matrix , and initialize the number of iterations of the Newton-Gauss algorithm , The initial value is ; for counter; , For the Short-term interference; in express The unit matrix of order; Indicates the maximum order of the basis function space; Indicates the length of short-term interference; S4.2: Transform the instantaneous angular frequency parameter vector Multiplication basis function space Get the estimated instantaneous angular frequency of this short-term interference : S4.3: Estimation of instantaneous angular frequency Perform cosine and multiplication operations to obtain time-varying filter coefficients ; S4.4: Calculating prediction error via time-varying filter transfer function and the instantaneous angular frequency parameter vector gradient ; The prediction error is calculated by the time-varying filter transfer function in step S4.4 and the instantaneous angular frequency parameter vector gradient , the specific formula is: in is the time-varying filter coefficient Relative prediction error The gradient of , the specific formula is: in, and is an intermediate variable; S4.5: Determine the The cost of the cycle Hedi The cost of the cycle Is the absolute error less than the threshold? : Jordi The cost of the cycle Hedi The cost of the cycle The absolute error is less than the threshold , then the current instantaneous angular frequency is considered to be is the final instantaneous angular frequency, go to step S3; Jordi The cost of the cycle Hedi The cost of the cycle The absolute error is greater than or equal to the threshold , then execute step S4.6; Cost Value The specific formula is: Among them, the threshold The value of ; Extract the final instantaneous angular frequency The formula is: in Indicates the extraction of The starting sequence number of the final instantaneous angular frequency of the short-term interference segment, Indicates the extraction of The ending sequence number of the final instantaneous angular frequency of the short-term interference segment; S4.6: Update the instantaneous angular frequency parameter vector using the Gauss-Newton algorithm As the first The instantaneous angular frequency parameter vector of the cycle is executed in step S4.2; Update the instantaneous angular frequency parameter vector The specific formula is: in It is The pseudo-Hessian matrix of the cost function of the sub-cycle is, It is The gradient of the cost function of the sub-cycle; S5: According to the final instantaneous angular frequency of the interference Calculate the filtering result with the time-varying filter transfer function ; According to the final instantaneous angular frequency of the interference Calculate the filtering result with the time-varying filter transfer function The specific steps are: in is the filter coefficient; filter coefficient The value is 0.

995.

2. The short-time adaptive time-varying filtering method based on the Gauss-Newton algorithm according to claim 1, characterized in that: The steps of setting the instantaneous angular frequency parameter vector in the Wigner-Wiley time-frequency analysis method are as follows: S1-1.1: Based on input interference and sampling rate , calculates the Wigner-Wiley distribution ; S1-1.2: Calculate the Wigner-Wiley distribution Moment vector The angular frequency vector with the maximum energy corresponding to each moment ; S1-1.3: Using time vectors The angular frequency vector with the maximum energy corresponding to each moment Calculate the estimated instantaneous angular frequency parameter vector.

3. The short-time adaptive time-varying filtering method based on the Gauss-Newton algorithm according to claim 1, characterized in that: The steps of the short-time Fourier transform time-frequency analysis method are: S1-2.1: Input interference and sampling rate , calculate the short-time Fourier transform ; ； Among them, the sampling point number , angular frequency , represents the window function; Indicates the length of the window function, the window function The expression is: S1-2.2: Compute the Short-Time Fourier Transform Moment vector The angular frequency vector with the maximum energy corresponding to each moment , the specific formula is: ； S1-2.3: Using time vectors The angular frequency vector with the maximum energy corresponding to each moment Calculate the estimated instantaneous angular frequency parameter vector , the specific formula is: in, Represents the time vector For each element Power, represents the maximum order of the basis function space, is the time vector The corresponding basis function space is represents the Moore-Penrose pseudoinverse.

4. The short-time adaptive time-varying filtering method based on the Gauss-Newton algorithm according to claim 1, characterized in that: In step S2, the interference The specific steps of segmenting into several short-term interferences are: Input interference The segments are divided into several short-term interferences, and the total number of segments is The starting sequence number of each short-term interference is , the end sequence number of each short-term interference , is the current segment number, for counter; Among them, the total number of segments 、The starting sequence number is , end sequence number , segment number The initial value of The initial values ​​are: ； ； ； ； ； in Indicates input interference The total length of Indicates the length of movement when extracting each short-term interference; Indicates rounding down.

5. The short-time adaptive time-varying filtering method based on the Gauss-Newton algorithm according to claim 2, characterized in that: The calculation of the Wigner-Wiley distribution The steps are: Wigner-Wiley distribution The specific formula is: Among them, the sampling point number The value range is , Indicates the length of short-term interference, angular frequency The value is , Represents the analytical signal, the specific formula is: in, Represents the imaginary number symbol.

6. The short-time adaptive time-varying filtering method based on the Gauss-Newton algorithm according to claim 2, characterized in that: Calculates the Wigner–Wiley distribution Moment vector The angular frequency vector with the maximum energy corresponding to each moment , the specific steps are: in, is the angular frequency vector with the maximum energy corresponding to each moment.

7. The short-time adaptive time-varying filtering method based on the Gauss-Newton algorithm according to claim 2, characterized in that: Using time vector The angular frequency vector with the maximum energy corresponding to each moment Calculate the estimated instantaneous angular frequency parameter vector , the specific steps are: in, Represents the time vector For each element Power, represents the maximum order of the basis function space, is the time vector The corresponding basis function space is represents the Moore-Penrose pseudoinverse.

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