MLFM signal parameter estimation method based on wavelet transform and frequency difference integrated processing

Abstract

A method for estimating MLFM signal parameters based on a combination of wavelet transform and frequency difference processing involves pulse width estimation of sorted MLFM single-pulse radar intrapulse signal data, followed by wavelet transform. Wavelet ridges are extracted through phase space reconstruction, singular value decomposition, and phase difference processing. The wavelet ridges are then subjected to mean and median filtering. The frequency difference method is used to identify the transition points of the wavelet ridges and eliminate false transition points. The MLFM signal is segmented based on the transition points. A FRFT is performed on each segment to estimate the starting frequency, bandwidth, center frequency, and frequency modulation slope parameters of each segment within the pulse. By combining the wavelet transform and FRFT time-frequency analysis methods, as well as phase space reconstruction, singular value decomposition, and transition point merging, the method effectively reduces the impact of noise on signal parameter estimation and improves the accuracy of signal parameter estimation under low signal-to-noise ratio conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing. Background Art

[0002] Radar countermeasure reconnaissance systems analyze radar signals in three key areas: signal interception, modulation recognition, and parameter estimation. To reduce the probability of radar signals being intercepted and correctly analyzed by reconnaissance equipment, radars are rapidly developing towards low probability of intercept (LPI) characteristics. These include increasing signal bandwidth, reducing peak transmit power, implementing power management, employing complex waveforms, and implementing rapid and random changes in radar signal parameters.

[0003] One such complex signal is the multi-component linear frequency modulation (MLFM) signal. The low probability of intercept (PPI) of radar poses significant challenges to signal interception, modulation recognition, and parameter estimation for radar countermeasure reconnaissance. Parameter estimation of MLFM signals remains challenging, especially when the signal-to-noise ratio (SNR) drops to 0 dB. Solving this problem is crucial for radar countermeasure reconnaissance efforts. Summary of the Invention

[0004] The purpose of the present invention is to propose a MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing, which can accurately estimate the starting frequency, bandwidth, frequency modulation slope and center frequency parameters in the MLFM signal pulse with a high probability above 0dB.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for estimating MLFM signal parameters based on wavelet transform and frequency difference integrated processing includes the following steps:

[0007] 1) Inputting the intercepted MLFM signal sequence containing intra-pulse modulation information and sorting it to obtain the MLFM signal sequence;

[0008] 2) performing pulse width estimation and dividing the sequence into individual pulses according to the pulse width;

[0009] 3) Perform wavelet transform on the single pulse signal and extract the wavelet ridges through phase space reconstruction, singular value decomposition and phase difference;

[0010] 4) Perform mean filtering and median filtering on the wavelet ridges;

[0011] Perform frequency difference processing on the wavelet ridge line to find the jump point of the frequency curve and eliminate the false jump points;

[0012] 5) Segment the MLFM signal according to the jump points; perform FRFT on each segment to estimate the starting frequency, bandwidth, center frequency and frequency modulation slope parameters of each segment in the pulse.

[0013] The parameter estimation method is as follows:

[0014] S1: Sort the intercepted signal to obtain the MLFM signal pulse sequence containing the intra-pulse modulation information. For any pulse, it is expressed as x(t), t = 1, 2, ..., T, T is the number of sampling points, and the sampling frequency is f s . The amplitude of x(t) is normalized, and the processed signal sequence is expressed as In the formula, |·| represents the absolute value, and this symbol has the same meaning in the following steps.

[0015] S2: Yes Pulse width estimation is performed using a radar pulse repetition interval estimation method based on blind source separation. The estimated pulse width is expressed as PW1, PW2, ..., PW N , where 1, 2, ..., N represents the pulse number. The signal sequence intercepted into a single pulse width is expressed as Where 1, 2, ..., N represent the pulse number, and the duration of each pulse is one pulse width.

[0016] S3: Yes Perform wavelet transform, expressed as cwt is the continuous wavelet transform function, 1 is the scale of the wavelet transform, cmor2-1 is the name of the wavelet basis function, and in addition to cmor2-1, other wavelet basis functions can also be used.

[0017] S4: For y1, filtering is performed through phase space reconstruction and singular value decomposition. The number of reconstructed rows is M, which can be set according to the number of points in y1, and the number of columns is Right now The number of sampling points is τ = 1. The absolute value of the reconstructed and filtered signal is taken as yy1. The phase of yy1 is calculated, and the phase difference is calculated using the phase difference method to obtain the wavelet ridge F(t,f), with the sampling points as the abscissa and the frequency as the ordinate. To further reduce the impact of noise on MLFM signal parameter estimation, the wavelet ridge is filtered using mean filtering and then median filtering.

[0018] S5: Perform frequency difference processing on the wavelet ridge. In order to reduce the influence of outliers caused by noise in the wavelet ridge, discard the first few dozen points of the wavelet ridge, generally 30 points. Let J be the order of frequency difference, generally J is 10, and perform the following difference processing on the wavelet ridge:

[0019] Let i=30:[length(F(t,f))-J],dF(i)=F(i+J)-F(i)

[0020] Among them, F is the wavelet ridge, and length(F(t,f)) represents the number of wavelet ridge values.

[0021] S6: Find the jump point of the frequency curve based on the wavelet ridge frequency difference result dF(i). First, find the maximum value of the frequency difference represented by the vertical axis of dF(i), and set the maximum value as Z max , set the threshold to Z y , according to a large number of simulation experiments, Z y =0.5Z max It can meet the requirements. Traverse all the value points of dF(i) vertical axis, when the value is greater than Z y When , this point is the jump point of the frequency curve. Let the jump point found be locs(j), j = 1, 2, ..., K, K is the number of jump points. Obviously, the jump point can represent the jump moment of the frequency curve.

[0022] S7: Identify and merge false transition points. For the transition point sequence locs(j), j = 1, 2, ..., K, if the interval between adjacent transition points is less than 20 sampling points, it indicates a false transition point and must be merged. This merging method is to average the sampling times represented by adjacent transition points with an interval less than 20 sampling points and treat them as true transition points. After this process, the remaining transition points are denoted as locs′(k), k = 1, 2, ..., K′, where K′ is the number of transition points.

[0023] S8: Estimate the parameters of the MLFM signal based on the transition point sequence locs′(k), k = 1, 2, …, K′. Since the MLFM signal pulse is typically divided into two or three segments, and the frequency modulation slope of each segment is positive, k′ should be 1 or 2. Without loss of generality, the method for estimating the parameters of the MLFM signal pulse is described using K′ = 1 as an example. K′ = 1 corresponds to the MLFM signal pulse being divided into two segments.

[0024] Obviously, the pulse width of the first segment in the MLFM signal pulse is pw1 = locs′(1)×1 / f s , whose unit is s. Take out the first segment of the MLFM signal and express it as Perform FRFT on it and estimate the frequency modulation slope K1 and starting frequency f according to the transformed time-frequency waveform. st1 , bandwidth B1 and center frequency f c1 .

[0025] The following is an explanation of the FRFT of a signal. For a signal x(t), we perform FRFT on it and get X p (u), whose expression is as follows:

[0026]

[0027] Where K p (u,t)=A α exp[jπ(u 2 cotα-2utcscα+t 2 cotα)] is FRFTX p (u) is the kernel function, where α=pπ / 2, where p and α represent the order of FRFT and the rotation angle, respectively.

[0028] After defining the FRFT, we can use it to estimate parameters of linear frequency modulated signals in both the time and frequency domains. Since the dimensions of the time and frequency domains are completely different, if we directly perform the FRFT on the LFM signal, the result will not be the true parameters. Therefore, before parameter estimation, we must first perform a dimension normalization operation on the time and frequency domains of the LFM signal to convert both the time and frequency domains of the LFM signal into dimensionless domains.

[0029] Before the dimension normalization operation, the time domain dimension of the LFM signal is The frequency domain dimension is Where T is the pulse width of the LFM signal, f s Is the sampling frequency of the signal. Before the normalization operation, the coordinate system of the time-frequency characteristics of the signal is (t, f). After the transformation, the new coordinate system of the time-frequency characteristics is (u, v), where the definition is is the scale factor of this conversion. After the coordinate system conversion, the time domain and frequency domain representation intervals of the LFM signal are and At this point, the dimension normalization of the LFM signal in the time domain and frequency domain has been completed. After normalization, the representation of the LFM center frequency changes from f0 to f0'. At the same time, the representation of the LFM signal's frequency modulation slope also changes from μ to μ'. The relationship before and after the change is as follows:

[0030]

[0031] When α=-arccot(μ), X p (u)=AAα exp(jπu 2 cotα), X p (u) is an impulse function in the fractional Fourier domain. When f0 = ucscα, X p (u) obtains the maximum impact. Based on this feature, the parameters p, u and A can be estimated. The expression is:

[0032]

[0033] According to formula (3), the center frequency f0 and the frequency modulation slope μ of the LFM signal can be estimated:

[0034]

[0035] The frequency modulation slope K1 is obtained from μ in equation (4). The center frequency f c1 Obtained from f0 in formula (4).

[0036] The bandwidth B1 is calculated as follows: B1 = pw1 × K1;

[0037] Starting frequency f st1 The calculation method is: f st1 =f c1 -B1 / 2.

[0038] S9: Parameter estimation of the second segment of the MLFM signal pulse. The pulse width of the second segment of the MLFM signal pulse is pw2 = PW1 - locs' (1) × 1 / fs s , whose unit is s, PW1 is the pulse width of the MLFM signal estimated by step S2. The second segment of the MLFM signal is taken out and expressed as Perform FRFT on it and estimate the frequency modulation slope K2 and starting frequency f according to the transformed time-frequency waveform. st2 , bandwidth B2 and center frequency f c2 .

[0039] The frequency modulation slope K2 is obtained from μ in equation (4). The center frequency f c2 Obtained from f0 in formula (4).

[0040] The bandwidth B2 is calculated as follows: B2 = pw2 × K2;

[0041] Starting frequency f st2 The calculation method is: f st2 =f c2 -B2 / 2.

[0042] When the MLFM signal pulse is divided into three or more segments, the method for finding the jump point and the parameter estimation method are similar to those when the MLFM signal is divided into two segments, and can be processed accordingly.

[0043] Compared with the prior art, the present invention has the following beneficial effects: first, the powerful time-frequency analysis capabilities of the wavelet transform, a "mathematical microscope," are utilized in combination with phase space reconstruction, singular value decomposition, and other methods to obtain wavelet ridges that reflect the essential characteristics of the MLFM signal. Based on the segmented nature of the MLFM signal pulse, frequency differential processing is performed on the MLFM signal wavelet ridges to accurately locate the transition points and achieve segmentation within the MLFM signal pulse. Then, the powerful FRFT processing capabilities of linear frequency modulation signals are utilized to accurately estimate the parameters of each segment within the MLFM signal pulse. By comprehensively utilizing the two time-frequency analysis methods of wavelet transform and FRFT, as well as phase space reconstruction, singular value decomposition, and transition point merging, the present invention can effectively reduce the impact of noise on signal parameter estimation and improve the effectiveness of signal parameter estimation under low signal-to-noise ratio conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Attachment Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] See also Figure 1 The present invention provides a method for estimating MLFM signal parameters based on wavelet transform and frequency difference comprehensive processing, and the specific scheme is as follows:

[0047] S1: Sort the intercepted signal to obtain the MLFM signal pulse sequence containing the intra-pulse modulation information. For any pulse, it is expressed as x(t), t = 1, 2, ..., T, T is the number of sampling points, and the sampling frequency is f s . The amplitude of x(t) is normalized, and the processed signal sequence is expressed as In the formula, |·| represents the absolute value, and this symbol has the same meaning in the following steps.

[0048] S2: Yes Pulse width estimation is performed using a radar pulse repetition interval estimation method based on blind source separation. The estimated pulse width is expressed as PW1, PW2, ..., PW N, where 1, 2, ..., N represents the pulse number. The signal sequence intercepted into a single pulse width is expressed as Where 1, 2, ..., N represent the pulse number, and the duration of each pulse is one pulse width.

[0049] S3: Yes Perform wavelet transform, expressed as cwt is the continuous wavelet transform function, 1 represents the scale of the wavelet transform, cmor2-1 represents the name of the wavelet basis function. In addition to cmor2-1, other wavelet basis functions can also be used.

[0050] S4: For y1, filtering is performed through phase space reconstruction and singular value decomposition. The number of reconstructed rows is M, which can be set according to the number of points in y1, and the number of columns is Right now The number of sampling points is τ = 1. The absolute value of the reconstructed and filtered signal is taken as yy1. The phase of yy1 is calculated, and the phase difference is calculated using the phase difference method to obtain the wavelet ridge F(t,f), with the sampling points as the abscissa and the frequency as the ordinate. To further reduce the impact of noise on MLFM signal parameter estimation, the wavelet ridge is filtered using mean filtering and then median filtering.

[0051] S5: Perform frequency difference processing on the wavelet ridge. In order to reduce the influence of outliers caused by noise in the wavelet ridge, discard the first few dozen points of the wavelet ridge, generally 30 points. Let J be the order of frequency difference, generally J is 10, and perform the following difference processing on the wavelet ridge:

[0052] Let i=30:[length(F(t,f))-J],dF(i)=F(i+J)-F(i)

[0053] Among them, F is the wavelet ridge, and length(F(t,f)) represents the number of wavelet ridge values.

[0054] S6: Find the jump point of the frequency curve based on the wavelet ridge frequency difference result dF(i). First, find the maximum value of the frequency difference represented by the vertical axis of dF(i), and set the maximum value as Z max , set the threshold to Z y , according to a large number of simulation experiments, Z y =0.5Z max It can meet the requirements. Traverse all the value points of dF(i) vertical axis, when the value is greater than Z yWhen , this point is the jump point of the frequency curve. Let the jump point found be locs(j), j = 1, 2, ..., K, K is the number of jump points. Obviously, the jump point can represent the jump moment of the frequency curve.

[0055] S7: Identify and merge false transition points. For the transition point sequence locs(j), j = 1, 2, ..., K, if the interval between adjacent transition points is less than 20 sampling points, it indicates a false transition point and must be merged. This merging method is to average the sampling times represented by adjacent transition points with an interval less than 20 sampling points and treat them as true transition points. After this process, the remaining transition points are denoted as locs′(k), k = 1, 2, ..., K′, where K′ is the number of transition points.

[0056] S8: Estimate the parameters of the MLFM signal based on the transition point sequence loss′(k), k = 1, 2, …, K′. Since the MLFM signal pulse is typically divided into two or three segments, and the frequency modulation slope of each segment is positive, K′ should be 1 or 2. Without loss of generality, the method for estimating the parameters of the MLFM signal pulse is described using K′ = 1 as an example. K′ = 1 corresponds to the MLFM signal pulse being divided into two segments.

[0057] Obviously, the pulse width of the first segment in the MLFM signal pulse is pw1 = locs′(1)×1 / f s , whose unit is s. Take out the first segment of the MLFM signal and express it as Perform FRFT on it and estimate the frequency modulation slope K1 and starting frequency f according to the transformed time-frequency waveform. st1 , bandwidth B1 and center frequency f c1 .

[0058] FM slope K1 and center frequency f c1 It is directly obtained by performing FRFT transformation on the first segment of MLFM signal.

[0059] The bandwidth B1 is calculated as follows: B1 = pw1 × K1;

[0060] Starting frequency f st1 The calculation method is: f st1 =f c1 -B1 / 2.

[0061] S9: Parameter estimation of the second segment of the MLFM signal pulse. The pulse width of the second segment of the MLFM signal pulse is pw2 = PW1 - locs' (1) × 1 / f s , whose unit is s, PW1 is the pulse width of the MLFM signal estimated by step S2. The second segment of the MLFM signal is taken out and expressed as Perform FRFT on it and estimate the frequency modulation slope K2 and starting frequency f according to the transformed time-frequency waveform. st2 , bandwidth B2 and center frequency f c2 .

[0062] FM slope K2 and center frequency f c2 It is directly obtained by performing FRFT transformation on the second segment signal of MLFM.

[0063] The bandwidth B2 is calculated as follows: B2 = pw2 × K2;

[0064] Starting frequency f st The calculation method is: f st2 =f c2 -B2 / 2.

[0065] When the MLFM signal pulse is divided into three or more segments, the method for finding the jump point and the parameter estimation method are similar to those when the MLFM signal is divided into two segments, and can be processed accordingly.

[0066] The present invention will be further described below in conjunction with experimental test diagrams.

[0067] 1. Experimental conditions setting:

[0068] The experimental verification of the present invention is carried out under computer simulation conditions, and the simulation software adopts MATLAB R2010a. The effectiveness of the present invention is verified through a set of experiments.

[0069] Example: The MLFM signal amplitude is 1V, the pulse width is 21μs, and the frequency within the pulse is divided into two sections. The pulse width of the first section is 7μs, the starting frequency is 18MHz, and the frequency modulation slope is 2.5×10 12 Hz / s; the pulse width of the second segment is 14μs, the starting frequency is 17MHz, and the frequency modulation slope is 1×10 12 Hz / s. The sampling frequency is 150MHz, and the simulation duration is one pulse width. Different signal-to-noise ratios are set, and the estimation is repeated five times at each signal-to-noise ratio. Using this patented solution, the signal parameter estimation results are shown in Tables 1 to 4.

[0070] Table 1 -6dB case MLFM signal parameter results with two pulse frequencies

[0071]

[0072] Table 2-3dB case MLFM signal parameter results with 2 segments of pulse frequency

[0073]

[0074] Table 3 MLFM signal parameter results with 2 pulse frequencies at 0 dB

[0075]

[0076] Table 4 MLFM signal parameter results with 2 pulse frequencies under 3dB condition

[0077]

[0078] From the comparison between the estimated parameters in Tables 1 to 4 and the true parameters of the signal, it can be seen that the parameters estimated by the patent solution are very close to the true parameters, so the parameter estimation results are ideal.

[0079] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating MLFM signal parameters based on wavelet transform and frequency difference integrated processing, characterized in that: The steps include: 1) Inputting the intercepted MLFM signal sequence containing intra-pulse modulation information and sorting it to obtain the MLFM signal sequence; 2) performing pulse width estimation and dividing the sequence into individual pulses according to the pulse width; 3) Perform wavelet transform on the single pulse signal and extract the wavelet ridges through phase space reconstruction, singular value decomposition and phase difference; 4) Perform mean filtering and median filtering on the wavelet ridges; Perform frequency difference processing on the wavelet ridge line to find the jump point of the frequency curve and eliminate the false jump points; 5) Segment the MLFM signal according to the jump points; perform FRFT on each segment to estimate the starting frequency, bandwidth, center frequency and frequency modulation slope parameters of each segment in the pulse.

2. The MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing according to claim 1 is characterized in that: The specific method of inputting the intercepted MLFM signal sequence containing intra-pulse modulation information and sorting it to obtain the MLFM signal sequence is as follows: The intercepted signal is sorted to obtain the MLFM signal pulse sequence containing the intra-pulse modulation information. For any pulse, it is expressed as x(t), t=1,2,…,T, T is the number of sampling points, and the sampling frequency is f s ; Perform amplitude normalization on x(t), and the processed signal sequence is expressed as In the formula, |·| represents the absolute value.

3. The MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing according to claim 2 is characterized in that: The specific method of performing pulse width estimation in step 2) and dividing the sequence into individual pulses according to the pulse width is as follows: right To estimate the pulse width, a radar pulse repetition interval estimation method based on blind source separation is selected. The estimated pulse width is expressed as PW1, PW2, ..., PW N , where 1, 2, ..., N represents the pulse number; The signal sequence intercepted into a single pulse width is expressed as Where 1, 2, ..., N represent the pulse number, and the duration of each pulse is one pulse width.

4. The MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing according to claim 3 is characterized in that: The specific method of step 3) performing wavelet transform on the single pulse signal and extracting the wavelet ridge line through phase space reconstruction, singular value decomposition and phase difference is: right Perform wavelet transform, expressed as cwt is the continuous wavelet transform function, 1 is the scale of the wavelet transform, and cmor2-1 represents the name of the wavelet basis function.

5. The MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing according to claim 4 is characterized in that: The specific method of performing mean filtering and median filtering on the wavelet ridge line in step 4) is as follows: For y1, filtering is performed through phase space reconstruction and singular value decomposition. The number of reconstructed rows is M, which can be set according to the number of points in y1, and the number of columns is Right now The number of sampling points is τ = 1; the absolute value of the reconstructed and filtered signal is taken, expressed as yy1; for yy1, its phase is calculated, and the phase difference is calculated by the phase difference method to obtain the wavelet ridge line F(t,f), whose horizontal coordinate is the sampling point and the vertical coordinate is the frequency value.

6. The MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing according to claim 5, characterized in that: In step 4), the specific method of performing frequency difference processing on the wavelet ridge line, finding the jump point of the frequency curve, and eliminating the false jump point is as follows: Discard the first dozens of points of the wavelet ridge line, set J as the order of frequency difference, and take it as 10, and perform the following difference processing on the wavelet ridge line: Let i=30:[length(F(t,f))-J],dF(i)=F(i+J)-F(i) Where F is the wavelet ridge, length(F(t,f)) represents the number of wavelet ridge values; Find the jump point of the frequency curve according to the wavelet ridge frequency difference result dF(i); find the maximum value of the frequency difference represented by the vertical axis of dF(i), and set the maximum value as Z max , set the threshold to Z y , according to a large number of simulation experiments, Z y =0.5Z max It can meet the requirements; traverse all the value points of the vertical axis of dF(i), when the value is greater than Z y When , this point is the jump point of the frequency curve; let the jump point found be locs(j), j = 1, 2, ..., K, K is the number of jump points; False transition points are identified and merged. For the transition point sequence locs(j), j = 1, 2, ..., K, if the interval between adjacent transition points is less than 20 sampling points, the sampling moments represented by adjacent transition points with an interval less than 20 sampling points are averaged and regarded as real transition points. The remaining transition points are denoted as locs′(k), k = 1, 2, ..., K′, where K′ is the number of transition points.

7. The MLFM signal parameter estimation method based on wavelet transform and frequency difference comprehensive processing according to claim 6, characterized in that: In step 5), the MLFM signal is segmented according to the jump point, and FRFT is performed on each segment to estimate the starting frequency, bandwidth, center frequency and frequency modulation slope parameters of each segment in the pulse: For the signal x(t), perform FRFT on it and get X p (u), whose expression is as follows: Where K p (u,t)=A α exp[jπ(u 2 cotα-2utcscα+t 2 cotα)] is FRFTX p (u) is the kernel function, where α=pπ / 2, where p and α represent the order of FRFT and the rotation angle respectively; The time domain and frequency domain of the LFM signal are dimensionally normalized and converted into dimensionless domains. The center frequency of the LFM signal is changed from f0 to f′0, and the frequency modulation slope of the LFM signal is changed from μ to μ′. The relationship before and after the change is as follows: When α=-arccot(μ), X p (u)=AA α exp(jπu 2 cotα), X p (u) is an impulse function in the fractional Fourier domain. When f0 = ucscα, X p (u) obtains the maximum impact. Based on this feature, the parameters p, u and A can be estimated. The expression is: According to formula (3), the center frequency f0 and the frequency modulation slope μ of the LFM signal can be estimated: The frequency modulation slope K1 is obtained from μ in formula (4); the center frequency f c1 Obtained from f0 in formula (4); The bandwidth B1 is calculated as follows: B1 = pw1 × K1; Starting frequency f st1 The calculation method is: f st1 =f c1 -B1 / 2; Parameter estimation is performed on the second segment of the MLFM signal pulse; the pulse width of the second segment of the MLFM signal pulse is pw2=PW1-locs′(1)×1 / f s , whose unit is s, PW1 is the pulse width of the MLFM signal estimated by step S2; the second segment of the MLFM signal is taken out and expressed as Perform FRFT on it and estimate the frequency modulation slope K2 and starting frequency f according to the transformed time-frequency waveform. st2 , bandwidth B2 and center frequency f c2 ; The frequency modulation slope K2 is obtained from μ in formula (4); the center frequency f c2 Obtained from f0 in formula (4); The bandwidth B2 is calculated as follows: B2 = pw2 × K2; Starting frequency f st2 The calculation method is: f st2 =f c2 -B2 / 2; When the MLFM signal pulse is divided into three or more segments, the method for finding the jump point and the parameter estimation method are similar to those when the MLFM signal is divided into two segments.

Images