CN111766444A - Multi-component linear frequency modulation signal parameter estimation method and system based on comprehensive algorithm - Google Patents

Multi-component linear frequency modulation signal parameter estimation method and system based on comprehensive algorithm Download PDF

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CN111766444A
CN111766444A CN202010653459.7A CN202010653459A CN111766444A CN 111766444 A CN111766444 A CN 111766444A CN 202010653459 A CN202010653459 A CN 202010653459A CN 111766444 A CN111766444 A CN 111766444A
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黄理杰
钱江
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Abstract

The invention discloses a multi-component linear frequency modulation signal parameter estimation method based on STFT, neural network and Radon transformation, which comprises the steps of firstly solving short-time Fourier transform (STFT) of a multi-component LFM signal; judging the number of LFM signal components by using a neural network; then eliminating the influence of signal intensity by unifying the height of the frequency peak; finally, estimating the initial frequency and the frequency modulation slope of each LFM component by a successive elimination method (using Radon transformation); the amplitude of the LFM signal is estimated. According to the method, the number of the LFM signal components is judged through the neural network, the influence of the signal intensity is eliminated through the height of the uniform frequency peak value, the number of the LFM signal components can be directly judged from the STFT diagram, the number of the LFM signal components is not judged from the Radon plane, and the judgment is more accurate; the method is not influenced by cross terms, and is not influenced by different signal component amplitudes or the change of the same signal component amplitude along with time.

Description

Multi-component linear frequency modulation signal parameter estimation method and system based on comprehensive algorithm
Technical Field
The invention relates to the technical field of multi-component linear frequency modulation signals, in particular to a multi-component linear frequency modulation signal parameter estimation method and system based on a comprehensive algorithm.
Background
For a Linear Frequency Modulation (LFM) signal which is changed in instantaneous frequency and contains a plurality of components, the traditional parameter estimation mostly utilizes Wigner-Hough transformation (firstly, Wigner-Ville distribution of the signal is obtained, and then Hough transformation is carried out) or Radon-Wigner transformation (firstly, Wigner-Ville distribution of the signal is obtained, and then Radon transformation is carried out), then a threshold is set, parameters (initial frequency and frequency modulation slope) of each component of the LFM signal are determined according to extreme value coordinates which are larger than the threshold on a Radon-Wigner plane, or parameters of strong LFM signal components are determined one by one, and the strong LFM signal components are eliminated one by one through demodulation and filtering.
The existing method firstly solves the short-time Fourier transform (STFT) of the signal, then carries out Radon transform, then sets a threshold value, determines the parameters (initial frequency and FM slope) of each component of the LFM signal according to the extreme value coordinate which is larger than the threshold value on the STFT-Radon plane, or determines the parameters of the strong LFM signal components one by one and eliminates the strong LFM signal components one by demodulation line and filtering.
Because of the existence of cross terms in the Wigner-Ville distribution (WVD), the cross terms can cause unnecessary peaks to appear on the Radon-Wigner plane, although the elimination of strong LFM signal components one by one through demodulation and filtering can avoid the unnecessary peaks to appear to a certain extent, when the strength of the cross terms is high, the peaks of the cross terms on the Radon-Wigner plane are even higher than the peaks of the signal terms, and the elimination method one by one can mistakenly take the cross terms as the signal terms, thereby eliminating the wrong LFM signal components. As shown in fig. 1a, two LFM signal components with chirp rates close to or equal to each other will cause WVD to have a strong cross term, while its Radon transform will have a higher peak than the signal term, as shown in fig. 1b and 1 c.
The Radon transform of the STFT also exhibits spikes that correspond to out of the line if the signal amplitude is time varying. As shown in fig. 2a, there are two lines corresponding to two LFM signal components, respectively, and when the integration line of the Radon transform coincides with the two lines (directions marked with 1 and 2), the Radon transform value has a spike, but when the integration line of the Radon transform passes through a part (direction marked with 3) where the amplitude of the line of the two LFM signal components is large, the Radon transform value also has a spike, as shown in fig. 2b, and the height of the spike may be even larger than that of the spike of the signal item, and the one-by-one cancellation method may also fail.
Due to the above disadvantages and the influence of signal noise, the number of peaks on the Radon plane is often greater than the number of actual LFM signal components, so the number of LFM signal components cannot be accurately determined through Radon transformation.
Disclosure of Invention
In view of the above, the present invention provides a method for estimating parameters of a multi-component chirp signal by using a synthesis algorithm.
In order to achieve the purpose, the invention provides the following technical scheme:
the invention provides a multi-component linear frequency modulation signal parameter estimation method based on a comprehensive algorithm, which comprises the following steps:
obtaining a multi-component LFM signal;
performing short-time Fourier transform on the multi-component LFM signal;
judging the number of LFM signal components through a neural network algorithm;
unifying the frequency peak values of the processed LFM signal components;
estimating the initial frequency and the frequency modulation slope of each multi-component LFM signal by a successive elimination method;
the amplitude of the multi-component LFM signal is calculated.
Further, the short-time fourier transform STFT of the multi-component LFM signal is performed according to the following formula:
Figure BDA0002575842030000021
wherein STFT (t, f) represents a short-time fourier transform of the signal;
z (u) represents a multi-component chirp signal;
g (t) is an analysis window function;
g*(t) is the conjugate function of g (t);
u represents an integral variable;
f represents a frequency;
t represents time.
Further, the determining the number n of LFM signal components by the neural network algorithm is implemented according to the following steps:
and inputting an STFT graph obtained by short-time Fourier transform of the multi-component LFM signals into a neural network, and processing the STFT graph by the neural network to obtain the number n of the multi-component LFM signals.
Further, the frequency peaks are uniformly processed according to the following steps:
obtaining frequency peak values of different time on a time frequency plane obtained after short-time Fourier transform of the multi-component LFM signal, obtaining a coordinate set P of the frequency peak values on an STFT plane, and obtaining a binaryzation time frequency plane according to the set P;
the peak distribution on the time-frequency plane is obtained according to the following formula:
Figure BDA0002575842030000022
wherein, F (t, F) represents a binary time-frequency plane, the value of 1 represents that the point coordinate is in the set P, otherwise, the point coordinate is not in the set P,
t represents the time of day and t represents the time of day,
f represents the frequency of the frequency,
p represents a set of coordinates of frequency peaks at different times on the time-frequency plane of the short-time fourier transform,
and smoothing the time-frequency plane of the obtained binaryzation frequency peak value, and then performing Radon transformation.
Further, the estimating the start frequency and chirp rate of each multi-component LFM signal by successive elimination is performed according to the following steps:
determining the highest peak of the multi-component LFM signal after short-time Fourier transform, the initial frequency and the frequency modulation slope of the LFM signal component corresponding to the highest peak and a corresponding straight line in a time-frequency plane of the short-time Fourier transform;
removing points in the set P near the straight line;
obtaining a binary time-frequency plane again for the updated set P, and carrying out Radon transformation on the plane; this process is repeated until the parameters for the n components are determined.
Further, the Radon transform is implemented according to the following formula:
PF(u,α)＝∫PQF(ucosα-vsinα,usinα+vcosα)dv；
wherein，PF(u, α) representing the Radon transform of a binary function F (t, F) on a plane;
f (t, F) is a binary function on a plane;
rotating the original rectangular coordinates (t, f) by an angle alpha to obtain new rectangular coordinates (u, v);
the value of a point with coordinates (u, alpha) on a Radon transformation plane is the value of PQ integral along a straight line on the original plane;
the distance of the straight line PQ to the origin is u;
the included angle between the normal direction and the positive direction of the t axis is alpha;
calculating the intercept and the slope of a straight line according to the following formula through the peak value coordinates of Radon transformation, thereby solving the initial frequency and the frequency modulation slope of the multi-component LFM signal;
Figure BDA0002575842030000031
wherein the expression of the multi-component LFM signal is:
Figure BDA0002575842030000032
wherein i is the LFM signal component serial number, t is time, f0 is the starting frequency, m is the FM slope,
n is the number of components;
Ai(t) is the signal amplitude of each LFM signal component;
f0ithe starting frequency of each LFM signal component;
mithe chirp rate of each multi-component LFM signal.
Further, the calculating the amplitude of the multi-component LFM signal is performed according to the following steps:
the amplitude estimate at time t0 is calculated according to the following equation:
Figure BDA0002575842030000041
where M is the multi-component L sampled in the STFT planeFM signal at t0The value of the time:
STFT(t0,f0+mt0)＝M；
t0represents a sampling instant;
A0STFT representing an ideal LFM signal of constant amplitude and of infinite duration0The value at + mt, i.e.:
STFT(t,f0+mt)＝A0；
t represents time on the time-frequency plane.
The invention provides a multi-component linear frequency modulation signal parameter estimation system based on a comprehensive algorithm, which comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor realizes the following steps when executing the program:
obtaining a multi-component LFM signal;
performing short-time Fourier transform on the multi-component LFM signal;
judging the number of LFM signal components through a neural network algorithm;
unifying the frequency peak values of the processed LFM signal components;
estimating the initial frequency and the frequency modulation slope of each multi-component LFM signal by a successive elimination method;
the amplitude of the multi-component LFM signal is calculated.
Further, the determining the number n of LFM signal components by the neural network algorithm is implemented according to the following steps:
and inputting an STFT graph obtained by short-time Fourier transform of the multi-component LFM signals into a neural network, and processing the STFT graph by the neural network to obtain the number n of the multi-component LFM signals.
Further, the frequency peaks are uniformly processed according to the following steps:
obtaining frequency peak values of different time on a time frequency plane obtained after short-time Fourier transform of the multi-component LFM signal, obtaining a coordinate set P of the frequency peak values on an STFT plane, and obtaining a binaryzation time frequency plane according to the set P;
the peak distribution on the time-frequency plane is obtained according to the following formula:
Figure BDA0002575842030000051
wherein, F (t, F) represents a binary time-frequency plane, the value of 1 represents that the point coordinate is in the set P, otherwise, the point coordinate is not in the set P,
t represents the time of day and t represents the time of day,
f represents the frequency of the frequency,
p represents a set of coordinates of frequency peaks at different times on the time-frequency plane of the short-time fourier transform,
smoothing the time-frequency plane of the obtained binaryzation frequency peak value, and then carrying out Radon transformation;
the estimating of the start frequency and chirp rate of each multi-component LFM signal by successive cancellation is performed according to the following steps:
determining the highest peak of the multi-component LFM signal after short-time Fourier transform, the initial frequency and the frequency modulation slope of the LFM signal component corresponding to the highest peak and a corresponding straight line in a time-frequency plane of the short-time Fourier transform;
removing points in the set P near the straight line;
obtaining a binary time-frequency plane again for the updated set P, and carrying out Radon transformation on the plane; repeating the process until parameters for the n components are determined;
the Radon transform is implemented according to the following formula:
PF(u,α)＝∫PQF(ucosα-vsinα,usinα+vcosα)dv；
wherein, PF(u, α) representing the Radon transform of a binary function F (t, F) on a plane;
f (t, F) is a binary function on a plane;
rotating the original rectangular coordinates (t, f) by an angle alpha to obtain new rectangular coordinates (u, v);
the value of a point with coordinates (u, alpha) on a Radon transformation plane is the value of PQ integral along a straight line on the original plane;
the distance of the straight line PQ to the origin is u;
the included angle between the normal direction and the positive direction of the t axis is alpha;
calculating the intercept and the slope of a straight line according to the following formula through the peak value coordinates of Radon transformation, thereby solving the initial frequency and the frequency modulation slope of the multi-component LFM signal;
Figure BDA0002575842030000061
wherein the expression of the multi-component LFM signal is:
Figure BDA0002575842030000062
wherein i is the LFM signal component serial number, t is time, f0 is the starting frequency, m is the FM slope,
n is the number of components;
Ai(t) is the signal amplitude of each LFM signal component;
f0ithe starting frequency of each LFM signal component;
mithe chirp rate of each multi-component LFM signal.
The invention has the beneficial effects that:
the invention provides a multi-component linear frequency modulation signal parameter estimation method based on STFT, neural network and Radon transformation, which comprises the steps of firstly solving short-time Fourier transform (STFT) of a multi-component LFM signal; judging the number of LFM signal components by using a neural network; then eliminating the influence of signal intensity by unifying the height of the frequency peak; finally, estimating the initial frequency and the frequency modulation slope of each LFM component by a successive elimination method (using Radon transformation); the amplitude of the LFM signal is estimated.
According to the method, the number of the LFM signal components is judged through the neural network, the influence of the signal intensity is eliminated through the height of the uniform frequency peak value, the number of the LFM signal components can be directly judged from the STFT diagram, the number of the LFM signal components is not judged from the Radon plane, and the judgment is more accurate; the method is not influenced by cross terms, and is not influenced by different signal component amplitudes or the change of the same signal component amplitude along with time.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
fig. 1a is a schematic diagram of the WVD of two LFM signal components.
FIG. 1b is a diagram of the Radon transform of FIG. 1 a.
FIG. 1c is a schematic three-dimensional view of FIG. 1 b.
Fig. 2a shows an STFT diagram of two LFM signal components.
Fig. 2b is a diagram of the Radon transform of fig. 2 a.
Fig. 3 is a flow chart of a method for estimating parameters of a multi-component chirp signal.
Fig. 4 is a diagram of Radon transform.
Fig. 5 is a structure of a neural network.
FIG. 6a is a binarized time-frequency plane.
Fig. 6b shows the result of the smoothing filter of fig. 6 a.
Fig. 6c shows the result of the Radon transform performed on fig. 6 b.
FIG. 7a is a short-time Fourier transform of a signal for a range bin.
Fig. 7b shows the STFT plot of the distance unit signal reconstructed with the estimated parameters.
Fig. 7c shows the result of imaging with the raw signal.
Fig. 7d results of imaging after signal reconstruction with estimated parameters.
Detailed Description
The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.
Example 1
As shown in fig. 3, in the multi-component chirp signal parameter estimation method based on STFT, neural network and Radon transform provided in this embodiment, first, a short-time fourier transform (STFT) of a multi-component LFM signal is obtained; judging the number of LFM signal components by using a neural network; then eliminating the influence of signal intensity by unifying the height of the frequency peak; estimating the start frequency and chirp rate of each LFM component by a successive elimination method (using Radon transform); finally, the amplitude of the LFM signal is estimated.
The uniform frequency peaks of the present embodiment are obtained by equalizing the magnitudes of the frequency peaks. The inconsistent size of the frequency peaks may cause that the peaks of the Radon transform cannot correspond to the parameters of the band estimation, and this problem is avoided after the same frequency peak. Therefore, the signal strength influence can be eliminated by unifying the frequency peaks.
As shown in fig. 3, the method specifically comprises the following steps:
the mathematical representation of a single component LFM signal is:
Figure BDA0002575842030000071
where t is time, f0 is the starting frequency, and m is the chirp rate.
If the amplitude of the signal varies over time, it can be expressed as:
Figure BDA0002575842030000072
where A (t) is the amplitude of the signal.
If the signal contains multiple LFM signal components, the number of components n, can be expressed as:
Figure BDA0002575842030000081
the technical goal is to estimate the signal amplitude A of each LFM signal componenti(t), starting frequency f0iAnd chirp slope mi。
The Radon transform is defined as follows:
assuming a binary function F (t, F) on the plane, its Radon transforms into:
PF(u,α)＝∫PQF(ucosα-vsinα,usinα+vcosα)dv (4)
the value of a point with coordinates (u, alpha) on the Radon transform plane is the value of integral along a straight line PQ on the original plane, the distance from the straight line PQ to the original point is u, and the included angle between the normal direction of the straight line PQ and the positive direction of the t axis is alpha. The Radon transform is equivalent to a projection integration of the image as shown in fig. 4.
The Radon transform can be used to detect straight lines in an image, and when the integration straight line coincides with the detected straight line, the Radon transform obtains a very high value. Therefore, the intercept and the slope of the straight line can be calculated through the peak coordinates of Radon transformation, and the initial frequency and the frequency modulation slope of the LFM signal can be obtained.
Figure BDA0002575842030000082
A short-time fourier transform (STFT) of the multi-component LFM signal is calculated, and the STFT can obtain a frequency spectrum of the visualized signal in a local time range, which is defined as:
Figure BDA0002575842030000083
wherein g (t) is an analysis window function, g*(t) is its conjugate function. The window functions used for STFT are all Hamming windows with a window length of one quarter of the signal length.
From the STFT time-frequency diagram, it is clear how many LFM signal components are. Therefore, the STFT map obtained by the short-time fourier transform may be input to a neural network, and the neural network outputs the LFM signal component number n.
The neural network structure used in the embodiment is a ResNet simplified version widely used for image recognition, and is obtained by modification on the basis of ResNet-50, the number of layers of the network is reduced, and the BatchNorm layer is omitted.
Fig. 5 shows the structure of the convolutional neural network used. The method solves the problem that the number of LFM signal components cannot be accurately judged through Radon transformation.
In fig. 5, CONV2D denotes a two-dimensional convolutional layer;
ReLU represents a linear rectification function;
conv _ block1 represents residual module 1 with convolutional layer on branch;
conv _ block2 represents convolution module 2 with convolution layer on branch line;
identity _ block represents the convolution module with no convolution layer on the branch;
AVG POOLING denotes the mean POOLING layer,
flatten denotes unfolding the output tensor into a one-dimensional vector,
FC denotes a full connection layer;
the data for training the neural network is generated by simulation, and signals with the component number n of 0 to 10 are randomly generated by the formula (3), the amplitude A (t) and the starting frequency f of each component0The chirp rate m is also random. Each signal is then noisy, making it closer to what is the case with the measured signal. The input of the neural network is the STFT diagram of the signal z (t), the output is the number n of LFM signal components, and n is more than or equal to 0 and less than or equal to 10.
The present embodiment is described in detail below with the effect of eliminating the signal intensity by unifying the frequency peak heights.
The magnitudes are different due to the amplitude of the same multi-component LFM signal at different times. Furthermore, the different magnitudes of the different LFM signal components may also create a "small magnitude" problem, i.e., the spikes of the large magnitude signal components overlap the spikes of the small magnitude signals in the Radon plane. This problem can be solved by a method comprising the steps of:
(1) for the STFT of a multi-component LFM signal, find the frequency peaks at different times (requiring the peak height to be greater than a set threshold, such as 3 times the average amplitude of noise), and take the maximum n of these peaks (if the number of peaks is greater than n, n is the number of LFM signal components obtained in step 2), record the coordinates (t, f) of these peaks on the STFT plane, and the coordinates of all peaks form the set P.
(2) In another time-frequency plane, let
Figure BDA0002575842030000091
The peak value distribution with uniform peak value height is obtained. The result shown in fig. 6a is obtained through these two parts, as is the signal STFT of fig. 2 a.
(3) Because the coordinates of these peaks are not strictly distributed on a straight line (especially the measured data), the plane obtained in step (2) is directly subjected to Radon transform, and these points cannot be well projected onto the u-axis in a centralized manner no matter what the rotation angle α is. It may be smoothed first to obtain the result shown in fig. 6b, and then subjected to Radon transform to obtain the result shown in fig. 6 c.
In the present embodiment, the initial frequency and the chirp rate of each LFM component are estimated by the successive elimination method, and through the above steps, although the number of peaks of the Radon transform of the STFT is still greater than that of the LFM signal component, it is ensured that the highest peak corresponds to a certain LFM signal component, rather than the integral straight line corresponding to the reference number 3 in fig. 2 a.
Therefore, the highest peak, such as the start frequency and chirp rate of the LFM component corresponding to peak 1 in fig. 6c and the corresponding line in the STFT diagram, can be determined according to equation (5), and then the points in the set of peak coordinates P near this line are removed.
Repeating steps (2) and (3), the Radon transform obtained again has no peaks 1, 3 and 4 in fig. 6c, because peaks 3 and 4 are caused by the integral straight line passing through the points on the two straight lines in fig. 2a at the same time during the Radon transform, now the points near one straight line are eliminated, and no peaks 3 and 4 are obtained.
If there are multiple LFM signal components, the above steps are repeated, each time determining the start frequency and chirp rate of one LFM component, until the parameters for the n components are determined.
The successive cancellation method provided in this embodiment is different from the successive cancellation method of the prior art, which performs line demodulation and band rejection filtering on a signal to cancel a component on the original signal, and the successive cancellation method provided in this embodiment cancels a frequency near a straight line on the STFT.
Estimating the amplitude of the LFM signal: since the amplitude a (t) of each LFM signal component is time-varying, a (t) cannot be estimated by the peak height of the Radon transform (only the average amplitude over the entire time period can be estimated). To estimate A (t), f may be determined0And m, sampling the value of the corresponding line on the STFT plane.
For an ideal LFM signal of constant amplitude and of infinite duration, the STFT of the signal is then equal to f in the straight line f0The value at + mt is a constant, i.e.
If it is
Figure BDA0002575842030000101
Then
STFT(t,f0+mt)＝A0(9)
Sampling on the STFT surface to obtain the value of a certain LFM signal component at the time t0 as STFT (t0,f0+mt0)＝M；
Then the amplitude estimate of this component at time t0 is
Figure BDA0002575842030000102
If the instantaneous frequencies of the component and the other components are close or equal at time t0, then the estimate has a large error (actually resulting in the amplitude of the signal resulting from the interference of the same frequency component of the different components at time t 0).
The following is the application of the method provided by the present embodiment in ISAR imaging. For a certain measured data, as shown, among others,
FIG. 7a is a graph of the short-time Fourier transform of a signal at a range bin in measured data;
FIG. 7b is a graph of STFT of the distance cell signal reconstructed with estimated parameters;
FIG. 7c shows the Doppler spectrum of each range bin after fast Fourier transform is performed on the signal of each range bin of the measured data;
fig. 7d shows the result of doppler spectrum stitching imaging at a certain time after short-time fourier transform of the signal reconstructed by the estimated parameters.
It can be seen that the signal reconstructed with the estimated parameters, after parameter estimation, has removed noise compared to the original signal.
The method provided by the embodiment can directly judge the number of the LFM signal components from the STFT diagram, but not judge the number of the LFM signal components from the Radon plane, so that the judgment is more accurate. Meanwhile, the method is not influenced by cross terms, and is not influenced by different signal component amplitudes or the change of the same signal component amplitude along with time.
Example 2
The present embodiment also provides a system for estimating parameters of a multi-component chirp signal based on a synthesis algorithm, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the following steps when executing the computer program:
obtaining a multi-component LFM signal;
performing short-time Fourier transform on the multi-component LFM signal;
judging the number of LFM signal components through a neural network algorithm;
unifying the frequency peak values of the processed LFM signal components;
estimating the initial frequency and the frequency modulation slope of each multi-component LFM signal by a successive elimination method;
the amplitude of the multi-component LFM signal is calculated.
The LFM signal component number n is judged through a neural network algorithm according to the following steps:
and inputting an STFT graph obtained by short-time Fourier transform of the multi-component LFM signals into a neural network, and processing the STFT graph by the neural network to obtain the number n of the multi-component LFM signals.
The frequency peak value is uniformly carried out according to the following steps:
obtaining frequency peak values of different time on a time frequency plane obtained after short-time Fourier transform of the multi-component LFM signal, obtaining a coordinate set P of the frequency peak values on an STFT plane, and obtaining a binaryzation time frequency plane according to the set P;
the peak distribution on the time-frequency plane is obtained according to the following formula:
Figure BDA0002575842030000111
wherein, F (t, F) represents a binary time-frequency plane, the value of 1 represents that the point coordinate is in the set P, otherwise, the point coordinate is not in the set P,
t represents the time of day and t represents the time of day,
f represents the frequency of the frequency,
p represents a set of coordinates of frequency peaks at different times on the time-frequency plane of the short-time fourier transform,
smoothing the time-frequency plane of the obtained binaryzation frequency peak value, and then carrying out Radon transformation;
the estimating of the start frequency and chirp rate of each multi-component LFM signal by successive cancellation is performed according to the following steps:
determining the highest peak of the multi-component LFM signal after short-time Fourier transform, the initial frequency and the frequency modulation slope of the LFM signal component corresponding to the highest peak and a corresponding straight line in a time-frequency plane of the short-time Fourier transform;
removing points in the set P near the straight line;
obtaining a binary time-frequency plane again for the updated set P, and carrying out Radon transformation on the plane; repeating the process until parameters for the n components are determined;
the Radon transform is implemented according to the following formula:
PF(u,α)＝∫PQF(ucosα-vsinα,usinα+vcosα)dv；
wherein, PF(u, α) representing the Radon transform of a binary function F (t, F) on a plane;
f (t, F) is a binary function on a plane;
rotating the original rectangular coordinates (t, f) by an angle alpha to obtain new rectangular coordinates (u, v);
the value of a point with coordinates (u, alpha) on a Radon transformation plane is the value of PQ integral along a straight line on the original plane;
the distance of the straight line PQ to the origin is u;
the included angle between the normal direction and the positive direction of the t axis is alpha;
calculating the intercept and the slope of a straight line according to the following formula through the peak value coordinates of Radon transformation, thereby solving the initial frequency and the frequency modulation slope of the multi-component LFM signal;
Figure BDA0002575842030000121
wherein the expression of the multi-component LFM signal is:
Figure BDA0002575842030000122
wherein i is the LFM signal component serial number, t is time, f0 is the starting frequency, m is the FM slope,
n is the number of components;
Ai(t) is the signal amplitude of each LFM signal component;
f0ithe starting frequency of each LFM signal component;
mithe chirp rate of each multi-component LFM signal.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (10)

1. The multi-component linear frequency modulation signal parameter estimation method based on the comprehensive algorithm is characterized by comprising the following steps: the method comprises the following steps:
obtaining a multi-component LFM signal;
performing short-time Fourier transform on the multi-component LFM signal;
judging the number of LFM signal components through a neural network algorithm;
unifying the frequency peak values of the processed LFM signal components;
estimating the initial frequency and the frequency modulation slope of each multi-component LFM signal by a successive elimination method;
the amplitude of the multi-component LFM signal is calculated.
2. The method of claim 1, wherein: the short time fourier transform, STFT, of the multi-component LFM signal is performed according to the following formula:
Figure FDA0002575842020000011
wherein STFT (t, f) represents a short-time fourier transform of the signal;
z (u) represents a multi-component chirp signal;
g (t) is an analysis window function;
g*(t) is the conjugate function of g (t);
u represents an integral variable;
f represents a frequency;
t represents time.
3. The method of claim 1, wherein: the LFM signal component number n is judged through a neural network algorithm according to the following steps:
and inputting an STFT graph obtained by short-time Fourier transform of the multi-component LFM signals into a neural network, and processing the STFT graph by the neural network to obtain the number n of the multi-component LFM signals.
4. The method of claim 1, wherein: the frequency peak value is uniformly carried out according to the following steps:
obtaining frequency peak values of different time on a time frequency plane obtained after short-time Fourier transform of the multi-component LFM signal, obtaining a coordinate set P of the frequency peak values on an STFT plane, and obtaining a binaryzation time frequency plane according to the set P;
the peak distribution on the time-frequency plane is obtained according to the following formula:
Figure FDA0002575842020000021
wherein, F (t, F) represents a binary time-frequency plane, the value of 1 represents that the point coordinate is in the set P, otherwise, the point coordinate is not in the set P,
t represents the time of day and t represents the time of day,
f represents the frequency of the frequency,
p represents a set of coordinates of frequency peaks at different times on the time-frequency plane of the short-time fourier transform,
and smoothing the time-frequency plane of the obtained binaryzation frequency peak value, and then performing Radon transformation.
5. The method of claim 1, wherein: the estimating of the start frequency and chirp rate of each multi-component LFM signal by successive cancellation is performed according to the following steps:
determining the highest peak of the multi-component LFM signal after short-time Fourier transform, the initial frequency and the frequency modulation slope of the LFM signal component corresponding to the highest peak and a corresponding straight line in a time-frequency plane of the short-time Fourier transform;
removing points in the set P near the straight line;
obtaining a binary time-frequency plane again for the updated set P, and carrying out Radon transformation on the plane; this process is repeated until the parameters for the n components are determined.
6. The method of claim 4, wherein: the Radon transform is implemented according to the following formula:
PF(u,α)＝∫PQF(u cosα-v sinα,u sinα+v cosα)dv；
wherein, PF(u, α) represents the Radon transform of a binary function F (t, F) on a plane；
F (t, F) is a binary function on a plane;
rotating the original rectangular coordinates (t, f) by an angle alpha to obtain new rectangular coordinates (u, v);
the value of a point with coordinates (u, alpha) on a Radon transformation plane is the value of PQ integral along a straight line on the original plane;
the distance of the straight line PQ to the origin is u;
the included angle between the normal direction and the positive direction of the t axis is alpha;
calculating the intercept and the slope of a straight line according to the following formula through the peak value coordinates of Radon transformation, thereby solving the initial frequency and the frequency modulation slope of the multi-component LFM signal;
Figure FDA0002575842020000022
wherein the expression of the multi-component LFM signal is:
Figure FDA0002575842020000031
wherein i is the LFM signal component serial number, t is time, f0 is the starting frequency, m is the FM slope,
n is the number of components;
Ai(t) is the signal amplitude of each LFM signal component;
f0ithe starting frequency of each LFM signal component;
mithe chirp rate of each multi-component LFM signal.
7. The method of claim 1, wherein: the calculation of the amplitude of the multi-component LFM signal is performed according to the following steps:
the amplitude estimate at time t0 is calculated according to the following equation:
Figure FDA0002575842020000032
wherein M is in the STFT planeSampling to obtain a multi-component LFM signal at t0The value of the time:
STFT(t0,f0+mt0)＝M；
t0represents a sampling instant;
A0STFT representing an ideal LFM signal of constant amplitude and of infinite duration0The value at + mt, i.e.:
STFT(t,f0+mt)＝A0；
t represents time on the time-frequency plane.
8. A system for multi-component chirp signal parameter estimation based on a synthesis algorithm, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the following steps when executing the program:
obtaining a multi-component LFM signal;
performing short-time Fourier transform on the multi-component LFM signal;
judging the number of LFM signal components through a neural network algorithm;
unifying the frequency peak values of the processed LFM signal components;
estimating the initial frequency and the frequency modulation slope of each multi-component LFM signal by a successive elimination method;
the amplitude of the multi-component LFM signal is calculated.
9. The system of claim 8, wherein: the LFM signal component number n is judged through a neural network algorithm according to the following steps:
and inputting an STFT graph obtained by short-time Fourier transform of the multi-component LFM signals into a neural network, and processing the STFT graph by the neural network to obtain the number n of the multi-component LFM signals.
10. The system of claim 8, wherein: the frequency peak value is uniformly carried out according to the following steps:
obtaining frequency peak values of different time on a time frequency plane obtained after short-time Fourier transform of the multi-component LFM signal, obtaining a coordinate set P of the frequency peak values on an STFT plane, and obtaining a binaryzation time frequency plane according to the set P;
the peak distribution on the time-frequency plane is obtained according to the following formula:
Figure FDA0002575842020000041
wherein, F (t, F) represents a binary time-frequency plane, the value of 1 represents that the point coordinate is in the set P, otherwise, the point coordinate is not in the set P,
t represents the time of day and t represents the time of day,
f represents the frequency of the frequency,
p represents a set of coordinates of frequency peaks at different times on the time-frequency plane of the short-time fourier transform,
smoothing the time-frequency plane of the obtained binaryzation frequency peak value, and then carrying out Radon transformation;
the estimating of the start frequency and chirp rate of each multi-component LFM signal by successive cancellation is performed according to the following steps:
determining the highest peak of the multi-component LFM signal after short-time Fourier transform, the initial frequency and the frequency modulation slope of the LFM signal component corresponding to the highest peak and a corresponding straight line in a time-frequency plane of the short-time Fourier transform;
removing points in the set P near the straight line;
obtaining a binary time-frequency plane again for the updated set P, and carrying out Radon transformation on the plane; repeating the process until parameters for the n components are determined;
the Radon transform is implemented according to the following formula:
PF(u,α)＝∫PQF(u cosα-v sinα,u sinα+v cosα)dv；
wherein, PF(u, α) representing the Radon transform of a binary function F (t, F) on a plane;
f (t, F) is a binary function on a plane;
rotating the original rectangular coordinates (t, f) by an angle alpha to obtain new rectangular coordinates (u, v);
the value of a point with coordinates (u, alpha) on a Radon transformation plane is the value of PQ integral along a straight line on the original plane;
the distance of the straight line PQ to the origin is u;
the included angle between the normal direction and the positive direction of the t axis is alpha;
calculating the intercept and the slope of a straight line according to the following formula through the peak value coordinates of Radon transformation, thereby solving the initial frequency and the frequency modulation slope of the multi-component LFM signal;
Figure FDA0002575842020000051
wherein the expression of the multi-component LFM signal is:
Figure FDA0002575842020000052
wherein i is the LFM signal component serial number, t is time, f0 is the starting frequency, m is the FM slope,
n is the number of components;
Ai(t) is the signal amplitude of each LFM signal component;
f0ithe starting frequency of each LFM signal component;
mithe chirp rate of each multi-component LFM signal.
CN202010653459.7A 2020-07-08 2020-07-08 Multi-component linear frequency modulation signal parameter estimation method and system based on comprehensive algorithm Pending CN111766444A (en)

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