CN109284690B - Multi-component LFM signal separation method based on Radon-Wigner transformation and REALX algorithm - Google Patents

Multi-component LFM signal separation method based on Radon-Wigner transformation and REALX algorithm Download PDF

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CN109284690B
CN109284690B CN201811004557.7A CN201811004557A CN109284690B CN 109284690 B CN109284690 B CN 109284690B CN 201811004557 A CN201811004557 A CN 201811004557A CN 109284690 B CN109284690 B CN 109284690B
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周一鹏
程嗣怡
董晓璇
陈游
张官荣
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Beijing Aerospace Keyi Technology Co ltd
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Abstract

Aiming at the problems of parameter estimation and signal separation of a multi-component Linear Frequency Modulation (LFM) signal, a method based on RWT (Radon-Wigner Transform) and RELAX ideas is provided. The algorithm firstly estimates strong signal component parameters according to the RWT domain characteristics of the multi-component LFM signal, then carries out circular optimization on the estimated signal component parameters based on the RELAX idea, finally realizes parameter estimation on all signal components and realizes separation of the signal components. Compared with the traditional method for estimating the LFM signal parameters based on time-frequency transformation, the RELAX application can greatly eliminate the influence of strong and weak signal interference and time-frequency surface spectrum peak broadening in the process of circularly estimating the signal parameters, and improve the parameter estimation precision.

Description

Multi-component LFM signal separation method based on Radon-Wigner transformation and REALX algorithm
Technical Field
The invention belongs to the signal and information processing technology, and particularly relates to a method for separating a multi-component line LFM signal.
Background
The linear frequency modulation signal has the characteristics of time-varying frequency, large time-width bandwidth product, good anti-interference performance and the like, and is a common signal applied to radar, sonar, missile fuze and the like. The electromagnetic environment in modern war is increasingly complex, and for airborne electronic countermeasure reconnaissance receivers working in a non-cooperative mode, how to accurately and effectively separate received multi-component linear frequency modulation signals (hereinafter referred to as multi-component LFM signals) and estimate parameters of each signal component becomes an important basis for realizing radiation source identification and threat level judgment, and is also a necessary condition for implementing precise electronic interference.
Aiming at the problems of separation and parameter estimation of linear frequency modulation signals, the traditional maximum likelihood estimation method and the traditional linear modulation method have contradiction between estimation precision and calculation complexity, and the estimation precision is not high under the condition of low signal-to-noise ratio. The method can reflect the time-frequency characteristics of the LFM signal based on Fractional Fourier transform (FrFT), Radon-Wigner transform (RWT), Radon-Ambiguy transform (RAT) and Wigner-Hough transform (WHT) time-frequency transform methods, and can transform a one-dimensional LFM signal to a two-dimensional time-frequency plane, so that the signal parameter estimation problem is transformed to a two-dimensional spectrum peak search problem of the time-frequency plane, and higher estimation precision of a modulation frequency and an initial frequency can be obtained when a single LFM signal is analyzed, and the method is widely applied to parameter estimation of the LFM signal. However, for a multi-component LFM signal, the estimation accuracy of the tuning frequency and the initial frequency is severely affected by the cross interference terms present in the time-frequency distribution of the multi-component LFM signal. While the improved methods such as the smooth pseudo-wigner transform and the time-frequency distribution series method effectively inhibit the influence of cross terms, the frequency resolution of the estimated parameters is reduced. Therefore, how to implement high-precision multi-component LFM signal separation and parameter estimation by using a time-frequency analysis method becomes a hot spot of current research. The RELAX algorithm is an estimation algorithm based on a non-linear minimum variance criterion, and has advantages in estimation accuracy compared with a successive elimination (CLEAN) algorithm. According to the method, the estimation precision is effectively improved by eliminating each component of the signal one by one and updating the estimation value of the correction signal parameter, and finally the parameter estimation of the mixed signal is realized.
Disclosure of Invention
The invention provides a multi-component LFM signal separation method based on Radon-Wigner transformation and RELAX algorithm, comprising the following steps:
s1, preprocessing, namely converting an initialized multi-component LFM signal to a RWT plane based on Radon-Wigner conversion;
s2, coarse estimation, namely searching a peak value of the RWT plane, and performing coarse estimation on a stronger LFM signal component in the multi-component LFM signal to obtain a coarse estimation LFM signal component;
s3, fine estimation, namely performing circular optimization fine estimation on the coarse estimation signal component based on an REALX algorithm until internal convergence to obtain a fine estimation LFM signal component;
s4, signal separation, namely removing the fine estimation LFM signal component from the multi-component LFM signal to obtain a residual LFM signal component;
s5, terminating the threshold judgment, and repeating S2-S4 for the rest of LFM signal components, wherein when the parameters of all LFM signal components in the multi-component LFM signal are effectively estimated.
In order to more clearly describe the multi-component LFM signal separation method based on Radon-Wigner transformation and REALX algorithm, the steps S2-S5 are further disclosed, namely:
in step S2, the peak is a peak coordinate, and a rough estimation center is derived according to the peak coordinate;
in step S3, calculating a variation of two adjacent loop optimizations, and determining internal convergence when the variation is lower than a convergence threshold; when the variation is higher than the convergence threshold, returning to the step of S2;
in step S4, the fine-estimated LFM signal components are removed from the multi-component LFM signal by using a time-domain cancellation method to obtain remaining LFM signals;
in step S5, the energy of the remaining LFM signal is first calculated and compared with a set threshold, and if the energy is lower than the threshold, it is determined that all LFM signal components in the multi-component LFM signal are separated.
The invention has the beneficial effects that: aiming at the parameter estimation problem of the multi-component LFM signal, a signal parameter estimation algorithm based on RWT and RELAX ideas is provided. The algorithm combines the characteristics that the RWT algorithm can carry out quick rough estimation on the signal parameters and the RELAX algorithm has high estimation precision, carries out rough estimation on the signal parameters through RWT transformation, and then carries out circular optimization estimation on the estimated signal parameters through the RELAX algorithm. The method can realize higher estimation precision than the traditional method and has stronger practicability.
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Fig. 1 shows a flow chart of multi-component LFM signal parameter estimation;
FIG. 2 shows a three-dimensional WVD diagram of the original signal S (t) in example 9;
FIG. 3 shows a two-dimensional WVD diagram of the original signal S (t) in example 9;
FIG. 4 shows a diagram of RWT of the original signal S (t) in example 9;
fig. 5 shows a three-dimensional WVD diagram of the residual signal S1(t) after the first signal separation in example 9;
fig. 6 shows a two-dimensional WVD diagram of the residual signal S1(t) after the first signal separation in example 9;
FIG. 7 shows a diagram of RWT of the signal S1(t) remaining after the first signal separation in example 9;
FIG. 8 shows a three-dimensional WVD of the residual signal S2(t) after the second signal separation in example 9;
FIG. 9 shows a two-dimensional WVD of the residual signal S2(t) after the second signal separation in example 9;
fig. 10 shows a RWT graph of the remaining signal S2(t) after the second signal separation in example 9.
Detailed Description
The invention is described in detail below with reference to the following examples and the accompanying drawings.
Example 1
Referring to fig. 1, the present invention provides a method for separating a multi-component LFM signal based on Radon-Wigner transform and RELAX algorithm, comprising the following steps:
s1, preprocessing, namely converting an initialized multi-component LFM signal to a RWT plane based on Radon-Wigner conversion;
s2, coarse estimation, namely searching a peak value of the RWT plane, and performing coarse estimation on a stronger LFM signal component in the multi-component LFM signal to obtain a coarse estimation LFM signal component;
s3, fine estimation, namely performing circular optimization fine estimation on the coarse estimation signal component based on an REALX algorithm until internal convergence to obtain a fine estimation LFM signal component;
s4, signal separation, namely removing the fine estimation LFM signal component from the multi-component LFM signal to obtain a residual LFM signal component;
s5, terminating the threshold judgment, and repeating S2-S4 for the rest of LFM signal components, wherein when the parameters of all LFM signal components in the multi-component LFM signal are effectively estimated.
Example 2
This example is substantially the same as example 1, except that:
in step S2, the peak is a peak coordinate, and a rough estimation center is derived according to the peak coordinate;
in step S3, calculating a variation of two adjacent loop optimizations, and determining internal convergence when the variation is lower than a convergence threshold; when the variation is higher than the convergence threshold, returning to the step of S2;
in step S4, the fine-estimated LFM signal components are removed from the multi-component LFM signal by using a time-domain cancellation method to obtain remaining LFM signal components;
in step S5, the energy of the remaining LFM signal is first calculated and compared with a set threshold, and if the energy is lower than the threshold, it is determined that all LFM signal components in the multi-component LFM signal are separated.
Example 3
This embodiment is basically the same as embodiment 2, except that the step S1 specifically includes:
s1.1 initializing a multi-component LFM signal;
the multi-component LFM signal s (t) is composed of N mutually uncorrelated and superimposable LFM signals and background noise N (t), such as the multi-component LFM signal received by the airborne platform,
the ith LFM signal is shown in formula I:
Figure BDA0001783712230000051
in the formula I, si(t) is the ith LFM signal, αi、kiAnd fiSequentially setting the amplitude, the frequency modulation slope and the initial frequency of the ith LFM signal, wherein t is sampling time;
the multi-component LFM signal S (t) is shown in equation II:
Figure BDA0001783712230000052
in formula II, S (t) is a multi-component LFM signal, αi、kiAnd fiThe amplitude, chirp rate and initial frequency of the ith LFM signal are sequentially set, t is sampling time, N is the total number of LFM signal components, N (t) is background noise,the background noise comprises interference and noise components in the detected mixed signal, i is a variable, i is 1,2 … N;
s1.2, converting the multi-component LFM signal to a RWT plane;
the Wigner-Ville (abbreviated as "WVD") distribution of the multi-component LFM signal S (t) is shown in formula III:
Figure BDA0001783712230000061
in the formula III, Wz(t, w) is the Wigner-Ville transformation of S (t), t is time, w is frequency, and tau is time delay;
the LFM signal appears as a straight line y ═ f + kt in the WVD plane, where the parameters f and k are the initial frequency and the tuning frequency of the signal, respectively. In the LFM signal processing, the time-frequency property of the WVD to a single LFM signal is better, but serious cross terms exist among signals and between the signals and noise when mixed signals are analyzed. In order to suppress the WVD cross terms, integral smoothing can be performed along a focused straight line in an LFM signal time-frequency plane, so that Radon transformation and WVD are combined to form Radon-Wigner transformation (called RWT for short). The signal S (t) is obtained after RWT transformation:
the multi-component LFM signal S (t) is shown in formula IV after Radon-Wigner transformation:
Figure BDA0001783712230000062
in formula IV, S (t) is a multi-component LFM signal, R (a, b) is Radon-Wigner transformation of S (t), (a, b) is an integral path parameter along a time-frequency straight line of the multi-component LFM signal, a is an origin vertical distance, and b is an inclination angle; k and f are the chirp rate and the initial frequency of the LFM signal in turn, and t is the sampling time.
Example 4
This embodiment is basically the same as embodiment 3, except that the step S2 specifically includes:
s2.1, searching the highest peak coordinate of the RWT plane, as shown in formula V:
Figure BDA0001783712230000071
in the formula V, the reaction solution is shown in the specification,
Figure BDA0001783712230000072
calculating the maximum value for Radon-Wigner transformation, (a, b) are integral path parameters along an LFM signal time-frequency straight line, a is the vertical distance of an original point, and b is an inclination angle; s.t. is that the condition is satisfied with the mathematical sign;
each signal component in the multi-component LFM signal forms a peak value on a RWT plane, and when the integral path parameters (a, b) are accurately matched with the frequency modulation parameters (k, f) of a certain LFM signal component, the maximum integral value is obtained, and a corresponding peak value appears on the RWT plane; the peak value of the signal component with the strongest energy is the highest, so the parameter of the strongest signal component can be obtained according to the coordinate of the highest peak value;
s2.2, deriving to obtain a rough estimation center according to the highest peak coordinate;
obtaining corresponding integral path parameters (a, b) through the coordinates of the highest peak, and calculating to obtain a rough estimation center of the strongest signal component through the integral path parameters (a, b), the initial frequency f of the highest peak and the frequency modulation slope k, as shown in formula VI:
Figure BDA0001783712230000073
in formula vi, f is the initial frequency of the LFM signal, k is the chirp rate of the LFM signal, (a, b) are the integral path parameters along the time-frequency line of the LFM signal, a is the vertical distance of the origin, and b is the tilt angle.
The chirp signal is in a linear shape on the WVD plane and in a spectral peak shape on the RWT plane. When estimating a plurality of LFM signal component parameters, the invention obtains signal parameter estimation by finding out the peak value of each LFM signal component. It should be noted that the LFM signal exhibits an impulse function at the corresponding parameters of the RWT plane only when it is infinite long, whereas in practice the impulse function is broadened and sidelobes are generated when the signal length is finite, which is particularly evident in the analysis of the multi-component LFM signal. Therefore, although Radon transformation introduced in RWT transformation can play a certain role in suppressing cross interference terms, errors can be generated in estimation of integral path parameters due to the influence of broadening of an impulse function and side lobes after integral smoothing, and the estimation accuracy of initial frequency is not high. If the RWT transform is directly applied to perform cyclic parameter estimation on the multi-component LFM signal, error accumulation may be caused, resulting in increased estimation error of subsequent signal components. The time-frequency transformation and RWT such as WHT, RAT and FrFT can be converted to each other in principle, and the same problem exists. Therefore, the present invention adopts the RELAX concept to perform a fine estimation of the signal parameters, and the following description will proceed with the fine estimation of S3.
In order to improve the parameter estimation precision of the multi-component LFM signal, the invention provides a parameter estimation method based on RWT rough estimation and RELAX algorithm fine estimation. According to the method, the RELAX idea is introduced into the traditional LFM signal parameter estimation method based on RWT, so that continuous iterative optimization estimation of signal component parameters is realized, and the parameter estimation precision is greatly improved. The main idea of the RELAX algorithm is to eliminate each component in the mixed signal one by one through loop optimization, and reduce the estimation error of the signal parameter through iterative operation.
Example 5
This embodiment is basically the same as embodiment 4, except that the step S3 specifically includes:
s3.1 obtaining residual signal S after parameter estimation and separation of the first n-1 signal components of the multi-component LFM signal S (t)n-1(t), the expression of which is:
Figure BDA0001783712230000081
in the formula VII, Sn-1(t) is the composition of the residual signal after eliminating the first n-1 signals and the background noise n (t), and S (t) is a multi-component LFM signal;
Figure BDA0001783712230000091
the first n-1 signals, i is a variable, i is 1,2 … n-1; n is a variable, N is 1,2 … N;
s3.2, when the parameter estimation is carried out on the nth component, according to a nonlinear minimum variance criterion in a RELAX algorithm:
Figure BDA0001783712230000092
in the formula VIII, CnRepresenting the energy of a residual signal obtained by removing the first n signal components; among the multi-component LFM signals are N LFM signals, Sn-1(t)-sn(t) obtaining a residual signal S with the first n signal components removedn(t) consisting of (N-N) signal components and noise N (t); sn-1(t) is the composition of the residual signal after the removal of the first n-1 signals and the background noise n (t), sn(t) is the nth LFM signal, N is a variable, N is 1,2 … N;
estimating the parameter of the nth signal component as (f)n,kn) By finding the smallest CnI.e. calculating the minimum residual energy minCn(fn,kn) The parameter estimate (f) for the nth signal component can be derivedn,kn) (ii) a At the parameter estimation (f)n,kn) Carrying out optimization on the basis; will (f)n,kn) As a parameter of the nth signal;
s3.3, carrying out iterative updating on the estimated first n signal parameters; the updating process comprises the following steps: separating the estimated residual signal S 'out of the mth signal from the optimized signal in the step S3.2'm(t)：
Figure BDA0001783712230000093
Formula IX, S (t) is a multi-component LFM signal,
Figure BDA0001783712230000101
is the time domain superposition, S ', of the remaining signals of the n signal components except the m signal'm(t) after removing the first n signals except the mth signal component,resulting residual signal S'm(t); n and m are variables, m is 1,2 … n; n is 1,2 … N;
s3.4 of the residual signal S'm(t), Radon-Wigner transformation is carried out according to a formula IV, and then the highest peak coordinates (a, b) of the RWT plane are searched according to a formula V;
s3.5 calculating the parameter (f) of the mth estimated signal according to the formula VIm,km) And updates s according to formula Im(t) a signal, n and m being variables, m being 1,2 … n; n is 1,2 … N.
The optimization is circulated until the interior converges, and s is included in the optimizationnAnd (t) finishing updating the parameters of the n signal components.
Example 6
This embodiment is substantially the same as embodiment 5, except that the step S4 specifically includes:
judging internal convergence, the condition of the internal convergence being a residual signal SnEnergy of (t)
Figure BDA0001783712230000102
After the two previous and subsequent updates, the variation is lower than the convergence threshold, and the convergence judgment process can be expressed as:
Figure BDA0001783712230000103
in the formula X, DmAfter updating the parameters for the mth signal component, the residual signal SnEnergy of (t), i.e.
Figure BDA0001783712230000104
Dm+1After updating the parameters for the m +1 th signal component, the residual signal SnEnergy of (t), i.e.
Figure BDA0001783712230000105
Sn(t) residual signals obtained after the first n signals are removed; delta is a threshold parameter; n and m are variables, m is 1,2 … n; n is 1,2 … N;
at internal convergence, including sn(t) inAfter the parameters of the n signal components are updated, the variable n is n + 1;
if not, the process returns to step S2.
For example, when estimating the 3 rd parameter (n is 2), the rejection s is calculated according to the formula VI1(t) and s2(t) obtaining a residual signal S2(t) of (d). By calculating S2(t) coarse estimation of RWT planar peak to obtain s3Parameter (f ') of (t)'3,k′3). In the iterative updating process, firstly, the data is updated by s2(t)、s3(t) re-estimating s by using the estimated parameters and formula VI1Parameter (f ') of (t)'1,k′1) From updated s1(t)、s3(t) parameter re-estimation s2Parameter (f ') of (t)'2,k'2) Then by the updated s1(t)、s2(t) estimated parameter update s3(t) parameter (f ″)3,k″3) And repeating iterative optimization until internal convergence, thereby effectively improving the precision of parameter estimation. Then, the estimated 3 signals are removed from the original signal, and the parameters of other components in the residual signal are continuously estimated.
Example 7
This embodiment is substantially the same as embodiment 6, except that the step S5 specifically includes:
s5.1, signal reconstruction; obtaining an accurate estimate (f) of the strong signal component parameter by RWT coarse and RELAX fine estimatesn,kn) Then, the signal components are reconstructed from the estimated values:
Figure BDA0001783712230000111
in formula XI, sn(t) is the nth LFM signal, αn、fn、knSequentially setting the amplitude, the frequency modulation slope and the initial frequency of the nth LFM signal, wherein t is sampling time; n and m are variables, m is 1,2 … n; n is 1,2 … N;
s5.2 Signal separation residual Signal S is separated by time-domain cancellationn(t)：
Figure BDA0001783712230000112
In formula XII, S (t) is a multicomponent LFM signal,
Figure BDA0001783712230000121
for time-domain superposition of n signal components, Sn(t) residual signal obtained after removing the first n signals, Sn-1(t) residual signal s obtained after removing the first n-1 signalsn(t) is the nth signal; n and m are variables, m is 1,2 … n; n is 1,2 … N.
The separation of the residual signal may adopt a time domain cancellation method or a frequency domain notching method, and since there may be overlap in the frequency modulation ranges of multiple LFM signal components, the frequency domain notching method may cause energy loss of other signals, thereby affecting the estimation of the energy of the residual signal, and the time domain cancellation method is preferably adopted to separate the residual signal in the present invention.
Example 8
This embodiment is substantially the same as embodiment 7, except that the step S6 specifically includes:
s6.1, judging a termination threshold; calculating a residual signal sres(t) energy, the calculation formula is
Figure BDA0001783712230000122
Wherein s isres(t) is the residual signal sres(t) and comparing with the set threshold value, if the threshold value is lower than the set threshold value
Figure BDA0001783712230000123
Judging that all the energy in the signal is separated, otherwise returning to S2 to continue the parameter estimation and separation of the signal components;
residual signal sresThe energy determination of (t) may be expressed as:
Figure BDA0001783712230000124
Figure BDA0001783712230000125
in the formula
Figure BDA0001783712230000126
Is a residual signal sres(ii) the energy of (t),
Figure BDA0001783712230000127
for the energy of the multi-component LFM signal, ξ is the threshold value and SNR is the signal-to-noise ratio.
Example 9: multi-component LFM signal separation
Setting simulation parameters: the multi-component LFM signal is composed of a mixture of 3 LFM signals. The signal length is 5us, and the signal-to-noise ratio SNR is 0 dB. The center frequency of the 1 st signal is 20MHz, and the bandwidth of the frequency modulation is 20 MHz; the 2 nd signal has the center frequency of 25MHz and the frequency modulation bandwidth of 40 MHz; the 3 rd signal has a center frequency of 30MHz and a bandwidth of 30 MHz. The ratio of the 3 signal amplitudes is 1:0.9: 0.8. The sampling frequency is 120 MHz. Thus, the initial frequency and the modulation frequency (f, k) of the 3 signals are (10MHz, 4X 10, respectively)6MHz/s)，(5MHz,6×106MHz/s)，(15MHz,8×106MHz/s). The noise is additive white gaussian noise. The internal convergence parameter δ in the RELAX algorithm is 0.05. And the judgment parameter xi of the algorithm termination threshold is according to a formula XIII and a formula XIV.
First, time-frequency characteristics of the original signal are calculated. Fig. 2, 3 and 4 are three-dimensional WVD, two-dimensional WVD and RWT diagrams of the original signal s (t), respectively. From fig. 2 and 3, the time-frequency distribution of 3 LFM signal components can be observed, but due to the influence of noise, part of the energy of the signal is submerged in the noise, and due to the interference of WVD cross terms, part of the time-frequency distribution of the signal is blurred. The peak of the protrusion can be observed from fig. 4, however the peak has already generated a certain spread and the effect of the side lobe can be observed. At this time, if the strongest component signal parameter is estimated directly by the traditional time-frequency method, errors are introduced and interference is caused to the estimation of subsequent components. Thus, searching for the peak coordinates in the RWT yields a coarse estimate of the optimal projection path parameters for the signal, forThe signal parameters are coarsely estimated. Reconstructing a signal s from estimated parameters1(t) and separating the reconstructed signal from the original signal S (t) to obtain a residual signal S1(t)。
FIG. 5, FIG. 6 and FIG. 7 show the residual signal S obtained after the strong signal component is separated by the first signal separation1(t) three-dimensional WVD map, two-dimensional WVD map, and RWT map. From fig. 6, it can be observed that there are two straight lines of cross-interference terms, while two peaks appear in the RWT distribution, comparing fig. 3, it can be seen that the effects of peak broadening and sidelobe interference are reduced due to the reduction of signal components. Based on the signal S1(t) RWT transformation to estimate the residual signal S1(t) the coordinates of the highest peak in the RWT plane, from which the signal s is calculated2(t) a coarse estimate of the parameter. The signal s is then filtered by the RELAX algorithm1(t) and s2And (t) carrying out fine estimation on the parameters. According to a signal s2(t) separating s from the mixed signal S (t)2(t) for s1(t) reestimation, then according to s1(t) pairs of reestimation results of s2(t) reestimating the signal parameters. Obtaining the signal s after reaching internal convergence1(t) and s2(t) the result of the estimation.
Reconstructing a signal s1(t) and s2(t) and separating from the original signal S (t) to obtain a new residual signal S2(t) of (d). FIG. 8, FIG. 9 and FIG. 10 show the residual signal S obtained after the strong signal component is separated by the second signal separation2(t) three-dimensional WVD map, two-dimensional WVD map, and RWT map. It can be seen that the first two signal parameters are effectively separated after being precisely estimated by RELAX algorithm, so that the peak broadening and the side lobe interference in the RWT plane of the residual signal component are smaller. Obtaining a signal s based on a coarse RWT estimate3(t) rough estimation of the parameters, and then applying the RELAX algorithm to the signal s1(t)、s2(t) and s3(t) performing iterative optimization until internal convergence.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solution of the present invention by those skilled in the art should fall within the protection scope defined by the claims of the present invention without departing from the spirit of the present invention.

Claims (8)

1. The multi-component LFM signal separation method based on Radon-Wigner transformation and REALX algorithm is characterized by comprising the following steps:
s1, preprocessing, namely converting an initialized multi-component LFM signal to a RWT plane based on Radon-Wigner conversion;
s2, coarse estimation, namely searching a peak value of the RWT plane, and performing coarse estimation on a stronger LFM signal component in the multi-component LFM signal to obtain a coarse estimation LFM signal component;
s3, fine estimation, namely performing circular optimization fine estimation on the coarse estimation signal component based on an REALX algorithm until internal convergence to obtain a fine estimation LFM signal component;
s4, signal separation, namely removing the fine estimation LFM signal component from the multi-component LFM signal to obtain a residual LFM signal component;
s5, judging a termination threshold, and repeating the steps S2-S4 for the rest LFM signal components, wherein when the parameters of all LFM signal components in the multi-component LFM signal are effectively estimated.
2. The method for multi-component LFM signal separation based on Radon-Wigner transform and REALX algorithm of claim 1,
in the step S2, the peak is a peak coordinate, and a rough estimation center is derived according to the peak coordinate;
in the step S3, calculating a variation of two adjacent loop optimizations, and determining that the loop optimization is internally converged when the variation is lower than a convergence threshold; when the variation is higher than the convergence threshold, returning to the step of S2;
in the step S4, the fine-estimated LFM signal components are removed from the multi-component LFM signal by using a time-domain cancellation method to obtain remaining LFM signals;
in the step S5, the energy of the remaining LFM signal is first calculated and compared with a set threshold, and if the energy is lower than the threshold, it is determined that all LFM signal components in the multi-component LFM signal are separated.
3. The method for separating the multi-component LFM signal based on the Radon-Wigner transform and the REALX algorithm as claimed in claim 2, wherein the step of S1 comprises:
s1.1 initializing a multi-component LFM signal;
the multi-component LFM signal s (t) is composed of N mutually uncorrelated and superposable LFM signals and background noise N (t), and the ith LFM signal is shown in formula i:
Figure FDA0003161213380000021
in the formula I, si(t) is the ith LFM signal, αi、kiAnd fiSequentially setting the amplitude, the frequency modulation slope and the initial frequency of the ith LFM signal, wherein t is sampling time;
the multi-component LFM signal S (t) is shown in equation II:
Figure FDA0003161213380000022
in formula II, S (t) is a multi-component LFM signal, αi、kiAnd fiSequentially setting the amplitude, the frequency modulation slope and the initial frequency of the ith LFM signal, wherein t is sampling time, N is the total number of LFM signal components, N (t) is background noise, the background noise comprises interference and noise components in the intercepted mixed signal, i is a variable, and i is 1,2 … N;
s1.2, converting the multi-component LFM signal to a RWT plane;
the Wigner-Ville distribution of the multi-component LFM signal S (t) is shown in equation III:
Figure FDA0003161213380000023
in the formula III, Wz(t, w) is the Wigner-Ville transformation of S (t), t is time, w is frequency, and tau is time delay;
the multi-component LFM signal S (t) is shown in formula IV after Radon-Wigner transformation:
Figure FDA0003161213380000031
in formula IV, S (t) is a multi-component LFM signal, R (a, b) is Radon-Wigner transformation of S (t), (a, b) is an integral path parameter along a time-frequency straight line of the multi-component LFM signal, a is an origin vertical distance, and b is an inclination angle; k and f are the chirp rate and the initial frequency of the LFM signal in turn, and t is the sampling time.
4. The method for separating the multi-component LFM signal based on Radon-Wigner transform and REALX algorithm of claim 3, wherein the step S2 comprises:
s2.1, searching the highest peak coordinate of the RWT plane, as shown in formula V:
Figure FDA0003161213380000032
in the formula V, the reaction solution is shown in the specification,
Figure FDA0003161213380000033
calculating the maximum value for Radon-Wigner transformation, (a, b) are integral path parameters along an LFM signal time-frequency straight line, a is the vertical distance of an original point, and b is an inclination angle; s.t. is that the condition is satisfied with the mathematical sign;
each signal component in the multi-component LFM signal forms a peak value on a RWT plane, and when the integral path parameters (a, b) are accurately matched with the frequency modulation parameters (k, f) of a certain LFM signal component, the maximum integral value is obtained, and a corresponding peak value appears on the RWT plane; the peak value of the signal component with the strongest energy is the highest, so the parameter of the strongest signal component can be obtained according to the coordinate of the highest peak value;
s2.2, deriving to obtain a rough estimation center according to the highest peak coordinate;
obtaining corresponding integral path parameters (a, b) through the coordinates of the highest peak, and calculating to obtain a rough estimation center of the strongest signal component through the integral path parameters (a, b), the initial frequency f of the highest peak and the frequency modulation slope k, as shown in formula VI:
Figure FDA0003161213380000041
in formula vi, f is the initial frequency of the LFM signal, k is the chirp rate of the LFM signal, (a, b) are the integral path parameters along the time-frequency line of the LFM signal, a is the vertical distance of the origin, and b is the tilt angle.
5. The method for multi-component LFM signal separation based on Radon-Wigner transform and REALX algorithm of claim 4, wherein the step S3 comprises:
s3.1 obtaining residual signal S after parameter estimation and separation of the first n-1 signal components of the multi-component LFM signal S (t)n-1(t), the expression of which is:
Figure FDA0003161213380000042
in the formula VII, Sn-1(t) is the composition of the residual signal after eliminating the first n-1 signals and the background noise n (t), and S (t) is a multi-component LFM signal;
Figure FDA0003161213380000043
the first n-1 signals, i is variable, i is 1,2 … n-1; n is a variable, N is 1,2 … N;
s3.2, when the parameter estimation is carried out on the nth component, according to a nonlinear minimum variance criterion in a RELAX algorithm:
Figure FDA0003161213380000051
in the formula VIII, CnRepresenting the energy of a residual signal obtained by removing the first n signal components; among the multi-component LFM signals are N LFM signals, Sn-1(t)-sn(t) obtaining a residual signal S with the first n signal components removedn(t) consisting of (N-N) signal components and noise N (t); sn-1(t) is the composition of the residual signal after the removal of the first n-1 signals and the background noise n (t), sn(t) is the nth LFM signal, N is a variable, N is 1,2 … N;
estimating the parameter of the nth signal component as (f)n,kn) By finding the smallest CnI.e. calculating the minimum residual energy minCn(fn,kn) The parameter estimate (f) for the nth signal component can be derivedn,kn) (ii) a At the parameter estimation (f)n,kn) Carrying out optimization on the basis; will (f)n,kn) As a parameter of the nth signal;
s3.3, carrying out iterative updating on the estimated first n signal parameters; the updating process comprises the following steps: separating the estimated residual signal S 'out of the mth signal from the optimized signal in the step S3.2'm(t)：
Figure FDA0003161213380000052
Formula IX, S (t) is a multi-component LFM signal,
Figure FDA0003161213380000053
is the time domain superposition, S ', of the remaining signals of the n signal components except the m signal'm(t) is a residual signal S 'obtained after removing the first n signals except the mth signal component'm(t); n and m are variables, m is 1,2 … n; n is 1,2 … N;
s3.4 of the residual signal S'm(t), Radon-Wigner transformation is carried out according to a formula IV, and then the highest peak coordinates (a, b) of the RWT plane are searched according to a formula V;
s3.5 calculating the mth estimated signal according to formula VIParameter (f)m,km) And updates s according to formula Im(t) a signal, n and m being variables, m being 1,2 … n; n is 1,2 … N.
6. The method for separating the multi-component LFM signal based on Radon-Wigner transform and REALX algorithm of claim 5, wherein the step S4 comprises:
judging internal convergence, the condition of the internal convergence being a residual signal SnEnergy of (t)
Figure FDA0003161213380000061
After the two previous and subsequent updates, the variation is lower than the convergence threshold, and the convergence judgment process can be expressed as:
Figure FDA0003161213380000062
in the formula X, DmAfter updating the parameters for the mth signal component, the residual signal SnEnergy of (t), i.e.
Figure FDA0003161213380000063
Dm+1After updating the parameters for the m +1 th signal component, the residual signal SnEnergy of (t), i.e.
Figure FDA0003161213380000064
Sn(t) residual signals obtained after the first n signals are removed; delta is a threshold parameter; n and m are variables, m is 1,2 … n; n is 1,2 … N;
at internal convergence, including sn(t) after updating the parameters of the n signal components, the variable n being n + 1;
if not, the process returns to step S2.
7. The method for separating the multi-component LFM signal based on Radon-Wigner transform and REALX algorithm of claim 6, wherein the step S5 comprises:
s5.1, signal reconstruction; obtaining an accurate estimate (f) of the strong signal component parameter by RWT coarse and RELAX fine estimatesn,kn) Then, the signal components are reconstructed from the estimated values:
Figure FDA0003161213380000065
in formula XI, sn(t) is the nth LFM signal, αn、fn、knSequentially setting the amplitude, the frequency modulation slope and the initial frequency of the nth LFM signal, wherein t is sampling time; n and m are variables, m is 1,2 … n; n is 1,2 … N;
s5.2 Signal separation residual Signal S is separated by time-domain cancellationn(t)：
Figure FDA0003161213380000071
In formula XII, S (t) is a multicomponent LFM signal,
Figure FDA0003161213380000072
for time-domain superposition of n signal components, Sn(t) residual signal obtained after removing the first n signals, Sn-1(t) residual signal s obtained after removing the first n-1 signalsn(t) is the nth signal; n and m are variables, m is 1,2 … n; n is 1,2 … N.
8. The method for separating the multi-component LFM signal based on the Radon-Wigner transform and the REALX algorithm as claimed in claim 7, wherein the step of S6 comprises:
s6.1, judging a termination threshold; calculating a residual signal sres(t) energy, the calculation formula is
Figure FDA0003161213380000073
Wherein s isres(t) is the residual signal sres(t) and comparing with a set threshold value, if below the threshold valueValue of
Figure FDA0003161213380000074
Judging that all the energy in the signal is separated, otherwise returning to S2 to continue the parameter estimation and separation of the signal components;
residual signal sresThe energy determination of (t) may be expressed as:
Figure FDA0003161213380000075
Figure FDA0003161213380000076
in the formula
Figure FDA0003161213380000081
Is a residual signal sres(ii) the energy of (t),
Figure FDA0003161213380000082
for the energy of the multi-component LFM signal, ξ is the threshold value and SNR is the signal-to-noise ratio.
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