CN109284690A - Multi-component LFM signalt separation method based on Radon-Wigner transformation and REALX algorithm - Google Patents
Multi-component LFM signalt separation method based on Radon-Wigner transformation and REALX algorithm Download PDFInfo
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Abstract
For the parameter Estimation and Signal separator problem of multi -components linear frequency modulation (Linear Frequency Modulation, LFM) signal, a kind of method for being based on RWT (Radon-Wigner Transform, RWT) and RELAX thought is proposed.The algorithm estimates strong signal component parameters according to the RWT characteristic of field of multi-component LFM signalt first, is then based on RELAX thought and carries out loop optimization, the final parameter Estimation realized to whole signal components to signal component parameter has been estimated, and realizes the separation of signal component.Compared to traditional method based on time-frequency conversion estimation LFM signal parameter, the application of RELAX can greatly eliminate the influence of strong and weak signals interference and the broadening of time frequency plane spectral peak during circulation estimates signal parameter, improve Parameter Estimation Precision.
Description
Technical field
The invention belongs to Signal and Information Processing technologies, and in particular to the separation method of a kind of pair of multi -components line LFM signal.
Background technique
Linear FM signal has the characteristics that frequency time-varying, big Timed automata and good interference free performance, is to answer
Convectional signals for radar, sonar, guide missile fuze etc..Electromagnetic environment is increasingly complicated in modern war, for non-approach to cooperation
For the airborne ECM reconnaissance receiver of lower work, the multi -components linear frequency modulation letter detectd and received how is accurately and effectively separated
Number (hereinafter referred to as " multi-component LFM signalt ") and the parameter for estimating each signal component, becomes and realizes Radar recognition and threat
The important foundation of grade judgement, and implement the necessary condition of Precise electronic interference.
The separation of linear FM signal and Parameter Estimation Problem, traditional Maximum Likelihood Estimation Method reconciliation line tune method are deposited
In the contradiction of estimated accuracy and computation complexity, and under Low SNR, estimated accuracy is not high.Based in fractional order Fu
Leaf transformation (Fractional Fourier transform, FrFT), Radon-Wigner convert (Radon-Wigner
Transform, RWT), Radon-Ambiguity transformation (Radon-Ambiguity transform, RAT) and Wigner-
The time-frequency conversions methods such as Hough transform (Radon-Hough transform, WHT) are able to reflect the time-frequency characteristics of LFM signal,
One-dimensional LFM signal is transformed to two-dimentional time-frequency plane by such methods, and Signal parameter estimation problem is made to be converted into the two of time-frequency plane
Spectrum peak search problem is tieed up, can get the estimated accuracy of higher frequency modulation rate and original frequency when analyzing single LFM signal, therefore
It is widely applied in the parameter Estimation of LFM signal.Intersect however for multi-component LFM signalt, present in time-frequency distributions dry
Disturb the estimated accuracy for seriously affecting frequency modulation rate and original frequency of item.And Smoothing Pseudo vital capacity index and time-frequency distribution series etc.
Although improved method effectively inhibits the influence of cross term, but can reduce the frequency resolution of estimation parameter.Therefore how to transport
Hot spot of the high-precision multi-component LFM signalt separation with parameter Estimation as current research is realized with Time-Frequency Analysis Method.RELAX
Algorithm is a kind of algorithm for estimating based on nonlinear least-squares problem criterion, smart in estimation compared to (CLEAN) algorithm is gradually eliminated
Advantage is had more on degree.This method passes through the estimated value one by one rejected each component of signal and update correction signal parameter, so that
Estimated accuracy effectively improves, the final parameter Estimation for realizing mixed signal.
Summary of the invention
The present invention provides a kind of based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of RELAX algorithm
Method, comprising the following steps:
S1. it pre-processes, is converted based on Radon-Wigner, the multi-component LFM signalt of initialization is transformed into RWT plane；
S2. the peak value of the RWT plane is searched in rough estimate, to LFM signal stronger in the multi-component LFM signalt point
The carry out rough estimate of amount obtains rough estimate LFM signal component；
S3. essence estimation carries out the estimation of loop optimization essence to the rough estimate signal component based on REALX algorithm, until interior
Portion's convergence obtains essence estimation LFM signal component；
S4. Signal separator obtains the essence estimation LFM signal component surplus after rejecting in the multi-component LFM signalt
Remaining LFM signal component；
S5. it terminates thresholding and determines that the residue LFM signal component repeats S2-S4, when institute in the multi-component LFM signalt
There is the parameter of LFM signal component to be effectively estimated.
Believe to more clearly describe the multi -components LFM of the invention based on Radon-Wigner transformation and REALX algorithm
Number separation method, further discloses S2-S5 step, it may be assumed that
In S2 step, the peak value is top coordinate, is derived by rough estimate center according to the top coordinate；
In the S3 step, the variable quantity for calculating adjacent loop optimization twice is sentenced when the variable quantity is lower than convergence threshold
Break as inside convergence；When the variable quantity is higher than convergence threshold, S2 step is returned；
In S4 step, estimate LFM signal component from the multi-component LFM signalt essence using time domain opposition method
Residue LFM signal is obtained after rejecting；
In S5 step, the energy of the residue LFM signal is calculated first, and is compared with the threshold value of setting, if
Lower than threshold value, then judge that all LFM signal components are separated in the multi-component LFM signalt.
The invention has the benefit that being directed to the Parameter Estimation Problem of multi-component LFM signalt, provide a kind of based on RWT
With the Signal parameter estimation algorithm of RELAX thought.The algorithm combine RWT algorithm signal parameter can be carried out quick rough estimate and
The high feature of RELAX algorithm estimated accuracy carries out rough estimate to signal parameter by RWT transformation, then passes through RELAX algorithm pair
Estimate that signal parameter carries out loop optimization estimation.The present invention can be realized estimated accuracy more higher than conventional method, have relatively strong
Practicability.
Detailed description of the invention
Fig. 1 shows multi-component LFM signalt parameter Estimation flow chart；
Fig. 2 shows the three-dimensional WVD figures of original signal S (t) in embodiment 9；
Fig. 3 shows the two-dimentional WVD figure of original signal S (t) in embodiment 9；
Fig. 4 shows the RWT figure of original signal S (t) in embodiment 9；
Fig. 5 shows the three-dimensional WVD figure of the residual signal S1 (t) after first time Signal separator in embodiment 9；
Fig. 6 shows the two-dimentional WVD figure of the residual signal S1 (t) after first time Signal separator in embodiment 9；
Fig. 7 shows the RWT figure of the residual signal S1 (t) after first time Signal separator in embodiment 9；
Fig. 8 shows the three-dimensional WVD figure of the residual signal S2 (t) after second of Signal separator in embodiment 9；
Fig. 9 shows the two-dimentional WVD figure of the residual signal S2 (t) after second of Signal separator in embodiment 9；
Figure 10 shows the RWT figure of the residual signal S2 (t) after second of Signal separator in embodiment 9.
Specific embodiment
The present invention is described in detail below with reference to embodiment, attached drawing.
Embodiment 1
As shown in connection with fig. 1, the present invention provides a kind of multi -components based on Radon-Wigner transformation and RELAX algorithm
LFM signal separating method, comprising the following steps:
S1. it pre-processes, is converted based on Radon-Wigner, the multi-component LFM signalt of initialization is transformed into RWT plane；
S2. the peak value of the RWT plane is searched in rough estimate, to LFM signal stronger in the multi-component LFM signalt point
The carry out rough estimate of amount obtains rough estimate LFM signal component；
S3. essence estimation carries out the estimation of loop optimization essence to the rough estimate signal component based on REALX algorithm, until interior
Portion's convergence obtains essence estimation LFM signal component；
S4. Signal separator obtains the essence estimation LFM signal component surplus after rejecting in the multi-component LFM signalt
Remaining LFM signal component；
S5. it terminates thresholding and determines that the residue LFM signal component repeats S2-S4, when institute in the multi-component LFM signalt
There is the parameter of LFM signal component to be effectively estimated.
Embodiment 2
The present embodiment is substantially the same manner as Example 1, except that:
In S2 step, the peak value is top coordinate, is derived by rough estimate center according to the top coordinate；
In the S3 step, the variable quantity for calculating adjacent loop optimization twice is sentenced when the variable quantity is lower than convergence threshold
Break as inside convergence；When the variable quantity is higher than convergence threshold, S2 step is returned；
In S4 step, estimate LFM signal component from the multi-component LFM signalt essence using time domain opposition method
Residue LFM signal component is obtained after rejecting；
In S5 step, the energy of the residue LFM signal is calculated first, and is compared with the threshold value of setting, if
Lower than threshold value, then judge that all LFM signal components are separated in the multi-component LFM signalt.
Embodiment 3
The present embodiment is substantially the same manner as Example 2, except that S1 step specifically includes:
S1.1 initializes multi-component LFM signalt；
The multi-component LFM signalt S (t) is by LFM signal and ambient noise n N number of irrelevant and with superposability
(t) it forms, for example airborne platform detects the multi-component LFM signalt received,
I-th of LFM signal is as shown in formula I:
In formula I, siIt (t) is i-th of LFM signal, αi、kiAnd fiBe followed successively by the amplitude of i-th of LFM signal, chirp rate and
Original frequency, t are the sampling time；
The multi-component LFM signalt S (t) is as shown in formula II:
In formula II, S (t) is multi-component LFM signalt, αi、kiAnd fiIt is followed successively by amplitude, the chirp rate of i-th of LFM signal
And original frequency, t are the sampling time, N is the total number of LFM signal component, and n (t) is ambient noise, and the ambient noise includes
The interference in the mixed signal of receipts and noise contribution are detectd, i is variable, i=1,2 ... N；
Multi-component LFM signalt is transformed to RWT plane by S1.2；
Wigner-Ville (referred to as " WVD ") distribution of the multi-component LFM signalt S (t) is as shown in formula III:
In formula III, WzThe Wigner-Ville that (t, w) is S (t) is converted, t is the time, w is frequency, and τ is time delay；
LFM signal shows as a skew lines y=f+kt in WVD plane, and wherein parameter f and k is respectively signal
Original frequency and frequency modulation rate.In to LFM signal processing, WVD is preferable to the time-frequency of single LFM signal, but analyzes mixing letter
Number when signal between, there is serious cross terms between signal and noise.In order to inhibit WVD cross term, when can be along LFM signal
The straight line focused in frequency face does integral smooth, therefore Radon is converted and is combined with WVD, forms Radon-Wigner transformation (referred to as
"RWT").Signal S (t) is obtained after being converted by RWT:
After the multi-component LFM signalt S (t) is converted by Radon-Wigner shown in formula IV:
In formula IV, S (t) is multi-component LFM signalt, and the Radon-Wigner that R (a, b) is S (t) is converted, and (a, b) is along institute
The path of integration parameter of multi-component LFM signalt time-frequency straight line is stated, a is origin vertical range, and b is inclination angle；K and f is followed successively by LFM letter
Number chirp rate and original frequency, t is the sampling time.
Embodiment 4
The present embodiment is substantially the same manner as Example 3, except that S2 step specifically includes:
S2.1 searches for the top coordinate of RWT plane, as shown in formula V:
In formula V,For Radon-Wigner transformation calculations maximum value, (a, b) is straight along LFM signal time-frequency
The path of integration parameter of line, a are origin vertical range, and b is inclination angle；It s.t. is " condition is satisfied with " mathematic sign；
Each signal component can form peak value in RWT plane in the multi-component LFM signalt, when path of integration parameter
When chirp parameter (k, f) accurate match of (a, b) and some LFM signal component, maximum integrated value is obtained, and in RWT plane
One corresponding peak value of upper appearance；The wherein peak value highest of the strongest signal component of energy, therefore can according to peak-peak coordinate
To obtain the parameter of peak signal component；
S2.2 is derived by rough estimate center according to top coordinate；
Corresponding path of integration parameter (a, b) is obtained by top coordinate, passes through path of integration parameter (a, b) and highest
The original frequency f and chirp rate k of peak value, are calculated the rough estimate center of the peak signal component, as shown in formula VI:
In formula VI, f is the original frequency of LFM signal, and k is the chirp rate of LFM signal, and (a, b) is along LFM signal time-frequency
The path of integration parameter of straight line, a are origin vertical range, and b is inclination angle.
Linear FM signal linear shape in WVD plane is in spectral peak shape in RWT plane.Estimating multiple LFM letters
When number component parameters, the present invention obtains Signal parameter estimation by finding out the peak value of each LFM signal component.It may be noted that
It is that only when LFM signal is endless, it can just show as shock pulse function at RWT plane relevant parameter, and practical
Signal length is limited in situation, then the impulse function can be broadened and generate secondary lobe, especially bright in multi-component LFM signalt analysis
It is aobvious.Thus while the Radon transformation introduced in RWT transformation can play certain inhibiting effect to cross-interference terms, but it is long-pending
Due to the broadening of impulse function and the influence of secondary lobe after dividing smoothly, error can be generated to the estimation of path of integration parameter, caused just
The estimated accuracy of beginning frequency is not high.It, may if directly carrying out loop parameter estimation to multi-component LFM signalt with RWT transformation
Error accumulation is caused, the evaluated error of follow-up signal component is caused to increase.The time-frequency conversions such as WHT, RAT and FrFT and RWT are former
It can mutually convert, there is a problem of same in reason.Therefore, the present invention carries out smart estimation to signal parameter using RELAX thought,
It continues with and the estimation of S3 essence is illustrated.
In order to improve the Parameter Estimation Precision to multi-component LFM signalt, the present invention proposes to be based on RWT rough estimate and RELAX
The method for parameter estimation of algorithm essence estimation.RELAX thought is introduced traditional LFM Signal parameter estimation based on RWT by this method
Method is realized and is estimated the continuous iteration optimization of signal component parameter, greatlys improve Parameter Estimation Precision.RELAX algorithm
Main thought is one by one to be rejected each component in mixed signal by loop optimization, reduces signal ginseng by interative computation
Number evaluated error.
Embodiment 5
The present embodiment is substantially the same manner as Example 4, except that S3 step specifically includes:
S3.1 multi-component LFM signalt S (t) obtains residual signal by parameter Estimation and after separating preceding n-1 signal component
Sn-1(t), expression formula are as follows:
In formula VII, Sn-1It (t) is the composition for rejecting residual signal and ambient noise n (t) after preceding n-1 signal, S (t) is
Multi-component LFM signalt；For preceding n-1 signal, i is variable, i=1,2 ... n-1；N is to become
Amount, n=1,2 ... N；
S3.2, when carrying out parameter Estimation to n-th of component, according to the nonlinear least-squares problem criterion in RELAX algorithm:
In formula VIII, CnIndicate the energy for the residual signal that n signal component obtains before rejecting；The multi-component LFM signalt
In have N number of LFM signal, Sn-1(t)-sn(t) that obtain is the residual signal S of n signal component before rejectingn(t), constituting is
(N-n) a signal component and noise n (t)；Sn-1It (t) is the residual signal and ambient noise n (t) after n-1 signal before rejecting
Composition, snIt (t) is n-th of LFM signal, n is variable, n=1,2 ... N；
The parameter for estimating n-th of signal component is (fn,kn), by finding the smallest Cn, that is, calculate least residue energy
minCn(fn,kn), the parameter Estimation (f of available n-th of signal componentn,kn)；In the parameter Estimation (fn,kn) basis
On optimize；By (fn,kn) parameter as n-th of signal；
S3.3 is iterated update to the preceding n signal parameter estimated；Renewal process are as follows: after optimizing in S3.2 step
Signal in isolate and estimated residual signal S ' outside m-th of signalm(t):
S (t) is multi-component LFM signalt in formula Ⅸ,To be removed in n signal component
The time domain superposition of remaining outer signal of m-th of signal, S'mIt (t) is the preceding n signal eliminated in addition to m-th of signal component
Afterwards, the residual signal S' obtainedm(t)；N and m is variable, m=1,2 ... n；N=1,2 ... N；
S3.4 is by the residual signal S'm(t), Radon-Wigner transformation is carried out according to formula IV, then according to formula
The top coordinate (a, b) of V search RWT plane；
S3.5 calculates m-th of parameter (f for having estimated signal according to formula VIm,km), and s is updated according to formula Im(t) signal,
N and m is variable, m=1,2 ... n；N=1,2 ... N.
Such loop optimization includes s until internal convergence at this timen(t) parameter of n signal component including has updated
Finish.
Embodiment 6
The present embodiment is substantially the same manner as Example 5, except that S4 step specifically includes:
The internal convergence of judgement, internal convergent condition are residual signal Sn(t) energyBy front and back two
Secondary updated variable quantity is lower than convergence threshold, and convergence deterministic process may be expressed as:
In Formula X, DmAfter the parameter update of m-th of signal component, residual signal Sn(t) energy, i.e.,
Dm+1After the parameter update of the m+1 signal component, residual signal Sn(t) energy, i.e.,SnIt (t) is to pick
In addition to the residual signal obtained after preceding n signal；δ is threshold parameter；N and m is variable, m=1,2 ... n；N=1,2 ... N；
When the convergence of inside, including sn(t) the parameter update of n signal component including finishes, variable n=n+1；
When not converged, S2 step is returned.
Such as it when the 3rd parameter of estimation (n=2), is calculated according to formula VI and rejects s1(t) and s2(t) residual signal S is obtained2
(t).By calculating S2(t) RWT plane peak value rough estimate obtains s3(t) parameter (f '3,k′3).In iteration renewal process,
First by s2(t)、s3(t) estimation parameter and formula VI reevaluates s1(t) parameter (f '1,k′1), by updated s1
(t)、s3(t) parameter reevaluates s2(t) parameter (f '2,k'2), then by updated s1(t)、s2(t) estimation parameter is more
New s3(t) parameter (f "3,k″3), iteration optimization can effectively improve the essence of parameter Estimation until inside convergence repeatedly
Degree.Then 3 signals that estimation is rejected from original signal continue the parameter for estimating other components in residual signal.
Embodiment 7
The present embodiment is substantially the same manner as Example 6, except that S5 step specifically includes:
S5.1 signal reconstruction；The fine estimation of strong signal component parameters is obtained by RWT rough estimate and the estimation of RELAX essence
(fn,kn) after, according to estimated value reconstruction signal component:
In formula Ⅺ, snIt (t) is n-th of LFM signal, αn、fn、knBe followed successively by the amplitude of n-th of LFM signal, chirp rate and
Original frequency, t are the sampling time；N and m is variable, m=1,2 ... n；N=1,2 ... N；
S5.2 Signal separator separates residual signal S using time domain opposition methodn(t):
In formula Ⅻ, S (t) is multi-component LFM signalt,For n signal component when
Domain superposition, SnIt (t) is the residual signal obtained after n signal before eliminating, Sn-1It (t) is to be obtained after n-1 signal before eliminating
Residual signal, snIt (t) is n-th of signal；N and m is variable, m=1,2 ... n；N=1,2 ... N.
Time domain opposition method or frequency domain wave trap method can be used in the separation of residual signal, due to the tune of multiple LFM signal components
Frequency range is there may be overlapping, therefore frequency domain wave trap method would potentially result in the energy loss of other signals, to influence to residue
The estimation of signal energy, present invention preferably employs time domain opposition methods to separate residual signal.
Embodiment 8
The present embodiment is substantially the same manner as Example 7, except that S6 step specifically includes:
S6.1 terminates thresholding and determines；Calculate residual signal sres(t) energy, calculation formula areWherein sres
It (t) is residual signal sres(t), it and with the threshold value of setting is compared, if being lower than threshold valueThen judge signal
In all energy it is separated, otherwise return to S2 and continue the parameter Estimation and separation of signal component；
Residual signal sres(t) energy judgement may be expressed as:
In formulaFor residual signal sres(t) energy,For the energy of the multi-component LFM signalt
Amount, ξ is threshold value, and SNR is signal-to-noise ratio.
Embodiment 9: multi-component LFM signalt separation
Simulation parameter setting: multi-component LFM signalt is made of 3 LFM signal mixing.Signal length is 5us, signal-to-noise ratio
SNR=0dB.1st signal center frequency is 20MHz, modulating bandwidth 20MHz；2nd signal center frequency is 25MHz, is adjusted
Bandwidth is 40MHz；3rd signal center frequency is 30MHz, modulating bandwidth 30MHz.The ratio between 3 signal amplitudes are 1:
0.9:0.8.Sample frequency is 120MHz.Therefore, the original frequency of 3 signals and frequency modulation rate (f, k) be respectively (10MHz, 4 ×
106MHz/s), (5MHz, 6 × 106MHz/s), (15MHz, 8 × 106MHz/s).Noise is additive white Gaussian noise.RELAX is calculated
Inside convergence parameter δ in method is 0.05.Algorithm terminates the critical parameter ξ of thresholding according to formula X III and formula X IV.
The time-frequency characteristics of original signal are calculated first.Attached drawing 2, Fig. 3 and Fig. 4 are respectively the three-dimensional WVD of original signal S (t)
Figure, two dimension WVD figure and RWT figure.The time-frequency distributions of 3 LFM signal components are observed that from Fig. 2 and Fig. 3, but due to making an uproar
The portion of energy of the influence of sound, signal is submerged in noise, simultaneously because the interference of WVD cross term, the few time-frequency of signal
Distribution is fuzzy.Be able to observe that the spike of protrusion from Fig. 4, however spike generated a degree of broadening and it is observed that
The influence of secondary lobe.At this time if directly estimating most strong component signal parameter by traditional Time-frequency method, error will be introduced and to rear
The estimation of continuous component interferes.Therefore, the peak coordinate searched in RWT obtains the rough estimate of the best projection path parameter of signal
Evaluation carries out rough estimate to signal parameter.According to the parameter reconstruction signal s of estimation1(t), weight and from original signal S (t) is separated
Structure signal obtains residual signal S1(t)。
Attached drawing 5, Fig. 6 and Fig. 7 are respectively to pass through first time Signal separator, obtain residual signal S after separating strong signal component1
(t) three-dimensional WVD figure, two dimension WVD figure and RWT figure.It is able to observe that there are the two of cross-interference terms straight lines from Fig. 6, together
When RWT distribution in occur two spikes, comparison diagram 3 seeing as signal component reduction, spike broadening and secondary lobe interference shadow
It rings and reduces.Based on signal S1(t) RWT transformation estimation residual signal S1(t) peak-peak coordinate in RWT plane, calculates accordingly
Signal s2(t) the rough estimate evaluation of parameter.Then by RELAX algorithm to signal s1(t) and s2(t) parameter carries out smart estimation.Root
It is believed that number s2(t) estimated result, from separation s in mixed signal S (t)2(t), to s1(t) revaluation is carried out, then according to s1(t)
Revaluation result to s2(t) signal parameter carries out revaluation.Signal s is obtained after reaching internal convergence1(t) and s2(t) estimation knot
Fruit.
Reconstruction signal s1(t) and s2(t) and from original signal S (t) it separates, obtains new residual signal S2(t).Attached drawing 8,
Fig. 9 and Figure 10 is respectively to pass through second of Signal separator, obtains residual signal S after separating strong signal component2(t) three-dimensional WVD
Figure, two dimension WVD figure and RWT figure.It can be seen that since the first two signal parameter is effectively divided after the estimation of RELAX algorithm essence
From, therefore spike broadening and secondary lobe interference are smaller in the RWT plane of residual signal component.Signal s is obtained based on RWT rough estimate3
(t) parameter rough estimate value, then with RELAX algorithm to signal s1(t)、s2(t) and s3(t) it is iterated optimization, until internal
Convergence.
Embodiment described above is only that the preferred embodiment of the present invention is described, not to the scope of the present invention into
Row limits, and without departing from the spirit of the design of the present invention, those of ordinary skill in the art make technical solution of the present invention
Various changes and improvements out, should fall within the scope of protection determined by the claims of the present invention.
Claims (8)
1. the multi-component LFM signalt separation method based on Radon-Wigner transformation and REALX algorithm, which is characterized in that including
Following steps:
S1. it pre-processes, is converted based on Radon-Wigner, the multi-component LFM signalt of initialization is transformed into RWT plane；
S2. the peak value of the RWT plane is searched in rough estimate, to LFM signal component stronger in the multi-component LFM signalt
Rough estimate is carried out, rough estimate LFM signal component is obtained；
S3. essence estimation carries out the estimation of loop optimization essence to the rough estimate signal component based on REALX algorithm, until inside is received
It holds back, obtains essence estimation LFM signal component；
The essence estimation LFM signal component is obtained remaining LFM after rejecting in the multi-component LFM signalt by S4. Signal separator
Signal component；
S5. it terminates thresholding and determines that the residue LFM signal component repeats S2-S4 step, when institute in the multi-component LFM signalt
There is the parameter of LFM signal component to be effectively estimated.
2. according to claim 1 based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of REALX algorithm
Method, which is characterized in that
In the S2 step, the peak value is top coordinate, is derived by rough estimate center according to the top coordinate；
In the S3 step, the variable quantity of adjacent loop optimization twice is calculated, is judged when the variable quantity is lower than convergence threshold
For inside convergence；When the variable quantity is higher than convergence threshold, S2 step is returned；
In the S4 step, the essence estimation LFM signal component is picked from the multi-component LFM signalt using time domain opposition method
Residue LFM signal is obtained after removing；
In the S5 step, the energy of the residue LFM signal is calculated first, and is compared with the threshold value of setting, if low
In threshold value, then judge that all LFM signal components are separated in the multi-component LFM signalt.
3. according to claim 2 based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of REALX algorithm
Method, which is characterized in that wherein S1 step includes:
S1.1 initializes multi-component LFM signalt；
The multi-component LFM signalt S (t) is by i LFM signal and ambient noise n N number of irrelevant and with superposability
(t) it forms, i-th of LFM signal is as shown in formula I:
In formula I, siIt (t) is i-th of LFM signal, αi、kiAnd fiIt is followed successively by the amplitude of i-th of LFM signal, chirp rate and initial
Frequency, t are the sampling time；
The multi-component LFM signalt S (t) is as shown in formula II:
In formula II, S (t) is multi-component LFM signalt, αi、kiAnd fiIt is followed successively by the amplitude of i-th of LFM signal, chirp rate and just
Beginning frequency, t are the sampling time, and N is the total number of LFM signal component, and n (t) is ambient noise, and the ambient noise includes detecing receipts
Mixed signal in interference and noise contribution, i be variable, i=1,2 ... N；
Multi-component LFM signalt is transformed to RWT plane by S1.2；
The Wigner-Ville distribution of the multi-component LFM signalt S (t) is as shown in formula III:
In formula III, WzThe Wigner-Ville that (t, w) is S (t) is converted, t is the time, w is frequency, and τ is time delay；
After the multi-component LFM signalt S (t) is converted by Radon-Wigner shown in formula IV:
In formula IV, S (t) is multi-component LFM signalt, and the Radon-Wigner that R (a, b) is S (t) is converted, and (a, b) is along described more
The path of integration parameter of LFM Signal time-frequency straight line, a are origin vertical range, and b is inclination angle；K and f is followed successively by LFM signal
Chirp rate and original frequency, t are the sampling time.
4. according to claim 3 based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of REALX algorithm
Method, which is characterized in that wherein S2 step includes:
S2.1 searches for the top coordinate of RWT plane, as shown in formula V:
In formula V,For Radon-Wigner transformation calculations maximum value, (a, b) is along LFM signal time-frequency straight line
Path of integration parameter, a are origin vertical range, and b is inclination angle；It s.t. is " condition is satisfied with " mathematic sign；
Each signal component can form peak value in RWT plane in the multi-component LFM signalt, when path of integration parameter (a, b)
When with chirp parameter (k, f) accurate match of some LFM signal component, maximum integrated value is obtained, and occur in RWT plane
One corresponding peak value；The wherein peak value highest of the strongest signal component of energy, therefore can be obtained according to peak-peak coordinate
The parameter of peak signal component；
S2.2 is derived by rough estimate center according to top coordinate；
Corresponding path of integration parameter (a, b) is obtained by top coordinate, passes through path of integration parameter (a, b) and peak-peak
Original frequency f and chirp rate k, the rough estimate center of the peak signal component is calculated, as shown in formula VI:
In formula VI, f is the original frequency of LFM signal, and k is the chirp rate of LFM signal, and (a, b) is along LFM signal time-frequency straight line
Path of integration parameter, a be origin vertical range, b is inclination angle.
5. according to claim 4 based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of REALX algorithm
Method, which is characterized in that wherein S3 step includes:
S3.1 multi-component LFM signalt S (t) obtains residual signal S by parameter Estimation and after separating preceding n-1 signal componentn-1
(t), expression formula are as follows:
In formula VII, Sn-1It (t) is the composition for rejecting residual signal and ambient noise n (t) after preceding n-1 signal, S (t) is more points
Measure LFM signal；For preceding n-1 signal, i is variable, i=1,2 ... n-1；N is variable, n
=1,2 ... N；
S3.2, when carrying out parameter Estimation to n-th of component, according to the nonlinear least-squares problem criterion in RELAX algorithm:
In formula VIII, CnIndicate the energy for the residual signal that n signal component obtains before rejecting；There is N in the multi-component LFM signalt
A LFM signal, Sn-1(t)-sn(t) that obtain is the residual signal S of n signal component before rejectingn(t), constituting is that (N-n) is a
Signal component and noise n (t)；Sn-1It (t) is the composition for rejecting residual signal and ambient noise n (t) after preceding n-1 signal,
snIt (t) is n-th of LFM signal, n is variable, n=1,2 ... N；
The parameter for estimating n-th of signal component is (fn,kn), by finding the smallest Cn, i.e. calculating least residue energy minCn
(fn,kn), the parameter Estimation (f of available n-th of signal componentn,kn)；In the parameter Estimation (fn,kn) on the basis of into
Row optimization；By (fn,kn) parameter as n-th of signal；
S3.3 is iterated update to the preceding n signal parameter estimated；Renewal process are as follows: after optimizing in S3.2 step
It is isolated in signal and has estimated residual signal S ' outside m-th of signalm(t):
S (t) is multi-component LFM signalt in formula Ⅸ,For in n signal component in addition to
The time domain superposition of remaining outer signal of m signal, S'm(t) it after to eliminate the preceding n signal in addition to m-th of signal component, obtains
The residual signal S' arrivedm(t)；N and m is variable, m=1,2 ... n；N=1,2 ... N；
S3.4 is by the residual signal S'm(t), Radon-Wigner transformation is carried out according to formula IV, is then searched according to formula V
The top coordinate (a, b) of rope RWT plane；
S3.5 calculates m-th of parameter (f for having estimated signal according to formula VIm,km), and s is updated according to formula Im(t) signal, n and
M is variable, m=1,2 ... n；N=1,2 ... N.
6. according to claim 5 based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of REALX algorithm
Method, which is characterized in that wherein S4 step includes:
The internal convergence of judgement, internal convergent condition are residual signal Sn(t) energyTwice more by front and back
Variable quantity after new is lower than convergence threshold, and convergence deterministic process may be expressed as:
In Formula X, DmAfter the parameter update of m-th of signal component, residual signal Sn(t) energy, i.e.,Dm+1
After the parameter update of the m+1 signal component, residual signal Sn(t) energy, i.e.,SnIt (t) is rejecting
The residual signal obtained after preceding n signal；δ is threshold parameter；N and m is variable, m=1,2 ... n；N=1,2 ... N；
When the convergence of inside, including sn(t) the parameter update of n signal component including finishes, variable n=n+1；
When not converged, S2 step is returned.
7. according to claim 6 based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of REALX algorithm
Method, which is characterized in that wherein S5 step includes:
S5.1 signal reconstruction；Fine estimation (the f of strong signal component parameters is obtained by RWT rough estimate and the estimation of RELAX essencen,
kn) after, according to estimated value reconstruction signal component:
In formula Ⅺ, snIt (t) is n-th of LFM signal, αn、fn、knIt is followed successively by the amplitude of n-th of LFM signal, chirp rate and initial
Frequency, t are the sampling time；N and m is variable, m=1,2 ... n；N=1,2 ... N；
S5.2 Signal separator separates residual signal S using time domain opposition methodn(t):
In formula Ⅻ, S (t) is multi-component LFM signalt,It is folded for the time domain of n signal component
Add, SnIt (t) is the residual signal obtained after n signal before eliminating, Sn-1(t) it is remained for what is obtained after n-1 signal before eliminating
Remaining signal, snIt (t) is n-th of signal；N and m is variable, m=1,2 ... n；N=1,2 ... N.
8. according to claim 7 based on Radon-Wigner transformation and the multi-component LFM signalt side of separation of REALX algorithm
Method, which is characterized in that wherein S6 step includes:
S6.1 terminates thresholding and determines；Calculate residual signal sres(t) energy, calculation formula areWherein sres
It (t) is residual signal sres(t), it and with the threshold value of setting is compared, if being lower than threshold valueThen judge
All energy are separated in signal, otherwise return to parameter Estimation and separation that S2 continues signal component；
Residual signal sres(t) energy judgement may be expressed as:
In formulaFor residual signal sres(t) energy,For the multi-component LFM signalt
Energy, ξ are threshold value, and SNR is signal-to-noise ratio.
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