CN105785324A - MGCSTFT-based chirp signal parameter estimation method - Google Patents

Abstract

The invention discloses a maximum-likehood-generalized-cauchy-short-time-fourier-transform (MGCSTFT)-based chirp signal parameter estimation method. On the basis of generalized Cauchy distribution, one kind of loss function suitable for an alpha stable distribution noise environment is constructed; and parameter estimation of a chirp signal is realized accurately by using a maximum likelihood estimation theory. The method comprises: step one; collecting a chirp signal; step two, determining a determination threshold; step three, determining whether a pulse noise is included; step five, setting a loss function; step five, carrying out maximum likehood generalized Cauchy short time fourier transform processing; and step six, extracting a parameter of a chirp signal. According to the invention, a problem of estimation signal parameter failure occurrence in an alpha stable distribution noise environment according to the traditional time frequency analysis technology can be solved; and the parameter estimation precision is improved.

Description

Linear frequency-modulated parameter estimating method based on MGCSTFT

Technical field

The invention belongs to signal of communication process field, further relate to the linear frequency-modulated parameter estimating method based on maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT (maxmium-likehoodgeneralizedCauchyShortTimeFourierTransfo rmMGCSTFT) of the one in Radar Signal Processing Technology field.The present invention utilizes time-frequency analysis technology, removes impulsive noise at time-frequency domain through iteration, it is possible to accurately realize the parameter extraction of linear FM signal in α Stable distritation noise circumstance.

Background technology

Linear FM signal LFM (LinearFrequencyModulationLFM), also known as chirp signal, as the Typical Representative of non-stationary signal, because retaining the characteristic of continuous signal and pulse, it is widely used in the aspects such as radar, voice, sonar and biomedicine.In the case of digital reception, linear FM signal original frequency and chirp rate parameter are accurately estimated, it is possible to achieve the Target detection and identification in electronic reconnaissance system.At present, researcher successively proposes multiple effective processing method for the parameter estimation of non-stationary signal, is distributed, including the Linear Time-Frequency Analysis method being representative with Short Time Fourier Transform (STFT) and Wigner-Ville, the bilinearity Time-Frequency Analysis Method that (WVD) is representative.Short Time Fourier Transform is as the class Time-Frequency Analysis Method proposed the earliest, because can in conjunction with the advantage of various window functions, and the process for multicomponent data processing have cross term interference, thus is widely used in the process of non-stationary signal.But the time-frequency locality of STFT is not sufficiently good, it is easy to be subject to the interference of noise, especially under α Stable distritation influence of noise, the estimation performance of non-stationary signal parameter is declined to a great extent by STFT method.

A kind of method of fractional lower-order statistics disclosed in the patent " the orthogonal wavelet blind balance method based on fractional lower-order statistics " (application number CN201110208437A, publication number CN102355435A) of Nanjing Information engineering Univ's application.The method utilizes fractional lower-order statistics to suppress α Stable distritation noise, utilize the prior information of information source, in an iterative process adaptive correction modulus value, and equalizer input signal has been carried out orthogonal wavelet transformation, while reducing input signal autocorrelation, improve the harmony of system.Although the reducing technique that the method utilizes inhibits bigger pulse to a certain extent, but the weak point that the method exists is, when the intensity enhancing of impulsive noise, the method performance degradation, and the value of fractional lower-order operator do not have strict selection standard.

The L-DFT method of estimation that Zhu Min et al. proposes is (based on the LFM-BPSK multiplex modulated signal parameter estimation of L-DFT under Alpha Stable distritation noise, vibration and impact, 2015.9), square frequency doubling method is utilized to eliminate coding phase modulation, while L-DFT method impulse noise mitigation, estimate initial frequency and the modulation slope of linear FM signal, and effect is substantially better than fractional lower-order statistics, but the deficiency that this type of method exists is, L estimates that solution procedure is complicated, high power pulse noise is comparatively sensitive, when broad sense signal to noise ratio reduces, the method hydraulic performance decline, it is difficult to meet the requirement of non-stationary signal parameter estimation.

In sum, for linear FM signal method for parameter estimation under impulsive noise, current existing time-frequency analysis technology does not have robustness under the environment of impulsive noise, it is easily subject to the interference of impulsive noise, so that the parameter estimation of signal does not reach the precision of actual requirement, especially, when broad sense signal to noise ratio reduces, based on the method performance degradation of nonlinear filtering, even lost efficacy.

Summary of the invention

It is an object of the invention to the deficiency overcoming above-mentioned existing time-frequency analysis technology cannot realize Signal parameter estimation under impulse noise environment, on the basis of traditional Short Time Fourier Transform time-frequency analysis technology, broad sense Cauchy is utilized to be distributed, construct a class and be applicable to the loss function of α Stable distritation noise circumstance, theoretical by maximal possibility estimation, obtain the Short Time Fourier Transform of a kind of improvement, i.e. maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT.This type of method estimates the parameter of linear FM signal, it is possible to improve the Stability and veracity of α Stable distritation noise lower linear FM signal parameter estimation, thus improving the parameter estimation performance of linear FM signal.

The concrete thought realizing the present invention is: broad sense Cauchy distribution being used for matching α Stable distritation noise, its probability density function obtains the loss function in maximal possibility estimation theory, this type of loss function can better adapt to α Stable distritation noise circumstance.At the time-frequency plane of Short Time Fourier Transform, the maximal possibility estimation of linear FM signal is realized by the process of an iteration.By iteration, obtain maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT time frequency distribution map of linear FM signal, time frequency distribution map is carried out Hough transformation straight-line detection, finally gives original frequency and the chirp rate of linear FM signal.

The concrete steps of the present invention include as follows:

(1) linear FM signal is gathered:

The signal acquiring system receiver device by Pulse-compression Radar, gathers any one section of linear FM signal containing actual noise in radar antenna；

(2) judgement threshold is determined:

Adopt partial amplitudes characterization method, obtain local threshold, using this threshold value as judgement threshold；

(3) judge that whether linear FM signal partial amplitudes that amplitude statistical module gathers is more than judgement threshold, if, then think in linear FM signal containing α Stable distritation noise, perform step (4), otherwise, after the linear FM signal gathered is done Short Time Fourier Transform, perform step (6b)；

(4) according to the following formula, the loss function of maximal possibility estimation is set:

F (e)=-logp_v(t)

Wherein, F (e) represents the loss function of maximal possibility estimation, and e represents that estimation difference, t represent the sampling time gathering signal, and v (t) represents the background noise gathered in signal, p_vT () represents the probability density function of background noise v (t)；

(5) maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT it is:

(5a) the pulse indication signal obtained in step (3) is done Short Time Fourier Transform, by the result of Short Time Fourier Transform, as the initial value of maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT iteration；

(5b) according to the following formula, iteration obtains maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value successively:

$M^{\left(i\right)}=\frac{1}{Q}\·\underset{m=0}{\overset{N-1}{\Σ}}\frac{\mathrm{\ω}(n\mathrm{\Δ}t-t)\·x\left(n\mathrm{\Δ}t\right)e^{-j2\mathrm{\π}fn\mathrm{\Δ}t}}{|e^{(i-1)}{|}^p+k^p}$

Wherein, M⁽ⁱ⁾Represent maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value that ith iteration obtains, i represents iterations, Q represents the window long function accumulated value at discrete time point, N represents the total sampling number gathering signal, the size of N is determined by the length and sampling interval gathering signal, m represents discrete time initial point, ω represents window function, n represents discrete-time sample, Δ t represents discrete time section, t represents the sampling time gathering signal, x represents collection signal, f represents the sample frequency gathering signal, e represents error function, k represents the scale parameter that broad sense Cauchy is distributed, the size of k is determined by the factor alpha of α Stable distritation noise, p represents the exponent number that broad sense Cauchy is distributed, span is [1, 2]；

(5c) judge that whether the relative error of adjacent twice iterative value is less than threshold value η, if so, then performs step (6), otherwise, perform step (5b)；

(6) parameter of linear FM signal is extracted:

(6a) time frequency distribution map corresponding with maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value is drawn in T/F plane；

(6b) adopt Hough transformation line detection method, in time frequency distribution map, extract the parameter of linear FM signal.

Compared with prior art, present invention have the advantage that

First, it is maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT due to what the present invention adopted, α Stable distritation noise is suppressed by iteration at time-frequency plane, overcome the time-frequency analysis technology shortcoming of performance degradation in α Stable distritation noise adopted in prior art, make the present invention can under relatively low broad sense signal to noise ratio, it is effectively improved the accuracy rate that linear frequency-modulated parameter is estimated, it is thus achieved that less root-mean-square error, thus improving the performance that linear frequency-modulated parameter is estimated.

Second, owing to whether the relative error judging adjacent twice iterative value of present invention employing is less than threshold value η, η value is more little, the estimated accuracy of signal parameter is more high, overcome the limitation that cannot adjust Signal parameter estimation precision in prior art neatly, make the present invention that the parameter estimation of linear FM signal is reached less precision, thus effectively highlighting the local message of linear FM signal.

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention；

Fig. 2 is the analogous diagram of the present invention；

Fig. 3 is the simulated effect comparison diagram of the present invention.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention will be further described.

With reference to Fig. 1, specific embodiment of the invention step is as follows:

Step 1, gathers linear FM signal.

The signal acquiring system receiver device by Pulse-compression Radar, gathers any one section of linear FM signal containing actual noise in radar antenna.

Signal acquiring system passes through reception antenna, choose any one section of reception signal containing original linear FM signal s (t) and impulsive noise v (t), using selected reception signal as gathering signal, namely receiving signal: x (t)=s (t)+v (t), wherein the model of linear FM signal s (t) is represented by:

S (t)=Aexp (j2 π ft+ (j π kt²),t∈[0,T]

Wherein, A, f, k represents the amplitude of signal, original frequency and chirp rate respectively, and T express time is interval.LFM signal frequency linearly changes in time.

Step 2, it is determined that judgement threshold:

Adopt partial amplitudes characterization method, obtain local threshold, using this threshold value as judgement threshold.

The determination step of local threshold is as follows:

The first step, will gather signal input discrimination module, as differentiating signal.

Second step, arranging a regular length is the detection window of W, and the span of length W is the value more than 0 less than linear FM signal total number of sample points.

3rd step, utilizes the time domain of detection window to smooth, linear FM signal is blocked on a time period, be divided into the subsignal of multiple equal length time period, non-overlapping copies, adopt partial amplitudes characterization method to calculate the amplitude equalizing value of subsignal, obtain local threshold.

Step 3, it is judged that amplitude statistical module gather linear FM signal partial amplitudes whether more than judgement threshold, if, then think containing α Stable distritation noise in linear FM signal, perform step 4, otherwise, after directly the signal gathered being done Short Time Fourier Transform, perform the second step of step 6；

Step 4, according to the following formula, arranges the loss function of maximal possibility estimation:

F (e)=-logp_v(t)

Wherein, F (e) represents the loss function of maximal possibility estimation, and e represents that estimation difference, t represent the sampling time gathering signal, and v (t) represents the background noise gathered in signal, p_vT () represents the probability density function of background noise v (t).

When estimating containing noisy signal parameter, the method theoretical based on maximal possibility estimation is optimum, its loss function F (e)=-logp_v(t), wherein, p_vT () represents the probability density function of noise v (t).In Gauss figure viewed from behind noise, its probability density function normal distribution can obtain loss function F (e)=| e |², maximum likelihood theory shows, it is possible to obtain the Minimum Mean Squared Error estimation of signal, and signal s (n) is obtained by the output of mean filter, it may be assumed that

$\widehat{s\left(n\right)}=\frac{1}{2M+1}\underset{k=n-M}{\overset{n+M}{\Σ}}x\left(k\right)=mean\left\{x\left(k\right)\right|k\∈\[n-M,n+M\]\}$

Wherein, s (n) represents signal to be estimated,Representing the maximal possibility estimation of signal s (n), M represents the mobile range of discrete sampling point, and n represents discrete sampling point, and x (k) represents containing noisy signal, and mean represents mean filter function.

But, deviation is supposed that the interference of noise model is very sensitive by maximal possibility estimation, which results under α Stable distritation noise, the conventional method of analysis performance degradation theoretical based on maximal possibility estimation is serious, therefore the present invention proposes the loss function that a class is new, this type of loss function is distributed based on broad sense Cauchy, and its probability density function is:

F (x)=a (k^p+|x|^p)^-2/p

Wherein,K represents scale parameter, interval (0,2] upper value；Γ () represents gamma function, and broad sense Cauchy distribution comprises two special cases, and Cauchy's distribution when namely Merid distribution during p=1 is with p=2, theoretical by maximal possibility estimation, can obtain loss function function is: F (e)=log (k^p+|e|^p), wherein k > 0,0 < p≤2, e represents error.

Step 5, is maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT:

The first step, makes i=0, is Short Time Fourier Transform STFT to gathering signal x (t), as the initial value of iteration, i.e. and M⁽⁰⁾=STFT_x, wherein, M⁽⁰⁾Represent the initial value of maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT, STFT_xRepresent the Short Time Fourier Transform gathering signal x (t).

Second step, makes i=i+1, and the step of iteration is as follows:

$M^{\left(i\right)}=\frac{1}{Q}\&CenterDot;\underset{m=0}{\overset{N-1}{\&Sigma;}}\frac{\mathrm{\&omega;}(n\mathrm{\&Delta;}t-t)\&CenterDot;x\left(n\mathrm{\&Delta;}t\right)e^{-j2\mathrm{\&pi;}fn\mathrm{\&Delta;}t}}{|e^{(i-1)}{|}^p+k^p}$

Wherein, M⁽ⁱ⁾The maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value obtained when representing i iteration, i represents that iterations, Q represent the window long function accumulated value at discrete time point, the value of Q byDetermine, N represents the total sampling number gathering signal, and the size of N is determined by the length and sampling interval gathering signal, and m represents discrete time initial point, ω represents window function, n represents discrete-time sample, and Δ t represents discrete time section, and t represents the sampling time gathering signal, x represents collection signal, f represents the sample frequency gathering signal, and e represents error function, e^(i-1)=x (n Δ t) e^-j2πfnΔt-M^(i-1), k represents the scale parameter that broad sense Cauchy is distributed, and the size of k is determined by the factor alpha of α Stable distritation noise, namelyP represents the exponent number that broad sense Cauchy is distributed, and span is [1,2]；

3rd step, it is judged that the relative error of adjacent twice iterative value whether less than threshold value η, ifWherein, M⁽ⁱ⁾The maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value obtained when representing i iteration, then perform step 6, otherwise, performs the second step of step 5；

Threshold value η, is determined by the estimated accuracy of signal parameter, is taken as 0.1；

Step 6, extracts the parameter of linear FM signal:

The first step: the maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT time-frequency figure obtained being carried out Hough transformation, retrieves the polar coordinate (ρ, θ) of peak point, wherein, ρ represents footpath, polar pole, and θ represents polar polar angle；

Second step: by coordinate transform formulaObtain the parameter of linear FM signal, wherein, f₀Represent the chirp rate of linear FM signal, k₀Representing the original frequency of linear FM signal, ρ represents footpath, polar pole, and θ represents polar polar angle.

Below in conjunction with emulation experiment, the present invention will be further described.

1, simulated conditions:

The emulation signal of the present invention is linear FM signal, and its parameter is: sample frequency f_s=10kHz, original frequency f₀=1kHz, chirp rate k₀=10kHz/s, sampling number N=1600.Simulation software environment is the Matlab7.8 under Intel (R) Pentium (TM) G3260CPU3.20GHz, Windows732bit operating system.

The present invention adopts normalization root-mean-square error NRMSE to carry out the performance of evaluating method of estimation, it is assumed that the number of times of MonteCarlo emulation experiment is R, and estimated parameter is θ, and the estimated value in i & lt is tested is, then the normalization root-mean-square error that parameter θ is estimated is

The present invention adopts broad sense signal to noise ratio to come metric signal and the size of impulsive noise energy, owing to α Stable distritation is absent from limited second moment, in conventional signal to noise ratioLower noise varianceLose meaning, therefore redefine broad sense signal to noise ratio:In formula,Represent signal energy；γ_vThe coefficient of dispersion for α Stable distritation noise.

2, emulation content and interpretation of result:

Emulation 1: adopt MGCSTFT method to estimate the parameter of linear FM signal.

Under the α Stable distritation noise of characteristic index α=0.8, linear FM signal adopts the Computer Simulation such as figure of MGCSTFT method, take p=1, η=0.1, Fig. 2 (a) is the Short Time Fourier Transform figure of the linear frequency modulation primary signal of not Noise, by Fig. 2 (a) it can be seen that linear FM signal is clearly obvious at time-frequency domain, frequency changes linearly over time, presents the feature of straight line.

Mixed signal, after adding white Gaussian noise in linear FM signal, is the time frequency distribution map of Short Time Fourier Transform, signal to noise ratio snr=3dB by Fig. 2 (b).STFT method has certain robustness for white Gaussian noise, and in time frequency distribution map, linear FM signal is clear-cut, it is seen that conventional time-frequency analysis technology can process the signal containing white Gaussian noise.

Fig. 2 (c) adds broad sense signal to noise ratio GSNR=3dB, after the α Stable distritation noise of pulse strength α=0.8, and the time-frequency figure of linear FM signal, it is seen that linear FM signal is flooded completely by noise, and time-frequency plane causes confusion.Linear FM signal is serious by impulse noise effect, time-frequency figure under affecting with white Gaussian noise is entirely different, therefore traditional Time-Frequency Analysis Method STFT is difficult to the linear FM signal containing impulsive noise is carried out parameter estimation, demonstrates the traditional treatment method based on Gauss model and lost efficacy under impulse noise environment.

Fig. 2 (d) is the linear FM signal application MGCSTFT method of α Stable distritation noise, after 4 iteration, and the time frequency distribution map obtained.From Fig. 2 (d) it will be seen that after MGCSTFT method processes, impulsive noise is removed, and linear FM signal is in time-frequency plane clear and definite.

Fig. 2 (e) is on the basis of Fig. 2 (c) time frequency distribution map, utilize Hough line detection method, extract the parameter of linear FM signal, can be seen that from Fig. 2 (e), Hough transformation has searched peak point, the coordinate (ρ, θ) of its vertex correspondence is through coordinate transform formulaAfter, obtain original frequency and the chirp rate of linear FM signal.

Emulation 2: the application condition of various methods.

Change broad sense signal to noise ratio GSNR, when broad sense signal to noise ratio changes from-2dB to 8dB, the linear FM signal original frequency that MGCSTFT method is drawn and the normalization root-mean-square error of chirp rate.By MGCSTFT method respectively with the STFT (MYRSTFT) based on Myriad wave filter, the STFT (MERSTFT) of Merid wave filter, the normalization root-mean-square error that traditional STFT processing method obtains contrasts, through 100 MonteCarlo emulation experiments, its simulation result such as Fig. 3 (a), Fig. 3 (b).

From Fig. 3 (a), Fig. 3 (b) it will be seen that as GSNR >=1dB, MGCSTFT method can accurately estimate chirp rate and the original frequency of linear FM signal；As GSNR >=6dB, based on the STFT of the Merid wave filter chirp rate that can accurately obtain linear FM signal, during GSNR >=5dB, can accurately estimate the original frequency of linear FM signal；As GSNR >=8dB, the STFT based on Myriad wave filter just can obtain linear FM signal chirp rate and the accurate of original frequency is estimated；Traditional STFT method is serious by high power pulse influence of noise, performance serious degradation, it is difficult to the parameter of signal is made accurate estimation.Although all can comparatively accurately carry out linear frequency-modulated parameter estimation in good signal to noise situations based on multiple methods such as Myriad wave filter and Merid wave filter, but under high power pulse noise and low signal-to-noise ratio, estimate that performance all declines to some extent.

In sum, traditional Time-Frequency Analysis Method STFT is unable to estimate the parameter of linear FM signal under high power pulse effect of noise, after Myriad wave filter and Merid wave filter impulse noise mitigation, although MYRSTFT and MERSTFT can impulse noise mitigation to a certain extent, but under relatively low broad sense signal to noise ratio, still there is bigger error in both estimations.MGCSTFT method need not be filtered in time domain, it is to avoid the linear frequency-modulated parameter that application wave filter causes estimates the shortcoming of hydraulic performance decline, at time-frequency plane by, after iteration, achieving the estimation of signal parameter exactly.Therefore, the MGCSTFT new method that the present invention proposes is applicable to the parameter estimation of α Stable distritation noise lower linear FM signal, and estimates that performance and precision are good, is better than the processing method of other routines.

Claims (3)

1., based on the linear frequency-modulated parameter estimating method of MGCSTFT, comprise the steps:

(1) linear FM signal is gathered:

The signal acquiring system receiver device by Pulse-compression Radar, gathers any one section of linear FM signal containing actual noise in radar antenna；

(2) judgement threshold is determined:

Adopt partial amplitudes characterization method, obtain local threshold, using this threshold value as judgement threshold；

(3) judge that whether linear FM signal partial amplitudes that amplitude statistical module gathers is more than judgement threshold, if, then it is assumed that containing α Stable distritation noise in linear FM signal, perform step (4), otherwise, perform step (6b)；

(4) according to the following formula, the loss function of maximal possibility estimation is set:

F (e)=-logp_v(t)

Wherein, F (e) represents the loss function of maximal possibility estimation, and e represents that estimation difference, t represent the sampling time gathering signal, and v (t) represents the background noise gathered in signal, p_vT () represents the probability density function of background noise v (t)；

(5) maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT it is:

(5a) the pulse indication signal obtained in step (3) is done Short Time Fourier Transform, by the result of Short Time Fourier Transform, as the initial value of maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT iteration；

(5b) according to the following formula, iteration obtains maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value successively:

$M^{\left(i\right)}=\frac{1}{Q}\&CenterDot;\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\frac{\mathrm{\&omega;}(n\mathrm{\&Delta;}t-t)\&CenterDot;x\left(n\mathrm{\&Delta;}t\right)e^{-j2\mathrm{\&pi;}fn\mathrm{\&Delta;}t}}{|e^{(i-1)}{|}^p+k^p}$

Wherein, M⁽ⁱ⁾Represent maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value that ith iteration obtains, i represents iterations, Q represents the window long function accumulated value at discrete time point, N represents the total sampling number gathering signal, the size of N is determined by the length and sampling interval gathering signal, m represents discrete time initial point, ω represents window function, n represents discrete-time sample, Δ t represents discrete time section, t represents the sampling time gathering signal, x represents collection signal, f represents the sample frequency gathering signal, e represents error function, k represents the scale parameter that broad sense Cauchy is distributed, the size of k is determined by the factor alpha of α Stable distritation noise, p represents the exponent number that broad sense Cauchy is distributed, span is [1, 2]；

(5c) judge that whether the relative error of adjacent twice iterative value is less than threshold value η, if so, then performs step (6), otherwise, perform step (5b)；

(6) parameter of linear FM signal is extracted:

(6a) time frequency distribution map corresponding with maximum likelihood broad sense Cauchy's Short Time Fourier Transform MGCSTFT value is drawn in T/F plane；

(6b) adopt Hough transformation line detection method, in time frequency distribution map, extract the parameter of linear FM signal.

2. the linear frequency-modulated parameter estimating method based on MGCSTFT according to claim 1, it is characterised in that: the threshold value η described in step (5c) is determined by the estimated accuracy of signal parameter, is taken as 0.1.

3. the linear frequency-modulated parameter estimating method based on MGCSTFT according to claim 1, it is characterised in that: specifically comprising the following steps that of the Hough transformation line detection method described in step (6b)

The first step: the maximum likelihood broad sense Cauchy Short Time Fourier Transform MGCSTFT time-frequency figure obtained being carried out Hough transformation, retrieves the polar coordinate (ρ, θ) of peak point, wherein, ρ represents footpath, polar pole, and θ represents polar polar angle；

Second step: by coordinate transform formulaObtain the parameter of linear FM signal, wherein, f₀Represent the chirp rate of linear FM signal, k₀Representing the original frequency of linear FM signal, ρ represents footpath, polar pole, and θ represents polar polar angle.