CN106772308B - Terahertz wideband radar micro-doppler ambiguity solution method based on arteries and veins internal interference - Google Patents
Terahertz wideband radar micro-doppler ambiguity solution method based on arteries and veins internal interference Download PDFInfo
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- CN106772308B CN106772308B CN201710167846.8A CN201710167846A CN106772308B CN 106772308 B CN106772308 B CN 106772308B CN 201710167846 A CN201710167846 A CN 201710167846A CN 106772308 B CN106772308 B CN 106772308B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
Abstract
The present invention provides a kind of Terahertz wideband radar micro-doppler ambiguity solution method based on arteries and veins internal interference, pass through the feature of (Dechirp) reception signal in the way of wideband radar solution line frequency modulation, micro-doppler ambiguity solution is realized based on arteries and veins internal interference, have the characteristics that Efficient robust, and does not increase system complexity simultaneously.
Description
Technical field
The present invention relates to radar system designs and Radar Signal Processing Technology field, are specifically related to a kind of based on dry in arteries and veins
The Terahertz wideband radar micro-doppler ambiguity solution method related to.
Background technique
It realizes that Target Motion Character extraction is a kind of widely used method using radar means, there is round-the-clock, whole day
Wait, high-precision the features such as, remote sensing survey, in terms of have highly important application.Terahertz (Terahertz,
THz) frequency range is often referred to electromagnetic wave of the frequency between 0.1THz to 10THz (30 μm of -3mm of corresponding wavelength), and frequency is between milli
Between metric wave and infrared light, in macroelectronics to the transition frequency range of microcosmic photonics, it is very special to occupy in electromagnetic spectrum
Position, have the special nature different from other wave bands.In recent years, with the breakthrough of THz source, detection and related device,
Terahertz Radar Technology is quickly grown, and gradually shows advantage in high-resolution imaging and in terms of moving fine measurement.
Fine motion (Micro-motion) refers to that vibration, the rotation of target or target component in addition to mass center translation etc. is small
Movement proposes that the Doppler frequency shift as caused by fine motion is known as micro- how general by professor V.C.Chen of US Naval Research Laboratory earliest
It strangles (Micro-Doppler).Fine motion phenomenon in nature and life is very universal, such as the breathing heartbeat of human body, helicopter
The rotation of rotor, the vibration etc. of vehicle bridge etc.,
However in actual measurement, according to sampling thheorem, pulse recurrence frequency (the pulse repetition of radar signal
Frequency, PRF) define that the frequency between only-PRF/2 to PRF/2 can be directly observed.When doppler values be located at-
When except PRF/2 to PRF/2, it will occur fuzzy.Terahertz radar is due to its higher carrier frequency, compared to conventional microwave radar,
There is its sensibility to target fine motion, this is the advantage of Terahertz radar；But higher carrier frequency is but also in Terahertz frequency range mesh
Mark micro-doppler value easily exceeds observation scope and obscures.
These rolling targets are monitored using radar equipment simultaneously and are of great significance.But these rotation mesh
Mark the often vibration along with vibration interference, to these targets due to mechanical reason or applied external force during exercise
Emotionally condition also needs to be monitored, and by the monitoring to vibration, can provide for equipment running status and safety important
Auxiliary information.
Realize that target fine motion parameter Estimation has had quite extensive research using radar means, however Terahertz frequency range
Research is also much insufficient.Have scholar in microwave section to study micro-doppler fuzzy problem, mainly from radar system
Two aspects of design and signal processing account for.
In the prior art:
In system design aspect, mainly progress multichannel and the measurement of multiple frequency.Multichannel is by by big antenna head
Different platforms is placed in for several miniature antennas or by several antennas to form multichannel, at the joint of multi-channel data
Reason is to realize Doppler ambiguity-resolution.Multiple frequency is fuzzy to realize by needing to emit multiple frequency (usually 2~3) train of pulse
Property.
In terms of signal processing, mainly by signal domain and time-frequency domain, using target prior information, using digital picture
The methods of the inverse Radon transform of process field, Hough transform are corrected or compensate to fuzzy time-frequency curve micro- to realize
Doppler ambiguity-resolution.
In above-mentioned existing micro-doppler ambiguity solution scheme, multichannel and the measurement of multiple frequency have its intrinsic problem, and serious
The complexity of radar system is increased, so that system stability and practicability deteriorate.For the means of existing signal processing are comprehensive
There is the problems such as process is complicated, computationally intensive, universality is poor, it is difficult to be widely applied in systems in practice.Therefore, how quickly high
The realization micro-doppler ambiguity solution of effect gives full play to the advantage of Terahertz radar micro-doppler sensibility and realizes ambiguity solution simultaneously
Problem is still require study the problem of, and for this problem, current there is no effective means.
Summary of the invention
The purpose of the present invention is to provide a kind of Terahertz wideband radar micro-doppler ambiguity solution side based on arteries and veins internal interference
Method, the invention solve the technical issues of wideband radar fine motion target micro-doppler ambiguity solution.
The present invention provides a kind of Terahertz wideband radar micro-doppler ambiguity solution method based on arteries and veins internal interference, including following
Step:
Step S100: receiving the wideband echoes signal of fine motion target to be monitored using wideband radar solution line frequency modulation mode, right
Gained wideband echoes signal carries out residual video phase compensation, obtains compensating wide band echo-signal；
Step S200: extracting the signal in compensating wide band echo-signal one by one, to the frequency point of each signal extracted into
Line frequency interference, obtains multiple interference signals；
Step S300: carrying out time frequency analysis to interference signal, obtains ambiguity solution micro-doppler curve, and utilize inverse Radon
Transform method handles ambiguity solution micro-doppler curve, obtains the fine motion estimation parameter of fine motion target to be monitored.
Further, include the steps that carrying out interference signal in step S200 cumulative.
Further, interference difference frequency used is B/2 in accumulation step.
Further, time frequency analysis is to be carried out using the Short Time Fourier Transform method in linear time-frequency distribution.
Further, fine motion target to be monitored is rolling target.
Technical effect of the invention:
1, the Terahertz wideband radar micro-doppler ambiguity solution method provided by the invention based on arteries and veins internal interference, passes through utilization
Wideband radar solution line frequency modulation mode (Dechirp) receives the feature of signal, utilizes the sampling of several frequency points inside frequency sweep cycle
Signal is interfered and is added up to realize micro-doppler ambiguity solution, realizes micro-doppler ambiguity solution based on arteries and veins internal interference, has
The features such as Efficient robust, and do not increase system complexity simultaneously.Solves fine motion target micro-doppler mould from field of signal processing
Paste problem reduces the increase to radar system complexity while realizing fine motion parameter Estimation.
2, the Terahertz wideband radar micro-doppler ambiguity solution method provided by the invention based on arteries and veins internal interference, utilizes broadband
Radar solution line frequency modulation mode receives mode and obtains fine motion target wideband echoes signal, carries out residual video phase to echo-signal
(residual video phase, PVP) compensation；Then the signal for extracting two different frequent points in broadband signal carries out frequency
Interference, and all interference signals are added up to eliminate the interference of cross term；Frequency division when finally being carried out to the signal after interference
Analysis, obtains unambiguous micro-doppler curve, and handled using the inverse Radon transform in field of image processing estimate to
Monitor the fine motion parameter of fine motion target.Using arteries and veins internal interference principle, the carrier frequency in micro-doppler expression formula is converted to interference
Difference frequency, drastically reduce micro-doppler value, while saving the other information in echo again, be conducive to subsequent analysis processing make
With.
3. the Terahertz wideband radar micro-doppler ambiguity solution method provided by the invention based on arteries and veins internal interference, can be quick
Stable realization micro-doppler ambiguity solution, and can be applied to multiple target scene, while giving full play to Terahertz frequency range advantage,
Solves the problems, such as doppler ambiguity.
Specifically please refer to the Terahertz wideband radar micro-doppler ambiguity solution method according to the present invention based on arteries and veins internal interference
The various embodiments proposed it is described below, will make apparent in terms of above and other of the invention.
Detailed description of the invention
Fig. 1 is the process of the Terahertz wideband radar micro-doppler ambiguity solution method provided by the invention based on arteries and veins internal interference
Schematic diagram；
Fig. 2 is preferred embodiment flow diagram provided by the invention；
Fig. 3 is rolling target structural schematic diagram used in preferred embodiment provided by the invention；
Fig. 4 is untreated corner reflector echo time-frequency distributions schematic diagram in preferred embodiment provided by the invention,
Middle a) is rolling target when revolving speed is 40r/min；It b) is rolling target when revolving speed is 60r/min；
Fig. 5 be in preferred embodiment provided by the invention using the method provided by the present invention treated corner reflector echo when
Frequency distribution schematic diagram a) is wherein rolling target when revolving speed is 40r/min；It b) is rolling target when revolving speed is 60r/min；
Fig. 6 is the parameter space result schematic diagram in preferred embodiment provided by the invention after inverse Radon transform, wherein
It a) is rolling target when revolving speed is 40r/min；It b) is rolling target when revolving speed is 60r/min.
Specific embodiment
The attached drawing constituted part of this application is used to provide further understanding of the present invention, schematic reality of the invention
It applies example and its explanation is used to explain the present invention, do not constitute improper limitations of the present invention.
Referring to Fig. 1~2, the Terahertz wideband radar micro-doppler ambiguity solution side provided by the invention based on arteries and veins internal interference
Method, comprising the following steps:
Step S100: receiving the wideband echoes signal of fine motion target to be monitored using wideband radar solution line frequency modulation mode, right
Gained wideband echoes signal carries out residual video phase compensation, obtains compensating wide band echo-signal；
Step S200: extracting the signal in compensating wide band echo-signal one by one, to the frequency point of each signal extracted into
Line frequency interference, obtains multiple interference signals；
Step S300: carrying out time frequency analysis to interference signal, obtains ambiguity solution micro-doppler curve, and utilize inverse Radon
Transform method handles ambiguity solution micro-doppler curve, obtains rolling target fine motion estimation parameter.
Gained ambiguity solution micro-doppler curve refers to unambiguous Doppler curve herein.This method can be used for handling all kinds of
The fine motion generated in target movement, such as rolling target.Wideband echoes signal herein refers to the letter that wideband radar system obtains
Number.
Preferably, fine motion target to be monitored is rolling target.Method provided by the invention is for handling rolling target timeliness
Fruit is best, since rolling target often has biggish radius of turn or angular speed, it is therefore desirable to which certain beam angle is
It can coverage goal；In addition, rolling target microwave section micro-doppler value generally in several hundred to tens of thousands of hertz of range, be in one
It is a clearly to observe the section that fine motion phenomenon is unlikely to serious aliasing again.Therefore, rolling target ginseng is carried out using microwave radar
Number estimation and imaging have some superiority.
The method provided by the present invention is described as follows:
The signal received in this method can be obtained by wideband radar system, and specific radar used can be broadband arteries and veins
Radar is rushed, Broadband FM continuous wave radar is also possible to.The signal of wideband radar system transmitting used has the mould that is shown below
Formula:
Wherein,For apart from fast time, tmFor the orientation slow time, t is total time, TpFor pulse radar pulse width or tune
The frequency sweep cycle of frequency continuous wave radar, fcFor radar carrier frequency, γ is frequency modulation rate, and j is imaginary unit.
The received thought of wideband radar solution line frequency modulation mode is by the echo-signal and echo signal at a reference distance
Carry out conjugate multiplication, it is assumed that reference distance Rref, reference signal can indicate are as follows:
Wherein, c is the light velocity.Assuming that apart from radar R0There are K and fine motion scattering center in place, these scattering centers are regarded in radar
Projection on line can generally be regarded as simple harmonic motion, then the distance R of simple harmonic motionkVariation expression formula are as follows:
Wherein ak, ωkWithRespectively the fine motion amplitude of k-th scattering center, fine motion angular speed and initial phase.Then root
According to transmitting signal expression (1), the fine motion echo monitored is written as:
The micro-doppler value of each fine motion scattering center can indicate are as follows:
Wideband radar solution line frequency modulation mode treated wideband echoes signal form are as follows:
Wherein RΔk=Rk-Rref。
It is received after obtaining wideband echoes signal by wideband radar solution line frequency modulation mode, it can be with according to its expression formula (6)
Find out, the first item in phase of echoIt is to move related point with fine motion target to be monitored
Amount, Section 2And Section 3For the tilting item of envelope and residual video phase, need to second
Item and Section 3 compensate.The comparison that compensation method used discusses in wideband-radar signal processing is more, can be found in [protect in detail
Polished, Xing Mengdao, Wang Tong radar imagery principle [M] Electronic Industry Press .2008.] basic ideas are by formula (6) to the fast time
Fourier transformation is carried out, then multiplied by following formula (7), inverse Fourier transform is finally carried out and obtains width after compensating shown in formula (8)
Band echo signal expression, acquired results are Section 2 and Section 3 through overcompensation.
Compensated wideband echoes signal expression are as follows:
Step S200: arteries and veins internal interference processing
After obtaining the wideband echoes signal such as formula (8), each sampled point inside pulse is that is, a single-frequency
Under echo, it is assumed that the number of samples of each pulse of radar system be N, be equivalent to N number of single-frequency echo, this N number of single-frequency is equal
Positioned at fc- B/2 and fcBetween+B/2, wherein B is signal bandwidth.The wherein expression formula of i-th of simple signal are as follows:
It chooses i-th and first of simple signal carries out interference processing, the signal form after handling are as follows:
Wherein, K are micro-doppler item relevant to K scattering center before, thus in formula (10)It is the information for needing to obtain.The
Binomial is cross term, is inhibited.
It preferably, further include to the interference in the step S200 in order to reduce the influence of cross term in formula (10)
Signal carries out cumulative step.Specifically: i=1,2 ... N/2, l=N/2+1, N/2+2 ... N are taken respectively, by i-th and first
Signal conjugate multiplication obtains total N/2 signal vector, and adds up, signal form after treatment are as follows:
By accumulation process, the accuracy of gained valuation can be effectively improved.
The echo-signal comprising K scattering center, and the micro-doppler value expression of this K scattering center are thus obtained
Formula becomes
Wherein B is transmitted signal bandwidth, generally much smaller than signal carrier frequency fc.Formula (12) can be seen that compared with formula (5)
Bigger value f in former expression formulacIt is replaced by a lesser value B/2, this is equivalent to reduce micro-doppler value
2fc/ B times, thus without departing from the not fuzzy ranges [- PRF/2, PRF/2] of micro-doppler, therefore originally fuzzy Doppler
Curve will not obscure again after above-mentioned processing.To improve monitoring accuracy.The step can eliminate the interference of cross term.
Step S300: the fine motion parameter Estimation based on time frequency analysis and inverse Radon transform.
After the fine motion target echo signal for being eliminated fuzzy, so that it may it is micro- how general to observe to carry out time frequency analysis to it
Strangle curve.The common linear time-frequency distributions of Time-Frequency Analysis Method and secondary Cohen class time-frequency distributions, it is preferred that in order to reduce
The interference of cross term, the present invention is using Short Time Fourier Transform method (the Short Time Fourier in linear time-frequency distribution
Transform, STFT), the STFT expression formula of signal s (t) are as follows:
Wherein h (t) is window function.After obtaining time-frequency distributions, due to fine motion target being projected as on radar line of sight
Simple harmonic motion, micro-doppler are sinusoidal form.According to this feature, the present invention using inverse Radon transform to time-frequency distributions into
Row processing, converts it to parameter space to realize parameter Estimation.Inverse Radon transform is normally used for being word image procossing neck
Domain, the spy that the sine curve for being located at picture centre can be converted into parameter space by it show point, and the position of the aobvious point of spy can be released
Sinusoidal parameter.Thus the method provided by the present invention utilize this method this characteristic, thus by Doppler curve into
It obtains estimating parameter accordingly after row processing.Inverse Radon transform method can be carried out by existing step.It specifically include following step
It is rapid:
If a sinusoidal two-dimentional expression formula in plane are as follows:
Wherein A is sinusoidal maximum value,For its first phase.
This includes the expression formula that sinusoidal image passes through inverse Radon transform are as follows:
By pushing over process as shown in formula (15), the expression of inverse Radon can will be passed through containing sinusoidal image
Formula, obtains parameter space figure, and the aobvious point of the spy for being included on parameter space figure respectively corresponds sinusoidal parameter.By above-mentioned change
It changes the point that sine curve can be converted to parameter space and then carries out parameter Estimation.The distance of i.e. special aobvious point to picture centre is positive
The maximum value of chord curve, the aobvious point of spy and the angle of picture centre line and image vertical line are sinusoidal first phase.Gained is special
Aobvious point position is equivalent to obtain micro-doppler value and first phase in fine motion parameter.Therefore, it can be incited somebody to action by inverse Radon transform
Problem is extracted in the position that fine motion target component estimation problem is converted into the aobvious point of inverse Radon transform field parameter space spy, can be direct
Estimation obtains micro-doppler value and first phase.
The method that the present invention is combined using time frequency analysis and inverse Radon transform, frequency division when being carried out to the signal after ambiguity solution
Analysis is to obtain complete time-frequency curve, the simple harmonic characteristic then moved according to fine motion target, using inverse Radon transform by sinusoidal time-frequency
Curve is transformed into the point of parameter space, to realize last parameter Estimation.
Terahertz wideband radar micro-doppler ambiguity solution method provided by the invention based on arteries and veins internal interference, based on dry in arteries and veins
The micro-doppler ambiguity solution related to, i.e., the wideband echoes signal after receiving wideband radar solution line frequency modulation mode are considered as several single-frequency
Echo-signal selects suitable difference frequency to be interfered, and the result of interference of all identical difference frequencies is added up, when finally carrying out
Frequency analysis and parameter extraction.It is different from traditional system level solution based on multichannel or multiple frequency, the method for the present invention
It is simple with realizing, do not increase the advantages such as system complexity；It is different from classical signal grade solution, this method has calculation amount
The features such as small, Robust Performance.
Preferably, several signals after interfering are added up to eliminate the influence of cross term, in practice in order to
Reach preferable cross term and inhibit purpose, suitable difference frequency signal is selected to carry out conjugate multiplication, so that carrier frequency is reduced to the two
The difference of carrier frequency, generally taking difference frequency signal in the implementation is the half of bandwidth, thus selecting interference difference frequency is B/2, in this case, such as
The each pulse of fruit has N number of sampling, just has N/2 group interference signal and adds up, cross term inhibitory effect is preferable.
Method provided by the invention is described in detail below in conjunction with specific example.
By taking a carrier frequency is the wideband radar system of 220GHz as an example, using rotating electric machine drive corner reflector as target,
Illustrate the validity of this method.System carrier frequency 221.59GHz in experiment, bandwidth 12.816GHz, pulse repetition period 1ms, i.e.,
PRF is 1000, and sampling number N is 4096 in each pulse, observes pulse number 8192.The rotation of two rotary reflectors
Radius is respectively 16cm and 24cm, and angular velocity of rotation setting value is 40r/min and 60r/min in experiment twice.This example is with thunder
It is illustrated for up to rolling target common in experimental system.Handled rolling target is as shown in figure 3, be the two of a four sides
Face angle structure has the scattering properties for being similar to ideal scattering point, can be considered as ideal point target in processes.
Under the above conditions, it is handled using method provided by the invention.Two corner reflectors when revolving speed is 40r/min
Micro-doppler theoretical value be respectively 990.08Hz and 1485.1Hz, the time-frequency of signal after wideband radar solution line frequency modulation mode receives
It is a) shown in distribution such as Fig. 4.The micro-doppler theoretical value of two corner reflectors is respectively 1485.1Hz when revolving speed is 60r/min
And 2227.7Hz, the time-frequency distributions such as the b in Fig. 4 of signal after wideband radar solution line frequency modulation mode receives) shown in.Revolving speed is 40r/
When min and 60r/min, the micro-doppler value of two corner reflectors is far more than PRF/2.
From the time-frequency distributions of Fig. 4 it is also seen that coming, since the micro-doppler value of rolling target is made considerably beyond PRF/2
At obscuring, complete sine curve is unable to get in time frequency distribution map.It is obtained after the method processing provided through the invention
The time frequency distribution map of interference signal is as shown in Figure 5.As can be seen that by arteries and veins internal interference processing after, rolling target it is micro- how general
Le value has been reduced 2fc/ B=34.58 times, it is fuzzy to occur micro-doppler in acquired results, can also from its time-frequency distributions
To find out complete sine curve.
It is as shown in Figure 6 to the parameter space after the time-frequency distributions progress inverse Radon transform after ambiguity solution.By inverse
Radon transformation extracts special aobvious point at a distance from picture centre, can estimate to obtain at 40r/min the micro- how general of two targets
Le value is 28.2Hz and 42.5Hz, multiplied by contracting than multiple 2fcMicro-doppler estimated value can be obtained after/B=34.58
975.157Hz and 1469.65Hz.
The micro-doppler value that two targets at 60r/min can be estimated to obtain is 42.4Hz and 64.7Hz, multiplied by contracting ratio
Multiple 2fcMicro-doppler estimated value 1466.192Hz and 2330.692Hz can be obtained after/B=34.58.
By estimated value it is found that parameter Estimation relative error of the invention demonstrates the present invention less than 2% compared with theoretical value
The validity of method.
Those skilled in the art will be clear that the scope of the present invention is not limited to example discussed above, it is possible to carry out to it
Several changes and modification, the scope of the present invention limited without departing from the appended claims.Although oneself is through in attached drawing and explanation
The present invention is illustrated and described in book in detail, but such illustrate and describe is only explanation or schematical, and not restrictive.
The present invention is not limited to the disclosed embodiments.
By to attached drawing, the research of specification and claims, those skilled in the art can be in carrying out the present invention
Understand and realize the deformation of the disclosed embodiments.In detail in the claims, term " includes " is not excluded for other steps or element,
And indefinite article "one" or "an" be not excluded for it is multiple.The certain measures quoted in mutually different dependent claims
The fact does not mean that the combination of these measures cannot be advantageously used.Any reference marker in claims is not constituted pair
The limitation of the scope of the present invention.
Claims (5)
1. a kind of Terahertz wideband radar micro-doppler ambiguity solution method based on arteries and veins internal interference, which is characterized in that including following
Step:
Step S100: the wideband echoes signal of fine motion target to be monitored is received using wideband radar solution line frequency modulation mode, to gained
After wideband echoes signal carries out residual video phase compensation, compensating wide band echo-signal is obtained；
Step S200: extracting the signal in the compensating wide band echo-signal one by one, to the frequency point of each signal extracted into
Line frequency interference, obtains multiple interference signals；
Step S300: time frequency analysis is carried out to the interference signal, obtains ambiguity solution micro-doppler curve, inverse Radon transform side
The method processing ambiguity solution micro-doppler curve obtains the fine motion estimation parameter of fine motion target to be monitored.
2. the Terahertz wideband radar micro-doppler ambiguity solution method according to claim 1 based on arteries and veins internal interference, special
Sign is, include thes steps that carrying out the interference signal in the step S200 cumulative.
3. the Terahertz wideband radar micro-doppler ambiguity solution method according to claim 2 based on arteries and veins internal interference, special
Sign is, interference difference frequency used is B/2 in the accumulation step, wherein B is signal bandwidth.
4. the Terahertz wideband radar micro-doppler solution mould described in any one of claim 1 to 3 based on arteries and veins internal interference
Formulating method, which is characterized in that the time frequency analysis is to be carried out using the Short Time Fourier Transform method in linear time-frequency distribution.
5. the Terahertz wideband radar micro-doppler ambiguity solution method according to claim 4 based on arteries and veins internal interference, special
Sign is that the fine motion target to be monitored is rolling target.
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| CN111427035A (en) * | 2020-03-25 | 2020-07-17 | 湖南国科锐承电子科技有限公司 | Radar actual measurement data set expansion method based on sub-band micro-Doppler difference |
| CN112147606B (en) * | 2020-09-23 | 2024-02-23 | 中国人民解放军国防科技大学 | Rotary target micro-motion feature extraction method and device based on multichannel radar |
| CN112150452B (en) * | 2020-09-30 | 2022-04-15 | 西南交通大学 | Millimeter wave imaging-based railway sleeper defect detection method |
| CN112462344B (en) * | 2020-11-12 | 2023-09-19 | 中国人民解放军空军预警学院 | Method for extracting characteristic parameters in radar signal pulse through time-frequency domain transformation processing |
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