CN106990405A - A kind of Vibration Targets feature extracting method based on slow temporal envelope - Google Patents

Abstract

A kind of Vibration Targets feature extracting method based on slow temporal envelope is provided, including：The first step：Radar produces linear FM signal waveform；Second step：The geometrical model of Airborne Dual-Channel SAR/DPCA fine motion target detections is set up, and dechirp and Range compress processing are carried out to obtained echo-signal, clutter cancellation processing is further carried out, obtains the slow temporal envelope of signal；3rd step：The modulus value of signal after clutter cancellation is extracted, the vibration performance of Vibration Targets is extracted according to the modulus value of slow temporal envelope.The Vibration Targets feature extracting method based on slow temporal envelope, on the basis of being suppressed using DPCA technologies to land clutter, the vibration frequency and amplitude in oscillation point are extracted by using STE, so can be without considering the integrality of micro-doppler curve with regard to the extraction of Vibration Targets vibration performance can be completed.

Description

A kind of Vibration Targets feature extracting method based on slow temporal envelope

Technical field

The present invention relates to Signal and Information Processing technology, and in particular to a kind of Vibration Targets feature based on slow temporal envelope Extracting method.

Background technology

Synthetic aperture radar (synthetic aperture radar, SAR) is due to round-the-clock, round-the-clock work Make ability, there is important application value in terms of area monitoring and battle reconnaissance.But SAR ground moving object is indicated (Ground Moving Target Indication, GMTI) technology can be only done to ground at the uniform velocity and even accelerated motional objects Effective detection, be difficult to realize to ground fine motion target（Radar antenna, the car engine of vibration such as rotation, Hovering Helicopter Rotor etc.）Effective detection.And target fine motion is characterized in target distinctive attribute in itself, contain reflection target identities mark Fine-feature, by the analysis and extraction to target fine motion feature, can effectively differentiate different ground sea-surface targets.Cause This, solving ground fine motion clarification of objective extractive technique turns into the major issue in SAR technical research.

For the test problems of fine motion target in ground in solution SAR technologies, R ü egg M etc. exist《Vibration and rotation in millimeter-wave SAR》(IEEE Trans. on Geoscience and Remote Sensing, 2007, 45(2):293-304), Zhang W etc. exist《Extraction of vibrating features with dual-channel fixed-receiver bistatic SAR》(IEEE Geoscience and Remote Sensing Letters, 2012, 9(3):Detection of the SAR technologies in ground fine motion target is proposed in 507-511) respectively Method, completes the detection of ground vibration target.But, foregoing ground fine motion mesh object detection method does not adapt to strong clutter, Because under strong clutter environment, strong clutter can be such that the echo-signal of Vibration Targets is submerged in strong clutter background, it is impossible to vibration Target is detected, it is possible to use DPCA (Displaced Phase Center Antenna, DPCA) skill Art can effectively suppress land clutter, and then pass through the characteristic information of Time-Frequency Analysis Method acquisition Vibration Targets.But, DPCA skills Art is while land clutter is suppressed, slow temporal envelope (Slow Time Envelope, STE) item of Vibration Targets echo-signal Also it can be affected, STE can influence the Energy distribution of fine motion target micro-doppler curve, cause micro-doppler curve endless Whole, the feature of Vibration Targets is extracted in influence using micro-doppler curve.

The content of the invention

It is a kind of based on slow temporal envelope it is an object of the invention to overcome above-mentioned weak point of the prior art to propose Vibrational feature extracting method.

The present invention is realized in the following way：

A kind of Vibration Targets feature extracting method based on slow temporal envelope, comprises the following steps：

The first step：Radar produces linear FM signal waveform；

Second step：The geometrical model of Airborne Dual-Channel SAR/DPCA fine motion target detections is set up, and obtained echo-signal is entered Row dechirp and Range compress processing, further carry out clutter cancellation processing, obtain the slow temporal envelope of signal；

3rd step：The modulus value of signal after clutter cancellation is extracted, it is special according to the vibration that the modulus value of slow temporal envelope extracts Vibration Targets Levy.

The first step is specially：

The expression formula of the linear FM signal of radar emission is：

(1)

In formula：For rectangular window function, whenWhen,,When,；For carrier frequency,For the chirp rate of signal, the pulse duration is, bandwidth, letter Number cycle is T_r；For the fast time,For the slow time,,,Represent transmitting is the Individual signal,For full-time, triadic relation is：。

The second step is specially：

Two transceiver channel A are being placed along course-and-bearing₁And A₂, A₂In A₁Front, two passages alternately transmitting and receive letter Number, the pulse repetition period of each passage is 2T_r, the pulse repetition period of whole system is T_r；The distance between two passage antennas For d, and meet：

(2)

In formula：For the flying speed of carrier aircraft；

Antenna A₂The echo-signal and antenna A received in t₁ () reception arrive echo letter Number phase center is overlapped just,For antenna A₁Antenna A is moved to from current location₂Time required for position, two The echo-signal for the static ground target that receiving channel is received can be completed to offset, and the information of moving target is retained.

The second step is specially：

The Vibration Targets point P that scene orientation center is present is observed, amplitude is A_v, vibration frequency is f_v（Angular frequency）, initial phase is, the distance between the centre of oscillation and radar platform are R₀, intended vibratory direction is put down with xoy The angle in face is, direction of vibration xoy planes projection withAxle clamp angle is, the flying speed of carrier aircraft is, oscillation point P With antenna A₁、A₂Between instantaneous oblique distance can be expressed as、：

(3)

(4)

Wherein, t_mThe slow time is represented,Represent oscillation point along distance to amplitude, Amplitude of the oscillation point along orientation is represented,

According to oscillation point P and antenna A₁、A₂Between instantaneous oblique distance can obtain the echo-signal of Vibration Targets, two passages are connect The echo-signal of receipts is through dechirp processing, and after row distance of going forward side by side compression, echo-signal can be expressed as、：

(5)

(6)

Wherein,For constant,For signal wavelength,

Two-way echo-signal is handled using DPCA methods, completes to offset in initial data domain, i.e.,：

(7)

Wherein：

(8)

, from formula (7), after two passage difference frequency signals are handled through DPCA, include one and slow timeRelevant envelope, i.e., slow temporal envelope (STE) item；This will influence the echo difference frequency signal after clutter cancellation Energy distribution, and work as, i.e.,,When, envelope is zero, that is, works as vibration Point vibration frequency will be simultaneously suppressed when meeting above-mentioned relation formula with static land clutter, to avoid the generation of such case, should be use up Amount improves carrier aircraft speed v, reduces the distance between dual-mode antenna d, under far field condition, STE can be approximately further：

(9)

3rd step is specially：

Slow temporal envelope is analyzed, after echo difference frequency signal is handled through DPCA, slow temporal envelope equally includes Vibration Targets Characteristic information, formula (7) modulus is obtained：

(10)

Wherein,；After being handled through modulus, the STE of range cell believes for the cycle where oscillation point Number, therefore it is represented by the form of Fourier space：

(11)

Wherein,,,For the coefficient of Fourier space：

(12)

(13)

WithThe respectively cycle of formula (11) and first harmonic angular frequency, and；Oscillation point vibration frequency can pass through Fourier transformation is carried out to the STE after modulus, it is to vibrate two times of dot frequency to extract first harmonic frequency, formula (10) it is discrete Form is represented by：

(14)

Wherein m is integer,For slow time sampling interval, from formula (14), STE modulus value is SIN function and cosine function The compound function of composition, is modulated by cosine function, and the value in SIN function existsBetween change, STE curves Form withValue it is relevant.

The m values rule is as follows：

When the time interval between two neighboring maximum of points is equal with STE cycle, i.e.,, sentence It is set to；When the time interval between two neighboring maximum of points is less than STE cycle, i.e.,, it is determined as。

The extracting method of the oscillation point amplitude is specially：

When, in this case, the maximum of STE modulus value is：

(15)

Wherein maximum of points positionMeet,, and in STE a cycles Only comprising a maximum of points, i.e.,

(16)

Extract STE another locations pointValue：

(17)

Wherein, take, then,Expression is approximately rounded Computing, definitionPosition be STE median point, formula (15) and the ratio of (17) are：

(18)

According to formula (18), oscillation point distance can be estimated to amplitude by following formula：

(19)

The extracting method of the oscillation point amplitude is specially：

When, in this case, the maximum of points of STE modulus value is：

(20)

Wherein,Meet,, and have

(21)

Under this condition, in a cycle, in addition to maximum of points, also comprising a minimum point in STE curves（Or maximum Point）, it is assumed that the position of the point is, then meet,

Analysis has following relational expression more than：

(22)

Wherein,, therefore, oscillation point distance can be estimated to amplitude by following formula：

(23)

For DPCA technologies can influence to extract using micro-doppler curve when suppressing land clutter Vibration Targets feature this One problem, the present invention using DPCA technologies to land clutter on the basis of being suppressed, by analyzing Vibration Targets echo-signal STE items, the vibration performance that oscillation point is also included in STE is drawn, so as to propose using STE to extract the vibration in oscillation point The method of frequency and amplitude, so can be special with regard to that can complete Vibration Targets vibration without analyzing the micro-doppler curve of Vibration Targets The extraction levied, so that the problem of solving the Vibration Targets feature extraction under strong clutter environment.

Brief description of the drawings

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

Fig. 2 shows Airborne Dual-Channel SAR/DPCA geometrical models；

Fig. 3 shows m₀With m_kRelation schematic diagram；

Fig. 4 (a), Fig. 4 (b) and Fig. 4 (c) show that DPCA clutter recognitions are analyzed, and wherein Fig. 4 (a) shows to offset prepass A₁Spectrogram, Fig. 4 (b) shows to offset rear spectrogram, and Fig. 4 (c) shows to offset rear spectrogram --- partial enlargement；

Fig. 5 (a) and Fig. 5 (b) show the extraction of vibration frequency, and wherein Fig. 5 (a) shows the slow time frequency spectrums of point P, and Fig. 5 (b) is shown a little The slow time frequency spectrums of Q；

Fig. 6 (a) and Fig. 6 (b) show extraction of the distance to amplitude, and wherein Fig. 6 (a) shows point P STE curves, and Fig. 6 (b) is shown Point Q STE curves；

Fig. 7 (a) and Fig. 7 (b) show amplitude estimation error analysis, and wherein Fig. 7 (a) shows the unitary mismatch, and Fig. 7 (b) shows to return One changes RMSE.

Embodiment

Below in conjunction with the accompanying drawings with the example of the present invention, the invention will be further described.

As shown in figure 1, the present invention is realized through the following steps：Launched using Airborne Dual-Channel antenna and receive signal, Dechirp and Range compress processing are carried out to the echo-signal received, clutter cancellation processing further is carried out to signal, to miscellaneous The signal modulus that ripple is offseted after processing obtains the slow temporal envelope of signal, by being carried to slow temporal envelope as Fourier transformation Take out the vibration frequency of target；The amplitude of target is extracted by the modulus value progress processing to slow temporal envelope；Illustrate as Under：

The first step：Radar produces linear FM signal waveform；

The expression formula of the linear FM signal of radar emission is：

(1)

In formula：For rectangular window function, whenWhen,,When,；For carrier frequency,For the chirp rate of signal, the pulse duration is, bandwidth, letter Number cycle is T_r；For the fast time,For the slow time,,,Represent transmitting is theIndividual signal,For full-time, triadic relation is：。

Second step：The geometrical model of Airborne Dual-Channel SAR/DPCA fine motion target detections is set up, and obtained echo is believed Number dechirp and Range compress processing are carried out, further carry out clutter cancellation processing, obtain the slow temporal envelope of signal；

The geometrical model of Airborne Dual-Channel SAR/DPCA fine motion target detections is as shown in Figure 2；Two receipts are being placed along course-and-bearing Send out passage A₁And A₂, A₂In A₁Front, two passages alternately transmitting and receive signal, and the pulse repetition period of each passage is 2T_r, the pulse repetition period of whole system is T_r；The distance between two passage antennas are d, and are met：

(2)

In formula：For the flying speed of carrier aircraft；

So, antenna A₂The echo-signal and antenna A received in t₁ () reception arrives Echo-signal phase center is overlapped just,For antenna A₁Antenna A is moved to from current location₂Required for position when Between；So, the echo-signal for the static ground target that two receiving channels are received can be completed to offset, and the information of moving target is obtained To retain；

Assuming that scene orientation center has a Vibration Targets point P, amplitude is A_v, vibration frequency is f_v（Angular frequency）, initial phase is, the distance between the centre of oscillation and radar platform are R₀；Put down with xoy in intended vibratory direction The angle in face is, direction of vibration xoy planes projection withAxle clamp angle is, the flying speed of carrier aircraft is, oscillation point P With antenna A₁、A₂Between instantaneous oblique distance can be expressed as、：

(3)

(4)

Wherein, t_mThe slow time is represented,Represent oscillation point along distance to amplitude,Represent amplitude of the oscillation point along orientation；

According to oscillation point P and antenna A₁、A₂Between instantaneous oblique distance can obtain the echo-signal of Vibration Targets, two passages are connect The echo-signal of receipts is through dechirp processing, and after row distance of going forward side by side compression, echo-signal can be expressed as、：

(5)

(6)

Wherein,For constant,For signal wavelength；

Two-way echo-signal is handled using DPCA methods, completes to offset in initial data domain, i.e.,：

(7)

Wherein：

(8)

, from formula (7), after two passage difference frequency signals are handled through DPCA, include one and slow timeRelevant envelope, i.e., slow temporal envelope (STE) item, this will influence clutter cancellation after echo difference frequency signal Energy distribution, and work as, i.e.,,When, envelope is zero；Work as vibration Point vibration frequency will be simultaneously suppressed when meeting above-mentioned relation formula with static land clutter；To avoid the generation of such case, it should use up Amount improves carrier aircraft speed v, reduces the distance between dual-mode antenna d.Under far field condition, STE can be approximately further：

(9)

3rd step：The modulus value of signal after clutter cancellation is extracted, it is special according to the vibration that the modulus value of slow temporal envelope extracts Vibration Targets Levy；

By the analysis to slow temporal envelope it can be found that after echo difference frequency signal is handled through DPCA, slow temporal envelope is equally wrapped Characteristic information containing Vibration Targets, is obtained to formula (7) modulus：

(10)

Wherein,；After being handled through modulus, the STE of range cell believes for the cycle where oscillation point Number, therefore it is represented by the form of Fourier space：

(11)

Wherein,,,For the coefficient of Fourier space：

(12)

(13)

WithThe respectively cycle of formula (11) and first harmonic angular frequency, and；Therefore, oscillation point vibration frequency Can be by carrying out Fourier transformation to the STE after modulus, it is vibrate dot frequency two times, formula (10) to extract first harmonic frequency Discrete form be represented by：

(14)

Wherein m is integer,For slow time sampling interval；From formula (14), STE modulus value is SIN function and cosine function The compound function of composition, is modulated by cosine function, and the value in SIN function existsBetween change, therefore STE Curve form withValue it is relevant, the extracting method of oscillation point amplitude is discussed in two kinds of situation below：

Case 1：；In this case, the maximum of STE modulus value is：

(15)

Wherein maximum of points positionMeet,；And in STE a cycles Only comprising a maximum of points, i.e.,

(16)

Extract STE another locations pointValue：

(17)

Wherein, take, then,Expression is approximately rounded Computing；DefinitionPosition be STE median point, formula (15) and the ratio of (17) are：

(18)

According to formula (18), oscillation point distance can be estimated to amplitude by following formula：

(19)

Case 2：；In this case, the maximum of points of STE modulus value is：

(20)

Wherein,Meet,, and have

(21)

Under this condition, in a cycle, in addition to maximum of points, also comprising a minimum point in STE curves（Or maximum Point）, it is assumed that the position of the point is, then meet；WithRelation it is as shown in Figure 3；

Analysis has following relational expression more than：

(22)

Wherein,；Therefore, oscillation point distance can be estimated to amplitude by following formula：

(23)

For the judgement of both the above situation, it can be sentenced by the time interval between the STE curve maximums point to extraction It is disconnected；When the time interval between two neighboring maximum of points is equal with STE cycle, i.e.,, judge For Case 1；If less than STE cycle, i.e.,, then it is determined as Case 2.

For DPCA technologies can influence to extract using micro-doppler curve when suppressing land clutter Vibration Targets feature this One problem, the present invention using DPCA technologies to land clutter on the basis of being suppressed, by analyzing Vibration Targets echo-signal STE items, the vibration performance that oscillation point is also included in STE is drawn, so as to propose using STE to extract the vibration in oscillation point The method of frequency and amplitude, so can be special with regard to that can complete Vibration Targets vibration without analyzing the micro-doppler curve of Vibration Targets The extraction levied.

Example：Multiple target method for parameter estimation

Emulation experiment：Airborne Dual-Channel SAR/DPCA geometrical models are as shown in Fig. 2 radar parameter is set to：Carrier frequency 35GHz, arteries and veins Rush repetition time 0.1ms, bandwidth 150MHz, sample frequency 0.4MHz.Platform speed is 30m/s, and the synthetic aperture time is 0.8s. Scene includes three vibration point targets and 7 static point targets, and oscillation point parameter is as shown in table 1.Noise is added in emulation Than the white Gaussian noise for -3dB.

The oscillation point parameter of table 1

Oscillation point（Parameter）					()
						P	11950m	0	0	10Hz	3mm(3mm)
Q	11994m	0		15Hz	3mm(1.5mm)
						R	12039m	0		30Hz	3mm(0)

Fig. 4 (a), Fig. 4 (b) and Fig. 4 (c) give echo-signal distance-spectrogram contrast of slow time before and after DPCA clutter recognitions.Its Middle Fig. 4 (a) is clutter recognition prepass distance-slow time spectrogram, wherein not only include Vibration Targets point information, in addition to it is quiet Only target point information；Fig. 4 (b) is distance-slow time spectrogram that back echo difference frequency signal is handled through DPCA clutter recognitions, through DPCA Land clutter is eliminated after processing, only remains Vibration Targets point information.And it is only capable of intuitively observing two in Fig. 4 (b) directly Line, i.e. oscillation point P and oscillation point Q distance-slow time spectrogram, are the target point vibrated along orientation, its time due to oscillation point R Wave energy is very weak, has almost been submerged in noise.It can be seen that by the partial enlarged drawing for offseting rear distance-slow time spectrogram, two Straight line shows as light and dark discontinuous straight line, i.e., influenceed by STE, and the amplitude of spectrogram cathetus is also to change over time 's.

Vibration Targets point STE modulus value to extraction carries out FFT calculating vibration frequencies, and such as Fig. 5 (a) and Fig. 5 (b) are shown.Fig. 5 (a) the echo STE modulus value frequency spectrums for being oscillation point P, Fig. 5 (b) is oscillation point Q echo STE modulus value frequency spectrums.First harmonic in frequency spectrum The vibration frequency of as two target points of 1/2nd of corresponding Frequency point, respectively 10Hz and 15Hz, it is consistent with theoretical value.

Shown in STE curves such as Fig. 6 (a) and Fig. 6 (b) of two target points, to improve extraction accuracy, STE curves are carried out 2.5 times of interpolation processing.Because be present white Gaussian noise in echo-signal and can not be suppressed by clutter cancellation, STE's Amplitude is influenceed by certain, but the variation tendency of whole STE curves and is not affected by too big influence, smooth using convolution herein The method of processing, is smoothed to STE curves, to extract the maximum of points and minimum point of curve（Or maximum point）Deng Information.Fig. 6 (a) is the STE curves of P points, extracts the maximum of points of curve, is calculated between the time between two neighboring maximum of points 0.025s is divided into, less than the cycle 0.05s of STE modulus value, therefore, it is determined that being Case2, the minimum point position of curve is further extracted Put, the average for calculating P point amplitudes according to formula (23) is 2.98mm；Fig. 6 (b) is the STE modulus value curves of Q points, extracts curve most Big value point, the time interval calculated between two neighboring maximum of points is 0.034s, is approximately equal to STE modulus value cycle 0.033s, because This is determined as Case 1, further extracts curve median point position and amplitude information, and calculating Q point amplitude averages according to formula (19) is 1.38mm.Two oscillation point distances for being computed obtaining are closer to amplitude with theoretical value.

Amplitude estimation error is analyzed below, 200 Monte-Carlo emulation experiments, letter are carried out to amplitude estimation Make an uproar than changing from -5dB to 5dB.The unitary mismatch and normalized mean squared error (root mean of two oscillation point amplitude estimations Square error, RMSE) as shown in Fig. 7 (a) and Fig. 7 (b).Fig. 7 (a) is inclined for the normalization of two oscillation point amplitude estimations Difference, Fig. 7 (b) is the normalized mean squared error of two oscillation point amplitude estimations.The unitary mismatch of two oscillation point amplitude estimations It is very small with normalization RMSE, show to improve the validity of dynamic point amplitude extraction method herein.

Simultaneously it can be seen that oscillation point P amplitude estimation value precision of the amplitude estimation value than oscillation point Q is higher, this is due to Maximum of points and the positional information of minimum point need to be only extracted when calculating P point amplitudes, and not only needs to carry when calculating Q point amplitudes Take maximum of points and intermediate value dot position information, in addition it is also necessary to its range value, and it is difficult that to extract its true that STE amplitudes are affected by noise Real range value, therefore, extraction accuracy is subject to certain restrictions.

The inventive method using DPCA technologies to land clutter on the basis of being suppressed, by analyzing Vibration Targets echo The STE items of signal, draw the vibration performance that oscillation point is also included in STE, so as to propose using STE to extract oscillation point The method of vibration frequency and amplitude, so can be without analyzing the micro-doppler curve of Vibration Targets with regard to that can complete vibration performance Extract, so that the problem of solving the Vibration Targets feature extraction under strong clutter environment.

Claims (8)

1. a kind of Vibration Targets feature extracting method based on slow temporal envelope, comprises the following steps：

The first step：Radar produces linear FM signal waveform；

Second step：The geometrical model of Airborne Dual-Channel SAR/DPCA fine motion target detections is set up, and obtained echo-signal is entered Row dechirp and Range compress processing, further carry out clutter cancellation processing, obtain the slow temporal envelope of signal；

3rd step：The modulus value of signal after clutter cancellation is extracted, it is special according to the vibration that the modulus value of slow temporal envelope extracts Vibration Targets Levy.

2. the Vibration Targets feature extracting method according to claim 1 based on slow temporal envelope, the first step is specific For：

The expression formula of the linear FM signal of radar emission is s (t_m,t_k)：

$s(t_m,t_k)=rect\left(\frac{t_k}{T_p}\right)\exp \left(j2\mathrm{\π}\right(f_{c}t+\frac{1}{2}{\mathrm{\μt}}_k^2\left)\right)---\left(1\right)$

In formula：rect(t_k/T_p) it is rectangular window function, when | t_k|≤T_pWhen/2, rect (t_k/T_p)=1, | t_k|>T_pWhen/2, rect (t_k/T_p)=0；f_cFor carrier frequency, μ is the chirp rate of signal, and the pulse duration is T_p, bandwidth B=μ T_p, the signal period is T_r； t_kFor fast time, t_mFor slow time, t_m=(m-1) T_r, (m=1,2 ...), what m represented transmitting is m-th of signal, and t is full-time Between, triadic relation is：T=t_k+t_m。

3. the Vibration Targets feature extracting method according to claim 1 based on slow temporal envelope, the second step is specific For：

Two transceiver channel A are being placed along course-and-bearing₁And A₂, A₂In A₁Front, two passages alternately transmitting and receive signal, The pulse repetition period of each passage is 2T_r, the pulse repetition period of whole system is T_r；The distance between two passage antennas are D, and meet：

D=MT_rV (M=1,3,5...) (2)

In formula：V is the flying speed of carrier aircraft；

Antenna A₂The echo-signal and antenna A received in t₁In t+ τ_d(τ_d=MT_r) the echo-signal phase that arrives of reception Position center is overlapped just, τ_dFor antenna A₁Antenna A is moved to from current location₂Time required for position, two receive logical The echo-signal for the static ground target that road is received can be completed to offset, and the information of moving target is retained.

4. the Vibration Targets feature extracting method according to claim 3 based on slow temporal envelope, the second step is specific For：

The Vibration Targets point P that scene orientation center is present is observed, amplitude is A_v, vibration frequency is f_v(angular frequency_v=2 π f_v), initial phase is θ₀, the distance between the centre of oscillation and radar platform are R₀, the angle of intended vibratory direction and xoy planes For α, direction of vibration is β in the projection of xoy planes and y-axis angle, and the flying speed of carrier aircraft is v, oscillation point P and antenna A₁、A₂It Between instantaneous oblique distance can be expressed as R₁(t_m；R₀)、R₂(t_m；R₀)：

$R_1(t_m;R_0)=R_0+A_{r}sin({\mathrm{\ω}}_v{t}_m+{\mathrm{\θ}}_0)+\frac{{({\mathrm{vt}}_m-A_{a}sin({\mathrm{\ω}}_v{t}_m+{\mathrm{\θ}}_0\left)\right)}^2}{2R_0}---\left(3\right)$

$R_2(t_m;R_0)=R_0+A_{r}sin({\mathrm{\ω}}_v{t}_m+{\mathrm{\θ}}_0)+\frac{{({\mathrm{vt}}_m+d-A_{a}sin({\mathrm{\ω}}_v{t}_m+{\mathrm{\θ}}_0\left)\right)}^2}{2R_0}---\left(4\right)$

Wherein, t_mRepresent slow time, A_r=A_vCos α cos β represent oscillation point along distance to amplitude, A_a=A_vCos α sin β are represented Amplitude of the oscillation point along orientation,

According to oscillation point P and antenna A₁、A₂Between instantaneous oblique distance can obtain the echo-signal of Vibration Targets, two passages are connect The echo-signal of receipts is through dechirp processing, and after row distance of going forward side by side compression, echo-signal can be expressed as S₁(t_m+τ_d)、S₂ (t_m)：

$S_1(t_m+{\mathrm{\τ}}_d)={\mathrm{\σ}}_P\exp (-j\frac{4{\mathrm{\πR}}_1(t_m+{\mathrm{\τ}}_d;R_0)}{\mathrm{\λ}})---\left(5\right)$

$S_2\left(t_m\right)={\mathrm{\σ}}_P\exp (-j\frac{4{\mathrm{\πR}}_2(t_m;R_0)}{\mathrm{\λ}})---\left(6\right)$

Wherein, σ_PFor constant, λ is signal wavelength,

Two-way echo-signal is handled using DPCA methods, completes to offset in initial data domain, i.e.,：

$\begin{array}{c}{S}_{DPCA}(f_r,t_m)=S_1(t_m+{\mathrm{\τ}}_d)-S_2\left(t_m\right)\\ ={\mathrm{\σ}}_{P}P\left(t_m\right)\exp \left(j\right(\frac{\mathrm{\π}}{2}-\frac{2\mathrm{\π}\left(R_1\right(t_m+{\mathrm{\τ}}_d;R_0)+R_2(t_m;R_0\left)\right)}{\mathrm{\λ}}\left)\right)\end{array}---\left(7\right)$

Wherein：

$P\left(t_m\right)=-2\sin \left(\left(\frac{4{\mathrm{\πA}}_r}{\mathrm{\λ}}+\frac{{\mathrm{\πA}}_a}{{\mathrm{\λR}}_0}\left(2{\mathrm{vt}}_m+d\right)\right)\sin \left(\frac{{\mathrm{\ω}}_v{\mathrm{\τ}}_d}{2}\right)\cos \left({\mathrm{\ω}}_v{t}_m+{\mathrm{\θ}}_0^{\′}\right)\right)---\left(8\right)$

θ′₀=ω_vτ_d/2+θ₀, from formula (7), after two passage difference frequency signals are handled through DPCA, include one and slow time t_mHave The envelope P (t of pass_m), i.e., slow temporal envelope (STE) item；This will influence the energy of the echo difference frequency signal after clutter cancellation Distribution, and as sin (ω_vτ_d/ 2)=0, i.e. f_v=nv/d, n=1,2, when 3 ..., envelope is zero, i.e., when oscillation point vibration frequency To simultaneously it be suppressed with static land clutter when meeting above-mentioned relation formula, to avoid the generation of such case, should try one's best raising carrier aircraft Speed v, reduces the distance between dual-mode antenna d, under far field condition, STE can be approximately further：

$P\left(t_m\right)\≈-2\sin \left(\frac{4{\mathrm{\πA}}_r}{\mathrm{\λ}}\sin \left(\frac{{\mathrm{\ω}}_v{\mathrm{\τ}}_d}{2}\right)\cos \left({\mathrm{\ω}}_v{t}_m+{\mathrm{\θ}}_0^{\′}\right)\right)---\left(9\right)$

5. the Vibration Targets feature extracting method according to claim 1 based on slow temporal envelope, the 3rd step is specific For：

Slow temporal envelope is analyzed, after echo difference frequency signal is handled through DPCA, slow temporal envelope equally includes Vibration Targets Characteristic information, formula (7) modulus is obtained：

|S_DPCA(t_m)|≈σ_P|P(t_m) |=2 σ_P|sin(A_rCcos(ω_vt_m+θ′₀))| (10)

Wherein, C=4 π sin (ω_vτ_d/2)/λ；After being handled through modulus, the STE of range cell where oscillation point is periodic signal, because This is represented by the form of Fourier space：

$\left|S_{DPCA}\left(t_m\right)\right|=\frac{a_0}{2}+\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{a}_{n}cos\left({\mathrm{n\ωt}}_m\right)+\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{b}_{n}sin\left({\mathrm{n\ωt}}_m\right)---\left(11\right)$

Wherein, a₀, a_n, b_nFor the coefficient of Fourier space：

$a_n=\frac{2}{T}{\∫}_{-\frac{T}{2}}^{\frac{T}{2}}\left|S_{DPCA}\left(t_m\right)\right|cos\left({\mathrm{n\ωt}}_m\right){\mathrm{dt}}_m,(n=0,1,2...)---\left(12\right)$

$b_n=\frac{2}{T}{\∫}_{-\frac{T}{2}}^{\frac{T}{2}}\left|S_{DPCA}\left(t_m\right)\right|\sin \left({\mathrm{n\ωt}}_m\right){\mathrm{dt}}_m,(n=1,2...)---\left(13\right)$

T and ω are respectively cycle and the first harmonic angular frequency of formula (11), the ω of and ω=2_v；Oscillation point vibration frequency can be by right STE after modulus carries out Fourier transformation, and it is vibrate dot frequency two times, the discrete shape of formula (10) to extract first harmonic frequency Formula is represented by：

|S_DPCA(m) |=2 σ_P|sin(A_rCcos(ω_vmΔ_t+θ′₀))| (14)

Wherein m is integer, Δ_tFor slow time sampling interval, from formula (14), STE modulus value is SIN function and cosine function group Into compound function, modulated by cosine function, the value in SIN function is in [- A_rC A_rC] between change, STE curve forms with A_rC value is relevant.

6. the Vibration Targets feature extracting method according to claim 5 based on slow temporal envelope, the m values rule is such as Under：

When the time interval between two neighboring maximum of points is equal with STE cycle, i.e. (m_l-m_l-1)Δ_t=T, is determined as | A_rC|≤π/2；When the time interval between two neighboring maximum of points is less than STE cycle, i.e., | (m_k-m_k-1)|Δ_t<T, sentences It is set to | A_rC|>π/2。

7. the Vibration Targets feature extracting method according to claim 6 based on slow temporal envelope, the oscillation point amplitude Extracting method be specially：

When | A_rC |≤pi/2, in this case, the maximum of STE modulus value is：

|S_DPCA(m₁)|_max=2 σ_P|sin(A_rC)| (15)

Wherein maximum of points position m_lMeet cos (ω_vm_lΔ_t+θ′₀)=± 1, l=1,2 ..., and only wrapped in STE a cycles Containing a maximum of points, i.e.,

(m_l-m_l-1)Δ_t=T (16)

Extract STE another location point m_aValue：

WhereinTakeThen m_a=[m_l+π/(3ω_vΔ_t)], [] represents approximately to round fortune Calculate, define m_aPosition be STE median point, formula (15) and the ratio of (17) are：

$S_{ratio}=\frac{|S_{DPCA}\left(m_a\right){|}_{max}}{|S_{DPCA}\left(m_l\right){|}_{mid}}=\frac{2{\mathrm{\&sigma;}}_P\left|sin\left(A_{r}C\right)\right|}{2{\mathrm{\&sigma;}}_P\left|\sin (A_{r}C/2)\right|}=2cos(A_{r}C/2)---\left(18\right)$

According to formula (18), oscillation point distance can be estimated to amplitude by following formula：

$A_r=\frac{2\arccos \left(S_{ratio}/2\right)}{\left|C\right|}---\left(19\right).$

8. the Vibration Targets feature extracting method according to claim 6 based on slow temporal envelope, the oscillation point amplitude Extracting method be specially：

When | A_rC|>Pi/2, in this case, the maximum of points of STE modulus value is：

|S_DPCA(m_k)|_max=2 σ_P (20)

Wherein, m_kMeet A_rCcos(ω_vm_kΔ_t+θ′₀)=± (2k-1) pi/2, k=1,2 ..., and have

|(m_k-m_k-1)|Δ_t<T (21)

Under this condition, in a cycle, in addition to maximum of points, also comprising minimum point (or maximum in STE curves Point), it is assumed that the position of the point is m₀, then cos (ω are met_vm₀Δ_t+θ′₀)=± 1,

Analysis has following relational expression more than：

$\left|A_{r}Ccos\left({\mathrm{\&omega;}}_v{m}_{\mathrm{\&Delta;}}{\mathrm{\&Delta;}}_t\right)\right|=\frac{(2k-1)\mathrm{\&pi;}}{2}---\left(22\right)$

Wherein, m_Δ=m_k-m₀, therefore, oscillation point distance can be estimated to amplitude by following formula：

$A_r=\frac{\left(2k-1\right)\mathrm{\&pi;}}{2\left|C\cos \left({\mathrm{\&omega;}}_v{m}_{\mathrm{\&Delta;}}{\mathrm{\&Delta;}}_t\right)\right|}---\left(23\right)$