CN103630899A - Method for high-resolution radar compressed sensing imaging of moving object on ground - Google Patents

Abstract

The invention provides a method for high-resolution radar compressed sensing imaging of a moving object on ground. The method obtains relatively accurate imaging results and speed and position information of azimuth of the moving object on the basis of greatly compressing ground motion target echo data, and provides important information for accurate identification of the moving object on ground.

Description

The method of ground moving object high resolution radar compressed sensing imaging

Technical field

The present invention relates to remote sensing and radar imagery technical field, relate in particular to the method for a kind of ground moving object high resolution radar compressed sensing imaging.

Background technology

That synthetic-aperture radar (Synthetic Aperture Radar, SAR) can realize is round-the-clock, the ground static target imaging of round-the-clock, high-gain, is specially by the design of bandwidth signals frequency band and realizes distance to high-resolution; By the motion of carrier of radar platform, thereby form equivalently very long linear array in space, realize orientation to high-resolution.Yet in a lot of Military Application situations, in observation scene, not only there is static target, also have some moving targets.Traditional SAR does not possess the detection of moving target and imaging capability, and moving target can only be superimposed upon with the form defocusing on static target image.There is moving-target perpendicular to the course speed component position of orientation on static target SAR image and will depart from its true bearing position, have along the moving-target of course speed component and on static target SAR image, will occur that orientation is to blooming effect.

Utilize SAR to obtain moving object detection and imaging results has become current military and civilian area research focus.Yet along with improving constantly of SAR precision, the echo data amount of moving target is sharply increased.Huge data volume has proposed very high requirement to the storage capacity of system, is also a very large challenge to the transmittability of data channel simultaneously.Guaranteeing high-quality motive target imaging result and accurately estimating under the prerequisite of kinematic parameter how significantly to reduce echo data amount and be of great significance for the development tool of SAR motive target imaging and detection technique.

Summary of the invention

(1) technical matters that will solve

For solving above-mentioned one or more problems, the invention provides the method for a kind of ground moving object high resolution radar compressed sensing imaging, so that the formation method in a kind of applicable data compression situation to be provided.

(2) technical scheme

According to an aspect of the present invention, provide the method for a kind of ground moving object high resolution radar compressed sensing imaging, the method comprises: steps A, the complex radical band echoed signal of data receiver to terrain object in imaging region

with

utilize distance to pulse compression and offset to process and obtain the signal that comprises moving target information

step B, data receiver is to the described signal that comprises moving target information

carry out the down-sampled compression of data Random sparseness and process, adopt random Gaussian observing matrix as the observing matrix of the down-sampled compression of data, obtain the signal after compression

and the signal after this compression is sent to data processing end; Step C, data processing termination is received the signal after described compression

according to it at fractional Fourier transform FRFT matrix Ψ _αunder sparse property and Minimum Entropy criteria, utilize compressed sensing algorithm reconstruct Y _α, obtain optimum anglec of rotation α and corresponding optimal result Y _α, determine speed and the positional information of moving target.

(3) beneficial effect

From technique scheme, can find out, in the method for ground moving object high resolution radar compressed sensing of the present invention imaging, excessive for Ground moving target imaging data volume, be not easy to the problem of data storage and transmission, propose to obtain down-sampled data and realize motive target imaging in conjunction with the motive target imaging algorithm based on compressed sensing along orientation to carrying out Random sparseness sampling.Than conventional motion target imaging, can significantly reduce the echo data amount of ground moving object.

Accompanying drawing explanation

Fig. 1 be the single-emission and double-receiving radar antenna that adopts of the embodiment of the present invention and with the geometric relationship figure of moving target;

Fig. 2 is that LFM signal is at the distribution plan of time-frequency domain and fractional order;

Fig. 3 is the process flow diagram of ground moving object high resolution radar compressed sensing formation method;

Fig. 4 is echo data amplitude and the result figure that disappears mutually, wherein:

Fig. 4 A is that antenna echo that A receives is in the map of magnitudes of the slow time domain of distance;

Fig. 4 B is the map of magnitudes that two passage clutters offset back echo signal;

Fig. 4 C does not process to velocity compensation through orientation, directly utilizes doppler frequency rate corresponding to static target to carry out the result that orientation pulse compression obtains;

Fig. 4 D is the result of directly utilizing Fourier Transform of Fractional Order to process;

Fig. 5 be the embodiment of the present invention to motive target imaging result figure, wherein:

Shown in Fig. 5 A is that ratio of compression η is 75% result;

Fig. 5 B is the result that the range unit search at moving target P1 place is obtained;

Fig. 5 C is the result that the range unit search at moving target P2 place is obtained;

Fig. 5 D is two imaging results that moving target is final.

Embodiment

For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.It should be noted that, in accompanying drawing or instructions description, similar or identical part is all used identical figure number.The implementation that does not illustrate in accompanying drawing or describe is form known to a person of ordinary skill in the art in affiliated technical field.

Consider that ground static target and clutter offset and in the echo data after processing, only have moving target signal, and the moving target quantity in observation scene is limited, therefore Moving Target Return signal meets the requirement of sparse property, thereby adopts the echoed signal after compressive sensing theory compressing data to carry out imaging and parameter estimation processing.Compressive sensing theory is pointed out, if signal is sparse or sparse at certain transform domain, available one projects to lower dimensional space with the incoherent observing matrix of transform-based by high dimensional signal, can be with high probability reconstruct original signal from low-dimensional observation by solving-optimizing problem.Can say that CS theory is to utilize intelligence sample to replace traditional signal sampling, so sampling rate no longer determines by signal bandwidth, but depend on structure and the content of information in signal.Therefore, CS theory is applied to Ground moving target imaging system, can effectively realizes compression and imaging processing to ground Moving Target Return data.

In recent years, fraction Fourier conversion (fractional Fourier transform is called for short FRFT) has been subject to paying close attention to widely as a kind of strong instrument of processing non-stationary signal, especially chirp signal.FRFT is the popularization of traditional F ourier conversion, and the FRFT that signal x (t) angle is α is defined as:

$X_{\mathrm{\α}}\left(u\right)=F_p\left[x\left(t\right)\right]={\∫}_{-\∞}^{+\∞}x\left(t\right)K_{\mathrm{\α}}(t,u)\mathrm{dt}$

Wherein, the exponent number that p is FRFT, can be arbitrary real number; α=p pi/2; F _p[ ] is the operator notation of FRFT, K _α(t, u) is the kernel function of FRFT,

$K_{\mathrm{\&alpha;}}(t,u)=\left\{\begin{array}{cc}\mathrm{\&delta;}(t-u),& \mathrm{\&alpha;}=2\mathrm{n\&pi;}\\ \mathrm{\&delta;}(t+u),& \mathrm{\&alpha;}=(2n\&PlusMinus;1)\mathrm{\&pi;}\\ \sqrt{(1-j\cot \mathrm{\&alpha;})/2\mathrm{\&pi;}}\&CenterDot;\exp (j({\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002986524700052.png,HDA00002986524700061.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+u^2)\cot \mathrm{\&alpha;}/2-\mathrm{jtu}\csc \mathrm{\&alpha;}).& \mathrm{otherwise}\end{array}\right.$

A time-limited LFM signal is rendered as the dorsal fin shape distribution of skew lines on time-frequency plane, and FRFT conversion is in essence to signal " rotation ", select the suitable anglec of rotation to carry out Fourier conversion to signal, can make signal on a certain specific Fractional Fourier Domain, be rendered as the gathering of energy, there is obvious peak value in its amplitude.

As document " Tao Ran; Zhang Feng; Wang Yue.Progress in the discretizationof fractional Fourier transform.Sci China Inf Sci; 2008; 38 (4): 481-503. " has been summarized the progress of Discrete Fractional Fourier transform, document " Deng Bin; Qin Yuliang; Wang Hongqiang; etc. a kind of improved SAR moving object detection and formation method based on FRFT. electronics and information journal; 2008,30 (2): 326-330. " improved Fourier Transform of Fractional Order is applied to SAR moving object detection and imaging.Because SAR moving target orientation can be approximately chirp signal to echoed signal, its expression on time frequency plane is oblique blade-like, has obvious time-frequency characteristic, and the imaging processing and the kinematic parameter that therefore utilize FRFT can realize moving target are estimated.

The invention provides a kind of ground moving object high resolution radar compressed sensing formation method, on Moving Target Return data basis, ground, obtain the estimation to positional information to movement velocity and orientation of imaging results and orientation accurately significantly compressing, for the accurate identification of ground moving object provides information.

For convenient, understand, first observation model is elaborated.SAR antenna adopts single-emission and double-receiving configuration mode.Wherein antenna A transmits, and antenna A and antenna B receive echoed signal simultaneously, and antenna A and antenna B phase center distance are d.As shown in Figure 1, SAR is operated in band pattern, and its antenna is positive side-looking, and carrier of radar flying speed is v _a, the radar of take is X-axis along course, vertical course is that Y-axis is set up coordinate system.Point O be starting point, making its X-axis coordinate is 0, with the bee-line of Texas tower be R ₀.Point P _nrepresent n moving target in scene, the X-axis coordinate of range points O is x _n, with the bee-line of Texas tower be R _n, perpendicular to course and the speed that is parallel to course, be respectively v _nyand v _nx.R _anfor antenna A and P _ndistance, R _bnfor antenna B and P _ndistance.

In one exemplary embodiment of the present invention, provide a kind of ground moving object high resolution radar compressed sensing formation method.As shown in Figure 4, the present embodiment method comprises:

Steps A: data receiver is to obtaining the complex radical band echoed signal of terrain object in imaging region

with

utilize distance to pulse compression, the signal that processings acquisition comprises moving target information such as offset

Wherein, this step can be divided into following sub-step again:

Sub-step A1: the complex radical band echoed signal that obtains terrain object in imaging region with $s_B(\hat{t},t_m);$

The baseband form of supposing radar transmitted pulse signal is:

$p(\hat{t},t_m)=\mathrm{rect}\left(\frac{\hat{t}}{T_p}\right)\exp \left[\mathrm{j\&pi;\&gamma;}{\hat{t}}^2\right]---\left(1\right)$

Wherein, rect () representation unit rectangular window function, γ is frequency modulation rate, T _p=1/PRF is fire pulse width, and PRF is pulse repetition rate,

for fast time, t _mfor the slow time, m is slow time series number.Transmit through the reflection of imaging region internal object, the complex radical band echoed signal that antenna A receives

the complex radical band echoed signal receiving with antenna B

can be expressed as respectively:

$s_A(\hat{t},t_m)=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_l\&CenterDot;p(\hat{t}-\frac{{2R}_{\mathrm{Al}}\left(t_m\right)}{c})\&CenterDot;\exp \left\{\frac{-j4\mathrm{\&pi;}{R}_{\mathrm{Al}}\left(t_m\right)}{\mathrm{\&lambda;}}\right\}---(2-1)$

$s_B(\hat{t},t_m)=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_l\&CenterDot;p(\hat{t}-\frac{{2R}_{\mathrm{Bl}}\left(t_m\right)}{c})\&CenterDot;\exp \left\{\frac{-j4\mathrm{\&pi;}{R}_{\mathrm{Bl}}\left(t_m\right)}{\mathrm{\&lambda;}}\right\}---(2-2)$

Wherein, L is the target sum in observation scene; σ _lit is target P _lbackscattering coefficient, λ is the wavelength that transmits.R _al(t _m) be t _mmoment antenna A and point target P _ldistance, R _bl(t _m) be t _mmoment antenna B and point target P _tdistance, can be expressed as:

$R_{\mathrm{Al}}\left(t_m\right)=\sqrt{{(R_{\mathrm{Al}}-v_{\mathrm{ly}}{t}_m)}^2+{(v_a{t}_m-d/2-v_{\mathrm{lx}}{t}_m-x_l)}^2}---(3-1)$

$R_{\mathrm{Bl}}\left(t_m\right)=\sqrt{{(R_{\mathrm{Bl}}-v_{\mathrm{ly}}{t}_m)}^2+{(v_a{t}_m+d/2-v_{\mathrm{lx}}{t}_m-x_l)}^2}---(3-2)$

Wherein, $R_{\mathrm{Al}}=\sqrt{R_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002986524700052.png,HDA00002986524700061.png"\; state="\{\{state\}\}">l</figure-callout>}}^2+{(d/2-x_l)}^2},$ $R_{\mathrm{Bl}}=\sqrt{R_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002986524700052.png,HDA00002986524700061.png"\; state="\{\{state\}\}">l</figure-callout>}}^2+{(-d/2-x_l)}^2}.$

Sub-step A2: the complex radical band echoed signal to antenna A and antenna B reception

with

carry out respectively distance to pulse compression, obtain

with

Right

do about the time

fourier transform, carry out conjugate multiplication with the frequency-region signal transmitting, and do about the time

inverse Fourier transform, obtain the range pulse compression signal after processing:

${\tilde{s}}_A(\hat{t},t_m)=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_l\sin c\left[B_r(\hat{t}-{2R}_{\mathrm{Al}}\left(t_m\right)/c)\right]\exp (-j4\mathrm{\&pi;}{R}_{\mathrm{Al}}\left(t_m\right)/\mathrm{\&lambda;})---(4-1)$

Wherein, B _r=| r|T _pfor transmitted signal bandwidth, sinc (x)=sin (π x)/(π x).In like manner, the echoed signal that antenna B is received is carried out range pulse compression processing, can obtain:

${\tilde{s}}_B(\hat{t},t_m)=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_l\sin c\left[B_r(\hat{t}-{2R}_{\mathrm{Bl}}\left(t_m\right)/c)\right]\exp (-j4\mathrm{\&pi;}{R}_{\mathrm{Bl}}\left(t_m\right)/\mathrm{\&lambda;})---(4-2)$

Sub-step A3: the complex radical band echoed signal of adjusting the distance after pulse compression

with

adopt twin-channel processing that offsets, obtain binary channels and offset the signal after processing

Known according to formula (3):

R _Al(t _m)≈R _Al-v _lyt _m+[(v _a-v _lx)t _m+d/2-x _l] ²/(2R _Al) (5)

Due to τ=d/v _a, t _m+ τ constantly antenna B moves to t _mantenna A place constantly, now antenna B and point target P _ldistance, can be expressed as: $R_{\mathrm{Bl}}(t_m+\mathrm{\&tau;})=\sqrt{{(R_{\mathrm{Al}}-v_{\mathrm{ly}}(t_m+\mathrm{\&tau;}))}^2+{(v_a{t}_m+d/2-v_{\mathrm{lx}}(t_m+\mathrm{\&tau;})-x_l)}^2}$ $\&ap;R_{\mathrm{Al}}-v_{\mathrm{ly}}(t_m+\mathrm{\&tau;})+[(v_a-v_{\mathrm{lx}})t_m-v_{\mathrm{lx}}\mathrm{\&tau;}+d/2-x_l{]}^2/\left({2R}_{\mathrm{Al}}\right)---\left(6\right)$

In order to realize land clutter, offset processing, use deduct the information that offsets static target in the observation scene after processing is cancelled out each other, and the phase information of moving target remains unchanged, and supposes that moving target number is wherein N, and the signal obtaining is: $s_{\mathrm{mov}}(\hat{t},t_m)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_n\sin c\left[B_r(\hat{t}-{2R}_{\mathrm{An}}\left(t_m\right)/c)\right]\exp (-j4\mathrm{\&pi;}{R}_{\mathrm{An}}\left(t_m\right)/\mathrm{\&lambda;})---\left(7\right)$

Steps A 4: right

carry out peak value searching, obtain the signal that comprises moving target information ${\tilde{s}}_{\mathrm{mov}}\left(t_m\right).$

Because data compression of the present invention is for Data in Azimuth Direction, for perpendicular to course speed v _lycan adopt classic method to estimate and compensation deals.For outstanding description step of the present invention, so locate to suppose v _ly=0, and put aside R _an(t _m) in about t _mthe impact of quadratic component, so, formula (7) can be reduced to about slow time t _mchirp signal form, $s_{\mathrm{mov}}(\hat{t},t_m)=\underset{n=1}{\overset{N}{\&Sum;}}{\mathrm{\&sigma;}}_n\sin c\left[B_r(\hat{t}-{2R}_{\mathrm{An}}/c)\right]\exp (-j4\mathrm{\&pi;}{R}_{\mathrm{An}}/\mathrm{\&lambda;})\exp (\mathrm{j\&pi;}{k}_a{\mathrm{<figure-callout\; id="2"\; label="t\; m"\; filenames="HDA00002986524700052.png,HDA00002986524700061.png"\; state="\{\{state\}\}">t</figure-callout>}}_m^{}+2\mathrm{j\&pi;f}{t}_m+j\mathrm{\&phi;})---\left(8\right)$

Wherein, $\left\{\begin{array}{c}{k}_a=-\frac{{2(v_a-v_{\mathrm{nx}})}^2}{R_{\mathrm{An}}\mathrm{\&lambda;}}\\ f=\frac{2(-d/2+x_n)(v_a-v_{\mathrm{nx}})}{R_{\mathrm{An}}\mathrm{\&lambda;}}\\ \mathrm{\&phi;}=\frac{-2\mathrm{\&pi;}{(-d/2+x_n)}^2}{R_{\mathrm{An}}\mathrm{\&lambda;}}\end{array}\right.---\left(9\right)$

Like this by right

peak value searching, can obtain fast time corresponding to moving target signal place range gate

and then obtain the distance of moving target and antenna A, thereby obtain its radial distance R _n.Formula (9) can further be reduced to simultaneously ${\tilde{s}}_{\mathrm{mov}}\left(t_m\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_n\exp (-j4\mathrm{\&pi;}{R}_{\mathrm{An}}/\mathrm{\&lambda;})\exp (\mathrm{j\&pi;}{k}_a{\mathrm{<figure-callout\; id="2"\; label="t\; m"\; filenames="HDA00002986524700052.png,HDA00002986524700061.png"\; state="\{\{state\}\}">t</figure-callout>}}_m^{}+2\mathrm{j\&pi;f}{t}_m+\mathrm{j\&phi;})---\left(10\right)$

From formula (10), can find out, can regard a plurality of chirp signal stacks as, because Fourier Transform of Fractional Order (FRFT) has good detection performance to chirp signal, therefore utilize FRFT to carry out motive target imaging processing below and process with parameter estimation.

Step B: data receiver is to comprising the signal of moving target information

carry out the down-sampled compression of data Random sparseness and process, adopt the random Gaussian observing matrix observing matrix that down-sampled compression is processed as data Random sparseness, obtain the signal after compression

and this signal is sent to data processing end;

Adopt random Gaussian observing matrix as the observing matrix of the down-sampled compression of data, be designated as Φ, size is

echo data after can compressing like this

its size is N ' * 1, than original echo data compression

ratio of compression

observation process can be expressed as by following expression formula like this ${{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right)=\mathrm{\&Phi;}\&CenterDot;{\tilde{s}}_{\mathrm{mov}}\left(t_m\right)---\left(11\right)$

Data after compression can reduce the pressure of disk storage device or data transmission link.

Step C: data processing termination is received the signal after compression according to it at fractional Fourier transform FRFT matrix Ψ _αunder sparse property and Minimum Entropy criteria, utilize compressed sensing algorithm reconstruct Y _α, obtain optimum anglec of rotation α and corresponding optimal result Y _α, determine speed and the positional information of moving target.

Wherein, this step C can be divided into following sub-step again:

Step C1: structure fractional Fourier transform FrFT matrix Ψ _α, the value of anglec of rotation α, at [π, π], be take 0.01 π as step-length.Make ${{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right)=\mathrm{\&Phi;}\&CenterDot;{\tilde{s}}_{\mathrm{mov}}\left(t_m\right)=\mathrm{\&Phi;}\&CenterDot;{\mathrm{\&Psi;}}_{\mathrm{\&alpha;}}^{-1}\&CenterDot;Y_{\mathrm{\&alpha;}}---\left(12\right)$

The anglec of rotation is the FRFT matrix Ψ of α _αbe configured with various ways, the make based on feature decomposition proposing in document " Tao Ran; ZhangFeng; Wang Yue.Progress in the discretization of fractional Fourier transform.Sci China Inf Sci; 2008; 38 (4): 481-503. ", because Doppler's unit number of original echo data is

matrix Ψ so _αsize be

it is specifically expressed as:

Wherein,

be the proper vector of utilizing the approximate continuity Hermite-Gauss function that matrix Ξ obtains, the expression formula of matrix Ξ is: $\mathrm{\&Xi;}=\left[\begin{array}{cccccc}2& 1& 0& ...& 0& 1\\ 1& 2\cos \left(w\right)& 1& ...& 0& 0\\ 0& 1& 2\cos \left(2w\right)& ...& 0& 0\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ 0& 0& 0& ...& 2\cos \left[(\hat{N}-2)w\right]& 1\\ 1& 0& 0& ...& 1& 2\cos \left[(\hat{N}-1)w\right]\end{array}\right]---\left(14\right)$

Wherein, $w=2\mathrm{\&pi;}/\hat{N}.$

Step C2: set up compressed sensing reconstruction model: $\min {\left|\right|Y_{\mathrm{\&alpha;}}\left|\right|}_{0}s.t.{{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right)={{\mathrm{\&Phi;\&Psi;}}_{\mathrm{\&alpha;}}}^{-1}{Y}_{\mathrm{\&alpha;}},---\left(15\right)$

Utilize level and smooth L0 algorithm to obtain Y _α.Wherein, level and smooth L0 algorithm is specific as follows:

(i) order $\mathrm{\&Omega;}=\mathrm{\&Phi;}\&CenterDot;{\mathrm{\&Psi;}}_{\mathrm{\&alpha;}}^{-1},$ $\tilde{X}={{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right),$ $Y_{\mathrm{\&alpha;}}^{\left(0\right)}={\mathrm{\&Omega;}}^{+}\&CenterDot;\tilde{X},$ Ω ⁺=Ω ^h(Ω Ω ^h) ^-1generalized inverse for Ω;

(ii) select descending series [θ ₁, θ ₂..., θ _j], general θ ₁be made as 2 to 4 times, θ _jbe 0.001, the ratio of successively decreasing η=θ _j/ θ _j+1=0.4,

expression rounds up, and gets j=1;

(iii) get

k=1;

(iv) compute gradient:

wherein, the hadamard product of symbol ο representing matrix; Make Y ' _α=Y ' _α-u δ _k, wherein u is little normal number, suggestion value is 2;

(v) order wherein, the conjugate transpose of symbol H representing matrix.If k≤K (K is positive integer, and suggestion value is 3), returns to step (iv), otherwise continues to carry out next step.

(vi) judgement, if j < J

j=j+1, returns to step (iii), otherwise stops circulation, output Y _α=Y ' _α.

Step C3: utilize minimum entropy method to choose the estimated value α of the optimum anglec of rotation _aes, wherein the result of entropy minimum is as final motive target imaging result, and the orientation that calculates ground moving object by following formula is to speed v _nxwith orientation to positional information x _n: ${\mathrm{\&alpha;}}_{\mathrm{aes}}=\underset{\mathrm{\&alpha;}}{\min }\{-\underset{N=1}{\overset{\hat{N}}{\mathrm{\&Sigma;}}}|{Y^{\&prime;}}_{\mathrm{\&alpha;}}\left(n\right){|}^2\ln \left({|Y^{\&prime;}}_{\mathrm{\&alpha;}}\left(n\right){|}^2\right)\}---\left(16\right)$ $\left\{\begin{array}{c}{v}_{\mathrm{nx}}=v_a-\sqrt{-\frac{{\mathrm{<figure-callout\; id="2"\; label="PRF"\; filenames="HDA00002986524700052.png,HDA00002986524700061.png"\; state="\{\{state\}\}">PRF</figure-callout>}}^2\&CenterDot;{\cot \mathrm{\&alpha;}}_{\mathrm{aes}}\&CenterDot;R_{\mathrm{An}}\&CenterDot;\mathrm{\&lambda;}}{2\hat{N}}}\\ x_n=\frac{\mathrm{PRF}\&CenterDot;u_{\mathrm{aes}}\&CenterDot;{\csc \mathrm{\&alpha;}}_{\mathrm{aes}}\&CenterDot;R_{\mathrm{An}}\&CenterDot;\mathrm{\&lambda;}}{2\hat{N}\&CenterDot;(v_a-v_{\mathrm{nx}})}+\frac{d}{2}\end{array}\right.---\left(17\right)$

Wherein, for aspect is to Doppler's unit number,

with it is the scale factor that dimension normalization is introduced.

Below provide the simulation experiment result based on above-described embodiment method.

Initial parameter relevant in emulation experiment is as follows: the positive side-looking work of radar, the speed v of carrier aircraft _afor 150m/s, carrier aircraft course line is to the distance R of ground imaging center ₀for 10km, carrier frequency f transmits ₀for 10GHz (wavelength 0.03m), pulse width T _pfor 1.2us, bandwidth B is 150MHz, and the range resolution obtaining is so 1m.Pulse repetition rate PRF is 500, and imaging integration time is 1s, and the azimuth resolution of acquisition is 1m.The spacing d of antenna A and B is 3m.Supposing, in observation scene, has 14 static targets, 2 moving targets, and reflection coefficient is 1.Static target random arrangement, the initial position that makes moving target P1 is that (9975m, 30m) movement velocity is (0m/s, 20m/s), and the initial position of moving target P2 is (10030m, 0m), and movement velocity is (0m/s ,-30m/s).Because static scattering point echo is the land clutter that will suppress, distance is about-6.36dB to the signal to noise ratio (SCR, signal clutter ratio) of each antenna echo before pulse compression.

First the echo data receiving is carried out to pulse pressure and land clutter offsets processing, Fig. 4 A be antenna echo that A receives in the map of magnitudes of the slow time domain of distance, Fig. 4 B is the map of magnitudes that two passage clutters offset back echo signal.From Fig. 4 A, in the echoed signal of antenna A, comprise land clutter and moving target signal simultaneously, cannot differentiate and come.Through two passage DPCA, offset after processing, in Fig. 4 B, only comprise moving target signal, therefore can carry out the estimation of subsequent motion target component.Fig. 4 C does not process to velocity compensation through orientation, directly utilizes doppler frequency rate corresponding to static target to carry out the result that Azimuth Compression obtains.Fig. 4 D is the result of directly utilizing Fourier Transform of Fractional Order to process.Contrast this two width figure visible, without over-compensation, process and to obtain result and in orientation, upwards there is no well focussed, can find out that moving target P2 defocuses than P1 even more serious simultaneously, this be due to the orientation of P2 to speed higher than the orientation of P1 to speed.And process based on FRFT, obtain good result, can obtain accurately the information of two moving targets.

Afterwards, the above-mentioned echo data that offsets processing is compressed, shown in Fig. 5 A is that ratio of compression η is 75% result, Fig. 5 B is the result that the range unit search at moving target P1 place is obtained, Fig. 5 C is the result that the range unit search at moving target P2 place is obtained, Fig. 5 D is two imaging results that moving target is final, from imaging results, can find out, utilizes the present invention in the situation that of compression and back wave datum significantly, accurately to realize the imaging processing of ground moving object.

Finally, utilize the optimum exponent number of the moving target of above-mentioned search acquisition, carry out the parameter estimation of moving target.By the optimum anglec of rotation and u value, utilize formula (15) to obtain: the centre frequency of moving target 1 is 27.43Hz, orientation to the frequency modulation rate of signal is-115.59Hz/s ²; The centre frequency that moving target 2 obtains is 2.63Hz, and orientation to the frequency modulation rate of signal is-218.64Hz/s ².Recycling formula (21) solves, and the orientation of the moving target 1 of acquisition is 18.33m/s to speed, and orientation is 32.75m to initial position.The orientation of moving target 2 is-31.10m/s that orientation is 2.32m to initial position to speed.Can find out that to estimate the moving target orientation obtain more approaching to speed and position and actual value, can realize the description to moving target motion state.

Above simulating, verifying the validity of the present embodiment institute extracting method.

So far, by reference to the accompanying drawings the method for the present embodiment ground moving object high resolution radar compressed sensing imaging be have been described in detail.According to above, describe, those skilled in the art should have clearly understanding to the present invention.

In sum, the present invention proposes a kind of ground moving object compressed sensing formation method based on Discrete Fractional Fourier transform, in significantly compression situation of data, realized the accurate imaging to ground moving object, the optimum exponent number simultaneously utilize obtaining has carried out the estimation of moving target parameter, thereby describes and identification provides information for the motion state of terrain object.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (11)

1. a method for ground moving object high resolution radar compressed sensing imaging, is characterized in that, comprising:

Steps A: the complex radical band echoed signal of data receiver to terrain object in imaging region with

utilize distance to pulse compression and offset to process and obtain the signal that comprises moving target information $s_{\mathrm{mov}}(\hat{t},t_m);$

Step B: data receiver adopts random Gaussian observing matrix as observing matrix, to the described signal that comprises moving target information

carry out the down-sampled compression of data Random sparseness and process, obtain the signal after compression

and the signal after this compression is sent to data processing end;

Step C: data processing termination is received the signal after described compression

according to it at fractional Fourier transform FRFT matrix Ψ _αunder sparse property and Minimum Entropy criteria, utilize compressed sensing algorithm reconstruct Y _α, obtain optimum anglec of rotation α and corresponding optimal result Y _α, determine speed and the positional information of moving target.

2. method according to claim 1, is characterized in that, described steps A comprises:

Sub-step A1: the complex radical band echoed signal that obtains terrain object in imaging region

with $s_B(\hat{t},t_m);$

Sub-step A2: the complex radical band echoed signal to antenna A and antenna B reception

with carry out respectively distance to pulse compression, obtain apart from the complex radical band echoed signal after pulse compression

with

wherein:

Sub-step A3: to described distance to the complex radical band echoed signal after pulse compression

with

carry out binary channels and offset processing, obtain binary channels and offset the signal after processing

Sub-step A4: binary channels is offseted to the signal after processing

carry out peak value searching, obtain the signal that comprises moving target information

3. method according to claim 2, is characterized in that, described sub-step A2 middle distance is as follows to the signal after pulse compression: ${\tilde{s}}_A(\hat{t},t_m)=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_l\&CenterDot;\sin c\left(B_r(\hat{t}-\frac{{2R}_{\mathrm{Al}}\left(t_m\right)}{c})\right)\&CenterDot;\exp \left\{\frac{-j4\mathrm{\&pi;}{R}_{\mathrm{Al}}\left(t_m\right)}{\mathrm{\&lambda;}}\right\}$ ${\tilde{s}}_B(\hat{t},t_m)=\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_l\&CenterDot;\sin c\left(B_r(\hat{t}-\frac{{2R}_{\mathrm{Bl}}\left(t_m\right)}{c})\right)\&CenterDot;\exp \left\{\frac{-j4\mathrm{\&pi;}{R}_{\mathrm{Bl}}\left(t_m\right)}{\mathrm{\&lambda;}}\right\}$

Wherein,

for fast time, t _mfor the slow time, m is slow time series number, σ _lbe l target backscattering coefficient (l=1,2 ..., L), L is the target sum in observation scene, B _rfor transmitted signal bandwidth, R _al(t _m), R _bl(t _m) be respectively t _mthe distance of moment antenna A, antenna B and l target,

c is the light velocity, and λ is carrier wavelength,

4. method according to claim 3, is characterized in that, carries out the signal that binary channels offsets after processing as follows in described sub-step A3: $s_{\mathrm{mov}}(\hat{t},t_m)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_n\&CenterDot;\sin c\left(\mathrm{Br}(\hat{t}-\frac{{2R}_{\mathrm{An}}\left(t_m\right)}{c})\right)\&CenterDot;\exp \left\{\frac{-j4\mathrm{\&pi;}{R}_{\mathrm{An}}\left(t_m\right)}{\mathrm{\&lambda;}}\right\}$

Wherein, σ _nbe observation scene in n moving target backscattering coefficient (n=1,2 ..., N), N is the moving target sum in observation scene.

5. method according to claim 4, is characterized in that, the signal that comprises moving target information in described sub-step A4 is as follows: ${\tilde{s}}_{\mathrm{mov}}\left(t_m\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_n\exp (-j4\mathrm{\&pi;}{R}_{\mathrm{An}}/\mathrm{\&lambda;})\exp (\mathrm{j\&pi;}{k}_a{t}_m^2+2\mathrm{j\&pi;f}{t}_m+\mathrm{j\&phi;})$

Wherein, R _anfor the distance of initial time antenna A and n moving target, $k_a=-\frac{2{(v_a-v_{\mathrm{nx}})}^2}{R_{\mathrm{An}}\mathrm{\&lambda;}},$ $f=\frac{2(-d/2+x_n)(v_a-v_{\mathrm{nx}})}{R_{\mathrm{An}}\mathrm{\&lambda;}},$ $\mathrm{\&phi;}=\frac{-2\mathrm{\&pi;}(-d/2+x_n{)}^2}{R_{\mathrm{An}}\mathrm{\&lambda;}},$ V _afor the movement velocity of Texas tower, v _{n χ}be n moving target orientation to translational speed, d is the distance between antenna A and antenna B, x _nbe n moving target orientation to initial position.

6. method according to claim 5, is characterized in that, the signal in described step B after compression

as follows: ${{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right)=\mathrm{\&Phi;}\&CenterDot;{\tilde{s}}_{\mathrm{mov}}\left(t_m\right)$

Wherein, Φ is gaussian random observing matrix, and size is

its each element is the random quantity that meets Gaussian distribution,

for column vector length, N ' is

length.

7. method according to claim 6, is characterized in that, described step C comprises:

Step C1: structure fractional Fourier transform FRFT matrix Ψ _α, the value of anglec of rotation α, at [π, π], be take 0.01 π as step-length, makes ${{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right)=\mathrm{\&Phi;}\&CenterDot;{\tilde{s}}_{\mathrm{mov}}\left(t_m\right)=\mathrm{\&Phi;}\&CenterDot;{\mathrm{\&Psi;}}_{\mathrm{\&alpha;}}^{-1}\&CenterDot;Y_{\mathrm{\&alpha;}};$

Step C2: set up compressed sensing reconstruction model: $\min {\left|\right|Y_{\mathrm{\&alpha;}}\left|\right|}_{0}s.t.{{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right)={{\mathrm{\&Phi;\&Psi;}}_{\mathrm{\&alpha;}}}^{-1}{Y}_{\mathrm{\&alpha;}},$ Utilize level and smooth L0 algorithm to obtain Y _α;

Step C3: utilize minimum entropy method to choose the estimated value α of the optimum anglec of rotation _aes, wherein the result of entropy minimum, as final motive target imaging result, calculates the orientation of ground moving object to speed v _nxwith orientation to positional information x _n.

8. method according to claim 7, is characterized in that, the matrix of fractional Fourier transform FRFT described in described step C1 Ψ _αsize be

it is specifically expressed as:

Wherein, symbol T representing matrix transposition,

be the proper vector of utilizing the approximate continuity Hermite-Gauss function that matrix Ξ obtains, the expression formula of matrix Ξ is: $\mathrm{\&Xi;}=\left[\begin{array}{cccccc}2& 1& 0& ...& 0& 1\\ 1& 2\cos \left(w\right)& 1& ...& 0& 0\\ 0& 1& 2\cos \left(2w\right)& ...& 0& 0\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ 0& 0& 0& ...& 2\cos \left[(\hat{N}-2)w\right]& 1\\ 1& 0& 0& ...& 1& 2\cos \left[(\hat{N}-1)w\right]\end{array}\right]$

Wherein, $w=2\mathrm{\&pi;}/\hat{N}.$

9. method according to claim 8, is characterized in that, utilizes level and smooth L0 algorithm to obtain Y in described step C1 _α ^hcomprise:

(i) order $\mathrm{\&Omega;}=\mathrm{\&Phi;}\&CenterDot;{\mathrm{\&Psi;}}_{\mathrm{\&alpha;}}^{-1},$ $\tilde{X}={{\tilde{s}}^{\&prime;}}_{\mathrm{mov}}\left(t_m\right),$ $Y_{\mathrm{\&alpha;}}^{\left(0\right)}={\mathrm{\&Omega;}}^{+}\&CenterDot;\tilde{X},$ Ω ⁺=Ω ^h(Ω Ω ^h) ^-1, wherein, the conjugate transpose of symbol H representing matrix;

(ii) select descending series [θ ₁, θ ₂..., θ _j], general θ ₁be made as 2 to 4 times, θ _jbe 0.001, the ratio of successively decreasing η=θ _j/ θ _j+1=0.4,

expression rounds up, and gets j=1;

(iii) get

k=1;

(iv) compute gradient: wherein, the hadamard product of symbol ο representing matrix, || ²the vector that represents square formation of its element amplitude during for vector; Make Y ' _α=Y ' _α-u δ _k, wherein u is little normal number, suggestion value is 2;

(v) order

if k < is K (K is positive integer, and suggestion value is 3), returns to step (iv), otherwise continue to carry out next step;

(vi) judgement, if j < J

j=j+1, returns to step (iii), otherwise stops circulation, output Y _α=Y ' _α.

10. method according to claim 9, is characterized in that, chooses the estimated value α of the optimum anglec of rotation in described step C3 by following formula _aes: ${\mathrm{\&alpha;}}_{\mathrm{aes}}=\underset{\mathrm{\&alpha;}}{\min }\{-\underset{n=1}{\overset{\hat{N}}{\mathrm{\&Sigma;}}}{\left|Y_{\mathrm{\&alpha;}}\left(n\right)\right|}^2\&CenterDot;\ln \left({\left|Y_{\mathrm{\&alpha;}}\left(n\right)\right|}^2\right)\}$

Wherein, Y _α(n) represent Y _αn element.

11. methods according to claim 10, is characterized in that, the orientation that calculates ground moving object by following formula in described step C3 is to speed v _nxwith orientation to positional information x _n: $\left\{\begin{array}{c}{v}_{\mathrm{nx}}=v_a-\sqrt{-\frac{\mathrm{PR}{F}^2\&CenterDot;\cot {\mathrm{\&alpha;}}_{\mathrm{aes}}\&CenterDot;R_{\mathrm{An}}\&CenterDot;\mathrm{\&lambda;}}{2\hat{N}}}\\ x_n=\frac{\mathrm{PRF}\&CenterDot;u_{\mathrm{aes}}\&CenterDot;{\csc \mathrm{\&alpha;}}_{\mathrm{aes}}\&CenterDot;R_{\mathrm{An}}\&CenterDot;\mathrm{\&lambda;}}{2\hat{N}\&CenterDot;(v_a-v_{\mathrm{nx}})}+\frac{d}{2}\end{array}\right.$

Wherein, PRF is pulse repetition rate, u _aesfor the anglec of rotation is α _aestime frequency corresponding to fractional order territory energy peak.

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