CN103105610A - DPC-MAB SAR imaging method based on non-uniform sampling - Google Patents

Abstract

The invention discloses a DPC-MAB SAR imaging method based on non-uniform sampling and belongs to the field of synthetic aperture radar signal processing. The DPC-MAB SAR imaging method based on the non-uniform sampling aims at the problem of azimuth cycle non-uniform sampling problem faced by a DPC-MAB SAR system, echo data of M channels is combined and is changed in an equivalent mode to be conventional single-channel SAR echo data to carry out distance-direction pulse compression, each row of simplified fraction order Fourier transform of the equivalent echo data is calculated according to cycle non-uniform sampling points, and imaging of an target object is achieved through rebuilding of simplified fraction order Fourier transform spectrum of a uniform sampling signal. The DPC-MAB SAR imaging method based on the non-uniform sampling can achieve accurate imaging of the target object under the condition of satisfying Qwest sampling rate. Compared with a traditional imaging mode, the DPC-MAB SAR imaging method based on the non-uniform sampling can further achieve target imaging under an under-sampled condition, and solves a DPC-MAB SAR imaging problem based on non-uniform sampling under low sampling rate.

Description

DPC-MAB SAR formation method based on nonuniform sampling

Technical field

The present invention relates to a kind of DPC-MAB SAR formation method based on nonuniform sampling, belong to synthetic aperture radar (SAR) signal process field.

Background technology

But synthetic aperture radar (SAR) is the imaging system of a kind of important round-the-clock, all weather operations.It by the distance to pulse compression and orientation realize two-dimentional high-resolution imaging to synthetic aperture processing, be widely used in many dual-use fields such as battlefield investigation, precise guidance, resource detection, topographic mapping and the condition of a disaster monitoring.For conventional SAR, high resolving power contradicts with wide swath, both is difficult to realize simultaneously.The leggy center hold by can effectively solve contradiction between high resolving power and wide swath in the orientation to the mode that adopts multicast, but has strictly limited the selection of paired pulses repetition frequency (PRF) to multi-beam (DPC-MAB) Mode S AR.Work as PRF=2V _a/ each wave beam of guarantee orientation is the uniform sampling signal after the echoed signal combination (Md) time, wherein M is that the orientation is to sub antenna number, V _aBe platform speed, d is sub antenna phase center spacing.In reality, the PRF of system tends to depart from this theoretical value, and at this moment the orientation after the combination is the periodically nonuniform sampling signal to signal, and direct imaging will cause the orientation false target upwards to occur, affects the SAR image quality.Therefore, the formation method based on nonuniform sampling is the emphasis that DPC-MAB SAR data are processed.

At first the formation method of traditional DPC-MAB SAR utilizes existing reconstructing method to realize the orientation to the reconstruct of uniform sampling signal, and then uses classical imaging mode to carry out imaging processing.Existing signal reconfiguring method based on the periodically nonuniform sampling signal can be divided into two classes substantially at present: time domain reconstruction and reconstruction in frequency-domain.The time domain reconstruction method is utilized nonuniform sampling reconstruct uniform sampling signal, and the reconstruction in frequency-domain method is the frequency spectrum of reconstruct uniform sampling signal.This two classes signal reconfiguring method all reconstruct orientation well to homogeneous signal, eliminate the orientation to the aliasing of Doppler frequency spectrum, thereby effectively remove the false target in imaging results.Yet this traditional DPC-MAB SAR formation method can not effectively be eliminated false target in the situation that the uniform sampling signal of reconstruct satisfies and to receive the accurate imaging that Qwest's sampling rate could realize target in the situation of owing to sample.

In order to solve the Sampling of owing that may face in reality, the imaging that therefore is necessary to study the DPC-MAB SAR under condition of low sampling rate realizes.Fourier Transform of Fractional Order (fractional Fourier transform, FRFT) is a kind ofly to process at signal the mathematical tool that the boundary causes extensive concern in recent years.As a kind of generalized form of Fourier transform (Fourier Transform, FT), it has Duoed a free parameter than traditional F T, is applicable to process non-stationary signal.FRFT can be understood as the chirp base and decomposes, and it has good aggregation to the chirp signal, has larger advantage to analyzing and process chirp class signal.And the signal of launching in the SAR system is generally the chirp signal, utilize this characteristics, and the phase-modulation product term of considering FRFT is for the not impact of amplitude of SAR imaging results, so the present invention utilizes the Fourier Transform of Fractional Order (SFRFT) of simplification to realize DPC-MAB SAR imaging based on nonuniform sampling.

Summary of the invention

The present invention is directed to orientation that DPC-MAB SAR faces to this problem of periodically nonuniform sampling signal, proposed a kind of novel DPC-MAB SAR formation method based on simplifying Fourier Transform of Fractional Order, the method satisfies at the uniform sampling signal of reconstruct receives all effective accurate imagings of realize target of the situation of Qwest's sampling rate and the situation of owing sampling rate.

A kind of DPC-MAB SAR formation method based on nonuniform sampling of the present invention comprises the steps:

Step 1:DPC-MAB SAR system receives from the echo data of each orientation to M passage of sub antenna, and wherein the distance of each passage is N to sampling number _r, the orientation is N to sampling number _a, namely the echo data of each passage is N _a* N _rMatrix; The echo data of M passage is made up the echo data [X after combination _r] distance be still N to sampling number _r, the orientation is L=MN to sampling number _a, namely the echo data after the combination is L * N _rMatrix [X _r], the 1st of this matrix walks to the capable respective channel 1 respectively of M to the first row of passage M echo data matrix, (M+1) of this matrix walks to the capable respective channel 1 respectively of 2M to the 2nd row of passage M echo data matrix, by that analogy, and the ((N of this matrix _a-1) M+1) walk to N _aThe capable respective channel 1 respectively of M is to the N of passage M echo data matrix _aOK;

Step 2: the echo data [X after combination _r] equivalence is conventional single-channel SAR echo data, to this equivalence echo data [X _r] carry out the distance to pulse compression, obtain matrix [X _r1];

Step 3: determine equivalent echo data [X _r] the orientation to the set { t of L time point of periodically nonuniform sampling _n}:

t _n=t _m+ ceil (n/M) PRT, n=0,1 ...., L-1, m=nmod M, (1) is t wherein ₀=0, t ₁=d/ (2V _a) ..., t _M-1=(M-1) d/ (2V _a), PRT be the orientation of actual DPC-MAB SAR system to the pulse repetition time, round under ceil () expression, modM represents mould M complementation, d is sub antenna phase center spacing, V _aIt is the platform flying speed;

Step 4: according to front M nonuniform sampling time point { t of step 3 acquisition _m, m=0,1 ... .M-1} obtain the matrix [A] of M * M, the capable k column element of i [A] of [A] _{I, k}Calculated by formula (2), wherein T=PRT/M;

${\left[A\right]}_{i,k}=\frac{1}{M}\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}{e}^{-j\frac{2\mathrm{\π}(i-k)}{\mathrm{MT}}{t}_m};i=1,...,M;k=1,...,M---\left(2\right)$

Step 5: the matrix [A] that step 4 obtains is asked its inverse matrix [A] ^-1

Step 6: make q=1;

Step 7: L time point { t of the periodically nonuniform sampling that obtains according to step 3 _n, the matrix [X to step 2 distance after the pulse compression _rl] q row to carry out order be p=2arccot (2 π K _aThe Fourier Transform of Fractional Order of)/π

Then will obtain $\{{\tilde{X}}_p\left(u_{i,k}\right),i=1,...M;k=1,...N_a\}$ Write as M * N _aMatrix

Matrix

The capable k column element of i For

${\left[{\tilde{X}}_p\right]}_{i,k}={\tilde{X}}_p\left(u_{i,k}\right);$

Step 8: utilize the T that step 4 obtains, the matrix [A] that step 5 obtains ^-1And the matrix that obtains of step 7

Calculate M * N by formula (3) _aMatrix [X _p];

$X_p{\left[A\right]}^{-1}\left[{\tilde{X}}_p\right]---\left(3\right)$

Step 9: the matrix [X that step 8 is obtained _p] every row carry out respectively transposition, obtain M column vector, and then with the end to end MN that obtains as the formula (4) of each row order _aLong column vector Y _p:

Y _p=[X _p(1,:)，X _p(2,:)，…，X _p(M,:)] ^T （4）

X wherein _p(i :) be M * N _aMatrix [X _p] i is capable, column vector Y _pBe the simplification fractional order Fourier spectrum of orientation to the uniform sampling signal, i.e. Y _pBe matrix [X _rl] the pulse compression result of q row;

Step 10: make the value of q add 1, the matrix [X to the distance of step 2 after the pulse compression _rl] q row carry out processing from step 7 to step 9, until q=N _rCarry out for the last time the processing from step 7 to step 9, the N that obtains after completing _rThe size that individual column vector consists of is L * N _rMatrix be namely the imaging results of institute observation area.

As preferably, calculate apart from the matrix [X after pulse compression described in step 7 _rl] the order of q row be p=2arccot (2 π K _aThe Fourier Transform of Fractional Order of)/π

Method as follows:

${\tilde{X}}_p\left(u_{i,k}\right)=\underset{n=0}{\overset{L-1}{\mathrm{\Σ}}}{X}_{\mathrm{rl}}(n+1,q)e^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·t_n^2-j\·u_{i,k}{t}_n};i=1,...M;k=1,...N_a;$

Wherein

Be the frequency modulation rate of orientation to signal, λ is radar wavelength, R ₀Be scape center oblique distance, X _rl(n, q) is apart from the matrix [X after pulse compression _rl] the capable q column element of n, and

$u_{i,k}=-\frac{\mathrm{\π}}{T}+\frac{2\mathrm{\π}}{\mathrm{MT}}(i-1+\frac{k-1}{N_a}),i=1,...M;k=1,...N_a.$

The contrast prior art, beneficial effect of the present invention is:

(1) the DPC-MAB SAR formation method based on the simplification Fourier Transform of Fractional Order of the present invention's proposition is also realized the SAR imaging processing when rebuilding the simplification fractional number order Fourier spectrum of uniform sampling signal;

(2) the DPC-MAB SAR formation method based on the simplification Fourier Transform of Fractional Order of the present invention's proposition, utilize FRFT to the aggregation of chirp signal, can the effectively imaging of realize target under condition of low sampling rate.

Description of drawings

The array mode of Fig. 1-M passage echo data;

DPC-MAB SAR imaging results when Fig. 2-orientation satisfies from nonuniform sampling in Nyquist sampling rate situation to sampling;

In Fig. 3-Fig. 2 leftmost side target place apart from the orientation of correspondence to amplitude;

Fig. 4-orientation to sampling satisfy employing in Nyquist sampling rate situation traditional based on the DPC-MAB SAR imaging results after the frequency spectrum reconfiguration algorithm;

In Fig. 5-Fig. 4 leftmost side target place apart from the orientation of correspondence to amplitude;

Fig. 6-orientation satisfies the DPC-MAB SAR imaging results of the employing algorithm that this patent is put forward in Nyquist sampling rate situation to sampling;

In Fig. 7-Fig. 6 leftmost side target place apart from the orientation of correspondence to amplitude;

Fig. 8-orientation is to the DPC-MAB SAR imaging results of sampling when Nyquist owes nonuniform sampling in the sampling situation;

In Fig. 9-Fig. 8 leftmost side target place apart from the orientation of correspondence to amplitude;

Figure 10-orientation to sampling Nyquist owe employing in the sampling situation traditional based on the DPC-MAB SAR imaging results after the frequency spectrum reconfiguration algorithm;

In Figure 11-Figure 10 leftmost side target place apart from the orientation of correspondence to amplitude;

The DPC-MAB SAR imaging results that Figure 12-orientation is owed the employing algorithm that this patent is carried in the sampling situation to sampling at Nyquist;

In Figure 13-Figure 12 leftmost side target place apart from the orientation of correspondence to amplitude.

Embodiment

Below in conjunction with the drawings and the specific embodiments, the present invention is described in detail, it is pointed out that described embodiment only is intended to be convenient to the understanding of the present invention, and do not play any restriction effect.

A kind of DPC-MAB SAR formation method based on nonuniform sampling, the specific implementation step of the method is as follows:

Step 1: the echo data that M passage of DPC-MAB SAR system obtained makes up by Fig. 1 mode, and the echo data after combination is L * N _rMatrix [X _r], its equivalence is conventional single-channel SAR echo data;

Step 2: the equivalent echo data [X that step 1 is obtained _r] carry out the distance to pulse compression, obtain matrix [X _rl];

Step 3: determine equivalent echo data [X _r] the orientation to periodically nonuniform sampling time set { t _n=t _m+ ceil (n/M) PRT, n=0,1 ... L-1, m=nmodM}, wherein t ₀=0, t ₁=d/ (2V _a) ..., t _M-1=(M-1) d/ (2V _a);

Step 4: front M the nonuniform sampling time point { t that obtains according to step 3 _m, m=0,1 ... .M-1} calculate M * Metzler matrix [A] by formula (2);

Step 5: ask its inverse matrix [A] according to the matrix [A] that step 4 obtains ^-1

Step 6: make q=1;

Step 7: L time point { t of the periodically nonuniform sampling that obtains according to step 3 _n, calculate apart from the matrix [X after pulse compression _rl] the order of q row be p=2arccot (2 π K _aThe simplification Fourier Transform of Fractional Order of)/π is namely according to the frequency modulation rate K of orientation to echoed signal _a, selected conversion order p=2arccot (the 2 π K that simplify Fourier Transform of Fractional Order _aThen)/π is calculated apart from the matrix [X after pulse compression by formula (5) _rl] q row X _rl(:, M * N that L point p rank simplification Fourier Transform of Fractional Order q) consists of _aMatrix

L time point { t of the periodically nonuniform sampling that obtains according to step 3 specifically, _n, calculate apart from the matrix [X after pulse compression _rl] q row be X _rl(:, order q) is p=2arccot (2 π K _aThe simplification Fourier Transform of Fractional Order of)/π

${\tilde{X}}_p\left(u_{i,k}\right)=\underset{n=0}{\overset{L-1}{\mathrm{\Σ}}}{X}_{r1}(n+1,q)e^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·t_n^2-j\·u_{i,k}{t}_n};i=1,...M;k=1,...N_a;$

Wherein

Be the frequency modulation rate of orientation to signal, λ is radar wavelength, R ₀Be scape center oblique distance (can be calculated by podium level and the angle of pitch), X _rl(n, q) is apart from the matrix [X after pulse compression _rl] the capable q column element of n, and

$u_{i,k}=-\frac{\mathrm{\π}}{T}+\frac{2\mathrm{\π}}{\mathrm{MT}}(i-1+\frac{k-1}{N_a}),i=1,...M;k=1,...N_a;$

Then obtain aforementioned $\{{\tilde{X}}_p\left(u_{i,k}\right),i=1,...M;k=1,...N_a\}$ Write as M * N _aMatrix

Matrix

The capable k column element of i For

${\left[{\tilde{X}}_p\right]}_{i,k}={\tilde{X}}_p\left(u_{i,k}\right)=\underset{n=0}{\overset{L-1}{\mathrm{\Σ}}}{X}_{\mathrm{rl}}(n+1,q)e^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·t_n^2-j\·[-\frac{\mathrm{\π}}{T}+\frac{2\mathrm{\π}}{\mathrm{MT}}(i-1+\frac{k-1}{N_a})]t_n},---\left(5\right)$

I=1 wherein ..., M, k=1 ..., N _a

Step 8: according to [A] of T=PRT/M, step 5 ^-1And step 7

Calculate M * N by formula (3) _aMatrix [X _p];

The step 9: [X that step 8 is obtained _p] operation carried out as the formula (4) obtains MN _aLong column vector Y _p, just obtain apart from the matrix [X after pulse compression _rl] the pulse compression result of q row.

Step 10: make the value of q increase by 1, matrix [X after pulse compression adjusts the distance _rl] q row carry out processing from step 7 to step 9, until q=N _rAfter completing, namely obtain the imaging results of institute observation area.

For making technical scheme of the present invention and advantage clearer, definition and character and traditional signal spectrum method for reconstructing based on nonuniform sampling below in conjunction with simplifying Fourier Transform of Fractional Order carry out detailed theory explanation to embodiment.

The p rank simplification Fourier Transform of Fractional Order (SFRFT) of signal x (t) are defined as:

Wherein $A_p=1/\sqrt{2\mathrm{\π}\·j}.$ Consider the chirp signal $x\left(t\right)=\mathrm{rect}(t/T_a)e^{-\mathrm{j\π}{K}_a{t}^2},$ T wherein _aBe pulse width, K _aBe the frequency modulation rate, so the p=2arccot of x (t) (2 π K _aThe simplification Fourier Transform of Fractional Order on)/π rank is

$X_p\left(u\right)=A_p{T}_a\frac{\sin ({\mathrm{uT}}_a/2)}{{\mathrm{uT}}_a/2}=A_a{T}_a\sin c({\mathrm{uT}}_a/2)---\left(7\right)$

By formula (7) as can be known, the simplification Fourier Transform of Fractional Order of chirp signal spectrum be the form of sinc function, and this illustrates that the SFRFT that the chirp signal is mated order namely obtains the result of pulse compression.Simultaneously because SFRFT has good aggregation to the chirp signal, being the chirp signal has narrower bandwidth in the SFRFT territory, this means the chirp signal is mated the required sampling rate of the SFRFT of order lower than the chirp signal being carried out the required Nyquist sampling rate of FT, therefore, can be in the situation that lower than the Nyquist sampling rate, the chirp signal be mated the SFRFT of order.

According to the characteristic of the simplification Fourier Transform of Fractional Order of above-mentioned chirp signal, the present invention will compose the imaging of realize target by rebuilding the orientation to the simplification fractional order Fourier of uniform sampling signal.Matrix [X for the distance of step 2 after the pulse compression _rl], its every row are all periodically nonuniform sampling signals, periodically nonuniform sampling is { t constantly _n.By formula (6), ignore constant coefficient A _p, periodically nonuniform sampling signal { x (t _n) p=2arccot (2 π K _aFourier Transform of Fractional Order is simplified on)/π rank For

${\tilde{X}}_p\left(u\right)=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}x\left(t_n\right)e^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·t_n^2-j\·u{t}_n}---\left(8\right)$

Order $g\left(t_n\right)=x\left(t_n\right)e^{j\frac{1}{2}\cot \left(\frac{\mathrm{p\π}}{2}\right)t_n^2},$ Obtain

${\tilde{x}}_p\left(u\right)=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}x\left(t_n\right)e^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·t_n^2-j\·{\mathrm{ut}}_n}=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}g{\left(t_n\right)}^{-j\·{\mathrm{ut}}_n}---\left(9\right)$

By formula (9) as can be known, { g (t _n) Fourier transform be { x (t _n) p rank simplify Fourier Transform of Fractional Order.The signal of FRFT territory, p rank band limit, i.e. X due to continuous signal x corresponding to non-uniformly sampled signals (t) _p(u) only (corresponding continuous signal g (t) is the Fourier bandlimited signal for π/T, the upper value non-zero of π/T).Utilize the relation between the Fourier spectrum of the Fourier spectrum of the non-homogeneous signal of cycle shown in formula (10) and homogeneous signal:

$\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}g\left(t_n\right)e^{-j\·{\mathrm{ut}}_n}=\frac{1}{T}\underset{k=-\∞}{\overset{k=\∞}{\mathrm{\Σ}}}A\left(k\right)G(u-k\frac{2\mathrm{\π}}{\mathrm{MT}})---\left(10\right)$

Wherein G (u) is the Fourier transform of g (t),

Can obtain

${\tilde{X}}_p\left(u\right)=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}x\left(t_n\right)e^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·t_n^2-j\·{\mathrm{ut}}_n}=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}g\left(t_n\right)e^{-j\·{\mathrm{ut}}_n}$

$=\frac{1}{T}\underset{k=-\∞}{\overset{k=\∞}{\mathrm{\Σ}}}A\left(k\right)G(u-k\frac{2\mathrm{\π}}{\mathrm{MT}})---\left(11\right)$

$=\frac{1}{T}\underset{k=-\∞}{\overset{k=\∞}{\mathrm{\Σ}}}A\left(k\right)X_p(u-k\frac{2\mathrm{\π}}{\mathrm{MT}})$

Formula (11) is the relation between the simplification fractional order Fourier spectrum of the simplification fractional order Fourier spectrum of periodically nonuniform sampling signal and homogeneous signal.Therefore, can utilize the simplification fractional order Fourier of non-uniformly sampled signals to compose to calculate the simplification fractional order Fourier spectrum X of homogeneous signal according to formula (11) _p(u), namely obtain the picture of target.

For formula (11), as given-π/T＜u ₀During＜-π/T+2 π/MT, due to X _p(u) only (the summation that is summed to finite term in formula (11), obtain for π/T, value non-zero on π T

${\tilde{X}}_p\left(u_0\right)=\frac{1}{T}\underset{k=-(M-1)}{\overset{k=0}{\mathrm{\Σ}}}A\left(k\right)X_p(u_0-k\frac{2\mathrm{\π}}{\mathrm{MT}})---\left(12\right)$

Similarly, then consider u ₀+ 2 π/MT has

${\tilde{X}}_p(u_0+\frac{2\mathrm{\π}}{\mathrm{MT}})=\frac{1}{T}\underset{k=-(M-2)}{\overset{k=1}{\mathrm{\Σ}}}A\left(k\right)X_p(u_0-(k-1)\frac{2\mathrm{\π}}{\mathrm{MT}})---\left(13\right)$

The rest may be inferred, and following general formula is arranged

${\tilde{X}}_p(u_0+i\frac{2\mathrm{\π}}{\mathrm{MT}})=\frac{1}{T}\underset{k=-(M-i-1)}{\overset{k=i}{\mathrm{\Σ}}}A\left(k\right)X_p(u_0-(k-i)\frac{2\mathrm{\π}}{\mathrm{MT}})---\left(14\right)$

I0 wherein, 1 ... .M-1.This M equation is write as the form of following matrix, had

$T\left[{\tilde{X}}_p\left(u_0\right)\right]=\left[A\right]\left[X_p\left(u_0\right)\right]---\left(15\right)$

M dimensional vector wherein

I element be ${\left[{\tilde{X}}_p\left(u_0\right)\right]}_i={\tilde{X}}_p(u_0+2\mathrm{\π}(i-1)/\mathrm{MT}),$ Formula (2) is seen in the definition of [A], M dimensional vector [Xp (u ₀)] i element be [X _p(u ₀)] _i=X _p(u ₀+ 2 π (i-1)/MT).

By formula (15) as seen, a given u0, the M point that can obtain the uniform sampling signal is simplified the fractional order Fourier spectrum, works as u ₀Value change N _aInferior, namely get u ₀(n)=-π/T+2 π n/MN _aT, n=0,1 ..N _a-1, just can obtain at (π/T, the upper MN of π/T) _aPoint is simplified the fractional order Fourier spectrum uniformly, namely obtains the picture of target.

According to above-mentioned analysis, the present invention also realizes the SAR imaging processing when the simplification fractional order Fourier spectrum that realizes homogeneous signal is rebuild, and at the condition of low sampling rate also effectively imaging of realize target.

Below in conjunction with concrete simulation example and accompanying drawing, the present invention is elaborated:

In this emulation experiment, suppose satellite orbital altitude H=800km, satellite flight speed V _a=7452m/s, radar carrier frequency F _c=9.054GHz, the sub antenna length d==5m, sub antenna number M=3 calculates theoretical PRF _Idea=2V _a/ (Md)=993.6Hz.Suppose scape center oblique distance R ₀923.76km, fire pulse width T _r=1 μ s, frequency modulation rate K _r=7 * 10 ¹³Hz/s, sampling rate F _s90MHz, and hypothesis has five point targets in scene, upwards there are three targets the distance center position of its Scene in the orientation.

When the PRF of actual transmission deviation theory value was 490Hz, the orientation was non-homogeneous signal of cycle to echoed signal, and direct imaging will cause the orientation to producing additional frequency spectrum, produces the false target (see figure 2) after pulse compression.At this moment adopt traditional based on the result of carrying out again target imaging after the frequency spectrum reconfiguration algorithm as shown in Figure 4, adopt the target imaging result of algorithm that this patent is put forward as shown in Figure 6.Fig. 3, Fig. 5 and Fig. 7 provided respectively target place, the leftmost side in Fig. 2, Fig. 4 and Fig. 6 apart from the orientation of correspondence to amplitude.This shows, adopt and traditional all can effectively eliminate false target based on frequency spectrum reconfiguration algorithm and algorithm that this patent is carried, and the imaging effect of algorithm that this patent is carried be better than adopt traditional based on the imaging effect after the frequency spectrum reconfiguration algorithm.

When the PRF of actual transmission deviation theory value was 300Hz, the uniform sampling signal of at this moment reconstruct did not satisfy the Nyquist sampling thheorem.Directly with the orientation to non-homogeneous signal of cycle carry out the pulse pressure imaging and still produce the false target (see figure 8).Adopt that traditional at this moment traditional frequency spectrum reconfiguration algorithm can not effectively be eliminated false target based on the result of carrying out again target imaging after the frequency spectrum reconfiguration algorithm as shown in figure 10, and adopt algorithm that this patent is carried still can effectively eliminate false target, as shown in figure 12.Fig. 9, Figure 11 and Figure 13 provided respectively target place, the leftmost side in Fig. 8, Figure 10 and Figure 12 apart from the orientation of correspondence to amplitude, can prove absolutely that algorithm that this patent is carried is in the advantage of owing in the sampling situation.

Therefore, satisfy the Nyquist sampling request at the PRF of system, deduction has realized the imaging of target when realizing the even reconstruct of signal as algorithm, when the PRF of system does not satisfy the Nyquist sampling request, deduction still can effectively be eliminated false target as algorithm, has solved under the low sampling rate DPC-MAB SAR imaging problem based on nonuniform sampling.

The above; it is only the specific embodiment of the present invention; but protection scope of the present invention is not limited to this; anyly be familiar with the people of this technology in the disclosed technical scope of the present invention; can understand conversion and the replacement expected; all should be encompassed in of the present invention comprise scope within, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (3)

1. the DPC-MAB SAR formation method based on nonuniform sampling, is characterized in that, comprises following steps:

Step 1:DPC-MAB SAR system receives from the echo data of each orientation to M passage of sub antenna, and wherein the distance of each passage is N to sampling number _r, the orientation is N to sampling number _a, namely the echo data of each passage is N _a* N _rMatrix; The echo data of M passage is made up the echo data [X after combination _r] distance be still N to sampling number _r, the orientation is L=MN to sampling number _a, namely the echo data after the combination is L * N _rMatrix [X _r], the 1st of this matrix walks to the capable respective channel 1 respectively of M to the first row of passage M echo data matrix, (M+1) of this matrix walks to the capable respective channel 1 respectively of 2M to the 2nd row of passage M echo data matrix, by that analogy, and the ((N of this matrix _a-1) M+1) walk to N _aThe capable respective channel 1 respectively of M is to the N of passage M echo data matrix _aOK;

Step 2: the echo data [X after combination _r] equivalence is conventional single-channel SAR echo data, to this equivalence echo data [X _r] carry out the distance to pulse compression, obtain matrix [X _r1];

Step 3: determine equivalent echo data [X _r] the orientation to the set { t of L time point of periodically nonuniform sampling _n}:

t _n=t _m+ceil(n/M)PRT；n=0，1,…，L-1；m=nmod M； （1）

T wherein ₀=0, t ₁=d/ (2V _a) ..., t _M-1=(M-1) d/ (2V _a), PRT be the orientation of actual DPC-MAB SAR system to the pulse repetition time, round under ceil () expression, mod M represents mould M complementation, d is sub antenna phase center spacing, V _aIt is the platform flying speed;

Step 4: according to front M nonuniform sampling time point { t of step 3 acquisition _m, m=0,1 ... M-1} obtains the matrix [A] of M * M, the capable k column element of i [A] of [A] _{I, k}Calculated by formula (2), wherein T=PRT/M;

${\left[A\right]}_{i,k}=\frac{1}{M}\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}{e}^{-j\frac{2\mathrm{\π}(i-k)}{\mathrm{MT}}{t}_m};$ i＝1,...,M；k＝1，...,M （2）

Step 5: the matrix [A] that step 4 obtains is asked its inverse matrix [A] ^-1

Step 6: make q=1;

Step 7: L time point { t of the periodically nonuniform sampling that obtains according to step 3 _n, the matrix [X of the distance that step 2 is obtained after the pulse compression _r1] q row to carry out order be p=2arccot (2 π K _aThe Fourier Transform of Fractional Order of)/π

Then will obtain

I=1 ... M; K=1 ... N _aWrite as M * N _aMatrix

Matrix

The capable k column element of i

For

$[{{\tilde{X}}_p]}_{i,k}={\tilde{X}}_p\left(u_{i,k}\right);$

Step 8: utilize the T that step 4 obtains, the matrix [A] that step 5 obtains ^-1And the matrix that obtains of step 7

Calculate M * N by formula (3) _aMatrix [X _p];

$[X_p]={T{\left[A\right]}^{-1}[\tilde{X}}_p]---\left(3\right)$

Step 9: the matrix [X that step 8 is obtained _p] every row carry out respectively transposition, obtain M column vector, and then with the end to end MN that obtains as the formula (4) of each row order _aLong column vector Y _p:

Y _p=[X _p(1,:)，X _p(2,:)，…，X _p(M,:)] ^T （4）

X wherein _p(i :) be M * N _aMatrix [X _p] i is capable, column vector Y _pBe the simplification fractional order Fourier spectrum of orientation to the uniform sampling signal, i.e. Y _pBe matrix [X _r1] the pulse compression result of q row;

Step 10: make the value of q add 1, the matrix [X to step 2 distance after the pulse compression _r1] q row carry out processing from step 7 to step 9, until q=N _rCarry out for the last time the processing from step 7 to step 9, the N that obtains after completing _rThe size that individual column vector consists of is L * N _rMatrix be namely the imaging results of institute observation area.

2. the DPC-MAB SAR formation method based on nonuniform sampling according to claim 1, is characterized in that, calculates apart from the matrix [A after pulse compression described in step 7 _r1] the order of q row be p=2arccot (2 π K _aThe Fourier Transform of Fractional Order of)/π

Method as follows:

${\tilde{X}}_p\left(u_{i,k}\right)=\underset{n=0}{\overset{L-1}{\mathrm{\Σ}}}{X}_{\mathrm{rl}}{(n+1,q)e}^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·t_n^2-{j\·u}_{{i,k}^{t}n}};$ i＝1，...M;k＝1，...N _a;

Wherein

Be the frequency modulation rate of orientation to signal, λ is radar wavelength, R ₀Be scape center oblique distance, X _r1(n, q) is apart from the matrix [X after pulse compression _r1] the capable q column element of n, and

$u_{i,k}=-\frac{\mathrm{\π}}{T}+\frac{2\mathrm{\π}}{\mathrm{MT}}(i-1+\frac{k-1}{N_a}),$ i＝1,...M;k＝1，...N _a

3. the DPC-MAB SAR formation method based on nonuniform sampling according to claim 2, is characterized in that, scape center oblique distance R ₀Calculated by podium level and the angle of pitch.

Images