CN104330786B - Arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying - Google Patents

Abstract

The invention discloses a kind of arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying；It comprises the following steps: initiation parameter, discretization GBSAR spectral phase, spectral phase spatial function approximation, spectral phase frequency function approximation and weighted sum are simplified expression formula.The invention has the beneficial effects as follows: the arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying of the present invention, utilize Discrete Linear least square method that the space compound function in GBSAR spectral phase, frequency multiplexed function are carried out linear fit respectively, GBSAR spectral phase is reduced to binomial sum by multinomial sum, and then efficient frequency domain imaging treatment technology can be applied to realize focal imaging efficiently according to this simplified style, the GBSAR frequency spectrum that achieves efficient, high-precision simplifies.

Description

Arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying

Technical field

The invention belongs to Radar Technology field, particularly relate to a kind of arbitrary configuration double-base synthetic aperture radar echo spectrum Method for simplifying.

Background technology

Arbitrary configuration double-base synthetic aperture radar (General bistatic synthetic aperture radar, It is called for short GBSAR) it is that transmitter, receiver are placed on the polytype platforms such as satellite, aircraft and stationary stations, and between platform The two-dimensional imaging system constituted with any geometric configuration.Due to multiformity and the arbitrariness of geometric configuration of system platform, GBSAR system can carry out multi-angle to interesting target region and scout flexibly, thus obtains abundant target scattering information.Cause This, GBSAR system can apply to the fields such as round-the-clock, round-the-clock aircraft independent navigation, target reconnaissance and identification, for state People's expanding economy and national security play an important role.Germany's NASA (FGAN) high-frequency physical and Radar Technology institute (FHR) airborne-airborne double-base synthetic aperture radar system experimentation, Yi Jixing are implemented respectively in 2006 and in November, 2009 Load-airborne double-base synthetic aperture radar system test, Chinese Academy of Sciences electron institute implemented spaceborne-static platform in 2012 Double-base synthetic aperture radar system experimentation, these system experimentations demonstrate multi-platform, multi-configuration double-base synthetic aperture radar The feasibility of two-dimensional imaging.

GBSAR system covers the double-base synthetic aperture radar system of multiple specific type, is that polytype is bistatic The general designation of synthetic aperture radar.GBSAR system echoes spectral model is to disclose multiple double-base synthetic aperture radar system echoes Signal frequency domain feature, the prerequisite building general frequency domain imaging algorithm and basis.Yet with system platform multiformity with And the arbitrariness of configuration, GBSAR system 2-d spectrum analytic expression form is compared to single base synthetic aperture radar and some spy The spectrum complex degree of the double-base synthetic aperture radar of different configuration is greatly increased.By document 1 (Y.L.Neo, F.Wong, and I.G.Cumming,“A two-dimensional spectrum for bistatic SAR processing using series reversion,”IEEE Geosci.Remote Sens.Lett.,vol.4,no.1,pp.93–96,Jan.2007) Understanding, the frequency spectrum of GBSAR system is the higher order polynomial sum about target two-dimensional position and echo two-dimensional frequency, and target The high-order that there is complexity between position with frequency couples, and the frequency domain imaging being currently based on fast Fourier transform (FFT) processes This complicated analytic expression cannot be efficiently treated through, therefore, it is impossible to directly utilize the GBSAR frequency spectrum of multinomial and form by technology Realize efficient frequency domain focal imaging.At present, representational GBSAR frequency spectrum method for simplifying has Xian Electronics Science and Technology University Li Dong etc. propose the Taylors approximation method for simplifying for target two-dimensional spatial location (D.Li, G.Liao, W.Wang, Q.Xu, “Extended azimuth nonlinear chirp scaling algorithm for bistatic SAR processing in high-resolution highly squinted mode geoscience and remote sensing letters,”IEEE Geosci.Rem.Sens.Lett.,vol.11,no.6,pp.1134–1138,June 2014.), and the proposition such as University of Electronic Science and Technology Zhang Xiaoling for approximate based on first order Taylor method for simplifying (C.Dai, X.Zhang,“Omega-K algorithm for bistatic SAR with arbitrary geometry configuration,”Journal of Electromagnetic waves and applications,vol.25, no.11-12,pp.1564-1576,2011).But, due to the locality of Taylors approximation, these methods are only used for target field In the double-base synthetic aperture radar system of some particular configuration that scape scope is little or space-variant is little.Therefore, existing double-basis Ground synthetic aperture radar frequency spectrum method for simplifying is unsuitable for kinds of platform, the reality of arbitrary configuration GBSAR large scene high-performance imaging Application demand.

Summary of the invention

The goal of the invention of the present invention is: in order to solve problem above, and the present invention proposes a kind of bistatic conjunction of arbitrary configuration Become aperture radar return frequency spectrum method for simplifying, cannot correctly simplify multi-platform, arbitrary configuration GBSAR large scene echo to overcoming The limitation of frequency spectrum, the versatility of extension frequency domain imaging Processing Algorithm, meet kinds of platform, arbitrary configuration GBSAR large scene height The practical application request of performance imaging.

Describe present disclosure for convenience, first make following term and define:

Definition 1, Discrete Linear least square method (DLLS)

If system of linear equations Ax=b, wherein A is the matrix of m row n row, and is the coefficient matrix of this system of linear equations, $A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& ...& a_{1n}\\ a_{21}& a_{22}& ...& a_{2n}\\ ...& ...& ...& ...\\ a_{m1}& a_{m2}& ...& a_{\mathrm{mn}}\end{array}\right],$ B=[b₁ ... b_m]^T, x is unknown column vector x=[x₁ x₂ ... x_n]^T, A, b are all it is known that and m >n.The solution then utilizing Discrete Linear least square method can obtain x is

X=(AA^T)^-1A^Tb (1)

The solution of this x can meet mean square error and the minimum of system of linear equations, i.e.

$x=\arg \underset{x}{\min }\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{|\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{x}_j-b_i|}^2---\left(2\right)$

About Discrete Linear least square method, seen in detail in list of references 3:R.L.Burden, J.D.Faires, Numerical analysis,Thomson Learning,Inc.,2001.

Definition 2, GBSAR system echoes 2-d spectrum analytic expression

GBSAR system Range compress back echo 2-d spectrum analytic expression is

D (ξ, η)=∫ ∫ σ (x, y) exp (-j2 π ψ (ξ, η；x,y))dxdy (3)

Wherein, ξ and η is emission signal frequency and Doppler frequency respectively.(x y) is in (x, y) scattering of place's target to σ Coefficient, ψ (ξ, η；X, y) is spectral phase, according to document 1 (document 1:Y.L.Neo, F.Wong, and I.G.Cumming, " A two-dimensional spectrum for bistatic SAR processing using series reversion,” IEEE Geosci.Remote Sens.Lett., vol.4, no.1, pp.93 96, Jan.2007) understand,

$\mathrm{\ψ}(\mathrm{\ξ},\mathrm{\η};x,y)=\underset{p=0}{\overset{P}{\mathrm{\Σ}}}{s}_p(x,y)\·f_p(\mathrm{\ξ},\mathrm{\η})---\left(4\right)$

Wherein, P is integer, can adjust the value of P according to frequency spectrum required precision, typically take P >=4.f_p, p=0,1 ..., P It it is the compound function about two-dimensional frequency

$f_p(\mathrm{\ξ},\mathrm{\η})={\left(\frac{1}{\mathrm{\ξ}}\right)}^{p-1}{\mathrm{\η}}^p---\left(5\right)$

s_p, p=0,1 ..., P is the compound function about two-dimensional spatial location

$\begin{array}{c}{s}_0(x,y)=(-k_0(x,y)+\underset{q=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\γ}}_q(x,y)\·k_1^q(x,y))/c\\ s_1(x,y)=-t_{\mathrm{cen}}(x,y)-\underset{q=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\γ}}_q(x,y)\·k_1^{p-1}(x,y)\\ s_p(x,y)=\underset{q=p}{\overset{P}{\mathrm{\Σ}}}\frac{q!c^{p-1}}{p!(q-p)!}{\mathrm{\γ}}_q(x,y)\·k_1^{q-p}(x,y),p\≥2\end{array}---\left(6\right)$

Wherein c is the light velocity, γ₂,γ₃,γ₄Expression formula is as follows

$\begin{array}{c}{\mathrm{\γ}}_2(x,y)=\frac{1}{{4k}_2(x,y)}\\ {\mathrm{\γ}}_3(x,y)=\frac{k_3(x,y)}{8{k_2}^3(x,y)}\\ {\mathrm{\γ}}_4(x,y)=\frac{9{k_3}^2(x,y)-4k_2(x,y)\·k_4(x,y)}{64{k_2}^5(x,y)}\end{array}---\left(7\right)$

In formula (7), k_p(x is y) about GBSAR system oblique distance history R (t；X, p order derivative y),R(t；X, y)=k₀(x, y)=r_T(x,y)/cosθ_T(x,y)+r_R(x,y)/cosθ_R(x, y).Wherein, t_cenIt is the synthetic aperture central instant of target, r_T, r_RBe respectively flat pad, receiving platform distance objective nearest Oblique distance, θ_T,θ_RIt is flat pad, the angle of strabismus of receiving platform relative target respectively, r_T, r_R, θ_TAnd θ_RAnalytical expression respectively For

Wherein, [x_T0,y_T0,z_T0] and [x_R0,y_R0,z_R0] it is the transmitting of GBSAR system, the initial position of receiving platform respectively, v_T,v_RIt is the transmitting of GBSAR system, the movement velocity size of receiving platform respectively,It is that GBSAR system is launched, receiving platform moves The corner dimension of velocity attitude.

K in formula (6) and formula (7)_p(x, y), the detailed expressions of p >=1 may refer to document 1:Y.L.Neo, F.Wong, and I.G.Cumming,“A two-dimensional spectrum for bistatic SAR processing using series reversion,”IEEE Geosci.Remote Sens.Lett.,vol.4,no.1,pp.93–96,Jan.2007。

The technical scheme is that a kind of arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying, bag Include following steps:

A, forward sight double-base synthetic aperture radar imaging systematic parameter is carried out initialization process,

Wherein, forward sight double-base synthetic aperture radar imaging systematic parameter specifically includes: in the signal that radar system is launched Frequency of heart ξ₀, radar emission signal wavelength lambda, radar system transmitted signal bandwidth B, radar system launches signal chirp rate μ, thunder Reaching system pulses repetition rate PRF, radar system distance is to sampling number M, and radar system orientation, to sampling number N, is launched flat Platform is at the locus [x of initial time_T0,y_T0,z_T0], receiving platform is at the locus [x of initial time_R0,y_R0,z_R0]；Send out Penetrate velocity magnitude v of platform_T, velocity magnitude v of receiving platform_R, launch and receiving platform movement velocity angular separation；

B, according to arbitrary configuration double-base synthetic aperture radar system Range compress back echo 2-d spectrum analytic expression, obtain Spectral phase ψ (ξ, η；X, y), and by spectral phase ψ (ξ, η；X, y) according to two-dimensional spatial location and two-dimensional frequency carry out uniformly from Dispersion, obtains the spectral phase of discretization

C, employing Discrete Linear least square method, the discretization spectral phase that will obtain in step B In spatial function s_p, p >=2, it is expressed as spatial function s₀With spatial function s₁Linear function；

D, employing Discrete Linear least square method, the discretization spectral phase that will obtain in step B In frequency function f_p, p >=2, it is expressed as frequency function g₀With frequency function g₁Linear function；

E, utilize the spatial function s that step C obtains₀With spatial function s₁Linear function and step D in the frequency letter that obtains Number g₀With frequency function g₁Linear function to discretization spectral phaseIt is weighted summation, obtains discretization The simplified expression of spectral phase.

Further, described arbitrary configuration double-base synthetic aperture radar system Range compress back echo 2-d spectrum resolves Formula, particularly as follows:

D (ξ, η)=∫ ∫ σ (x, y) exp (-j2 π ψ (ξ, η；x,y))dxdy

Wherein, ξ is emission signal frequency, and η is Doppler frequency, σ (x, y) for being positioned at (x, y) scattering coefficient of place's target, ψ(ξ,η；X, y) is spectral phase.

Further, described spectral phase ψ (ξ, η；X, expression formula y), particularly as follows:

$\mathrm{\ψ}(\mathrm{\ξ},\mathrm{\η};x,y)=\underset{p=0}{\overset{P}{\mathrm{\Σ}}}{s}_p(x,y)\·f_p(\mathrm{\ξ},\mathrm{\η})$

Wherein, P is integer, P >=4, s_pFor the compound function about two-dimensional spatial location, f_pFor answering about two-dimensional frequency Conjunction function, p=0,1 ..., P.

Further, described discretization spectral phaseExpression formula, particularly as follows:

Wherein, ξ_m,η_nIt is respectively two-dimensional frequency discrete point position, x_i,y_lIt is respectively two-dimensional spatial location discrete point position, M, n are respectively two-dimensional frequency numbering, and i, l are respectively two-dimensional spatial location numbering.

Further, the described discretization spectral phase that will obtain in step BIn spatial function s_p, P > 2, is expressed as spatial function s₀With spatial function s₁Linear function, particularly as follows:

$s_p(x_i,y_l)={\mathrm{\α}}_p^s\·s_0(x_i,y_l)+{\mathrm{\β}}_p^s\·s_1(x_i,y_l)+\mathrm{\Δ}{s}_p(x_i,y_l).$

Further, the described discretization spectral phase that will obtain in step BIn frequency function f_p, P > 2, is expressed as frequency function g₀With frequency function g₁Linear function, particularly as follows:

$f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)={\mathrm{\α}}_p^f\·g_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+{\mathrm{\β}}_p^f\·g_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+\mathrm{\Δ}{f}_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n).$

Further, the simplified expression of described discretization spectral phase, particularly as follows:

Further, described Discrete Linear least square method, particularly as follows:

Set system of linear equations Ax=b, wherein, A be the matrix of L row K row and A be system of linear equations Ax=b be Matrix number, $A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& ...& a_{1K}\\ a_{21}& a_{22}& ...& a_{2K}\\ ...& ...& ...& ...\\ a_{L1}& a_{L2}& ...& a_{\mathrm{LK}}\end{array}\right],$ B=[b₁ ... b_L]^T, x is unknown column vector x=[x₁ x₂ ... x_K]^T, A, b For known quantity, L > K；The solution solving x is x=(AA^T)^-1A^TB, x meet

The invention has the beneficial effects as follows: the arbitrary configuration double-base synthetic aperture radar echo spectrum simplification side of the present invention Method, utilizes Discrete Linear least square method to enter the space compound function in GBSAR spectral phase, frequency multiplexed function respectively Line linearity matching, is reduced to binomial sum by GBSAR spectral phase by multinomial sum, and then can apply according to this simplified style Efficiently frequency domain imaging treatment technology realizes focal imaging efficiently, and the GBSAR frequency spectrum that achieves efficient, high-precision simplifies, and overcomes Prior art cannot correctly simplify multi-platform, the limitation of arbitrary configuration GBSAR large scene echo spectrum, have greatly expanded frequency The versatility of domain imaging Processing Algorithm, meets kinds of platform, the actual application of arbitrary configuration GBSAR large scene high-performance imaging Demand.

Accompanying drawing explanation

Fig. 1 is the arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying schematic flow sheet of the present invention.

Fig. 2 is the target scene midpoint Target space position distribution schematic diagram of the embodiment of the present invention.

Fig. 3 is the letter that obtains after the arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying of the present invention processes Change the error schematic diagram of spectral phase and actual spectrum phase place.

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, right The present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, not For limiting the present invention.

As it is shown in figure 1, the arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying flow process for the present invention is shown It is intended to.A kind of arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying, comprises the following steps:

A, forward sight double-base synthetic aperture radar imaging systematic parameter is carried out initialization process,

Wherein, forward sight double-base synthetic aperture radar imaging systematic parameter specifically includes: in the signal that radar system is launched Frequency of heart ξ₀, radar emission signal wavelength lambda, radar system transmitted signal bandwidth B, radar system launches signal chirp rate μ, thunder Reaching system pulses repetition rate PRF, radar system distance is to sampling number M, and radar system orientation, to sampling number N, is launched flat Platform is at the locus [x of initial time_T0,y_T0,z_T0], receiving platform is at the locus [x of initial time_R0,y_R0,z_R0]；Send out Penetrate velocity magnitude v of platform_T, velocity magnitude v of receiving platform_R, launch and receiving platform movement velocity angular separation。

As in figure 2 it is shown, be the target scene midpoint Target space position distribution schematic diagram of the embodiment of the present invention.The present invention is real Executing in example, forward sight double-base synthetic aperture radar imaging systematic parameter is known quantity, specifically includes: the letter that radar system is launched Number mid frequency ξ₀, ξ₀=9.5GHz；Radar emission signal wavelength lambda, λ=0.032m；Radar system transmitted signal bandwidth B, B= 200MHz；Radar system launches signal chirp rate μ, μ=2e+14；Radar system pulse recurrence frequency PRF, PRF= 6100Hz；Radar system distance is to sampling number M, M=4096；Radar system orientation is to sampling number N, N=8192；Launch flat Platform is at the locus [x of initial time_T0,y_T0,z_T0] it is [-300 ,-500,514] km, receiving platform is in the space of initial time Position [x_R0,y_R0,z_R0] it is [4.5 ,-5,6] km；Velocity magnitude v of flat pad_T, v_T=7600m/s；The speed of receiving platform Size v_R, v_R=101.98m/s；Launch and receiving platform movement velocity angular separation,

B, according to arbitrary configuration double-base synthetic aperture radar system Range compress back echo 2-d spectrum analytic expression, obtain Spectral phase ψ (ξ, η；X, y), and by spectral phase ψ (ξ, η；X, y) according to two-dimensional spatial location and two-dimensional frequency carry out uniformly from Dispersion, obtains the spectral phase of discretization

Arbitrary configuration double-base synthetic aperture radar system Range compress back echo 2-d spectrum analytic expression in the present invention, tool Body is:

D (ξ, η)=∫ ∫ σ (x, y) exp (-j2 π ψ (ξ, η；x,y))dxdy

Wherein, ξ is emission signal frequency, and η is Doppler frequency, σ (x, y) for being positioned at (x, y) scattering coefficient of place's target, ψ(ξ,η；X, y) is spectral phase.

According to arbitrary configuration double-base synthetic aperture radar system Range compress back echo 2-d spectrum analytic expression, obtain frequency Spectrum phase place ψ (ξ, η；X, expression formula y), particularly as follows:

$\mathrm{\ψ}(\mathrm{\ξ},\mathrm{\η};x,y)=\underset{p=0}{\overset{P}{\mathrm{\Σ}}}{s}_p(x,y)\·f_p(\mathrm{\ξ},\mathrm{\η})$

Wherein, P is integer, it is possible to adjusting P value size according to frequency spectrum required precision, usual value is P >=4, s_pFor closing In the compound function of two-dimensional spatial location, f_pFor the compound function about two-dimensional frequency, p=0,1 ..., P.

f_pExpression formula particularly as follows:

$f_p(\mathrm{\ξ},\mathrm{\η})={\left(\frac{1}{\mathrm{\ξ}}\right)}^{p-1}{\mathrm{\η}}^p$

s_pExpression formula particularly as follows:

$\begin{array}{c}{s}_0(x,y)=(-k_0(x,y)+\underset{q=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\γ}}_q(x,y)\·k_1^q(x,y))/c\\ s_1(x,y)=-t_{\mathrm{cen}}(x,y)-\underset{q=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\γ}}_q(x,y)\·k_1^{p-1}(x,y)\\ s_p(x,y)=\underset{q=p}{\overset{P}{\mathrm{\Σ}}}\frac{q!c^{p-1}}{p!(q-p)!}{\mathrm{\γ}}_q(x,y)\·k_1^{q-p}(x,y),p\≥2\end{array}$

Wherein, c is the light velocity, γ_q, q=2,3,4, expression formula be respectively as follows:

$\begin{array}{c}{\mathrm{\γ}}_2(x,y)=\frac{1}{{4k}_2(x,y)}\\ {\mathrm{\γ}}_3(x,y)=\frac{k_3(x,y)}{8{k_2}^3(x,y)}\\ {\mathrm{\γ}}_4(x,y)=\frac{9{k_3}^2(x,y)-4k_2(x,y)\·k_4(x,y)}{64{k_2}^5(x,y)}\end{array}$

Wherein, k_p(x is y) about GBSAR system oblique distance history R (t；X, p order derivative y),R(t；X, y)=k₀(x, y)=r_T(x,y)/cosθ_T(x,y)+r_R(x,y)/cosθ_R (x, y), t_cenFor the synthetic aperture central instant of target, r_TFor the nearest oblique distance of flat pad distance objective, r_RFor receiving platform The nearest oblique distance of distance objective, θ_TFor the angle of strabismus of flat pad relative target, θ_RFor the angle of strabismus of receiving platform relative target, r_T、r_R、θ_TAnd θ_RExpression formula be respectively as follows:

Wherein, [x_T0,y_T0,z_T0] it is the initial position of GBSAR system flat pad, [x_R0,y_R0,z_R0] it is GBSAR system The initial position of receiving platform, v_TFor the movement velocity size of GBSAR system flat pad, v_RFor GBSAR system receiving platform Movement velocity size,It is the transmitting of GBSAR system, the corner dimension in receiving platform movement velocity direction.

By spectral phase ψ (ξ, η；X, y) carries out uniform discrete according to two-dimensional spatial location and two-dimensional frequency, obtains discrete The spectral phase changedDiscretization spectral phaseExpression formula, particularly as follows:

Wherein, ξ_m,η_nIt is respectively two-dimensional frequency discrete point position, ξ_m=ξ₀+mΔξ,η_n=η₀+ n Δ η, ξ₀,η₀It is respectively and sends out Penetrating signal center frequency and echo-signal doppler centroid, Δ ξ, Δ η are respectively two-dimensional frequency interval, Δ ξ=B/M, Δ η =PRF/N, m, n are respectively two-dimensional frequency and number, m=-M/2 ..., M/2-1, n=-N/2 ..., N/2-1, x_i,y_lIt is respectively Two-dimensional spatial location discrete point position, x_i=x_ref+iΔx,y_l=y_ref+ l Δ y, Δ x, Δ y are respectively between two-dimensional spatial location Every, i, l are respectively two-dimensional spatial location and number, i=-M/2 ..., M/2-1, l=-N/2 ..., N/2-1, x_ref,y_refFor ginseng Examination point target two-dimensional spatial location.

The embodiment of the present invention takes P=4, is calculated ξ₀=9.5GHz, η₀=99.5KHz, Δ ξ=48828Hz, Δ η= 0.74Hz, m=-2048 ..., 2047, n=-4096 ..., 4095, i=-2048 ..., 2047, l=-4096 ..., 4095, x_ref=0, y_ref=0.

C, employing Discrete Linear least square method, the discretization spectral phase that will obtain in step B In spatial function s_p, p >=2, it is expressed as spatial function s₀With spatial function s₁Linear function.

The present invention uses Discrete Linear least square method, particularly as follows:

Set system of linear equations Ax=b, wherein, A be the matrix of L row K row and A be system of linear equations Ax=b be Matrix number, $A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& ...& a_{1K}\\ a_{21}& a_{22}& ...& a_{2K}\\ ...& ...& ...& ...\\ a_{L1}& a_{L2}& ...& a_{\mathrm{LK}}\end{array}\right],$ B=[b₁ ... b_L]^T, x is unknown column vector x=[x₁ x₂ ... x_K]^T, A, b For known quantity, L > K；The solution solving x is x=(AA^T)^-1A^TB, x meetI.e. x meets linear The mean square error of equation group and minimum.

The present invention uses Discrete Linear least square method, the discretization spectral phase that will obtain in step BIn spatial function s_p, p >=2, it is expressed as spatial function s₀With spatial function s₁Linear function, particularly as follows:

$s_p(x_i,y_l)={\mathrm{\α}}_p^s\·s_0(x_i,y_l)+{\mathrm{\β}}_p^s\·s_1(x_i,y_l)+\mathrm{\Δ}{s}_p(x_i,y_l)$

Wherein, ${\mathrm{\α}}_p^s,{\mathrm{\β}}_p^s=\arg \underset{{\mathrm{\α}}_p^s,{\mathrm{\β}}_p^s}{\min }\underset{i=-M/2}{\overset{M/2-1}{\mathrm{\Σ}}}\underset{l=-M/2}{\overset{M/2-1}{\mathrm{\Σ}}}{\left|\mathrm{\Δ}{s}_p(x_i,y_l)\right|}^2.$

In the embodiment of the present invention, p=2,3,4, then

$s_p(x_i,y_l)={\mathrm{\α}}_p^s\·s_0(x_i,y_l)+{\mathrm{\β}}_p^s\·s_1(x_i,y_l)+\mathrm{\Δ}{s}_p(x_i,y_l)$

Wherein, ${\mathrm{\α}}_p^s,{\mathrm{\β}}_p^s=\arg \underset{{\mathrm{\α}}_p^s,{\mathrm{\β}}_p^s}{\min }\underset{i=-2048}{\overset{2047}{\mathrm{\Σ}}}\underset{l=-4096}{\overset{4095}{\mathrm{\Σ}}}{\left|\mathrm{\Δ}{s}_p(x_i,y_l)\right|}^2.$

D, employing Discrete Linear least square method, the discretization spectral phase that will obtain in step B In frequency function f_p, p >=2, it is expressed as frequency function g₀With frequency function g₁Linear function.

The present invention uses Discrete Linear least square method, the discretization spectral phase that will obtain in step BIn frequency function f_pIt is expressed as frequency function g₀With frequency function g₁Linear function, particularly as follows:

$f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)={\mathrm{\α}}_p^f\·g_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+{\mathrm{\β}}_p^f\·g_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+\mathrm{\Δ}{f}_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)$

Wherein, $g_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)=f_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+\underset{p=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\α}}_p^s\·f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n),g_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)=f_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+\underset{p=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\β}}_p^s\·f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n),$ ${\mathrm{\α}}_p^f,{\mathrm{\β}}_p^f=\arg \underset{{\mathrm{\α}}_p^f,{\mathrm{\β}}_p^f}{\min }\underset{m=-M/2}{\overset{M/2-1}{\mathrm{\Σ}}}\underset{n=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}{\left|\mathrm{\Δ}{f}_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)\right|}^2.$

In the embodiment of the present invention, p=2,3,4, then

$f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)={\mathrm{\α}}_p^f\·g_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+{\mathrm{\β}}_p^f\·g_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+\mathrm{\Δ}{f}_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)$

Wherein, $g_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)=f_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+\underset{p=2}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_p^s\·f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n),g_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)=f_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+\underset{p=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\β}}_p^s\·f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n),$ ${\mathrm{\α}}_p^f,{\mathrm{\β}}_p^f=\arg \underset{{\mathrm{\α}}_p^f,{\mathrm{\β}}_p^f}{\min }\underset{m=-2048}{\overset{2047}{\mathrm{\Σ}}}\underset{n=-4096}{\overset{4095}{\mathrm{\Σ}}}{\left|\mathrm{\Δ}{f}_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)\right|}^2.$

E, utilize the spatial function s that step C obtains₀With spatial function s₁Linear function and step D in the frequency letter that obtains Number g₀With frequency function g₁Linear function to discretization spectral phaseIt is weighted summation, obtains discretization The simplified expression of spectral phase.

The present invention utilizes the spatial function s that step C obtains₀With spatial function s₁Linear function and step D in the frequency that obtains Rate function g₀With frequency function g₁Linear function to discretization spectral phaseBe weighted summation, obtain from The simplified expression of dispersion spectral phase, is expressed as:

Wherein, $w_0(x_i,y_l)=s_0(x_i,y_l)+\underset{p=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\α}}_p^f\·\mathrm{\Δ}{s}_p(x_i,y_l),w_1(x_i,y_l)=s_1(x_i,y_l)+\underset{p=2}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\β}}_p^f\·\mathrm{\Δ}{s}_p(x_i,y_l).$

As it is shown on figure 3, after being the arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying process of the present invention The error schematic diagram simplifying spectral phase and actual spectrum phase place obtained.From the figure 3, it may be seen that be 1km × km for scene domain Targeted imaging region, simplify the difference between 2-d spectrum phase place and actual spectrum phase place the least and can ignore, therefore, It is special that the arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying of the present invention can correctly describe GBSAR system echoes Levy, can be used for realizing the application such as its high-resolution focal imaging.

Those of ordinary skill in the art it will be appreciated that embodiment described here be to aid in reader understanding this Bright principle, it should be understood that protection scope of the present invention is not limited to such special statement and embodiment.This area It is each that those of ordinary skill can make various other without departing from essence of the present invention according to these technology disclosed by the invention enlightenment Planting concrete deformation and combination, these deform and combine the most within the scope of the present invention.

Claims (8)

1. an arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying, it is characterised in that comprise the following steps:

A, forward sight double-base synthetic aperture radar imaging systematic parameter is carried out initialization process,

Wherein, forward sight double-base synthetic aperture radar imaging systematic parameter specifically includes: signal center's frequency that radar system is launched Rate ξ₀, radar emission signal wavelength lambda, radar system transmitted signal bandwidth B, radar system launches signal chirp rate μ, radar system System pulse recurrence frequency PRF, radar system distance exists to sampling number N, flat pad to sampling number M, radar system orientation Locus [the x of initial time_T0,y_T0,z_T0], receiving platform is at the locus [x of initial time_R0,y_R0,z_R0]；Launch flat Velocity magnitude v of platform_T, velocity magnitude v of receiving platform_R, launch and receiving platform movement velocity angular separation

B, according to arbitrary configuration double-base synthetic aperture radar system Range compress back echo 2-d spectrum analytic expression, obtain frequency spectrum Phase place ψ (ξ, η；X, y), and by spectral phase ψ (ξ, η；X, y) carries out the most discrete according to two-dimensional spatial location and two-dimensional frequency Change, obtain the spectral phase of discretizationWherein, ξ is emission signal frequency, and η is Doppler frequency, (x, y) For target location, ξ_m,η_nIt is respectively two-dimensional frequency discrete point position, x_i,y_lIt is respectively two-dimensional spatial location discrete point position；

C, employing Discrete Linear least square method, the discretization spectral phase that will obtain in step BIn Spatial function s_p, p >=2, it is expressed as spatial function s₀With spatial function s₁Linear function；

D, employing Discrete Linear least square method, the discretization spectral phase that will obtain in step BIn frequency Rate function f_p, p >=2, it is expressed as frequency function g₀With frequency function g₁Linear function；

E, utilize the spatial function s that step C obtains₀With spatial function s₁Linear function and step D in the frequency function g that obtains₀ With frequency function g₁Linear function to discretization spectral phaseIt is weighted summation, obtains discretization frequency spectrum The simplified expression of phase place.

2. arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying as claimed in claim 1, it is characterised in that: Described arbitrary configuration double-base synthetic aperture radar system Range compress back echo 2-d spectrum analytic expression, particularly as follows:

D (ξ, η)=∫ ∫ σ (x, y) exp (-j2 π ψ (ξ, η；x,y))dxdy

Wherein, ξ is emission signal frequency, and η is Doppler frequency, σ (x, y) for being positioned at (x, y) scattering coefficient of place's target, ψ (ξ, η；X, y) is spectral phase, and j is imaginary unit.

3. arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying as claimed in claim 1, it is characterised in that: Described spectral phase ψ (ξ, η；X, expression formula y), particularly as follows:

$\mathrm{\ψ}(\mathrm{\ξ},\mathrm{\η};x,y)=\underset{p=0}{\overset{P}{\Σ}}{s}_p(x,y)\·f_p(\mathrm{\ξ},\mathrm{\η})$

Wherein, P is integer, P >=4, s_pFor the compound function about two-dimensional spatial location, f_pFor the compound letter about two-dimensional frequency Number, p=0,1 ..., P.

4. arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying as claimed in claim 1, it is characterised in that: Described discretization spectral phaseExpression formula, particularly as follows:

Wherein, ξ_m,η_nIt is respectively two-dimensional frequency discrete point position, x_i,y_lBeing respectively two-dimensional spatial location discrete point position, m, n divide Not numbering for two-dimensional frequency, i, l are respectively two-dimensional spatial location numbering.

5. arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying as claimed in claim 1, it is characterised in that: The described discretization spectral phase that will obtain in step BIn spatial function s_p, p > 2, it is expressed as space letter Number s₀With spatial function s₁Linear function, particularly as follows:

$s_p(x_i,y_l)={\mathrm{\α}}_p^s\·s_0(x_i,y_l)+{\mathrm{\β}}_p^s\·s_1(x_i,y_l)+{\mathrm{\Δs}}_p(x_i,y_l)$

Wherein,It is the weight coefficient utilizing least square method to obtain,

${\mathrm{\α}}_p^s,{\mathrm{\β}}_p^s=\arg \underset{{\mathrm{\α}}_p^s,{\mathrm{\β}}_p^s}{min}\underset{i=-I/2}{\overset{M/2-1}{\Σ}}\underset{l=-L/2}{\overset{M/2-1}{\Σ}}|{\mathrm{\Δs}}_p(x_i,y_l){|}^2,$

${\mathrm{\Δs}}_p(x_i,y_l)=s_p(x_i,y_l)-{\mathrm{\α}}_p^s\·s_0(x_i,y_l)-{\mathrm{\β}}_p^s\·s_1(x_i,y_l).$

6. arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying as claimed in claim 5, it is characterised in that: The described discretization spectral phase that will obtain in step BIn frequency function f_p, p > 2, it is expressed as frequency letter Number g₀With frequency function g₁Linear function, particularly as follows:

$f_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)={\mathrm{\α}}_p^f\·g_0({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+{\mathrm{\β}}_p^f\·g_1({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)+{\mathrm{\Δf}}_p({\mathrm{\ξ}}_m,{\mathrm{\η}}_n)$

Wherein, It is the weight coefficient utilizing least square method to obtain, f_p, p=0,1 ..., P is about two-dimensional frequency Compound function:

7. arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying as claimed in claim 6, it is characterised in that: The simplified expression of described discretization spectral phase, particularly as follows:

Wherein,

8. arbitrary configuration double-base synthetic aperture radar echo spectrum method for simplifying as claimed in claim 1, it is characterised in that: Described Discrete Linear least square method, particularly as follows:

Setting system of linear equations Ax=b, wherein, A is the matrix that a L row K arranges and the coefficient square that A is system of linear equations Ax=b Battle array,B=[b₁ ... b_L]^T, x is unknown column vector x=[x₁ x₂ ... x_K]^T, A, b are The amount of knowing, L > K；The solution solving x is x=(AA^T)^-1A^TB, x meet