CN112698279A - One-station fixed bistatic SAR echo signal rapid generation method - Google Patents

One-station fixed bistatic SAR echo signal rapid generation method Download PDF

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CN112698279A
CN112698279A CN202011307790.XA CN202011307790A CN112698279A CN 112698279 A CN112698279 A CN 112698279A CN 202011307790 A CN202011307790 A CN 202011307790A CN 112698279 A CN112698279 A CN 112698279A
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谢洪途
陈凯鹏
王国倩
梁康
胡俊
姜新桥
李金堂
林奕全
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Sun Yat Sen University
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Abstract

The invention provides a method for quickly generating a stationary bistatic SAR echo signal, which comprises the steps of firstly generating a radar emission signal and calculating FFT of the radar emission signal; secondly, dividing the synthetic aperture of the motion station into a plurality of sub apertures, and dividing the scene into a plurality of equidistant elliptical ring domains and elliptical polar scenes; then, calculating equivalent scattering coefficients of the elliptical polar scene corresponding to the central position of the sub-aperture of the motion station, simultaneously calculating the scattering coefficients of equidistant elliptical ring domains corresponding to all the sub-aperture positions by using FFT operation, and calculating system impulse response functions corresponding to all the sub-apertures and FFT thereof; and finally, multiplying the FFT of the radar emission signal and the FFT of the system impulse response function, then transforming the product to a time domain by utilizing IFFT operation to obtain a sub-aperture echo signal, and repeating the previous operation according to the sequence of the sub-apertures to finally obtain the echo signal of the scene.

Description

One-station fixed bistatic SAR echo signal rapid generation method
Technical Field
The invention relates to the technical field of radars, in particular to a method for quickly generating a stationary bistatic SAR echo signal.
Background
The Synthetic Aperture Radar (SAR) echo signal simulation technology is one of the key technologies of SAR system research and development, and is mainly used for system parameter verification, processing algorithm (including imaging algorithm, motion compensation algorithm, target detection algorithm and the like) test, scattering characteristic research and the like. To ensure that the performance of the designed SAR system meets the practical requirements, echo signal simulation and imaging processing should be implemented before the SAR system is developed. To ensure that the simulated echo signal is closer to the actual echo signal, the actual track effect (e.g., radar motion error) and the actual scene (e.g., extended scene) are considered in the echo signal simulation. Generally, for an extended scene containing a large number of scattering points, the echo signal simulation mainly includes two aspects: and (3) expanding scene scattering characteristic simulation and generating a fast echo signal. Many scholars have conducted intensive research on the scattering characteristics of the SAR model and the extended scene, and successfully extended the application to bistatic SAR systems. In addition, the scattering coefficient of the extended scene can be obtained through SAR experiments according to parameters such as special frequency, polarization and the like. The bistatic SAR rapid echo signal generation method is mainly researched, and extended scene scattering characteristic simulation is not considered, which means that the scene scattering coefficient is known.
The SAR echo signal generation method mainly comprises a time domain pulse-by-pulse point-by-point (TBT) algorithm, a one-dimensional fast Fourier (1DFFT) algorithm, a two-dimensional fast Fourier (2DFFT) algorithm and an inverse imaging processing (IMIP) algorithm. The time-domain TBT algorithm is used for generating SAR echo signals in a point-by-point pulse-by-pulse mode according to an SAR imaging configuration. The TBT algorithm can generate SAR echo signals with high accuracy, but it has a large amount of calculation. Therefore, the TBT algorithm is only suitable for SAR echo signal generation for a few discrete point targets. Franciscetti first proposed a 2DFFT algorithm, developed into a series of SAR echo signal simulators, and extended for application to bistatic SAR echo signal generation. The 2DFFT algorithm multiplies the two-dimensional spectrum of the scene scattering characteristic and the two-dimensional spectrum of the system transmission function, and then obtains SAR echo signals through two-dimensional Inverse Fast Fourier Transform (IFFT). Compared with a time-domain TBT algorithm, the generation efficiency of the 2DFFT algorithm is greatly improved, but the motion trail of the radar is difficult to consider. The IMIP method obtains SAR echo signal data by transforming image data into a signal space through an inverse process, and the generation efficiency of the algorithm is higher than that of the TBT algorithm, but the motion trajectory of radar is difficult to be considered. The 1DFFT algorithm uses FFT operations to compute the convolution of the transmit signal and the SAR system transfer function to obtain the SAR echo signal. The algorithm still generates the SAR echo signal pulse by pulse, so its generation efficiency is higher than the TBT algorithm, but is less efficient than the 2DFFT algorithm and the IMIP algorithm. In order to further improve the SAR echo signal generation efficiency, a sub-aperture technology is introduced to SAR echo signal generation, and a SAR echo signal fast generation method based on equivalent scatterer and sub-aperture processing is provided, so that the generation efficiency can be improved while the generation of high-precision echo signals is kept. However, the algorithm is mainly proposed for the generation of the monostatic SAR echo signal, and is not suitable for the rapid generation of the stationary bistatic SAR echo signal of one station. Therefore, how to solve the fast method suitable for generating the echo signal of the fixed bistatic SAR of one station is just a technical problem to be solved urgently.
The application number 201811078709.8 discloses a high-efficiency bistatic SAR echo generation method suitable for any platform track, which comprises the steps of firstly modeling bistatic SAR points and surface target echoes in a complex geometric mode, then carrying out Doppler characteristic analysis, Doppler phase space distribution characteristic analysis and wavenumber domain analysis on the bistatic SAR points and the surface target echoes to obtain the bistatic SAR surface target echo generation method suitable for the complex geometric mode, and finally realizing the high-efficiency echo generation of the bistatic SAR. However, this patent does not realize the improvement of the generation efficiency of the present application while maintaining the high-precision generation of the echo signal.
Disclosure of Invention
The invention provides a method for quickly generating a stationary bistatic SAR echo signal, which can keep high-precision generation of the echo signal and improve the generation efficiency.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
a method for quickly generating a stationary bistatic SAR echo signal comprises the following steps:
s1: setting system simulation parameters and scene scattering coefficients, generating radar emission signals and carrying out FFT calculation on the radar emission signals;
s2: dividing the synthetic aperture of the motion station into a plurality of sub-apertures, and dividing the scene into a plurality of equidistant elliptical ring domains;
s3: calculating equivalent scattering coefficients of the elliptical polar scene corresponding to the central position of the sub-aperture of the motion station, calculating the scattering coefficients of equidistant elliptical ring domains corresponding to all the sub-aperture positions by using FFT, and calculating system impulse response functions corresponding to all the sub-apertures and FFT thereof;
s4: the FFT of the radar transmitting signal is multiplied by the FFT of the system impulse response function, then the product is transformed to a time domain by IFFT operation to obtain a sub-aperture echo signal, and the previous operation is repeated according to the sequence of the sub-apertures, so that the echo signal of the scene is finally obtained.
Further, the specific process of step S1 is:
let the motion station move along a line parallel to the Y-axis and the coordinates of the motion station at the time of the slow time eta be (0, Y)M(η),zM) The fixed station is located on a high tower and has the coordinate (x)S,0,zS) The scene is composed of a plurality of targets distributed on grid points, the size of the scene grid is MxN, namely the distance direction and the azimuth direction, the distance direction and the azimuth direction interval between adjacent grid points are respectively delta x and delta y, then the eta moment, the sum of the distances from the mobile station and the fixed station to the scene grid point (M, N) is R (eta, M, N), and the transmitting signal is set as a chirp signal p (tau) wr(τ)exp(j2πfcτ+jπKrτ2) Wherein w isr(. h) is the distance envelope, τ is the fast time, fcCarrier frequency, K, for transmitting signalsrThe frequency is adjusted in the distance direction, because the scene is distributed by a plurality of grid pointsThe scene echo signal is subjected to orthogonal demodulation to obtain:
Figure BDA0002788770180000031
wherein σmnThe scattering coefficients of scene grid points (m, n).
Further, the process of dividing the equidistant elliptical ring domain in step S2 is:
let Rmin(η) and Rmax(η) is the minimum and maximum of the sum of the distances from the mobile station and the fixed station to the scene at the time of η, Δ s is the interval between two adjacent equidistant elliptical rings, and then the number of equidistant elliptical rings in the scene is:
Np(η)＝round((Rmax(η)-Rmin(η))/Δs)+1；
if p-1 and p represent two adjacent equidistant elliptical rings, the sum of their distances to the radar is Rmin(η) + (p-1) Δ s and Rmin(η) + p Δ s, the spacing between the p-1 and p equidistant elliptical rings defining a p equidistant elliptical ring field, the sum of the distances from the centerline of the p equidistant elliptical ring field to the radar being:
R(η,p)＝Rmin(η)+(p-12)Δs；
in order to calculate the scattering coefficient of the pth equidistant elliptical ring domain, the sum of the distances from the center line of the pth equidistant elliptical ring domain to the radar is approximately used to replace the sum of the distances from all the targets in the pth equidistant elliptical ring domain to the radar, an equivalent scatterer is used to replace all the targets in the pth equidistant elliptical ring domain, and then the scattering coefficient of the equivalent scatterer is:
Figure BDA0002788770180000032
wherein, IpNumber of targets in the p-th equidistant elliptical ring, σiThe scattering coefficient of the ith target in the equidistant elliptical ring; Δ Ri(η, p) is the p-th equidistant elliptical ring summed with the distance from the i-th target to the radarThe difference between the sum of the distances from the center line of the domain to the radar, i.e.:
ΔRi(η,p)＝Ri(η)-(Rmin(η)+(p-12)Δs)
based on the equivalent scatterer model, the scene echo signal is represented as:
Figure BDA0002788770180000041
wherein, the symbol
Figure BDA0002788770180000044
For convolution with a fast time τ, since the convolution operation can be quickly implemented by FFT and IFFT operations, the above equation is expressed as:
Figure BDA0002788770180000042
according to the above formula, a fixed bistatic SAR echo signal can be quickly generated by using an equivalent scatterer and FFT/IFFT operation, so that the generation efficiency of the echo signal can be improved, but the above formula belongs to a pulse-by-pulse mode, and is not suitable for generation of a large number of pulse scene echo signals.
Further, the process of calculating the equivalent scattering coefficient of the elliptical polar scene corresponding to the central position of the sub-aperture of the motion station in step S3 is as follows:
let AηPosition of moving station at time η, AηcIs etacThe position of the moving station at the moment, namely the synthetic aperture center, B is the position of the fixed station, and the position of any grid point (m, n) of the scene is set as (x)m,yn0), grid points (m, n) to the synthetic aperture center a of the motion stationηcA distance of rM，rSLet ρ be η for the distance of the scene grid point (m, n) to the fixed station BcThe sum of the distances from the scene grid point (m, n) to the mobile station and the transmitting station at the moment of time, theta being the distance rMThe included angle between the positive direction of the Y axis, delta theta is the sampling interval of the scene ellipse polar angle, and the ellipse polar coordinates of the scene grid points (m, n)Defined as (ρ, θ), i.e.:
Figure BDA0002788770180000043
wherein Θ is the azimuth beam width of the motion station, the scene can be divided into a plurality of elliptical polar scenes, the scene targets are distributed in the elliptical polar scenes, and R (η, ρ) is assumedp,θk) For the aperture position A of the motion stationηAnd the sum of the distances from the fixed station B to the kth elliptical polar scene of the pth equidistant elliptical ring domain, the scene echo signal is:
Figure BDA0002788770180000051
wherein N isk(eta) is the number of elliptical polar sub-scenes in the p-th equidistant elliptical ring at the time of eta, and sigma (eta, rho)p,θk) The scattering coefficient of the kth elliptical polar scene of the pth equidistant elliptical ring domain is as follows:
Figure BDA0002788770180000052
wherein, Ip,kThe number of the targets in the kth elliptical polar scene of the pth equidistant elliptical ring domain.
Further, the process of calculating the scattering coefficients of the equidistant elliptical ring domains corresponding to all the sub-aperture positions by using FFT in step S3 is as follows:
setting etanFor the slow time of the n-th motion station sub-aperture, ηncFor the nth motion station sub-aperture center time,
Figure BDA0002788770180000053
is etancThe location of the mobile station is at the moment,
Figure BDA0002788770180000054
is etanThe position of the motion station at the moment defines the ellipse corresponding to the sub-aperture of the nth motion stationCircular polar coordinates (ρ)n,θn)，ΔθnFor the corresponding scene ellipse polar angle sampling interval,
Figure BDA0002788770180000055
is a straight line
Figure BDA0002788770180000056
Length of (d), T (ρ)np,θn0) And T' (ρ)np,θnk) For two elliptical polar scenes in the pth equidistant elliptical ring, and thetank＝θn0+kΔθn，rMnpIndicating a mobile station position
Figure BDA0002788770180000057
To an elliptical polar scene T (ρ)np,θn0) A distance of rSnpRepresenting a fixed station to an elliptical polar scene T (p)np,θn0) Distance of moving station
Figure BDA0002788770180000058
And a fixed station to an elliptical polar scene T' (ρ)np,θnk) Are each rM′npAnd rS′np；
For the sport station position
Figure BDA0002788770180000059
Sum of distances R (η, ρ)p,θk) Needs to be rewritten into R (eta)nc,ρnp,θnk) And it is equal for all elliptical polar scenes in the pth equidistant elliptical ring because it is equal to the variable θnkIndependently of one another, therefore, the sum of distances R (η)nc,ρnp,θnk) Simplified to R (eta)nc,ρnp) I.e. the location of the moving station
Figure BDA00027887701800000510
And the sum of the distances from the fixed station position B to the pth equidistant elliptical ring domain;
according to
Figure BDA00027887701800000511
Kinematic station position AηncThe corresponding scene echo signal is:
Figure BDA00027887701800000512
for other mobile station positions
Figure BDA00027887701800000513
Sum of distances R (η, ρ)p,θk) Need to be rewritten into R (eta)n,ρnp,θnk) But it is not equal for all elliptical polar scenes in the pth equidistant elliptical ring because it is equal to the variable θnkCorrelation, however, sum of distances R (η)n,ρnp,θnk) By sum of distances R (η)nc,ρnp) Represents:
Figure RE-GDA0002913934120000061
thus, the position of the exercise station
Figure BDA0002788770180000062
The corresponding scene echo signals are:
Figure BDA0002788770180000063
due to R (eta)nc,ρnp) And Δ R2And the variable k or thetakIndependently of Δ R1And the variable k or thetakIs related to
Figure BDA0002788770180000064
And
Figure BDA0002788770180000065
scattering coefficient σ (η)n,ρnp,θnk) Approximate generationIs instead σ (η)nc,ρnp,θnk) When the azimuth beam width of the antenna of the mobile station is sufficiently narrow, delta [ tau-2R (eta) ] is used in the digital signal processingn,ρnp,θnk)/c]And δ [ τ -2R (η)n,ρnp,θn0)/c]Is almost equal, the mobile station position
Figure BDA0002788770180000066
The corresponding scene echo signals are:
Figure BDA0002788770180000067
thus, the position of the exercise station
Figure BDA0002788770180000068
The scattering coefficient of the pth equidistant elliptical ring domain of (a) may be defined as:
Figure BDA0002788770180000069
according to the imaging geometry and the cosine theorem, | AnηT | + | BT | can be calculated and approximated as:
Figure BDA00027887701800000610
same distance
Figure BDA00027887701800000611
Can be calculated and approximated as:
Figure BDA0002788770180000071
thus, the distance difference Δ R1Calculated and approximated as:
Figure BDA0002788770180000072
since the azimuth beam width of the mobile station is assumed to be sufficiently narrow, k Δ θnIs relatively small, and thus, cos (θ)n0+kΔθn)-cos(θn0)≈-kΔθnsin(θn0) It is also reasonable, therefore, that Δ R1A further approximation is:
ΔR1≈-dηnkΔθnsin(θn0)
then:
Figure BDA0002788770180000073
if the scene polar angle sampling interval delta thetanThe following relationship can be satisfied:
Figure BDA00027887701800000711
wherein
Figure BDA0002788770180000074
For the position of a sports station
Figure BDA0002788770180000075
Distance to nth sub-aperture edge position, then:
Figure BDA0002788770180000076
let the nth sub-aperture be 2L in lengthnAnd corresponding reference numeral is ln＝-Ln…LnAnd then:
Figure BDA0002788770180000077
wherein
Figure BDA0002788770180000078
Is as followslnAt the position of a sports station
Figure BDA0002788770180000079
For the ith sub-aperturenScattering coefficient σ (l) of pulse, p-th equidistant elliptic ring equivalent scatterern,ρnp) Is the scattering coefficient sigma (eta)nc,ρnp,θnk) L-th obtained by FFT operationnThe number of the equivalent scatterers of the p-th equidistant elliptic ring domain can be calculated simultaneously through FFT operationn,ρnp) Thus, the position of the exercise station
Figure BDA00027887701800000710
The corresponding scene echo signal is calculated as:
Figure BDA0002788770180000081
when Δ R is satisfied1＝ΔR2When 0, the above formula can be simplified as:
Figure BDA0002788770180000082
thus, the scene echo signal of the nth sub-aperture is collectively represented as:
Figure BDA0002788770180000083
further, the calculation process for finally obtaining the echo signal of the scene in step S4 is:
the formula is calculated using FFT/IFFT operations:
Figure BDA0002788770180000084
obtaining:
Figure BDA0002788770180000085
compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention adopts equivalent scatterers, sub-apertures and sub-scene processing technology, can effectively solve the problem that the precision and the efficiency cannot be considered at the same time in the generation of the one-station fixed bistatic SAR echo signal, and greatly improves the generation efficiency while maintaining the high-precision generation of the echo signal, thereby realizing the high-efficiency high-precision generation of the one-station fixed bistatic SAR echo signal and obtaining the high-quality one-station fixed bistatic SAR echo signal. The method is suitable for echo signal generation of one-station fixed bistatic SAR of various carrying platforms, such as a vehicle-mounted platform, an airborne platform, a satellite-mounted platform and the like.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a fixed bistatic SAR imaging geometry of the present invention;
FIG. 3 is a schematic diagram of the distribution of two adjacent equidistant elliptical ring inner point targets according to the present invention;
FIG. 4 is a geometric schematic of elliptical polar imaging according to the present invention;
FIG. 5 is a schematic view of the sub-aperture and elliptical pole scene processing of the present invention;
FIG. 6 shows simulation system parameters in a simulation experiment;
FIG. 7 is a diagram of a scene echo signal generated by the TBT method and the present invention;
fig. 8 shows the imaging result of the BP algorithm on the echo signals in fig. 7.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the present embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
As shown in fig. 1, a method for rapidly generating a stationary bistatic SAR echo signal includes the following steps:
s1: setting system simulation parameters and scene scattering coefficients, generating radar emission signals and carrying out FFT calculation on the radar emission signals;
s2: dividing the synthetic aperture of the motion station into a plurality of sub-apertures, and dividing the scene into a plurality of equidistant elliptical ring domains;
s3: calculating equivalent scattering coefficients of the elliptical polar scene corresponding to the central position of the sub-aperture of the motion station, calculating the scattering coefficients of equidistant elliptical ring domains corresponding to all the sub-aperture positions by using FFT, and calculating system impulse response functions corresponding to all the sub-apertures and FFT thereof;
s4: the FFT of the radar transmitting signal is multiplied by the FFT of the system impulse response function, then the product is transformed to a time domain by IFFT operation to obtain a sub-aperture echo signal, and the previous operation is repeated according to the sequence of the sub-apertures, so that the echo signal of the scene is finally obtained.
The imaging geometry of a stationary bistatic SAR is shown in FIG. 2, and the coordinate axes are X-axis, Y-axis and Z-axis. Let the motion station move along a line parallel to the Y-axis and the coordinates of the motion station at the time of the slow time eta be (0, Y)M(η),zM) (ii) a The fixed station is located on a high tower and has the coordinate (x)S,0,zS) (ii) a Assuming that a scene can be considered to be composed of several objects distributed at grid points, the scene grid size is M × N (distance direction × azimuth direction), and the distance direction and azimuth direction intervals between adjacent grid points are Δ x and Δ y, respectively, then the sum of the distances from the mobile station and the fixed station to the scene grid point (M, N) at time η is:
R(η,m,n)＝RM(η,m,n)+RS(η,m,n),1≤m≤M,1≤n≤N (1)
wherein R isM(η, m, n) and RS(η, m, n) are the distances of the mobile station and the fixed station to the scene grid points (m, n) at time η, respectively.
Setting the transmitted signal to chirpSignal p (τ) ═ wr(τ)exp(j2πfcτ+jπKrτ2) Wherein w isr(. h) is the distance envelope, τ is the fast time, fcCarrier frequency, K, for transmitting signalsrIs the range chirp. Since the scene can be considered to be composed of a plurality of targets distributed at the grid points, the scene echo signal is, after orthogonal demodulation:
Figure BDA0002788770180000101
wherein σmnThe scattering coefficients of scene grid points (m, n).
Firstly, equidistant elliptic ring domain division and scatterer equivalence:
let Rmin(η) and Rmax(η) is the minimum and maximum of the sum of the distances from the mobile station and the fixed station to the scene at the time of η, Δ s is the interval between two adjacent equidistant elliptical rings, and then the number of equidistant elliptical rings in the scene is:
Np(η)＝round((Rmax(η)-Rmin(η))/Δs)+1 (3)
as shown in fig. 3, the target distribution of points in two adjacent equidistant elliptical rings is shown. p-1 and p represent two adjacent equidistant elliptical rings, the sum of their distances to the radar being Rmin(η) + (p-1) Δ s and Rmin(η) + p.DELTA.s. The interval between the p-1 and the p equidistant elliptical rings is defined as the p equidistant elliptical ring domain. The dotted circle line represents the center line of the pth equidistant elliptical ring domain, and the sum of the distances from the pth equidistant elliptical ring domain to the radar is:
R(η,p)＝Rmin(η)+(p-1/2)Δs (4)
in order to calculate the scattering coefficient of the p-th equidistant elliptical ring domain, the sum of the distances from the center line of the p-th equidistant elliptical ring domain to the radar is approximately used for replacing the sum of the distances from all the targets in the p-th equidistant elliptical ring domain to the radar. Therefore, an equivalent scatterer can be used to replace all targets in the p-th equidistant elliptical ring, and the scattering coefficient of the equivalent scatterer is:
Figure BDA0002788770180000102
wherein, IpNumber of targets in the p-th equidistant elliptical ring, σiThe scattering coefficient of the ith target in the equidistant elliptical ring. Δ Ri(η, p) is the difference between the sum of the distances from the ith target to the radar and the sum of the distances from the center line of the pth equidistant elliptical ring to the radar, namely:
ΔRi(η,p)＝Ri(η)-(Rmin(η)+(p-1/2)Δs) (6)
based on the equivalent scatterer model, the scene echo signal can be represented as:
Figure BDA0002788770180000111
wherein, the symbol
Figure BDA0002788770180000114
Is a convolution with respect to the fast time tau. Since the convolution operation can be rapidly implemented by FFT and IFFT operations, equation (7) can be expressed as:
Figure BDA0002788770180000112
as can be seen from equation (8), a stationary bistatic SAR echo signal can be generated quickly by using an equivalent scatterer and FFT/IFFT operation, and therefore, the generation efficiency of the echo signal can be improved. However, equation (8) still adopts a pulse-by-pulse method, and thus is not suitable for scene echo signal generation with a large number of pulses.
In order to improve the generation efficiency of scene echo signals of a large number of pulses, the invention introduces sub-aperture and sub-scene processing technologies into echo signal generation.
Secondly, sub-aperture and polar scene processing:
a one-station stationary bistatic SAR elliptical polar imaging geometry is shown in figure 4. Let AηPosition of the station at time η, AηcIs etacThe position of the mobile station (i.e. the synthetic aperture centre) at the moment and B is the position of the fixed station. Let the position of any grid point (m, n) of the scene be (x)m,yn,0). Grid point (m, n) to the center of the synthetic aperture of the motion station AηcA distance of rM，rSThe distance of the scene grid point (m, n) to the fixed station B. Let ρ be ηcThe sum of the distances from the time scene grid point (m, n) to the mobile station and the transmitting station, theta being the distance rMAnd the positive direction of the Y axis. And delta theta is the sampling interval of the scene ellipse polar angle. Thus, the elliptical polar coordinates of the scene grid points (m, n) are defined as (ρ, θ), i.e.:
Figure BDA0002788770180000113
where Θ is the mobile station azimuth beam width. In fig. 3, the scene may be divided into several elliptical pole scenes (areas divided by red arcs and dashed lines), and thus the scene objects may be considered to be distributed in these elliptical pole scenes. Let R (eta, rho)p,θk) For the aperture position A of the motion stationηAnd the sum of the distances from the fixed station B to the kth elliptical polar scene of the pth equidistant elliptical ring domain, the scene echo signal is:
Figure BDA0002788770180000121
wherein N isk(eta) is the number of elliptical polar sub-scenes in the p-th equidistant elliptical ring at the time of eta, and sigma (eta, rho)p,θk) The scattering coefficient of the kth elliptical polar scene of the pth equidistant elliptical ring domain is as follows:
Figure BDA0002788770180000122
wherein, Ip,kThe number of the targets in the kth elliptical polar scene of the pth equidistant elliptical ring domain.
Dividing the radar pulse train into groups, i.e. moving stationsThe synthetic aperture is divided into a number of sub-apertures, and each sub-aperture contains the same number of radar pulses. When the sub-aperture time is relatively short, all pulses in the same sub-aperture can be considered to illuminate the same scene range. Fig. 5 is a sub-aperture processing in a station stationary bistatic SAR echo signal generation. Setting etanFor the slow time of the n-th motion station sub-aperture, ηncFor the nth mobile station sub-aperture center time,
Figure BDA0002788770180000123
is etancThe location of the mobile station is at the moment,
Figure BDA0002788770180000124
is etanThe location of the mobile station is moved at that time. Similar to the elliptical polar coordinates (ρ, θ) in FIG. 3, the elliptical polar coordinates (ρ, θ) corresponding to the nth motion station sub-aperture may be definedn,θn)。ΔθnFor the corresponding scene ellipse polar angle sampling interval,
Figure BDA0002788770180000125
is a straight line
Figure BDA0002788770180000126
Length of (d). Let T (ρ)np,θn0) And T' (ρ)np,θnk) For two elliptical polar scenes in the pth equidistant elliptical ring, and thetank＝θn0+kΔθn。rMnpIndicating a mobile station position
Figure BDA0002788770180000127
To an elliptical polar scene T (ρ)np,θn0) A distance of rSnpRepresenting a fixed station to an elliptical polar scene T (p)np,θn0) The distance of (c). Also, the station position
Figure BDA0002788770180000128
And a fixed station to an elliptical polar scene T' (ρ)np,θnk) Are each r'MnpAnd r'Snp。
For the sport station position
Figure BDA0002788770180000129
Sum of distances R (eta, rho) in the formula (10)p,θk) Needs to be rewritten into R (eta)nc,ρnp,θnk) And it is equal for all elliptical polar scenes in the pth equidistant elliptical ring because it is equal to the variable θnkIs irrelevant. Therefore, the sum of distances R (η)nc,ρnp,θnk) Can be simplified to R (eta)nc,ρnp) I.e. the position of the moving station
Figure BDA00027887701800001210
And the sum of the distances of the fixed station location B to the p-th equidistant elliptical ring field. According to
Figure BDA00027887701800001211
Motion station location
Figure BDA00027887701800001212
The corresponding scene echo signals are:
Figure BDA00027887701800001213
for other mobile station positions
Figure BDA0002788770180000131
Similarly, the sum of distances R (η, ρ) in equation (10)p,θk) Need to be rewritten into R (eta)n,ρnp,θnk) But it is not equal for all elliptical polar scenes in the pth equidistant elliptical ring because it is equal to the variable θnkAnd (4) correlating. However, the sum of distances R (η)n,ρnp,θnk) Sum of available distances R (η)nc,ρnp) Represents:
Figure RE-GDA0002913934120000131
thus, the position of the exercise station
Figure BDA0002788770180000133
The corresponding scene echo signals are:
Figure BDA0002788770180000134
it is known that R (. eta.)nc,ρnp) And Δ R2And a variable k (or θ)k) Independently of Δ R1And a variable k (or θ)k) And (4) correlating.
To simplify equation (14), the present invention uses some reasonable assumptions: (1) and imaging the far-field scene. Thus, it is possible to provide
Figure BDA0002788770180000135
And
Figure BDA0002788770180000136
is reasonable in one-station fixed bistatic SAR far-field scene imaging. (2) The sub-aperture time is sufficiently short. Therefore, it can be considered that all pulses in the same sub-aperture irradiate the same scene range, and the scattering coefficient σ (η) in equation (14)n,ρnp,θnk) Can be approximately substituted by sigma (eta)nc,ρnp,θnk). (3) The azimuth beamwidth of the mobile station antenna is sufficiently narrow. Thus, delta [ tau-2R (eta) in digital signal processingn,ρnp,θnk)/c]And δ [ τ -2R (η)n,ρnp,θn0)/c]The values of (a) and (b) are almost equal. Based on the above assumptions, equation (14) can be approximated as:
Figure BDA0002788770180000137
thus, the position of the exercise station
Figure BDA0002788770180000141
The scattering coefficient of the pth equidistant elliptical ring domain can be defined as:
Figure BDA0002788770180000142
according to the imaging geometry and the cosine theorem, | AnηT | + | BT | can be calculated and approximated as:
Figure BDA0002788770180000143
same distance
Figure BDA0002788770180000144
Can be calculated and approximated as:
Figure BDA0002788770180000145
therefore, the distance difference Δ R in the formula (15)1Can be calculated and approximated as:
Figure BDA0002788770180000146
since the azimuth beam width of the mobile station is assumed to be sufficiently narrow, k Δ θnThe value of (a) is generally small. Thus, cos (θ)n0+kΔθn)-cos(θn0)≈-kΔθnsin(θn0) It is also reasonable. Therefore,. DELTA.R1A further approximation is:
Figure BDA0002788770180000147
equation (16) can be approximated as:
Figure BDA0002788770180000148
if the scene polar angle sampling interval delta thetanThe following relationship can be satisfied:
Figure BDA00027887701800001412
wherein
Figure BDA0002788770180000149
For the position of a sports station
Figure BDA00027887701800001410
The distance to the nth sub-aperture edge position, equation (21) can be written as:
Figure BDA00027887701800001411
suppose that the nth sub-aperture is 2L in lengthnAnd corresponding reference numeral is ln＝-Ln…LnThen equation (23) can be written as:
Figure BDA0002788770180000151
wherein
Figure BDA0002788770180000152
Is the firstnAt the position of a sports station
Figure BDA0002788770180000153
A discrete value of (d). Compared to the FFT formula, the formula (24) can be calculated quickly and accurately using the FFT operation. For the l in the n sub-aperturenScattering coefficient σ (l) of pulse, p-th equidistant elliptic ring equivalent scatterern,ρnp) Can be regarded as the scattering coefficient sigma (eta)nc,ρnp,θnk) L-th obtained by FFT operationnAnd (4) the number. That is, the scattering coefficient σ (l) of the p-th equidistant elliptic region equivalent scatterer can be simultaneously calculated by the FFT operationn,ρnp) This will greatly improve the generation efficiency of the one-station stationary bistatic SAR echo signal.Thus, the position of the exercise station
Figure BDA0002788770180000154
The corresponding scene echo signal may be calculated as:
Figure BDA0002788770180000155
when Δ R is satisfied1＝ΔR2When 0, equation (25) can be simplified to equation (12). Thus, the scene echo signal of the nth sub-aperture can be collectively expressed as:
Figure BDA0002788770180000156
and finally, rapidly generating a scene echo signal:
in summary, equation (26) can be calculated using FFT/IFFT operations, namely:
Figure BDA0002788770180000157
therefore, a fixed bistatic SAR echo signal can be generated rapidly through equivalent scatterers, sub-aperture processing, FFT/IFFT operation and the like, so that the generation efficiency of a scene echo signal is improved.
The simulation experiment is carried out by using the method, and the simulation system parameters in the method are shown in figure 6. The 81 discrete point targets are located in a scene of size 200m × 200m (distance direction × azimuth direction), arranged in 9 rows and 9 columns. The distance and azimuth interval between two adjacent point targets are 20.98m and 22.44m respectively. The position of the scene center point object is (1100,0,0) m. The scattering coefficient for all point targets in the scene is assumed to be 1m 2.
As shown in fig. 7, the TBT method and the scene echo signal generated by the present invention are given. As can be seen from fig. 7(a) and 7(b), the echo signals generated by the two methods are very similar. Fig. 7(c) shows the amplitude and phase errors of the echo signals generated by the two methods, and it can be found that the maximum relative amplitude error of the two echo signals is 0.01 and the maximum absolute phase error is 0.3 rad. The amplitude error and the phase error are caused by the approximation of the sub-aperture processing in the present invention. Furthermore, both methods produce echo signals with a correlation coefficient of 0.9814, very close to 1. Therefore, the invention can effectively generate high-precision scene echo signals.
The echo signals in fig. 7(a) and 7(b) are subjected to imaging processing by using the high-precision BP algorithm, and the obtained imaging result is shown in fig. 8. As can be seen from fig. 8(a) and 8(b), the imaging results of the two echo signals are very similar, and all discrete point targets achieve good focus. Fig. 8(c) and 8(d) show the profile of the center-point objects in the scenes of fig. 8(a) and 8(b), respectively, where the center-point objects in the scenes can be seen to be imaged very closely, but the focus quality of the image in fig. 8(d) is slightly lower than that of the image in fig. 8 (c). This is because the present invention has a certain approximation but has little effect on the main lobe and only a slight effect on the side lobes.
Under the same simulation condition, the time of generating the echo signal by the TBT method and the invention is measured. The TBT method and the time of the present invention are 201671.3s and 1425.4s, respectively. Compared with the TBT method, the generation efficiency of the echo signal is improved by nearly 141.5 times. Therefore, the invention can quickly generate a high-precision one-station fixed bistatic SAR echo signal.
The same or similar reference numerals correspond to the same or similar parts;
the positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications can be made on the basis of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. A method for quickly generating a stationary bistatic SAR echo signal is characterized by comprising the following steps:
s1: setting system simulation parameters and scene scattering coefficients, generating radar emission signals and carrying out FFT calculation on the radar emission signals;
s2: dividing the synthetic aperture of the motion station into a plurality of sub-apertures, and dividing the scene into a plurality of equidistant elliptical ring domains;
s3: calculating equivalent scattering coefficients of the elliptical polar scene corresponding to the central position of the sub-aperture of the motion station, calculating the scattering coefficients of equidistant elliptical ring domains corresponding to all the sub-aperture positions by using FFT, and calculating system impulse response functions corresponding to all the sub-apertures and FFT thereof;
s4: the FFT of the radar transmitting signal is multiplied by the FFT of the system impulse response function, then the product is transformed to a time domain by utilizing IFFT operation to obtain a sub-aperture echo signal, and the previous operation is repeated according to the sequence of the sub-apertures, so that the echo signal of the scene is finally obtained.
2. The method for rapidly generating the fixed bistatic SAR echo signal according to claim 1, wherein the specific process of the step S1 is:
let the motion station move along a line parallel to the Y-axis and the coordinates of the motion station at the time of the slow time eta be (0, Y)M(η),zM) The fixed station is located on a high tower and has the coordinate (x)S,0,zS) The scene is composed of a plurality of targets distributed on grid points, the size of the scene grid is MxN, namely the distance direction and the azimuth direction, the distance direction and the azimuth direction interval between adjacent grid points are respectively delta x and delta y, then the eta moment, the sum of the distances from the mobile station and the fixed station to the scene grid points (M, N) is R (eta, M, N), and the transmitting signal is set as a chirp signal p (tau) wr(τ)exp(j2πfcτ+jπKrτ2) Wherein w isr(. h) is the distance envelope, τ is the fast time, fcCarrier frequency, K, for transmitting signalsrFor adjusting the frequency in the range direction, the scene is composed of a plurality of targets distributed at grid pointsThen, the scene echo signal is subjected to orthogonal demodulation to be:
Figure FDA0002788770170000011
wherein σmnThe scattering coefficients of scene grid points (m, n).
3. The method for rapidly generating the one-station stationary bistatic SAR echo signal according to claim 2, wherein the dividing of the equidistant elliptical ring domain in the step S2 is:
let Rmin(η) and Rmax(η) is the minimum and maximum of the sum of the distances from the mobile station and the fixed station to the scene at the time of η, Δ s is the interval between two adjacent equidistant elliptical rings, and then the number of equidistant elliptical rings in the scene is:
Np(η)＝round((Rmax(η)-Rmin(η))/Δs)+1。
4. a method for fast generation of a stationary bistatic SAR echo signal according to claim 3, characterized in that if p-1 and p represent two adjacent equidistant elliptical rings, the sum of their distances to the radar is Rmin(η) + (p-1) Δ s and Rmin(η) + p Δ s, the interval between the p-1 and p equidistant elliptical rings is defined as the p equidistant elliptical ring domain, and the sum of the distances from the center line of the p equidistant elliptical ring domain to the radar is:
R(η,p)＝Rmin(η)+(p-1/2)Δs。
5. the method as claimed in claim 4, wherein to calculate the scattering coefficient of the p-th equidistant elliptical ring domain, the sum of the distances from the center line of the p-th equidistant elliptical ring domain to the radar is used to approximately replace the sum of the distances from all targets in the p-th equidistant elliptical ring domain to the radar, and an equivalent scatterer is used to replace all targets in the p-th equidistant elliptical ring domain, so that the scattering coefficient of the equivalent scatterer is:
Figure FDA0002788770170000021
wherein, IpNumber of targets in the p-th equidistant elliptical ring, σiThe scattering coefficient of the ith target in the equidistant elliptical ring.
6. The method for rapidly generating the SAR echo signal of claim 5, wherein Δ R isi(η, p) is the difference between the sum of the distances from the ith target to the radar and the sum of the distances from the center line of the pth equidistant elliptical ring to the radar, namely:
ΔRi(η,p)＝Ri(η)-(Rmin(η)+(p-1/2)Δs)。
7. the method for rapidly generating the one-station stationary bistatic SAR echo signal according to claim 6, characterized in that based on the equivalent scatterer model, the scene echo signal is expressed as:
Figure FDA0002788770170000022
wherein, the symbol
Figure FDA0002788770170000023
For convolution with a fast time τ, since the convolution operation can be quickly implemented by FFT and IFFT operations, the above equation is expressed as:
Figure FDA0002788770170000031
according to the above formula, a fixed bistatic SAR echo signal can be quickly generated by using an equivalent scatterer and FFT/IFFT operation, so that the generation efficiency of the echo signal can be improved.
8. The method for rapidly generating the one-station stationary bistatic SAR echo signal according to claim 1, wherein the step S3 of calculating the equivalent scattering coefficient of the moving station sub-aperture center position corresponding to the elliptical polar sub-scene is as follows:
let AηIs the position of the mobile station at time η,
Figure FDA0002788770170000032
is etacThe position of the moving station at the moment, namely the synthetic aperture center, B is the position of the fixed station, and the position of any grid point (m, n) of the scene is set as (x)m,yn0), grid points (m, n) to the synthetic aperture center of the motion station
Figure FDA0002788770170000033
A distance of rM，rSLet ρ be η for the distance of the scene grid point (m, n) to the fixed station BcThe sum of the distances from the scene grid point (m, n) to the mobile station and the transmitting station at the moment of time, theta being the distance rMThe angle between the positive direction of the Y axis is, Δ θ is the sampling interval of the scene ellipse polar angle, and the ellipse polar coordinates of the scene grid points (m, n) are defined as (ρ, θ), that is:
Figure FDA0002788770170000034
wherein Θ is the azimuth beam width of the motion station, the scene can be divided into a plurality of elliptical polar scene scenes, the scene targets are distributed in the elliptical polar scenes, and R (η, ρ) is assumedp,θk) For the aperture position A of the motion stationηAnd the sum of the distances from the fixed station B to the kth elliptical polar scene of the pth equidistant elliptical ring domain, the scene echo signal is:
Figure FDA0002788770170000035
wherein N isk(eta) is the number of elliptical polar sub-scenes in the p-th equidistant elliptical ring at the time of eta, and sigma (eta, rho)p,θk) The scattering coefficient of the kth elliptical polar scene of the pth equidistant elliptical ring domain is as follows:
Figure FDA0002788770170000036
wherein, Ip,kThe number of the targets in the kth elliptical polar scene of the pth equidistant elliptical ring domain.
9. The method for rapidly generating the stationary bistatic SAR echo signal according to claim 1, wherein the step S3 of calculating the scattering coefficients of the equidistant elliptical ring domain corresponding to all the sub-aperture positions by using FFT comprises:
setting etanFor the slow time of the n-th motion station sub-aperture, ηncFor the nth motion station sub-aperture center time,
Figure RE-FDA0002913934110000041
is etancThe location of the mobile station is at the moment,
Figure RE-FDA0002913934110000042
is etanDefining the position of the motion station at the moment, and defining the elliptical polar coordinate (rho) corresponding to the sub-aperture of the nth motion stationn,θn)，ΔθnFor the corresponding scene ellipse polar angle sampling interval,
Figure RE-FDA0002913934110000043
is a straight line
Figure RE-FDA0002913934110000044
Length of (d), T (ρ)np,θn0) And T' (ρ)np,θnk) For two elliptical polar scenes in the pth equidistant elliptical ring, and thetank＝θn0+kΔθn，rMnpIndicating a mobile station position
Figure RE-FDA0002913934110000045
To an elliptical polar scene T (ρ)np,θn0) A distance of rSnpRepresenting a fixed station to an elliptical polar scene T (p)np,θn0) Distance of moving station
Figure RE-FDA0002913934110000046
And a fixed station to an elliptical polar scene T' (ρ)np,θnk) Are each rM′npAnd rS′np；
For the sport station position
Figure RE-FDA0002913934110000047
Sum of distances R (η, ρ)p,θk) Needs to be rewritten into R (eta)nc,ρnp,θnk) And it is equal for all elliptical polar scenes in the pth equidistant elliptical ring because it is equal to the variable θnkIndependently of one another, therefore, the sum of distances R (η)nc,ρnp,θnk) Simplified to R (eta)nc,ρnp) I.e. the location of the moving station
Figure RE-FDA0002913934110000048
And the sum of the distances from the fixed station position B to the p-th equidistant elliptical ring domain;
according to
Figure RE-FDA0002913934110000049
Motion station location
Figure RE-FDA00029139341100000410
The corresponding scene echo signals are:
Figure RE-FDA00029139341100000411
for other mobile station positions
Figure RE-FDA00029139341100000412
Sum of distances R (η, ρ)p,θk) Need to be rewritten into R (eta)n,ρnp,θnk) But it is not equal for all elliptical polar scenes in the pth equidistant elliptical ring because it is equal to the variable θnkCorrelation, however, sum of distances R (η)n,ρnp,θnk) By sum of distances R (η)nc,ρnp) Represents:
Figure RE-FDA00029139341100000413
thus, the position of the exercise station
Figure RE-FDA00029139341100000414
The corresponding scene echo signals are:
Figure RE-FDA0002913934110000051
due to R (eta)nc,ρnp) And Δ R2And the variable k or thetakIndependently of Δ R1And the variable k or thetakIs related to
Figure RE-FDA0002913934110000052
And
Figure RE-FDA0002913934110000053
scattering coefficient σ (η)n,ρnp,θnk) Approximated by σ (η)nc,ρnp,θnk) Delta [ tau-2R (eta) in digital signal processing when the azimuth beam width of the mobile station antenna is sufficiently narrown,ρnp,θnk)/c]And δ [ τ -2R (η)n,ρnp,θn0)/c]Is almost in phaseWhen equal, then move the station position
Figure RE-FDA0002913934110000054
The corresponding scene echo signals are:
Figure RE-FDA0002913934110000055
thus, the position of the exercise station
Figure RE-FDA0002913934110000056
The scattering coefficient of the pth equidistant elliptical ring domain of (a) may be defined as:
Figure RE-FDA0002913934110000057
according to the imaging geometry and the cosine theorem, | AnηT | + | BT | can be calculated and approximated as:
Figure RE-FDA0002913934110000058
same distance
Figure RE-FDA0002913934110000059
Can be calculated and approximated as:
Figure RE-FDA00029139341100000510
thus, the distance difference Δ R1Calculated and approximated as:
Figure RE-FDA00029139341100000511
since the azimuth beam width of the mobile station is assumed to be sufficiently narrow, k Δ θnIs relatively small, and thus, cos (θ)n0+kΔθn)-cos(θn0)≈-kΔθnsin(θn0) It is also reasonable, therefore, that Δ R1A further approximation is:
Figure RE-FDA0002913934110000061
then:
Figure RE-FDA0002913934110000062
if the scene polar angle sampling interval delta thetanThe following relationship can be satisfied:
Figure RE-FDA0002913934110000063
wherein
Figure RE-FDA0002913934110000064
For the position of a sports station
Figure RE-FDA0002913934110000065
Distance to nth sub-aperture edge position, then:
Figure RE-FDA0002913934110000066
let the nth sub-aperture be 2L in lengthnAnd corresponding reference numeral is ln＝-Ln…LnAnd then:
Figure RE-FDA0002913934110000067
wherein
Figure RE-FDA0002913934110000068
Figure RE-FDA0002913934110000069
Is the firstnAt the position of a sports station
Figure RE-FDA00029139341100000610
For the ith sub-aperturenScattering coefficient σ (l) of pulse, p-th equidistant elliptic ring equivalent scatterern,ρnp) Is the scattering coefficient sigma (eta)nc,ρnp,θnk) L-th obtained by FFT operationnThe number of the equivalent scatterers of the p-th equidistant elliptic ring domain can be calculated simultaneously through FFT operationn,ρnp) Thus, the position of the exercise station
Figure RE-FDA00029139341100000611
The corresponding scene echo signal is calculated as:
Figure RE-FDA00029139341100000612
when Δ R is satisfied1＝ΔR2When 0, the above formula can be simplified as:
Figure RE-FDA00029139341100000613
thus, the scene echo signal of the nth sub-aperture is collectively represented as:
Figure RE-FDA00029139341100000614
10. the method for rapidly generating the echo signal of the fixed bistatic SAR of claim 1, wherein the calculation process for finally obtaining the echo signal of the scene in step S4 is as follows:
the formula is calculated using FFT/IFFT operations:
Figure FDA0002788770170000071
obtaining:
Figure FDA0002788770170000072
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