CN108562902B - High-low orbit bistatic SAR configuration design method based on simulated annealing algorithm - Google Patents

High-low orbit bistatic SAR configuration design method based on simulated annealing algorithm Download PDF

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CN108562902B
CN108562902B CN201810618721.7A CN201810618721A CN108562902B CN 108562902 B CN108562902 B CN 108562902B CN 201810618721 A CN201810618721 A CN 201810618721A CN 108562902 B CN108562902 B CN 108562902B
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CN108562902A (en
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李真芳
马秀露
王跃锟
吕争
索志勇
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9058—Bistatic or multistatic SAR
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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    • G01S13/9088—Circular SAR [CSAR, C-SAR]

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Abstract

The invention discloses a high-low orbit bistatic SAR configuration design method based on a simulated annealing algorithm, which belongs to the technical field of signal processing and mainly comprises the following steps: determining high-orbit SAR satellite and low-orbit SAR satellite, and establishing earth-fixed coordinateDetermining a target position vector PTThen determining a target position vector PTCorresponding synthetic aperture center time t0(ii) a Calculating to obtain t0Time ground scene distance resolution, t0Time ground scene orientation resolution, t0Time ground scene two-dimensional resolution direction angle and t0After the time noise equivalent backscattering coefficient, then constructing t0A time-of-day nonlinear multivariable objective function; finally solving t based on simulated annealing algorithm0Obtaining a target position vector P by a target function of time nonlinear multivariableTAnd the corresponding optimal central moment of the synthetic aperture, the optimal downward viewing angle of the low-orbit SAR satellite and the optimal ground squint angle of the low-orbit SAR satellite are used as the design result of the high-low orbit bistatic SAR configuration based on the simulated annealing algorithm.

Description

High-low orbit bistatic SAR configuration design method based on simulated annealing algorithm
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a high-low orbit bistatic SAR configuration design method based on a simulated annealing algorithm, which is suitable for configuration planning and design of a bistatic SAR system which takes a cooperative signal emitted by a high-orbit SAR satellite as an active irradiation source and passively receives a ground scattering signal by a low-orbit SAR satellite.
Background
The satellite-borne Synthetic Aperture Radar (SAR) is one of the most rapidly and effectively developed sensors in microwave remote sensing equipment, and can be used as an active sensor which is not limited by illumination and climatic conditions and can realize all-time and all-weather earth observation.
The orbit height of a high-orbit SAR (GEO SAR) satellite is 35786km, the survivability is strong, the ground coverage range is wide, the time resolution is high, but the spatial resolution is low, and the resolution within 1m can hardly be achieved; the low-orbit SAR (LEO SAR) satellite orbit height is usually 500 km-1000 km, the spatial resolution is high and can reach sub-meter level, but the time resolution is low, large-scale networking flight is required to improve the revisit capability, the system is complex, and the cost is high; in order to fully utilize the advantages of the GEO SAR satellite and the LEO SAR satellite, the high-low orbit double-base configuration can be reasonably designed, a cooperation signal transmitted by the GEO SAR satellite is used as an active irradiation source, and the LEO SAR satellite passively receives a double/multi-base cooperation system of a ground scattering signal to carry out networking observation.
In recent years, a high-orbit SAR satellite is used as an active irradiation source, and a high-low orbit bistatic SAR cooperation system for passively receiving ground scattering signals by a low-orbit SAR satellite gradually enters the visual field of people. Therefore, compared with the current satellite-borne SAR system, the high-low orbit bistatic SAR system can remarkably improve the earth observation capability and has wide application prospect.
At present, machine-to-machine, LEO SAR satellite formation and satellite-to-machine double-base configuration are sufficiently researched at home and abroad, however, the research of the high-low orbit double-base SAR system is still in a starting stage, and methods and conclusions under other double-base systems cannot be directly applied to the high-low orbit system, and still face many new technical problems.
Due to the characteristics of large track difference, large space and large scale isomerism and the like of a receiving and transmitting platform, how to reasonably design a double-base configuration is a big problem. In the article "GEO-LEO double-station time-frequency SAR system several problem research" (modern radar, 2017, 39 (3): 17-20), beam key and the like, a bistatic ground resolution expression is deduced for a bistatic SAR system transmitted by geostationary orbit satellites and received by low orbit satellites, however, the bistatic ground resolution expression does not make further research on configuration design; liuwenkang and the like provide a satellite-machine double-base parameter optimization design method based on a high-rail radiation source in an article 'high-rail satellite-machine BiSAR resolution analysis and imaging parameter optimization design' (electronics and informatics report, 2016, 38 (12): 3152 and 3158). The method mainly aims at carrying out optimization analysis on a satellite-machine double-base system and is not suitable for high-low rail double-base configuration design.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a high-low orbit bistatic SAR configuration design method based on a simulated annealing algorithm, which is a bistatic configuration design technology of a high-low orbit SAR system, and provides imaging performance parameter expressions such as ground two-dimensional resolution, a resolution direction angle, a noise equivalent backscattering coefficient and the like from a space geometric relationship of a receiving and transmitting platform, establishes a mathematical model between each imaging performance parameter and a bistatic configuration parameter, provides a nonlinear multivariable objective function according to the mathematical model, and optimally designs the high-low orbit bistatic SAR configuration through the simulated annealing algorithm.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
A high-low orbit bistatic SAR configuration design method based on a simulated annealing algorithm comprises the following steps:
step 1, determining a high-orbit SAR satellite and a low-orbit SAR satellite, establishing a ground-fixed coordinate system, and determining a target position vector PTThen determining a target position vector PTCorresponding synthetic aperture center time t0；
Step 2, calculating to obtain t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector sum t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTThe unit slope distance vector of (1);
step 3, according to t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector sum t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of (1) to obtain t0Time ground scene distance resolution, t0Time ground scene orientation resolution, t0Time ground scene two-dimensional resolution direction angle and t0Time of day noise equivalent backscattering coefficient and then constructing t0A time-of-day nonlinear multivariable objective function;
step 4, solving t based on simulated annealing algorithm0Obtaining a target position vector P by a target function of time nonlinear multivariableTCorresponding synthetic aperture optimal central time, optimal downward viewing angle of low-orbit SAR satellite and low-orbit SThe ground optimal squint angle of the AR satellite, and the target position vector PTAnd the corresponding optimal central moment of the synthetic aperture, the optimal downward viewing angle of the low-orbit SAR satellite and the optimal ground squint angle of the low-orbit SAR satellite are design results of the high-low-orbit bistatic SAR configuration based on the simulated annealing algorithm.
The invention has the beneficial effects that:
the invention aims to provide an effective solution for the design of high-low orbit bistatic SAR configuration; the method takes the imaging performance indexes such as ground two-dimensional resolution, resolution direction angle, noise equivalent backscattering coefficient and the like into consideration, so that the high-low orbit bistatic SAR configuration designed based on the method perfectly conforms to the observation task requirements of the SAR system; the nonlinear multivariable equation is optimized and solved through the simulated annealing algorithm, so that the equation can be prevented from falling into a local optimal solution, and the situations of non-convergence and non-solution can be avoided.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a high-low orbit bistatic SAR configuration design method based on a simulated annealing algorithm of the invention;
FIG. 2 is a geometric figure of high and low orbit bistatic SAR satellite earth observation under a geostationary coordinate system;
FIG. 3(a) is a diagram of a point target simulation result under a right-view condition of a low-orbit SAR satellite;
fig. 3(b) is a diagram of a point target simulation result in a left view situation of the low-orbit SAR satellite.
Detailed Description
Referring to fig. 1, a flow chart of a high-low orbit bistatic SAR configuration design method based on a simulated annealing algorithm is shown in the invention; the design method of the high-low orbit bistatic SAR configuration based on the simulated annealing algorithm comprises the following steps:
step 1, establishing observation geometry of a high-low orbit bistatic SAR system according to prior information, and providing configuration parameters capable of representing any space configuration of the high-low orbit.
Determining a high-orbit SAR satellite and a low-orbit SAR satellite, respectively taking the satellite with the orbit height of 35786km and carrying an SAR sensor as the high-orbit SAR satellite, and taking the satellite with the orbit height of 500-1000 km as the low-orbit SAR satellite.
Establishing a ground-fixed coordinate system OXYZ, wherein the ground-fixed coordinate system OXYZ points to the north pole by taking the earth center as an origin O, Z axis, the X axis points to the 0-degree meridian, and the Y axis is determined according to a right-hand rule; the geometric configuration of the high-low orbit bistatic SAR satellite earth observation under the earth-fixed coordinate system OXYZ is shown in figure 2.
Recording the orbit position of the high-orbit SAR satellite at the time t as PG(t), recording the orbit speed of the high-orbit SAR satellite at the time t as VG(t) the downward view angle of the high-orbit SAR satellite is thetaG(ii) a Recording the orbit position of the low-orbit SAR satellite at the time t as PL(t), recording the orbit speed of the low-orbit SAR satellite at the time t as VL(t) low-earth SAR satellite downward view angle is thetaL(ii) a The method comprises the steps that electromagnetic wave signals transmitted by a high-orbit SAR satellite are reflected by a ground scene and then are received by a low-orbit SAR satellite, wherein the ground scene is in the irradiation range of the high-orbit SAR satellite and is used for reflecting the ground area of the high-orbit SAR satellite for transmitting the electromagnetic wave signals; a plurality of targets exist in the ground scene, and the position vector of any one target in the ground scene is selected and recorded as a target position vector PT。
Vector P of target positionTThe corresponding imaging time is recorded as the synthetic aperture time TsWherein the target position vector PTCorresponding to a synthetic aperture center time t0(ii) a Vector P pointing from high-orbit SAR satellite to target position at time tTIs RG(t) pointing from the low-orbit SAR satellite to a target position vector P at time tTIs RL(t); vector P pointing from high-orbit SAR satellite to target position at time tTIs a slope distance vector RG(t) projection vector of ground scene is R'G(t) pointing from the low-orbit SAR satellite to a target position vector P at time tTIs a slope distance vector RL(t) projection vector in ground scene is RLLow-orbit SAR satellite orbit velocity V at time point of' (t), tL(t) projection vector on ground scene is VL' (t) the ground squint angle of a low-orbit SAR satellite is
Figure BDA0001697536300000042
Where t represents a time variable.
The orbit of the high-orbit SAR satellite and the low-orbit SAR satellite is determined after the high-orbit SAR satellite and the low-orbit SAR satellite are transmitted, so the configuration parameter t0、θLAnd
Figure BDA0001697536300000043
can determine any space configuration of high-low orbit bistatic SAR satellite earth observation, and the distance resolution d between each configuration parameter and ground scenegrGround scene orientation resolution dgaGround scene two-dimensional resolution direction angle omega and noise equivalent backscattering coefficient NE sigma0The four imaging performance indicators are closely related.
Step 2, according to the high-low orbit bistatic SAR satellite earth observation geometric configuration under the earth fixed coordinate system shown in figure 2, aiming at the target position vector PTPositioning to obtain a target position vector PTAnd (x, y, z) and find t0Moment high-orbit SAR satellite-to-target position vector PTUnit slope distance vector xi ofG(t0) And t0Time-of-day low-orbit SAR satellite-to-target position vector PTUnit slope distance vector of
Figure BDA0001697536300000044
The substep of step 2 is:
2a) for the target position vector PTAt the target position vector PTCorresponding synthetic aperture center time t0Then, get t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0)：
Figure BDA0001697536300000041
Where, | | · | | denotes a vector modulo operation, t0Representing a target position vector PTCorresponding synthetic aperture center time, PG(t0) Represents t0High-orbit SAR satellite orbital position at time, RG(t0) Represents t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTThe pitch vector of (a).
t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTHas a unit slope distance vector of
Figure BDA0001697536300000045
Figure BDA0001697536300000051
Therein, ζL(t0) Represents t0Time-of-day low-orbit SAR satellite orbital velocity VL(t0) Tan represents a tangent function, η represents the satellite squint angle of the low-orbit SAR satellite, which can be expressed as
Figure BDA00016975363000000510
sin denotes a sine function, arcsin denotes an arcsine function, thetaLRepresenting the downward view of the low-orbit SAR satellite,
Figure BDA00016975363000000511
representing the ground squint angle of the low-orbit SAR satellite;
Figure BDA0001697536300000052
represents a center slope vector, whose expression is:
Figure BDA0001697536300000053
where η represents the satellite squint angle of the low-orbit SAR satellite, which can be expressed as
Figure BDA0001697536300000054
PL(t0) Represents t0The orbital position of the low-orbit SAR satellite at the moment, cos represents the cosine function, arccos represents the inverse residueA chord function;
Figure BDA0001697536300000055
represents the center velocity vector, expressed as:
Figure BDA0001697536300000056
wherein, VL(t0) Represents t0The orbital velocity of the low-orbit SAR satellite at the moment, LEO SAR denotes the low-orbit SAR satellite,
Figure BDA0001697536300000057
is a vector cross product operation.
2b) According to the high-low orbit bistatic SAR satellite earth observation geometric configuration and t under the earth-fixed coordinate system OXYZ0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure BDA0001697536300000058
The following system of equations can be obtained:
Figure BDA0001697536300000059
wherein R iseRepresenting the equatorial radius of the earth, RpThe radius of the earth polar region is represented, h represents the set target elevation distance, and the value of h is 0m in the embodiment; x represents a target position vector PTThe coordinate of X axis in the earth fixed coordinate system OXYZ, y represents the vector P of the target positionTY-axis coordinate in earth-fixed coordinate system OXYZ, z represents target position vector PTZ-axis coordinate, xi, in the earth-fixed coordinate system OXYZL(1) Represents t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure BDA0001697536300000061
X-axis coordinate, xi, in the earth-fixed coordinate system OXYZL(2) Represents t0Pointing from a low-orbit SAR satellite to a target position at a timeVector PTUnit slope distance vector of
Figure BDA0001697536300000062
Y-axis coordinate, xi, in the earth-fixed coordinate system OXYZL(3) Represents t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure BDA0001697536300000063
Z-axis coordinate, P, in the earth-fixed coordinate system OXYZL(1) Represents t0Low-orbit SAR satellite orbital position P of momentL(t0) X-axis coordinate, P, in the earth-fixed coordinate system OXYZL(2) Represents t0Low-orbit SAR satellite orbital position P of momentL(t0) Y-axis coordinate, P, in the earth-fixed coordinate system OXYZL(3) Represents t0Low-orbit SAR satellite orbital position P of momentL(t0) Z-axis coordinates in a ground-fixed coordinate system OXYZ; by solving the system of equations, a target position vector P can be obtainedTTo find t further from the three-dimensional coordinates (x, y, z) of (A)0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0) And t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure BDA0001697536300000064
Step 3, according to the t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0) And t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure BDA0001697536300000065
Establishing an imaging Performance index dgr、dgaOmega and NE sigma0And a configuration parameter t0、θLAnd
Figure BDA0001697536300000066
mathematics of (2) betweenAnd (4) relationship.
3a) According to the t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0) And t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure BDA0001697536300000067
To obtain t0Temporal ground scene distance resolution
Figure BDA0001697536300000068
The expression of (c) can be written as:
Figure BDA0001697536300000069
wherein, w1Represents a first set constant, taken to be 0.886; c represents the speed of light, and is taken to be 3X 108m/s; b represents the bandwidth of the electromagnetic wave signal emitted by the high-orbit SAR satellite, the superscript T represents the transposition operation of the vector or matrix, G⊥Representing ground projection matrices, i.e.
Figure BDA00016975363000000610
I denotes a 3X 3 identity matrix and μ T denotes a vector P from the target positionTUnit vector, mu, pointing to origin O of earth-fixed coordinate system OXYZT＝-PT/||PTAnd | l, | · | represents a vector modulo operation.
3b) According to t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure BDA00016975363000000611
To obtain t0Temporal ground scene orientation resolution
Figure BDA00016975363000000612
The expression of (c) can be written as:
Figure BDA0001697536300000071
wherein, TsRepresenting the synthetic aperture time, the superscript T representing the transpose operation of the vector or matrix; w is a2Represents a second set constant, taken to be 0.886; λ represents the wavelength of an electromagnetic wave signal emitted by a high-orbit SAR satellite;
Figure BDA0001697536300000072
represents t0Time of day low-orbit SAR satellite relative to target position vector PTThe unit angular velocity vector of (a), expressed as:
Figure BDA0001697536300000073
wherein, VL(t0) Represents t0Time of day low-orbit SAR satellite orbital speed, PL(t0) Represents t0A low-orbit SAR satellite orbital position at time.
3c) According to the t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0) And t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of (1) to obtain t0Time ground scene two-dimensional resolution direction angle
Figure BDA0001697536300000074
The expression of (c) can be written as:
Figure BDA0001697536300000075
wherein arccos represents an inverse cosine function,<·>it is shown that the operation of the inner product of the vectors,
Figure BDA0001697536300000076
represents t0Temporal ground scene distance resolution
Figure BDA0001697536300000077
The unit direction vector of (a) is,
Figure BDA0001697536300000078
represents t0Temporal ground scene orientation resolution
Figure BDA0001697536300000079
The expression of the unit direction vector of (1) is expressed as:
Figure BDA00016975363000000710
wherein the content of the first and second substances,
Figure BDA00016975363000000711
represents t0Time of day low-orbit SAR satellite relative to target position vector PTThe unit angular velocity vector of.
3d) According to the t0Temporal ground scene distance resolution
Figure BDA00016975363000000712
t0Temporal ground scene orientation resolution
Figure BDA00016975363000000713
And t0Time ground scene two-dimensional resolution direction angle
Figure BDA00016975363000000714
To obtain t0Time ground scene distinguishing unit area
Figure BDA00016975363000000715
Can be expressed as:
Figure BDA00016975363000000716
and then obtain t0Time of day noise equivalent backscattering coefficient
Figure BDA0001697536300000081
Expression (2)Can be written as:
Figure BDA0001697536300000082
wherein, PmRepresents the average transmitting power of the high-orbit SAR satellite, k represents Boltzmann constant and is 1.38 multiplied by 10-23J/K；TaRepresenting the noise temperature of the high-orbit SAR satellite, L representing the loss of the high-orbit SAR satellite, F representing the noise coefficient of the high-orbit SAR satellite, GGRepresenting the antenna gain, G, of a high-orbit SAR satelliteLRepresenting the antenna gain of a low-orbit SAR satellite.
At this time, the imaging performance index d) is established from 3a), 3b), 3c) and 3d)gr、dgaOmega and NE sigma0And a configuration parameter t0、θLAnd
Figure BDA0001697536300000083
a mathematical relationship therebetween.
Step 4, converting the objective function, namely converting each imaging performance index dgr、dgaOmega and NE sigma0And a configuration parameter t0、θLAnd
Figure BDA0001697536300000084
the mathematical relationship between them translates into a nonlinear multivariable objective function.
Given each imaging performance requirement is dgr_c，dga_c，ΩcAnd NE σ0_c，dgr_cRepresenting a given specific ground scene distance resolution, dga_cRepresenting a given specific ground scene azimuth resolution, ΩcRepresenting the direction angle and NE sigma of a given two-dimensional resolution of a particular terrestrial scene0_cRepresenting a given specific noise equivalent backscattering coefficient.
Then according to the t0Temporal ground scene distance resolution
Figure BDA0001697536300000085
t0Temporal ground scene orientation resolution
Figure BDA0001697536300000086
And t0Time ground scene two-dimensional resolution direction angle
Figure BDA0001697536300000087
And t0Time of day noise equivalent backscattering coefficient
Figure BDA0001697536300000088
And a configuration parameter t0、θLAnd
Figure BDA0001697536300000089
the mathematical relationship between them, the following equation is obtained:
Figure BDA00016975363000000810
where, let k be {1,2,3,4},
Figure BDA00016975363000000811
representing the kth equation.
From the above formula, t can be obtained0Target function of time-of-day nonlinear multivariable
Figure BDA00016975363000000812
Comprises the following steps:
Figure BDA00016975363000000813
wherein s.t. represents a constraint condition, e represents belonging, | is an absolute value operation, ω iskExpressing the kth equation
Figure BDA0001697536300000091
The value of the weight coefficient of (a) is {1,2,3,4}, and the value of the weight coefficient of each equation in this embodiment is the same, that is, the value of the weight coefficient of each equation is 0.25; e1As a target position vector PTCorresponding synthetic aperture center time t0According to the actual SAR satellite determination and the actual user needs, E1>0s；E2Down view theta for low-earth-orbit SAR satellitesLValue range of (1), 0 °<E2<90°；E3Ground squint angle for low-earth-orbit SAR satellites
Figure BDA0001697536300000092
The value range can be determined according to the SAR satellite observation visual angle and the actual needs of users, and is at 90 DEG below zero<E3<90°。
Solving for the t by using a simulated annealing algorithm0Target function of time-of-day nonlinear multivariable
Figure BDA0001697536300000093
Obtaining the optimal configuration parameter xp_optNamely:
Figure BDA0001697536300000094
wherein the content of the first and second substances,
Figure BDA0001697536300000095
t0_optrepresenting a target position vector PTCorresponding to the optimum center time of the synthetic aperture, thetaL_optRepresents the optimal downward viewing angle of the low-orbit SAR satellite,
Figure BDA0001697536300000096
represents the ground optimal squint angle of the low-orbit SAR satellite,
Figure BDA0001697536300000097
t corresponding to when expressing or taking the minimum value0、θLAnd
Figure BDA0001697536300000098
the value of (a).
The effect of the present invention will be further explained with the simulation experiment.
Height adopted by simulationThe low-orbit bistatic SAR orbit parameters are shown in table 1, wherein the high-orbit SAR satellite transmits electromagnetic wave signals, the electromagnetic wave signals are reflected by the ground scene surface, and the low-orbit SAR satellite receives echo signals; the parameters of the adopted high-low orbit bistatic SAR system are shown in table 2, and a target position vector P is given in simulationTCorresponding synthetic aperture center time t0Value range E of1Lower view angle theta of low-orbit SAR satelliteLValue range E of2And ground squint angle of low-orbit SAR satellite
Figure BDA00016975363000000912
Value range E of3Comprises the following steps:
Figure BDA0001697536300000099
TABLE 1
Figure BDA00016975363000000910
TABLE 2
Figure BDA00016975363000000911
Figure BDA0001697536300000101
Given the required imaging performance (d) in the low-orbit SAR satellite right and left view casesgr_c,dga_c,Ωc,NEσ0_c) Respectively (2.4m,2m,90 °, -22dB) and (3.1m,3m,90 °, -21dB), high-low orbit bistatic SAR configuration design simulation is performed by the above simulation conditions, and configuration design is performed by the method of the present invention, and configuration design results are shown in table 3.
TABLE 3
Figure BDA0001697536300000102
In order to verify the validity of the result of the invention, point target SAR imaging simulation is carried out under the configuration parameters of the designed table 3, the point target simulation results under the conditions of the right view of the low-orbit SAR satellite and the left view of the low-orbit SAR satellite are respectively shown in fig. 3(a) and fig. 3(b), and the simulation results show that each imaging performance index is not greatly different from the required imaging performance, and the calculation error is not more than 3%. Simulation experiments prove that the invention can realize the configuration design of the high-low orbit bistatic SAR.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (4)

1. A high-low orbit bistatic SAR configuration design method based on a simulated annealing algorithm is characterized by comprising the following steps:
step 1, determining a high-orbit SAR satellite and a low-orbit SAR satellite, establishing a ground-fixed coordinate system, and determining a target position vector PTThen determining a target position vector PTCorresponding synthetic aperture center time t0；
Step 2, calculating to obtain t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector sum t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTThe unit slope distance vector of (1);
step 3, according to t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector sum t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of (1) to obtain t0Time ground scene distance resolution, t0Time ground scene orientation resolution, t0Time ground scene two-dimensional resolution direction angle and t0Time of day noise equivalent backscattering coefficient and then constructing t0A time-of-day nonlinear multivariable objective function;
step 4, according to the t0Temporal ground scene distance resolution
Figure FDA0003049130660000011
t0Temporal ground scene orientation resolution
Figure FDA0003049130660000012
And t0Time ground scene two-dimensional resolution direction angle
Figure FDA0003049130660000013
And t0Time of day noise equivalent backscattering coefficient
Figure FDA0003049130660000014
The following equation is obtained:
Figure FDA0003049130660000015
where, let k be {1,2,3,4},
Figure FDA0003049130660000016
represents the kth equation;
according to the equation, t is obtained0Target function of time-of-day nonlinear multivariable
Figure FDA0003049130660000017
Comprises the following steps:
Figure FDA0003049130660000018
wherein E is1As a target position vector PTCorresponding synthetic aperture center time t0A value range of (E)1＞0s；E2Down view theta for low-earth-orbit SAR satellitesLThe value range of (1), 0 DEG < E2＜90°；E3Ground squint angle for low-earth-orbit SAR satellites
Figure FDA0003049130660000019
The value range of-90 DEG < E3< 90 °; s.t. represents a constraint condition, belongs to by e, is an absolute value operation, omegakExpressing the kth equation
Figure FDA0003049130660000021
K ═ 1,2,3,4, the weighting coefficients of each equation take the same value,
solving for the t using a simulated annealing algorithm0Target function of time-of-day nonlinear multivariable
Figure FDA0003049130660000022
Further obtaining the optimal configuration parameter xp_optNamely:
Figure FDA0003049130660000023
wherein the content of the first and second substances,
Figure FDA0003049130660000024
t0_optrepresenting a target position vector PTCorresponding to the optimum center time of the synthetic aperture, thetaL_optRepresents the optimal downward viewing angle of the low-orbit SAR satellite,
Figure FDA0003049130660000025
represents the ground optimal squint angle of the low-orbit SAR satellite,
Figure FDA0003049130660000026
t corresponding to when expressing or taking the minimum value0、θLAnd
Figure FDA0003049130660000027
the value of (a).
2. The design method of the high-low orbit bistatic SAR configuration based on the simulated annealing algorithm as claimed in claim 1, characterized in that in step 1, the high-orbit SAR satellite and the low-orbit SAR satellite specifically have an orbit height of 35786km, the satellite carrying the SAR sensor is used as the high-orbit SAR satellite, and the satellite having an orbit height of 500-1000 km is used as the low-orbit SAR satellite;
the earth-fixed coordinate system is a coordinate system which takes the earth center as an origin point O, Z axis and points to the north pole, the X axis points to 0-degree meridian, and the Y axis is determined according to the right-hand rule;
the target position vector PTThe determination process is as follows: the method comprises the steps that electromagnetic wave signals transmitted by a high-orbit SAR satellite are reflected by a ground scene and then are received by a low-orbit SAR satellite, wherein the ground scene is in the irradiation range of the high-orbit SAR satellite and is used for reflecting the ground area of the high-orbit SAR satellite for transmitting the electromagnetic wave signals; a plurality of targets exist in the ground scene, and the position vector of any one target in the ground scene is selected and recorded as a target position vector PT；
The target position vector PTCorresponding synthetic aperture center time t0The determination process is as follows: vector P of target positionTThe corresponding imaging time is recorded as the synthetic aperture time TsWherein the target position vector PTCorresponding to a synthetic aperture center time t0。
3. The SAR configuration design method based on simulated annealing algorithm as claimed in claim 2, characterized in that in step 2, t is0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector sum t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTThe unit pitch vector of (2) is obtained by the substeps of:
2a) calculating t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0)：
Figure FDA0003049130660000031
Where, | | · | | denotes a vector modulo operation, t0Representing a target position vector PTCorresponding synthetic aperture center time, PG(t0) Represents t0High-orbit SAR satellite orbital position at time, RG(t0) Represents t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTThe pitch vector of (a);
calculating t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA0003049130660000032
Figure FDA0003049130660000033
Therein, ζL(t0) Represents t0Time-of-day low-orbit SAR satellite orbital velocity VL(t0) Tan represents a tangent function, η represents a satellite squint angle of the low-orbit SAR satellite,
Figure FDA0003049130660000034
sin denotes a sine function, arcsin denotes an arcsine function, thetaLRepresenting the downward view of the low-orbit SAR satellite,
Figure FDA0003049130660000035
representing the ground squint angle of the low-orbit SAR satellite;
Figure FDA0003049130660000036
represents a center slope vector, whose expression is:
Figure FDA0003049130660000037
wherein, PL(t0) Represents t0The orbit position of the low-orbit SAR satellite at the moment, cos represents a cosine function, and arccos represents an inverse cosine function;
Figure FDA0003049130660000038
represents the center velocity vector, expressed as:
Figure FDA0003049130660000039
wherein, VL(t0) Represents t0The orbital velocity of the low-orbit SAR satellite at the moment, LEO SAR denotes the low-orbit SAR satellite,
Figure FDA00030491306600000310
is a vector cross product operation;
2b) according to t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA00030491306600000311
The following system of equations is obtained:
Figure FDA0003049130660000041
wherein R iseRepresenting the equatorial radius of the earth, RpRepresents the earth polar region radius, h represents the set target elevation distance, and x represents the target position vector PTThe coordinate of X axis in the earth fixed coordinate system OXYZ, y represents the vector P of the target positionTY-axis coordinate in earth-fixed coordinate system OXYZ, z represents target position vector PTZ-axis coordinate, xi, in the earth-fixed coordinate system OXYZL(1) Represents t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA0003049130660000042
X-axis coordinate, xi, in the earth-fixed coordinate system OXYZL(2) Represents t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA0003049130660000043
Y-axis coordinate, xi, in the earth-fixed coordinate system OXYZL(3) Represents t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA0003049130660000044
Z-axis coordinate, P, in the earth-fixed coordinate system OXYZL(1) Represents t0Low-orbit SAR satellite orbital position P of momentL(t0) X-axis coordinate, P, in the earth-fixed coordinate system OXYZL(2) Represents t0Low-orbit SAR satellite orbital position P of momentL(t0) Y-axis coordinate, P, in the earth-fixed coordinate system OXYZL(3) Represents t0Low-orbit SAR satellite orbital position P of momentL(t0) Z-axis coordinates in a ground-fixed coordinate system OXYZ;
by solving the system of equations, a target position vector P can be obtainedTTo find t further from the three-dimensional coordinates (x, y, z) of (A)0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0) And t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA0003049130660000045
4. The SAR configuration design method based on simulated annealing algorithm as claimed in claim 3, characterized in that in step 3, t is0Time ground scene distance resolution, t0Time ground scene orientation resolution, t0Time ground scene two-dimensional resolution direction angle and t0The method comprises the following steps of distinguishing unit areas of the ground scene at a moment, wherein the substeps are as follows:
3a) according to the t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0) And t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA0003049130660000046
To obtain t0Temporal ground scene distance resolution
Figure FDA0003049130660000047
Figure FDA0003049130660000048
Wherein, w1Representing a first set constant, c representing the speed of light, B representing the bandwidth of the electromagnetic wave signal emitted by the high-orbit SAR satellite, superscript T representing the transposition of a vector or matrix, G⊥A ground projection matrix is represented that represents the ground projection matrix,
Figure FDA0003049130660000051
i represents a 3X 3 identity matrix, μTRepresenting a vector P from a target positionTUnit vector, mu, pointing to origin O of earth-fixed coordinate system OXYZT＝-PT/||PT| l, | | |, | | represents the vector modulo operation;
3b) according to t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of
Figure FDA0003049130660000052
To obtain t0Temporal ground scene orientation resolution
Figure FDA0003049130660000053
Figure FDA0003049130660000054
Wherein, TsRepresenting the synthetic aperture time, the superscript T representing the transpose operation of the vector or matrix; w is a2A second set constant is represented, and lambda represents the wavelength of an electromagnetic wave signal emitted by the high-orbit SAR satellite;
Figure FDA0003049130660000055
represents t0Time of day low-orbit SAR satellite relative to target position vector PTThe unit angular velocity vector of (a), expressed as:
Figure FDA0003049130660000056
wherein, VL(t0) Represents t0Time of day low-orbit SAR satellite orbital speed, PL(t0) Represents t0A low-orbit SAR satellite orbit position at a time;
3c) according to the t0Pointing a target position vector P from a high-orbit SAR satellite at a timeTUnit slope distance vector xi ofG(t0) And t0Pointing a target position vector P from a low-orbit SAR satellite at a timeTUnit slope distance vector of (1) to obtain t0Time ground scene two-dimensional resolution direction angle
Figure FDA0003049130660000057
Figure FDA0003049130660000058
Wherein arccos represents an inverse cosine function,<·>it is shown that the operation of the inner product of the vectors,
Figure FDA0003049130660000059
represents t0Temporal ground scene distance resolution
Figure FDA00030491306600000510
The unit direction vector of (a) is,
Figure FDA00030491306600000511
represents t0Temporal ground scene orientation resolution
Figure FDA00030491306600000512
The expression of the unit direction vector of (1) is expressed as:
Figure FDA0003049130660000061
wherein the content of the first and second substances,
Figure FDA0003049130660000062
represents t0Time of day low-orbit SAR satellite relative to target position vector PTThe unit angular velocity vector of (c);
3d) according to the t0Temporal ground scene distance resolution
Figure FDA0003049130660000063
t0Temporal ground scene orientation resolution
Figure FDA0003049130660000064
And t0Time ground scene two-dimensional resolution direction angle
Figure FDA0003049130660000065
To obtain t0Time ground scene distinguishing unit area
Figure FDA0003049130660000066
Figure FDA0003049130660000067
And then obtain t0Time of day noise equivalent backscattering coefficient
Figure FDA0003049130660000068
Figure FDA0003049130660000069
Wherein, PmRepresents the average transmitting power of the high-orbit SAR satellite, k represents Boltzmann constant, and is 1.38 multiplied by 10-23J/K；TaRepresenting the noise temperature of the high-orbit SAR satellite, L representing the loss of the high-orbit SAR satellite, F representing the noise coefficient of the high-orbit SAR satellite, GGRepresenting the antenna gain, G, of a high-orbit SAR satelliteLRepresenting the antenna gain of a low-orbit SAR satellite.
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