CN116088319B - Distributed SAR configuration design method suitable for guidance detection - Google Patents

Distributed SAR configuration design method suitable for guidance detection Download PDF

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CN116088319B
CN116088319B CN202310369859.9A CN202310369859A CN116088319B CN 116088319 B CN116088319 B CN 116088319B CN 202310369859 A CN202310369859 A CN 202310369859A CN 116088319 B CN116088319 B CN 116088319B
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shaft
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CN116088319A (en
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汪宗福
吕金虎
刘克新
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Beihang University
Academy of Mathematics and Systems Science of CAS
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Academy of Mathematics and Systems Science of CAS
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention relates to a distributed SAR configuration design method suitable for guidance detection, belongs to the technical field of distributed cluster control, and solves the problems of inaccurate target positioning and complex track planning in the prior art. According to the method, based on the arbitrary shift geometry relation of the terminal guided distributed SAR, a model between the motion information and the imaging performance of the distributed platform is directly constructed, the design process of the distributed optimal configuration is converted into the design problem of the optimal track of the distributed platform, a nonlinear multi-element objective function is established, the design problem of the optimal track is further converted into the optimization problem of the nonlinear multi-objective function, the accuracy of target positioning is improved, and the complexity of track planning is reduced.

Description

Distributed SAR configuration design method suitable for guidance detection
Technical Field
The invention belongs to the technical field of distributed cluster control, and relates to a distributed SAR configuration design method suitable for guidance detection.
Background
With the increasing intensity of the game countermeasure of the two parties of the modern battlefield, the battlefield environment is quite complex, which provides new challenges for the detection and guidance means of the current accurate guided weapon. Because of the requirements of guidance control, the tail end trajectory is generally in forward looking detection, the traditional detection lacks resolution in azimuth, so that the target identification tracking precision is greatly reduced, the last section often cannot accurately find the target, and particularly when the target is aimed at a large target, such as a complex target of aircraft carrier combat group, large-scale expelling ship, near-shore ship formation and the like, the target tracking is lost due to angle anti-interference or change of a target scattering center, and the accurate hit of the target in a complex scene cannot be realized.
The missile-borne distributed SAR imaging detection technology formed by combining the distributed SAR imaging detection system and the missile platform has incomparable information acquisition advantages in a plurality of specific occasions, particularly in the tail end guidance stage of the warhead, the distributed SAR imaging detection technology can realize high-resolution imaging of a target by a receiver in front view, and can separate the target in a complex environment by combining the target sorting and recognition technology, so that the target can be precisely hit. There has been a great deal of research in the prior art on distributed SAR imaging detection techniques, such as chinese patents CN103901430B, CN108562902B and CN111273678B.
However, the complex warhead geometry and trajectory diversity characteristics imposed by warhead maneuvers and guidance constraints present challenges to the design of distributed SAR configurations for the guidance phases, particularly the end guidance phases.
Disclosure of Invention
In view of the above problems, the invention provides a distributed SAR configuration design method suitable for guidance detection, which solves the problems of inaccurate target positioning and complex track planning in the prior art.
The invention provides a distributed SAR configuration design method suitable for guidance detection, which is characterized by comprising the following specific steps:
step 1, constructing a spatial model of a random shift configuration of the distributed SAR;
step 2, constructing a distance-direction resolution model and a ground distance azimuth resolution model of a random shift configuration of the distributed SAR based on a gradient theory;
step 3, establishing a nonlinear multi-objective optimization equation based on a distance-direction resolution model and a ground distance azimuth resolution model of a random shift configuration of the distributed SAR;
and 4, solving the nonlinear multi-objective optimization equation obtained in the step 3 to obtain an optimal track under the optimal resolution.
Optionally, the distributed SAR arbitrary shift configuration is changed into a double-base forward-looking SAR model; the bistatic forward-looking SAR model comprises a dynamic space model of the receiver and the unmanned aerial vehicle.
Optionally, the specific steps of step 1 are as follows:
establishing a transmitting coordinate system of the receiver, taking a projection point of a starting position of the receiver projected to a local horizontal plane as a coordinate origin of the transmitting coordinate system, and taking a course of a speed of the starting position of the receiver in a projection speed direction of the local horizontal plane as the transmitting coordinate systemxAn axis of the emission coordinate system in a direction perpendicular to the local horizontal planeyShaft based onxyAxis-determining emission coordinate systemzA shaft; the detection target scene is positioned right in front of the receiver, and the receiver looks aheadMeasuring a target scene area;
acquiring position information, speed information and acceleration information of a receiver:
the position information of the receiver isP rk =（x rk ,y rk ,z rk ) The speed information isV rk =（v rxk ,v ryk ,v rzk ) And acceleration information isA rk =（a rxk ,a ryk ,a rzk ) Wherein, the method comprises the steps of, wherein,kis the firstkAt the moment of time of day,x rk ,y rk andz rk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezThe initial coordinates of the axes are set to be,v rxk ,v ryk andv rzk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezThe speed of the shaft is such that,a rxk ,a ryk anda rzk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezAcceleration of the shaft;
acquiring position information, speed information and acceleration information of an unmanned aerial vehicle:
the position information of the unmanned aerial vehicle is thatP tk =（x tk ,y tk ,z tk ) The speed information isV tk =（v txk ,v tyk ,v tzk ) And acceleration information isA tk =（a txk ,a tyk ,a tzk ) Wherein, the method comprises the steps of, wherein,x tk ,y tk andz tk respectively the firstkUnmanned plane at each momentxA shaft(s),yShaft and method for producing the samezThe initial coordinates of the axes are set to be,v txk ,v tyk andv tzk respectively the firstkThe time is that the unmanned aerial vehicle is inxA shaft(s),yShaft and method for producing the samezThe speed of the shaft is such that,a txk ,a tyk anda tzk respectively the firstkUnmanned plane at each momentxA shaft(s),yShaft and method for producing the samezAcceleration of the shaft;
step 14, establishing grid points of an imaging scene of the detection target:
setting the scene level of a detection target, wherein the detection target is positioned on the horizontal plane, and acquiring initial position information of the detection target as followsP p =（x p ,0,z p ），x p To detect the object inxInitial coordinates of axes, detection target inyThe coordinates of the axes are 0 and,z p to detect the object inzInitial coordinates of the shaft;
according to the preset imaging breadth, carrying out grid division on an imaging scene of the detection target, wherein the grid division is carried outxShaft step sizezThe axial step length is respectively%xAnd deltazThe position information of each grid point of the imaging scene of the detection target is thatP i j(,) =（x i ,0,z j ）：
P i j(,) =（x i ,0,z j ）=（x p +M·△x,0,z p +N·△z）；
Wherein, the liquid crystal display device comprises a liquid crystal display device,M=-m：1：m，N=-n：1：n，mandngrid divided into imaging breadth and starting from initial position of detected targetxCell number sum of axeszThe number of bars of the shaft;x i at the ground grid pointxThe coordinates of the axes are used to determine,z j at the ground grid pointzCoordinates of the axes.
Optionally, the specific steps of step 2 are as follows:
the specific steps of constructing the distance resolution model are as follows:
based on the steps of1, obtaining a first base-based forward-looking SAR modelkThe distances from the receiver and the unmanned aerial vehicle at each moment are all constantMIs equal to the equidistant ground coordinate point of (2)P Mk =（x Mk ,0,z Mk ) Position information, constant of (a)MWith equidistant ground coordinate pointsP Mk The following relationship is satisfied:
Figure SMS_1
all equidistant ground coordinate pointsP Mk Constitute the firstkEquidistant line for each momentM bk ；
Obtain the firstkEquidistant line of time of dayM bk Equidistant ground coordinate points onP Mk Gradient of%M k The expression is:
Figure SMS_2
wherein, the liquid crystal display device comprises a liquid crystal display device,i x 、i y andi z respectively representing the emission coordinate systemxA shaft(s),yShaft and method for producing the samezA unit vector of the axis;
obtain the firstkEquidistant line for each momentM bk Equidistant ground coordinate points onP Mk Ground range resolution along gradient directionρ rgk The expression is:
Figure SMS_3
wherein, the liquid crystal display device comprises a liquid crystal display device,cis the speed of light;B r the bandwidth of transmitting pulse signals for the radar detection system of the unmanned aerial vehicle;
the specific steps of constructing the azimuth resolution model are as follows:
based on the bistatic forward-looking SAR model established in the step 1, obtaining the first stepkEquidistant line from receiver and unmanned aerial vehicle at individual momentsM bk Ground coordinate point onP Mk Unit pitch vector of (a)
Figure SMS_4
And->
Figure SMS_5
The expression is:
Figure SMS_6
obtain the firstkEquidistant line at each momentM bk Ground coordinate point onP Mk Doppler of (2)F dk The expression is:
Figure SMS_7
wherein, the liquid crystal display device comprises a liquid crystal display device,V Rk andV Tk respectively the receiver firstkSpeed information at each timeV rk =（v rxk ,v ryk ,v rzk ) And speed information of unmanned aerial vehicleV tk =（v txk ,v tyk ,v tzk ）；λIs the wavelength of the radar detection system;
based on the firstkEquidistant line at each momentM bk Ground coordinate point onP Mk Doppler of (2)F dk， Acquisition of the firstkEqual Doppler line at each momentf dk The expression is:
f dk =const；
obtain the firstkGround coordinate point of equal Doppler line on equidistant line at each momentP Mk Gradient of%f dk The expression is:
Figure SMS_8
Figure SMS_9
Figure SMS_10
Figure SMS_11
obtaining the synthetic aperture time delta of the radartIn, the firstkGround coordinate points on equidistant lines at each moment are in ground distance azimuth resolution along the Doppler gradient direction, and the expression is as follows:
Figure SMS_12
wherein, is deltatIs the synthetic aperture time of the radar, i.e. the dwell time of the beam in the imaging area.
Optionally, the specific steps of step 3 are as follows:
obtain the firstkThe distance resolution of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure SMS_13
Figure SMS_14
Figure SMS_15
wherein, is VM k (i,j) Represent the firstkImaging scene of object detection at each momenti,j) Distance of individual grid pointsA gradient;
obtain the firstkThe azimuth resolution of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure SMS_16
Figure SMS_17
Figure SMS_18
Figure SMS_19
wherein, is Vf dk (i,j) Represent the firstkDetecting Doppler gradients of grid points of an imaging scene of the target at each moment;
obtain the firstkThe gradient included angle between the distance gradient and the Doppler gradient of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure SMS_20
obtain the first based on the most stringent detection criteriakImaging detection results of track segmentation at each moment:
maxρ rg_k =max(max(ρ rg_k ))；
maxρ a_k =max(max(ρ a_k ))；
minψ k =min(min(ψ k ))；
wherein maxρ rg_k 、maxρ ak And minψ k Respectively represent the firstkImaging of a detection target at various moments in timeMaximum distance resolution, maximum azimuth resolution and minimum gradient included angle of each grid point of the scene;
extraction of the firstkOptimization variables for individual momentsX k The expression is:
X k =(x tk ,y tk ,z tk ,v txk ,v tyk ,v tzk ) T ；
based on the firstkOptimization variables for individual momentsX k Constructing a nonlinear multi-element target optimization function, wherein the expression is as follows:
Figure SMS_21
wherein, the liquid crystal display device comprises a liquid crystal display device,f 1 (X k ) A distance resolution optimization function is represented and,f 2 (X k ) Representing the azimuth resolution optimization function,f 3 ( k X) Representing an azimuth resolution optimization function;ρ rg_opt representing the ground distance resolution expectation of back calculation according to the positioning accuracy requirement,ρ a_opt representing the ground clearance azimuth resolution expectation of back calculation according to the positioning accuracy requirement,ψ opt representing a desired two-dimensional resolution angle;
constructing a first objective optimization function based on nonlinear multiple objective optimization functionskIndividual time weighted optimization functionF(X k ) The expression is:
Figure SMS_22
wherein, the liquid crystal display device comprises a liquid crystal display device,ω k is the firstkWeighting coefficients for each time instant;f n (X k ) Represent the firstnA single objective optimization function;Uspace of solutions optimized for the target;
optimizing the function by weightingF(X k ) Conversion to an optimal solution problem for nonlinear multi-objective optimization equationsX opt k, The expression is:
Figure SMS_23
wherein, the liquid crystal display device comprises a liquid crystal display device,Pis a set of parameter spaces.
Compared with the prior art, the invention has at least the following beneficial effects:
(1) According to the configuration design method, in the bullet group based on the distributed SAR imaging guidance process, the optimal distributed platform motion track can be obtained in real time, so that the optimal target detection spatial resolution is obtained, good detection information is provided for accurate guidance striking of the target, and the accurate striking efficiency of the bullet group on the enemy target in a complex environment is improved.
(2) The configuration design method of the invention directly builds a model between the motion information and the imaging performance of the distributed platform based on the arbitrary shift geometry relation of the terminal guided distributed SAR, builds a nonlinear multi-element objective function, utilizes a nonlinear multi-objective optimization method to plan the track of the distributed platform, and has simple and efficient planning process.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention.
FIG. 1 is a geometric model of dual-base forward-looking SAR imaging detection of the present invention;
fig. 2 is a flow chart of a distributed SAR configuration design method of the present invention.
Reference numerals:
1. imaging each grid point of the scene; 2. a receiver; 3. unmanned aerial vehicle.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. It should be noted that, without conflict, the embodiments of the present invention and features in the embodiments may be combined with each other. In addition, the invention may be practiced otherwise than as specifically described and thus the scope of the invention is not limited by the specific embodiments disclosed herein.
In one embodiment of the present invention, as shown in fig. 1, a distributed SAR configuration design method suitable for guided detection is disclosed, comprising the following specific steps:
step 1, constructing a spatial model of a random shift configuration of the distributed SAR;
optionally, as shown in fig. 1, the distributed SAR is arbitrarily changed into a dual-base forward-looking SAR model, and the dual-base forward-looking SAR model comprises a dynamic space model of the receiver 2 and the unmanned aerial vehicle 3;
step 101, establishing a transmitting coordinate system of the receiver, taking a projection point of a starting position of the receiver projected to a local horizontal plane as a coordinate origin of the transmitting coordinate system, and taking a heading of a speed of the starting position of the receiver in a projection speed direction of the local horizontal plane as the transmitting coordinate systemxAn axis of the emission coordinate system in a direction perpendicular to the local horizontal planeyShaft, based on right-hand screw rulexyAxis-determining emission coordinate systemzA shaft; the detection target scene is positioned right in front of the receiver, and the receiver looks ahead at the detection target scene area; unmanned aerial vehicle is the illumination node, and unmanned aerial vehicle strabismus detects target scene area.
It can be understood that the receiver is a section of curved dive track meeting guidance and detection when looking forward at the detection target scene area; the unmanned aerial vehicle strabismus detects the target scene area and is a section of roundabout curve flight track.
102, acquiring position information, speed information and acceleration information of a receiver;
the position information of the receiver isP rk =（x rk ,y rk ,z rk ) The speed information isV rk =（v rxk ,v ryk ,v rzk ) And acceleration information isA rk =（a rxk ,a ryk ,a rzk ) Wherein, the method comprises the steps of, wherein,kis the firstkAt the moment of time of day,x rk ,y rk andz rk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezThe initial coordinates of the axes are set to be,v rxk ,v ryk andv rzk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezThe speed of the shaft is such that,a rxk ,a ryk anda rzk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezAcceleration of the shaft.
It will be appreciated that the position, velocity and acceleration information of the receiver at the initial time are respectivelyP r0 、V r0 AndA r0 （x r0 ,y r0 ,z r0 ）、（v rx0 ,v ry0 ,v rz0 ) And%a rx0 ,a ry0 ,a rz0 ）。
Step 103, acquiring position information, speed information and acceleration information of the unmanned aerial vehicle;
the position information of the unmanned aerial vehicle is thatP tk =（x tk ,y tk ,z tk ) The speed information isV tk =（v txk ,v tyk ,v tzk ) And acceleration information isA tk =（a txk ,a tyk ,a tzk ) Wherein, the method comprises the steps of, wherein,x tk ,y tk andz tk respectively the firstkUnmanned plane at each momentxA shaft(s),yShaft and method for producing the samezThe initial coordinates of the axes are set to be,v txk ,v tyk andv tzk respectively the firstkThe time is that the unmanned aerial vehicle is inxA shaft(s),yShaft and method for producing the samezThe speed of the shaft is such that,a txk ,a tyk anda tzk respectively the firstkUnmanned plane at each momentxA shaft(s),yShaft and method for producing the samezAcceleration of the shaft.
It can be understood that the position, speed and acceleration information of the unmanned aerial vehicle at the initial moment are respectivelyP t0 、V t0 AndA t0 （x t0 ,y t0 ,z t0 ）、（v tx0 ,v ty0 ,v tz0 ) And%a tx0 ,a ty0 ,a tz0 ）。
104, establishing grid points of an imaging scene of a detection target;
setting the scene level of a detection target, wherein the detection target is positioned on the horizontal plane, and acquiring initial position information of the detection target as followsP p =（x p ,0,z p ），x p To detect the object inxInitial coordinates of axes, detection target inyThe coordinates of the axes are 0 and,z p to detect the object inzInitial coordinates of the shaft;
according to the preset imaging breadth, carrying out grid division on an imaging scene of the detection target, wherein the grid division is carried outxShaft step sizezThe axial step length is respectively%xAnd deltazThe position information of each grid point 1 of the imaging scene of the detection target is thatP i j(,) =（x i ,0,z j ）：
P i j(,) =（x i ,0,z j ）=（x p +M·△x,0,z p +N·△z）；
Wherein, the liquid crystal display device comprises a liquid crystal display device,M=-m：1：m，N=-n：1：n，mandngrid divided into imaging breadth and starting from initial position of detected targetxCell number sum of axeszThe number of bars of the shaft;x i at the ground grid pointxThe coordinates of the axes are used to determine,z j at the ground grid pointzCoordinates of the axes.
Step 2, constructing a distance-direction resolution model and a ground distance azimuth resolution model of a random shift configuration of the distributed SAR based on a gradient theory;
the specific steps of constructing the distance resolution model are as follows:
based on the bistatic forward-looking SAR model established in the step 1, obtaining the first stepkThe distances from the receiving bullet and the unmanned aerial vehicle at each moment are all constantMIs equal to the equidistant ground coordinate point of (2)P Mk =（x Mk ,0,z Mk ) Position information, constant of (a)MWith equidistant ground coordinate pointsP Mk The following relationship is satisfied:
Figure SMS_24
all equidistant ground coordinate pointsP Mk Constitute the firstkEquidistant line for each momentM bk 。
It will be appreciated that assuming the positions of the drone and receiver are fixed, all range drones and receivers areMIs formed into an ellipsoid in space, and the intersection line of this ellipsoid and ground surface is formed into the first place on the ground surfacekEquidistant line for each momentM bk . Ground range resolution is the firstkEquidistant line for each momentM bk Is a distributed intensity level of (c).
Obtain the firstkEquidistant line of time of dayM bk Equidistant ground coordinate points onP Mk Gradient of%M k The expression is:
Figure SMS_25
wherein, the liquid crystal display device comprises a liquid crystal display device,i x 、i y andi z respectively representing the emission coordinate systemxA shaft(s),yShaft and method for producing the samezA unit vector of the axis;
obtain the firstkEquidistant line for each momentM bk Equidistant ground coordinate points onP Mk Ground range resolution along gradient directionρ rgk The expression is:
Figure SMS_26
wherein, the liquid crystal display device comprises a liquid crystal display device,cis the speed of light;B r the bandwidth of the pulse signal is transmitted for the unmanned radar detection system.
The specific steps of constructing the azimuth resolution model are as follows:
based on the bistatic forward-looking SAR model established in the step 1, obtaining the first stepkEquidistant line from receiver and unmanned aerial vehicle at individual momentsM bk Ground coordinate point onP Mk Unit pitch vector of (a)
Figure SMS_27
And->
Figure SMS_28
The expression is:
Figure SMS_29
obtain the firstkEquidistant line at each momentM bk Ground coordinate point onP Mk Doppler of (2)F dk The expression is:
Figure SMS_30
wherein, the liquid crystal display device comprises a liquid crystal display device,V Rk andV Tk respectively the receiver firstkSpeed information at each timeV rk =（v rxk ,v ryk ,v rzk ) And speed information of unmanned aerial vehicleV tk =（v txk ,v tyk ,v tzk ）；λIs the wavelength of the radar detection system.
It will be appreciated that the doppler of the ground coordinate points on equidistant lines is obtained from the projected components of the respective velocity vectors of the receiver and the drone onto the pitch vector.
Based on the firstkEquidistant line at each momentM bk Ground coordinate point onP Mk Doppler of (2)F dk， Acquisition of the firstkEqual Doppler line at each momentf dk The expression is:
f dk =const；
it will be appreciated that the firstkThe ground coordinate points on equidistant lines with equal Doppler at each moment form Doppler lines.
Obtain the firstkGround coordinate point of equal Doppler line on equidistant line at each momentP Mk Gradient of%f dk The expression is:
Figure SMS_31
Figure SMS_32
/>
Figure SMS_33
Figure SMS_34
obtaining the synthetic aperture time delta of the radartIn, the firstkGround coordinate points on equidistant lines at each moment are in ground distance azimuth resolution along the Doppler gradient direction, and the expression is as follows:
Figure SMS_35
wherein, is deltatIs the synthetic aperture time of the radar, i.e. the dwell time of the beam in the imaging area.
Step 3, establishing a nonlinear multi-objective optimization equation based on a distance-direction resolution model and a ground distance azimuth resolution model of a random shift configuration of the distributed SAR;
obtain the firstkThe distance resolution of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure SMS_36
Figure SMS_37
/>
Figure SMS_38
wherein, is VM k (i,j) Represent the firstkImaging scene of object detection at each momenti,j) A distance gradient of the grid points;
obtain the firstkThe azimuth resolution of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure SMS_39
Figure SMS_40
Figure SMS_41
Figure SMS_42
wherein, is Vf dk (i,j) Represent the firstkDetecting Doppler gradients of grid points of an imaging scene of the target at each moment;
obtain the firstkThe gradient included angle between the distance gradient and the Doppler gradient of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure SMS_43
obtain the first based on the most stringent detection criteriakImaging detection results of track segmentation at each moment:
maxρ rg_k =max(max(ρ rg_k ))；
maxρ a_k =max(max(ρ a_k ))；
minψ k =min(min(ψ k ))；
wherein maxρ rg_k 、maxρ ak And minψ k Respectively represent the firstkMaximum distance resolution, maximum azimuth resolution and minimum gradient included angle of each grid point of an imaging scene of the detection target at each moment;
it can be understood that the most stringent detection criteria is to use the maximum distance resolution, azimuth resolution and gradient angles of each grid point of the imaging scene of the detection target as optimization indexes.
Bandwidth of pulse signal emitted by unmanned aerial vehicle systemB r And synthetic apertureTimeT s Is a known parameter, assuming that the position and speed of the receiver are known, the first is extractedkOptimization variables for individual momentsX k The expression is:
X k =(x tk ,y tk ,z tk ,v txk ,v tyk ,v tzk ) T ；
based on the firstkOptimization variables for individual momentsX k Constructing a nonlinear multi-element target optimization function, wherein the expression is as follows:
Figure SMS_44
wherein, the liquid crystal display device comprises a liquid crystal display device,f 1 (X k ) A distance resolution optimization function is represented and,f 2 (X k ) Representing the azimuth resolution optimization function,f 3 ( k X) Representing an azimuth resolution optimization function;ρ rg_opt representing the ground distance resolution expectation of back calculation according to the positioning accuracy requirement,ρ a_opt representing the ground clearance azimuth resolution expectation of back calculation according to the positioning accuracy requirement,ψ opt representing the desired two-dimensional resolution angle.
Constructing a first objective optimization function based on nonlinear multiple objective optimization functionskIndividual time weighted optimization functionF(X k ) The expression is:
Figure SMS_45
wherein, the liquid crystal display device comprises a liquid crystal display device,ω k is the firstkThe weighting coefficients of the respective moments are given different weights according to the requirements used at the different moments, optionally the weights at the respective moments are set to be the same, preferably,ω k =1/3；f n (X k ) Represent the firstnA single objective optimization function;Uand (3) restricting the optimization parameters according to the requirements of the motion characteristics of the transmission solution of the bistatic SAR model for the space of the target optimization solution, and limiting the optimizing size of the optimization parameters.
Optimizing the function by weightingF(X k ) Conversion to an optimal solution problem for nonlinear multi-objective optimization equationsX opt The expression is:
Figure SMS_46
/>
wherein, the liquid crystal display device comprises a liquid crystal display device,Pis a parameter space set;
therefore, the design problem of the double-base SAR configuration is converted into the design problem of the emission track, and finally the design problem is changed into the problem of nonlinear objective function optimization with constraint.
Step 4, solving the nonlinear multi-objective optimization equation obtained in the step 3 to obtain an optimal track under the corresponding optimal resolution;
the method comprises the following specific steps:
step 401, loading unmanned aerial vehiclek-motion parameters for 1 moment:
X k -1 =(x tk-1 ,y tk-1 ,z tk-1 ,v txk-1 ,v tyk-1 ,v tzk-1 ) T ；
wherein, the liquid crystal display device comprises a liquid crystal display device,X k-1 represent the firstkPosition and speed information of the drone at 1 moment,k=1,2,…N，Nrepresenting the total number of optimization iteration steps; when (when)kWhen=1, the firstk-1 instant represents an initial instant.
Step 402, giving a value of an imaging resolution index:
the imaging resolution index comprises a ground distance resolution expectation which is reversely calculated according to the positioning accuracy requirementρ rg_opt Back calculation according to the positioning accuracy requirementIs desired for ground range azimuth resolutionρ a_opt Included angle with desired two-dimensional resolutionψ opt 。
Preferably, the method comprises the steps of,ρ rg_opt =1，ρ a_opt =1，ψ opt =0.5；
step 403, establishing a motion constraint condition of the unmanned aerial vehicle:
Figure SMS_47
wherein, the liquid crystal display device comprises a liquid crystal display device,a tx ，a ty anda tz respectively in a transmitting coordinate system of unmanned aerial vehiclexA shaft(s),yShaft and method for producing the samezThe acceleration of the shaft is such that,a tx_max ，a ty_max anda tz_max respectively in a transmitting coordinate system of unmanned aerial vehiclexA shaft(s),yShaft and method for producing the samezMaximum acceleration of the shaft.
Step 404, build the firstkThe optimal variable range of the unmanned plane at each moment is expressed as follows:
Figure SMS_48
wherein, when + -number in the expression is taken as + number, it is the firstkOptimizing variables at each momentX k Upper bound of (2); when the + -number in the expression is taken as the-number, it is the firstkOptimizing variables at each momentX k Is defined below.
Step 405, construct the firstkA time penalty function:
Q k (σ,X k )=σ·max{0,(X k -X k-1 ) 2 -R k 2 }；
wherein, the liquid crystal display device comprises a liquid crystal display device,Q k is the firstkOptimizing variables at each momentX k Is used in the field of the (c),σa penalty function factor;R k is the firstkRadius of the feasible region at each moment.
It can be appreciated that by the firstkObtaining the optimal variable range of the unmanned plane at each momentkOptimizing variables at each momentX k Maximum upper bound, get the firstkRadius of each time feasible regionR k 。
Further, whenX k ∈Q k When, i.e. the firstkWhen the individual time-of-day optimization variables are in the feasible domain,Q k (σ,X k ) =0, i.e. no penalty term, when the optimal solution of the problem is the optimal solution of the original problem; when (when)X k ∉Q k In the time-course of which the first and second contact surfaces,Q k (σ,X k ) Not equal to 0, and the function value is very large under the action of the penalty function factor, the obtained solution is not the optimal solution of the original problem, and the first iskAdding the time weighted optimization function and the penalty function to obtain the first time weighted optimization functionkNew optimization function at each moment:
Figure SMS_49
at this time, the firstkThe optimal solution problem of the new optimization function at each moment is as follows:
Figure SMS_50
wherein, the liquid crystal display device comprises a liquid crystal display device,R 6 is a 6-dimensional European space;
the feasible region of the optimization variables becomes the whole at this timeR 6 Changing into an unconstrained optimization problem, and solving by adopting an unconstrained optimization problem method;
step 406, initializing optimized calculation parameters;
initializing penalty factorsσImprecise search step size factorβStep size scaling factorγAnd a non-precision line search thresholdsIs used for the value of (a) and (b),wherein the imprecise line search thresholdsIs a positive integer; the initial point of the unmanned plane isX 0 =(x t0 ,y t0 ,z t0 ,v txk-1 ,v ty0 ,v tz0 ) T The method comprises the steps of carrying out a first treatment on the surface of the The termination error is 0 to less than or equal toεThe method comprises the steps of carrying out a first treatment on the surface of the Initial symmetric positive definite matrix isB 0 ；
Preferably, the termination error is 0.ltoreq.ε<<1。
Step 407, calculate the firstkOptimizing function for each momentF’(X k ) Is expressed as:
g k =▽F’(X k )；
Figure SMS_51
wherein, is deltaX k Is the firstkStep sizes of discrete gradients at each moment;
IIg k ‖≤εWhen the iteration is stopped, outputX k As an approximate minimum; IIg k ‖>εWhen it is, go to step 408;
step 408, obtain the firstkSearch direction of time:
B k d=-g k ；
d k =-B k -1 g k ；
wherein, the liquid crystal display device comprises a liquid crystal display device,B k is the firstkBlack plug matrix at each moment;dfor the direction vector in the optimization process;d k is the firstkThe search direction of the moment;
step 409: first, thekObtaining a search step at a time based on the search stepFirst, thekAn optimization variable of +1 moments;
F’(X k +β s d k )≤F’(X k )+γβ s g k T d k ；
X k +1 =X k +β s d k ；
wherein, the liquid crystal display device comprises a liquid crystal display device,β s the step length is the searching step length;X k+1 is the firstk+1 time optimization variables;
the first to be obtainedkOptimization variable for +1 time instantsX k+1 Substituting into step 407 to obtain the firstkOptimizing function for each momentF’(X k+1 ) Gradient of (2)g k+1 。
Step 410, using quasi-Newton BFGS methodkBlack plug matrix at each momentB k Correction is carried out to obtain a corrected black plug matrixB k+1 The method comprises the following steps:
Figure SMS_52
wherein, the liquid crystal display device comprises a liquid crystal display device,S k in order to optimize the displacement of the spot,S k =X k+1 -X k ；y k is the gradient difference between the two function values,y k =g k+1 -g k 。
step 411: the iteration number is increased by 1, and the process returns to step 407 until IIg k ‖≤εObtaining the trajectory of the unmanned aerial vehicle;
further, if the number of iterative steps is atNObtaining a converged optimization variable in the step, ending the iteration loop to obtain the trajectory of the unmanned aerial vehicle, and taking the converged optimization variable as the final optimizationAs a result, taking the final optimization result as an initial value to perform the optimization solution of the next track;
if the number of iterative steps is atNIn step, no converged optimization variables are obtained, and step 406 is returned to, and penalty factors are increasedσContinuing iteration until the trajectory of the unmanned aerial vehicle is obtained; if the penalty factor is increasedσWhen the penalty threshold is reached, outputting the current resolution optimization without solution, modifying the resolution index, and iterating again.
Step 412, optimizing the trajectory of the unmanned aerial vehicle obtained in the step 4 by using the constraint condition of the interpolation points;
the constraint conditions of the interpolation points are as follows:
Figure SMS_53
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_54
deriving a synthetic aperture time for the radar for the position of the unmanned aerial vehicle; />
Figure SMS_55
The synthetic aperture time of the radar is derived for the speed of the unmanned aerial vehicle;V max is the maximum speed of the unmanned aerial vehicle;a max is the maximum acceleration of the unmanned aerial vehicle.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.

Claims (3)

1. The distributed SAR configuration design method suitable for guidance detection is characterized by comprising the following specific steps of:
step 1, constructing a space model of a double-base forward-looking SAR model; the double-base forward-looking SAR model comprises a dynamic space model of a receiver and an unmanned aerial vehicle;
step 11, establishing a receptionThe transmitting coordinate system of the machine takes a projection point of the starting position of the receiver projected to the local horizontal plane as a coordinate origin of the transmitting coordinate system, and takes the course of the speed of the starting position of the receiver in the projection speed direction of the local horizontal plane as the transmitting coordinate systemxAn axis of the emission coordinate system in a direction perpendicular to the local horizontal planeyShaft based onxyAxis-determining emission coordinate systemzA shaft; the detection target scene is positioned right in front of the receiver, and the receiver looks ahead at the detection target scene area;
step 12, acquiring position information, speed information and acceleration information of a receiver:
the position information of the receiver isP rk =（x rk ,y rk ,z rk ) The speed information isV rk =（v rxk ,v ryk ,v rzk ) And acceleration information isA rk =（a rxk ,a ryk ,a rzk ) Wherein, the method comprises the steps of, wherein,kis the firstkAt the moment of time of day,x rk ,y rk andz rk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezThe initial coordinates of the axes are set to be,v rxk ,v ryk andv rzk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezThe speed of the shaft is such that,a rxk ,a ryk anda rzk respectively the firstkReceiver at each momentxA shaft(s),yShaft and method for producing the samezAcceleration of the shaft;
step 13, acquiring position information, speed information and acceleration information of the unmanned aerial vehicle:
the position information of the unmanned aerial vehicle is thatP tk =（x tk ,y tk ,z tk ) The speed information isV tk =（v txk ,v tyk ,v tzk ) And acceleration information isA tk =（a txk ,a tyk ,a tzk ) Wherein, the method comprises the steps of, wherein,x tk ,y tk andz tk respectively the firstkUnmanned plane at each momentxA shaft(s),yShaft and method for producing the samezThe initial coordinates of the axes are set to be,v txk ,v tyk andv tzk respectively the firstkThe time is that the unmanned aerial vehicle is inxA shaft(s),yShaft and method for producing the samezThe speed of the shaft is such that,a txk ,a tyk anda tzk respectively the firstkUnmanned plane at each momentxA shaft(s),yShaft and method for producing the samezAcceleration of the shaft;
step 14, establishing grid points of an imaging scene of the detection target:
setting the scene level of a detection target, wherein the detection target is positioned on the horizontal plane, and acquiring initial position information of the detection target as followsP p =（x p ,0,z p ），x p To detect the object inxInitial coordinates of axes, detection target inyThe coordinates of the axes are 0 and,z p to detect the object inzInitial coordinates of the shaft;
according to the preset imaging breadth, carrying out grid division on an imaging scene of the detection target, wherein the grid division is carried outxShaft step sizezThe axial step length is respectively%xAnd deltazThe position information of each grid point of the imaging scene of the detection target is thatP i j(,) =（x i ,0,z j ）：
P i j(,) =（x i ,0,z j ）=（x p +M·△x,0,z p +N·△z）；
Wherein, the liquid crystal display device comprises a liquid crystal display device,M=-m：1：m，N=-n：1：n，mandngrid divided into imaging swathsStarting from the initial position of the detection targetxCell number sum of axeszThe number of bars of the shaft;x i at the ground grid pointxThe coordinates of the axes are used to determine,z j at the ground grid pointzCoordinates of the axes;
step 2, constructing a distance-direction resolution model and a ground distance azimuth resolution model of a random shift configuration of the distributed SAR based on a gradient theory;
the specific steps of constructing the distance resolution model are as follows:
based on the bistatic forward-looking SAR model established in the step 1, obtaining the first stepkThe distances from the receiver and the unmanned aerial vehicle at each moment are all constantMIs equal to the equidistant ground coordinate point of (2)P Mk =（x Mk ,0,z Mk ) Position information, constant of (a)MWith equidistant ground coordinate pointsP Mk The following relationship is satisfied:
Figure QLYQS_1
all equidistant ground coordinate pointsP Mk Constitute the firstkEquidistant line for each momentM bk ；
Obtain the firstkEquidistant line of time of dayM bk Equidistant ground coordinate points onP Mk Gradient of%M k The expression is:
Figure QLYQS_2
wherein, the liquid crystal display device comprises a liquid crystal display device,i x 、i y andi z respectively representing the emission coordinate systemxA shaft(s),yShaft and method for producing the samezA unit vector of the axis;
obtain the firstkEquidistant line for each momentM bk Equidistant ground coordinate points onP Mk Ground range resolution along gradient directionρ rgk The expression is:
Figure QLYQS_3
wherein, the liquid crystal display device comprises a liquid crystal display device,cis the speed of light;B r the bandwidth of transmitting pulse signals for the radar detection system of the unmanned aerial vehicle;
step 3, establishing a nonlinear multi-objective optimization equation based on a distance-direction resolution model and a ground distance azimuth resolution model of a random shift configuration of the distributed SAR;
and 4, solving the nonlinear multi-objective optimization equation obtained in the step 3 to obtain an optimal track under the optimal resolution.
2. The distributed SAR configuration design method according to claim 1, wherein the specific steps of constructing the azimuth resolution model in step 2 are:
based on the bistatic forward-looking SAR model established in the step 1, obtaining the first stepkEquidistant line from receiver and unmanned aerial vehicle at individual momentsM bk Ground coordinate point onP Mk Unit pitch vector of (a)
Figure QLYQS_4
And->
Figure QLYQS_5
The expression is:
Figure QLYQS_6
obtain the firstkEquidistant line at each momentM bk Ground coordinate point onP Mk Doppler of (2)F dk The expression is:
Figure QLYQS_7
wherein, the liquid crystal display device comprises a liquid crystal display device,V Rk andV Tk respectively the receiver firstkSpeed information at each timeV rk =（v rxk ,v ryk ,v rzk ) And speed information of unmanned aerial vehicleV tk =（v txk ,v tyk ,v tzk ）；λIs the wavelength of the radar detection system;
based on the firstkEquidistant line at each momentM bk Ground coordinate point onP Mk Doppler of (2)F dk， Acquisition of the firstkEqual Doppler line at each momentf dk The expression is:
f dk =const；
obtain the firstkGround coordinate point of equal Doppler line on equidistant line at each momentP Mk Gradient of%f dk The expression is:
Figure QLYQS_8
Figure QLYQS_9
Figure QLYQS_10
Figure QLYQS_11
obtaining the synthetic aperture time delta of the radartIn, the firstkGround coordinate points on equidistant lines at each moment are in ground distance azimuth resolution along the Doppler gradient direction, and the expression is as follows:
Figure QLYQS_12
wherein, is deltatIs the synthetic aperture time of the radar, i.e. the dwell time of the beam in the imaging area.
3. The distributed SAR configuration design method according to claim 2, wherein the specific steps of step 3 are as follows:
obtain the firstkThe distance resolution of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure QLYQS_13
Figure QLYQS_14
Figure QLYQS_15
wherein, is VM k (i,j) Represent the firstkImaging scene of object detection at each momenti,j) A distance gradient of the grid points;
obtain the firstkThe azimuth resolution of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure QLYQS_16
Figure QLYQS_17
Figure QLYQS_18
Figure QLYQS_19
wherein, is Vf dk (i,j) Represent the firstkDetecting Doppler gradients of grid points of an imaging scene of the target at each moment;
obtain the firstkThe gradient included angle between the distance gradient and the Doppler gradient of each grid point of the imaging scene of the detection target at each moment is expressed as follows:
Figure QLYQS_20
obtain the first based on the most stringent detection criteriakImaging detection results of track segmentation at each moment:
maxρ rg_k =max(max(ρ rg_k ))；
maxρ a_k =max(max(ρ a_k ))；
minψ k =min(min(ψ k ))；
wherein maxρ rg_k 、maxρ ak And minψ k Respectively represent the firstkMaximum distance resolution, maximum azimuth resolution and minimum gradient included angle of each grid point of an imaging scene of the detection target at each moment;
extraction of the firstkOptimization variables for individual momentsX k The expression is:
X k =(x tk ,y tk ,z tk ,v txk ,v tyk ,v tzk ) T ；
based on the firstkOptimization variables for individual momentsX k Constructing a nonlinear multi-element target optimization function, wherein the expression is as follows:
Figure QLYQS_21
wherein, the liquid crystal display device comprises a liquid crystal display device,f 1 (X k ) A distance resolution optimization function is represented and,f 2 (X k ) Representing the azimuth resolution optimization function,f 3 (X k ) Representing an azimuth resolution optimization function;ρ rg_opt representing the ground distance resolution expectation of back calculation according to the positioning accuracy requirement,ρ a_opt representing the ground clearance azimuth resolution expectation of back calculation according to the positioning accuracy requirement,ψ opt representing a desired two-dimensional resolution angle;
constructing a first objective optimization function based on nonlinear multiple objective optimization functionskIndividual time weighted optimization functionF(X k ) The expression is:
Figure QLYQS_22
wherein, the liquid crystal display device comprises a liquid crystal display device,ω k is the firstkWeighting coefficients for each time instant;f n (X k ) Represent the firstnA single objective optimization function;Uspace of solutions optimized for the target;
optimizing the function by weightingF(X k ) Conversion to an optimal solution problem for nonlinear multi-objective optimization equationsX opt k, The expression is:
Figure QLYQS_23
wherein, the liquid crystal display device comprises a liquid crystal display device,Pis a set of parameter spaces.
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