CN115877318B - Radiation source positioning method based on multi-aperture cross positioning - Google Patents
Radiation source positioning method based on multi-aperture cross positioning Download PDFInfo
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Abstract
The invention discloses a radiation source positioning method based on multi-aperture cross positioning. The positioning method comprises the following steps: based on a back projection algorithm, obtaining azimuth angle estimated values of targets under a plurality of sub-apertures with different positions in a multi-aperture search model through coarse search and fine search; based on the obtained azimuth angle estimated value, the distance direction distance and the azimuth direction distance of the target are obtained through a least square solution linear equation set, and the target positioning is realized. Compared with the positioning method of two apertures, the multi-aperture cross positioning of the invention increases the positioning accuracy.
Description
Technical Field
The invention relates to a radiation source positioning technology, in particular to a multi-aperture-based cross positioning method.
Background
Compared with the radiation source positioning technology based on a plurality of position information, the positioning method based on the passive synthetic aperture has remarkable advantages in sensitivity and resolution due to the coherent accumulation characteristic. In the synthetic aperture positioning method, the azimuth angle of the target under the sub-aperture can be obtained based on a back projection algorithm, and the position of the target can be obtained by utilizing the azimuth angle information of the target under the two apertures. However, the two-aperture target positioning result based on the back projection algorithm has larger fluctuation and poor target positioning precision.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a novel radiation source positioning method based on multi-aperture cross positioning, which can solve the problem of poor positioning precision in the positioning of a dual-aperture-based back projection algorithm in the prior art and improve the positioning accuracy of the whole target.
The technical scheme of the invention is as follows:
A method of positioning a radiation source based on multi-aperture cross positioning, comprising:
Step 101: performing down-conversion and de-modulation processing on a radiation source target signal received by a receiver, namely a received signal, so as to obtain a Doppler received signal of the radiation source target;
Step 102: sampling the de-modulated Doppler received signal according to a signal sampling model, intercepting and searching the obtained sampled signal based on a multi-synthetic aperture searching model, obtaining azimuth angle estimated values of targets under a plurality of sub apertures with different central aperture positions through a back projection algorithm in searching, and constructing the searching model based on a searching strategy which is sequentially carried out by coarse searching and fine searching;
Step 103: obtaining the distance and azimuth distance of the radiation source target by a least square method according to the azimuth angle estimated values of the target under a plurality of sub-apertures with different central aperture positions;
the search model is constructed as follows:
The sub-apertures participating in the search comprise 1 st, 2 nd, … th, I th and … th I-th sub-apertures, the central moment positions of the corresponding sub-apertures are T ci, i=1, 2, …, I, the central space positions of the corresponding sub-apertures are L i＝vTci, v is the movement speed of a platform, coarse search and fine search for targets are sequentially carried out under the aperture arrays of the plurality of sub-apertures to obtain azimuth angles phi i of any I-th sub-aperture and the targets, wherein the aperture search duration of the coarse search is T short, the aperture search duration of the fine search is T long,Tlong＞Tshort, and the search center of the fine search is the initial positioning position of the targets obtained through the coarse search.
According to some embodiments of the invention, the signal sampling model is set as follows:
rd(l)＝r2(lTs),l＝0,1,…,L-1
Wherein, rd () represents a discretized signal sequence obtained after sampling, which is a 1×l-dimensional complex matrix, that is, rd e C 1 ×L; l represents the first sampling point signal of the one-dimensional vector, and L represents the number of signal sampling points; Represents a signal sampling time interval, where f s represents a sampling frequency, and the corresponding signal sampling time range is t=lt s, l=0, 1, …, L-1.
According to some embodiments of the invention, in step 101, obtaining the doppler received signal of the radiation source target includes:
(1) Setting related parameters of a radiation source, which specifically comprises: setting a radiation source signal modulation mode as Binary Phase Shift Keying (BPSK), wherein carrier frequencies are f c, the radiation source signal is s (t) =g (t) exp (j 2 pi f c t), t represents time, and g (t) is a baseband code element signal of the radiation source signal;
(2) Setting scene and platform receiver parameters, specifically comprising: under a rectangular coordinate system, the platform moves linearly at a constant speed v, the motion track is [ x (t), y (t), z (t) ], and the speed vector is [ v x,vy,vz ]. The radiation source target radiates electromagnetic signals around the earth surface, and the corresponding coordinates are [ x 0,y0, 0];
(3) According to the settings of (1) and (2), a radiation source target signal received by an onboard receiver, namely a received signal r (t), is obtained as follows:
Where a represents the intensity of the received signal, w (t) is zero mean, variance is sigma 2 gaussian white noise, c represents the speed of light, represents the instantaneous distance of the radiation source target to the receiver;
(4) And performing down-conversion processing on the received signal r (t) according to the signal carrier frequency to obtain a down-conversion processed signal r 1 (t), wherein the down-conversion processing signal r 1 (t) is as follows:
wherein w 1(t)＝w(t)exp(-j2πfc t) represents the down-converted interference signal, represents the baseband symbol signal of the radiation source signal at the moment ;
(5) Square-de-modulating the down-converted processed signal r 1 (t) to obtain a Doppler received signal r 2 (t) of the radiation source target:
wherein, C is a normal complex number, represents the interference signal after demodulation.
According to some embodiments of the invention, the step 102 includes:
sampling the Doppler received signal according to the signal sampling model to obtain a discretized sampled received signal;
Intercepting and sampling the discretized sampling received signal according to the coarse search aperture time length T short to obtain a target Doppler signal under a short synthetic aperture;
Performing first meshing subdivision according to azimuth angles and distances in azimuth angles of a search area for performing target search, namely coarse meshing subdivision;
Taking grid points obtained by coarse meshing subdivision as a first target point, and obtaining a de-modulated Doppler signal of the first target point, namely a de-modulated Doppler signal under short synthesis duration;
Performing correlation processing on the Doppler signal of the target under the short synthetic aperture and the de-modulated Doppler signal under the short synthetic duration within a short synthetic aperture range to obtain a positioning result of the first target point;
searching the peak position of the positioning result under coarse gridding sectioning according to the positioning result of the first target point, and obtaining the positioning position of the first target point under coarse searching according to the first azimuth index and the distance index in the first azimuth direction which are correspondingly obtained, wherein the positioning position comprises a coarse first azimuth and the distance in the first azimuth direction;
obtaining a frequency and a tuning frequency corresponding to the target according to the first azimuth angle and the distance calculation in the first azimuth angle direction;
performing down-conversion processing on the discretized sampling received signal according to the frequency corresponding to the target to obtain a down-converted sampling received signal;
carrying out low-pass filtering treatment on the sampling signal subjected to the down-conversion treatment according to the frequency modulation to obtain a sampling receiving signal subjected to filtering;
Performing up-conversion processing on the filtered sampling received signal according to the frequency corresponding to the target to obtain an up-converted sampling signal;
Intercepting and sampling the up-converted sampling signal according to the finely searched searching aperture duration T long to obtain a target Doppler signal under a long synthetic aperture;
taking the positioning position of the first target point under the rough search as a center, and performing second meshing subdivision on a search area for performing target search according to the azimuth angle and the distance in the azimuth direction, namely fine meshing subdivision;
Taking grid points obtained by fine meshing subdivision as a second target point, and obtaining a de-modulated Doppler signal of the second target point, namely a de-modulated Doppler signal under long synthesis duration;
performing correlation processing on the Doppler signal of the target under the long synthetic aperture and the de-modulated Doppler signal under the long synthetic duration within the range of the long synthetic aperture to obtain a positioning result of the second target point;
Searching the peak position of the positioning result under the fine grid segmentation according to the positioning result of the second target point, and obtaining the azimuth angle of the second target point under the fine search, namely the azimuth angle estimated value, according to the second azimuth angle index and the distance index in the second azimuth angle direction which are correspondingly obtained;
wherein the distance in the azimuth direction is the distance between the sub-aperture center and the target.
According to some embodiments of the invention, the step 102 specifically includes:
based on the search model, taking the central moment position T ci of the sub-aperture as the center, taking T short as the interception length, intercepting the discretized signal rd obtained by sampling the signal sampling model to obtain Doppler signals of the target under the short synthetic aperture, wherein the Doppler signals are as follows:
rdshort(l;Tci)＝rd(l),l＝Ns1,Ns1+1,…,Ns2
Where rd short represents the Doppler signal of the target under the short synthetic aperture of the ith sub-aperture, which is a1× (N sk2-Nsk1 +1) -dimensional complex matrix, i.e., Ns1＝round(Tsi1fs) represents the start sampling point of the intercepted signal rd of the ith sub-aperture under short synthetic aperture interception, N s2＝round(Tsi2fs) represents the end sampling point of the intercepted signal rd of the ith sub-aperture under short synthetic aperture interception, round (·) represents the nearest rounding,/> represents the time starting point of the intercepted signal, and/> represents the time ending point of the intercepted signal, i.e., the Doppler signal interception time range t si(l;Tci,Tshort)＝t(lTs),l＝Ns1,Ns1+1,…,Ns2 of the ith sub-aperture under short synthetic aperture interception;
(2) Setting the central position coordinates of the search area as [ X 0,Y0, 0], and calculating a squint angle theta ci and a squint distance R ci corresponding to the central position of the search area by combining the central position coordinates of the synthetic aperture [ X ci,yci,zci ] and a velocity vector [ v x,vy,vz ], wherein the squint angle theta ci and the squint distance R ci are as follows:
(3) Taking the squint angle theta ci and the squint distance R ci as the center, carrying out coarse meshing subdivision of the azimuth angle and the distance in the azimuth direction, namely the azimuth distance,
Wherein, coarse meshing subdivision of azimuth angle is as follows:
represents azimuth grid points obtained by coarse meshing subdivision under the ith sub-aperture, and the azimuth grid points are M s multiplied by 1-dimensional real matrices; θ si is the azimuth split range; m s is the grid cell number over the total azimuth, and θ si＝Msdθsi,dθsi is the azimuth split interval; m denotes the mth azimuth grid cell.
Coarse meshing subdivision of azimuth distance is as follows:
represents azimuth distance grid points obtained by coarse meshing dissection under the ith sub-aperture, and the azimuth distance grid points are N s multiplied by 1-dimensional real matrices; r si is the azimuth distance subdivision range; n s is the grid cell number of the total azimuth distance, and R si＝NsdRsi,dRsi is the azimuth distance subdivision interval; n represents the nth range grid cell in azimuth;
(4) Taking grid points with an azimuth angle of theta smi,m＝1,…,Ms and an azimuth distance of R sni,n＝1,…,Ns as target points, namely a first target point, and combining the motion track of a platform to obtain Doppler signals R short(l;m,n,Tci under the short synthesis duration of the ith sub-aperture considering the de-modulation effect, wherein the Doppler signals R short(l;m,n,Tci are as follows:
Wherein R (l; m, n, T ci,Tshort) represents the instantaneous distance between the target with a sampling interval of T s, an azimuth angle of θ smi (m), and an azimuthal distance of R sni (n) and the satellite trajectory at the short synthetic aperture of the ith sub-aperture, an
(5) And carrying out correlation processing on the Doppler signal rd short(l;Tci of the target under the short synthetic aperture of the ith sub-aperture and the Doppler signal r short(l;m,n,Tci) under the short synthetic duration of the ith sub-aperture in a short synthetic aperture range to obtain a positioning result of the first target point, wherein the positioning result is as follows:
Wherein I short(m,n;Tci) represents the target grid point positioning result obtained by rough search under the short synthetic aperture of the ith sub-aperture, which is an M s×Ns -dimensional real matrix, namely represents correlation calculation, |·| represents a modulus value,/> represents the complex conjugate of the doppler signal rd short(l;Tci) of the target under the short synthetic aperture of the ith sub-aperture;
(6) Searching the peak position of I short(m,n;Tci) according to the positioning result of the first target point, and correspondingly obtaining the coarse positioning azimuth angle theta smi(msi) and the azimuth distance R sni(nsi of the first target point through the azimuth index m si and the azimuth distance index n si of the grid point of the position;
(7) Calculate the corresponding frequency and frequency modulation of the target at the first target point based on the resulting azimuth θ smi(msi) and azimuth distance R sni(nsi), as follows:
Wherein v represents the platform running speed, and lambda represents the signal carrier wavelength;
(8) According to the frequency corresponding to the obtained target, performing down-conversion processing on the discretized signal sequence rd obtained by sampling by the signal sampling model to obtain a sampled received signal rd1 after the down-conversion processing, wherein the down-conversion processing is as follows:
rd1＝rd·exp(-j2πfdt)；
(9) And according to the frequency modulation corresponding to the obtained target, performing low-pass filtering processing on the sampling received signal rd1 after the down-conversion processing to obtain a sampling received signal rd2 after the filtering processing, wherein the following steps are performed:
rd2＝ifft(fft(filter,length(rd1))·fft(rd1))
wherein, fft (·) is fourier transform, ifft (·) is inverse fourier transform, |·| represents modulus, length (·) represents signal length, filter represents filter time domain expression, as follows:
filter＝cfirpm(No,[-1 -F2 -F1 F1 F21],@lowpass)；
Wherein cfirpm represents the order for function ;F1＝2|Ka|Tlong/fs,F2＝3|Ka|Tlong/fs;No used to generate the filter time domain expression for the corresponding band range, @ lowpass represents the low pass filter call function;
(10) And according to the frequency corresponding to the obtained target, performing up-conversion processing on the filtered sampling signal rd 2 to obtain an up-converted sampling signal rd3, wherein the up-converted sampling signal rd3 is as follows:
rd3＝rd2·exp(j2πfdt)；
(11) Taking T ci as a center, taking T long as a interception length, taking down as a downsampling multiple of a positive integer, intercepting and sampling the up-converted sampling signal rd3 to obtain a Doppler signal of a target under a long synthetic aperture, wherein the Doppler signal is as follows:
rdlong(l;Tci,down)＝rd3(l·down),l＝Nl1,Nl1+1,…,Nl2
Where rd long(l;Tci, down) represents a target Doppler signal obtained by downsampling the long synthetic aperture of the ith sub-aperture by 1× (N l2-Nl1 +1) dimensional complex matrix, i.e., Nl1＝round(Tli1fs/down) represents a start sampling point of downsampling signal of the ith sub-aperture truncated by the long synthetic aperture, N l2＝round(Tli2fs/down) represents a stop sampling point of downsampling signal of the ith sub-aperture truncated by the long synthetic aperture, round (·) represents a nearest integer,/> represents a time start point of downsampling signal of the truncated down times,/> represents a time end point of downsampling signal of the truncated down times, and the interception time range of Doppler signal of the target under the ith sub-aperture is the long synthetic aperture ：tli(l;Tci,Tlong,down)＝t(l·Ts·down),l＝Nl1,Nl1+1,…,Nl2;
(12) Azimuth angle theta smi(msi) and azimuth distance R sni(nsi) of the first target point obtained by the rough search are used as search centers of the fine search, and fine meshing subdivision based on azimuth angles and azimuth distances is performed on a search area near the center, wherein the fine meshing subdivision is as follows:
azimuth angle subdivision is:
Wherein θ lmi (M) represents azimuth grid points obtained by fine meshing subdivision under the ith sub-aperture, which is an M l ×1-dimensional real matrix, i.e., θli is an azimuth subdivision range; m l is the grid cell number over the total azimuth, and θ li＝Mldθli,dθli is the azimuth split interval;
The azimuthal distance is split as follows:
Wherein R lni (N) represents an azimuthal distance grid point obtained by fine meshing subdivision under the ith sub-aperture, which is an N l ×1-dimensional real matrix, i.e., Rli is an azimuthal distance subdivision range; n l is the grid cell number of the total azimuth distance, and R li＝NldRli,dRli is the azimuth distance subdivision interval;
(13) Taking a grid point with an azimuth angle of theta lmi and an azimuth distance of R lni as a target point, namely a second target point, and combining the platform track to obtain a Doppler signal R long of the grid target point in a long synthesis duration, wherein the Doppler signal R long(l;m,n,Tci is a demodulation Doppler signal R57down under the long synthesis duration, and the Doppler signal R long is obtained by taking the demodulation effect into consideration as follows:
wherein R (l; m, n, T ci,Tlong, down) represents the instantaneous distance between the target with the sampling interval of Down.T s, the azimuth angle being θ lmi (m), the azimuthal distance being R lni (n), and the satellite trajectory, under the long synthetic aperture of the ith sub-aperture, and:
Wherein, t li(l;Tci,Tlong, down) represents the Doppler received signal interception time range of the ith sub-aperture under the long synthetic aperture;
(14) And performing correlation processing on the Doppler signals rd long(l;Tci and down) intercepted under the long synthetic aperture and the de-modulated Doppler signals r long(l;m,n,Tci and down) under the long synthetic duration within the range of the long synthetic aperture to obtain a positioning result of the second target point, wherein the positioning result is as follows:
Wherein represents the second mesh target point positioning result under the i-th sub-aperture under the long synthetic aperture, which is an M l×Nl -dimensional real matrix,/> represents the correlation calculation, |·| represents the modulus value,/> represents the complex conjugate of the doppler signal rd long(l;Tci, down) representing the target under the i-th sub-aperture under the long synthetic aperture;
(15) Searching for the peak position of I long(m,n;Tci, down) according to the positioning result of the second target point, and obtaining the azimuth angle phi i, i=1, 2, …, the estimated value phi i of the target under the ith sub-aperture by the azimuth index m li of the grid point of the position, as follows:
φi＝θlmi(mli)。
according to some embodiments of the invention, the step 103 includes:
Based on the obtained azimuth angle estimated values of the targets under the plurality of sub-apertures with different central aperture positions, according to the geometrical relationship between different distances and azimuth angles, A system of equations R for solving the positions of the radiation source targets with the distance R, the azimuth distance A z and the distances R1, R2, …, ri, … and RI in the azimuth direction is established, wherein the system of equations R is as follows:
The sub-aperture center distance L i＝v·Lci,Ri is the distance between the sub-aperture center and the target, i.e. the azimuth direction distance, i=1, 2, …, I, Φ i, i=1, 2, …, I represents the target azimuth;
Solving the equation set through a least square method to obtain the distance R and the azimuth distance A s of the target.
According to some embodiments of the invention, the distance to distance R and the azimuth distance A s of the target are solved as follows:
A z =x (1), r=x (2), x (1), x (2) represent the first row element and the second row element of the solution matrix x of the following equation set:
x= (a *A)\(A* b), wherein:
a * represents the conjugate transpose of matrix a.
Compared with the two-aperture target positioning method of the back projection algorithm, the method has the advantages that the stability and the positioning precision of the positioning result are obviously improved, the number and the positions of the sub-apertures can be flexibly designed according to actual engineering requirements, the use is flexible, and the real-time performance is good.
Drawings
Fig. 1 is a schematic diagram of a radiation source positioning process according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of the azimuth search according to the embodiment of the present invention.
FIG. 3 is a schematic representation of a solution to the target position of the radiation source in an embodiment of the present invention.
Fig. 4 is a schematic diagram of a simulation positioning scenario in embodiment 1 of the present invention.
FIG. 5 is a diagram showing the result of 2-aperture azimuth positioning error in example 1 of the present invention.
FIG. 6 is a diagram showing the result of 2-aperture distance positioning error in embodiment 1 of the present invention.
FIG. 7 is a graph showing the result of 21-aperture azimuth positioning error in example 1 of the present invention.
FIG. 8 is a graph showing the result of 21-aperture distance positioning error in example 1 of the present invention.
Detailed Description
The present invention will be described in detail with reference to the following examples and drawings, but it should be understood that the examples and drawings are only for illustrative purposes and are not intended to limit the scope of the present invention in any way. All reasonable variations and combinations that are included within the scope of the inventive concept fall within the scope of the present invention.
Referring to fig. 1, according to the technical scheme of the invention, an embodiment of a multi-aperture-based radiation source cross positioning method comprises the following procedures:
Step 101: and receiving the radiation source target signal through a receiver, and performing down-conversion and de-modulation processing on the received radiation source target signal, namely the received signal, so as to obtain a Doppler received signal of the radiation source target.
In some embodiments, the radiation source target signal received by the receiver may be obtained for instrument reading and/or generated by simulation.
Further, in some embodiments, step 101 includes:
(1) Setting related parameters of a radiation source, which specifically comprises: the modulation mode of the radiation source signal is binary phase shift keying BPSK, the carrier frequencies are f c, the radiation source signal is s (t) =g (t) exp (j 2 pi f c t), t represents time, and g (t) is a baseband code element signal of the radiation source signal.
(2) Setting scene and platform receiver parameters, specifically comprising: under a rectangular coordinate system, the platform moves linearly at a constant speed v, the motion track is [ x (t), y (t), z (t) ], the speed vector is , the radiation source target radiates electromagnetic signals around the earth surface, and the corresponding coordinate is [ x 0,y0, 0].
(3) According to the settings of (1) and (2), a radiation source target signal received by an onboard receiver, namely a received signal r (t), is obtained as follows:
Where a represents the intensity of the received signal, w (t) is zero mean, variance is σ 2 gaussian white noise, c represents the speed of light, represents the instantaneous distance of the radiation source target to the receiver.
In the above steps, r (t) is a radiation source signal received by an actual receiver instrument in an actual scene, and in a simulation scene, r (t) is a received signal generated according to the simulation of the actual scene, and is the scene reproduction of the actual scene, and the subsequent positioning modes of the r (t) and the receiving signal are the same.
(4) And performing down-conversion processing on the received signal r (t) according to the signal carrier frequency to obtain a down-conversion processed signal r 1 (t), wherein the down-conversion processing signal r 1 (t) is as follows:
Where w 1(t)＝w(t)exp(-j2πfc t) represents the down-converted interference signal, represents the baseband symbol signal of the radiation source signal at time .
(5) Square-de-modulating the down-converted processed signal r 1 (t) to obtain a Doppler received signal r 2 (t) of the radiation source target:
Wherein, C is a normal complex number, represents the interference signal after demodulation.
Step 102: and sampling the de-modulated Doppler received signal according to a signal sampling model, intercepting and searching the obtained sampled signal based on a multi-synthetic aperture searching model, obtaining azimuth angle estimated values of targets under a plurality of sub apertures with different central aperture positions through a back projection algorithm in searching, and constructing the searching model based on a searching strategy which is sequentially carried out by coarse searching and fine searching.
Wherein, in some embodiments, the signal sampling model is as follows:
the Doppler signal r 2 (t) is truncated and sampled to obtain a discrete signal:
rd(l)＝r2(lTs),l＝0,1,…,L-1
Wherein, rd () represents a discretized signal sequence obtained after sampling, which is a 1×l-dimensional complex matrix, that is, rd e C 1 ×L; l represents the first sampling point signal of the one-dimensional vector, and L represents the number of signal sampling points; Represents a signal sampling time interval, where f s represents a sampling frequency, and the corresponding signal sampling time range is t=lt s, l=0, 1, …, L-1.
In some embodiments, referring to fig. 2, the search model is constructed as follows:
The sub-apertures participating in searching comprise 1 st, 2 nd, … th, I th and … th I-th sub-apertures, the central moment positions of the corresponding sub-apertures are T ci, i=1, 2, …, I, the central space positions of the corresponding sub-apertures are L i＝vTci, and coarse searching and fine searching aiming at targets are sequentially carried out under the aperture arrays of the plurality of sub-apertures to obtain azimuth angles phi i of any I-th sub-aperture and the targets, wherein the aperture searching duration of the coarse searching is T short, and the aperture searching duration of the fine searching is T long,Tlong＞Tshort.
Wherein, in some embodiments, the intercepting and searching comprises:
(1) Based on the search model, firstly taking the central moment position T ci of the sub-aperture as the center, taking T short as the interception length, intercepting the discretized signal sequence obtained by sampling the signal sampling model to obtain Doppler signals of the target under the short synthetic aperture, wherein the Doppler signals are as follows:
rdshort(l;Tci)＝rd(l),l＝Ns1,Ns1+1,…,Ns2
Where rd short represents the Doppler signal of the target under the short synthetic aperture of the ith sub-aperture, which is a1× (N sk2-Nsk1 +1) -dimensional complex matrix, i.e., Ns1＝round(Tsi1fs) represents the start sampling point of the truncated signal rd of the ith sub-aperture under short synthetic aperture truncation, N s2＝round(Tsi2fs) represents the end sampling point of the truncated signal rd of the ith sub-aperture under short synthetic aperture truncation, round (·) represents the nearest rounding,/> represents the time starting point of the truncated signal, and/> represents the time ending point of the truncated signal, i.e., the Doppler signal truncated time range t si(l;Tci,Tshort)＝t(lTs),l＝Ns1,Ns1+1,…,Ns2 of the ith sub-aperture under short synthetic aperture truncation.
(2) Setting the central position coordinates of the search area as [ X 0,Y0, 0], and calculating a squint angle theta ci and a squint distance R ci corresponding to the central position of the search area by combining the central position coordinates of the synthetic aperture [ X ci,yci,zci ] and a speed vector , wherein the squint angle theta ci and the squint distance R ci are as follows:
(3) Coarse gridding subdivision of the search area in azimuth and azimuthal distance (i.e., distance between the sub-aperture center and the target) is performed with the squint angle θ ci and the squint distance R ci as the center.
Wherein, coarse meshing subdivision of azimuth angle is as follows:
represents azimuth grid points obtained by coarse meshing subdivision under the ith sub-aperture, and the azimuth grid points are M s multiplied by 1-dimensional real matrices; θ si is the azimuth split range; m s is the grid cell number over the total azimuth, and θ si＝Msdθsi,dθsi is the azimuth split interval; m denotes the mth azimuth grid cell.
The azimuthal distance is split as follows:
represents azimuth distance grid points obtained by coarse meshing dissection under the ith sub-aperture, and the azimuth distance grid points are N s multiplied by 1-dimensional real matrices; r si is the azimuth distance subdivision range; n s is the grid cell number of the total azimuth distance, and R si＝NsdRsi,dRsi is the azimuth distance subdivision interval; n represents the nth range grid cell in azimuth.
(4) Taking grid points with an azimuth angle of theta smi,m＝1,…,Ms and an azimuth distance of R sni,n＝1,…,Ns as target points, namely first grid target points, referring to a receiving signal acquisition flow in step 101, and combining a platform motion track to obtain Doppler signals R short(l;m,n,Tci under the short synthesis duration of an ith sub-aperture considering a de-modulation effect, wherein the following steps are as follows:
Wherein R (l; m, n, T ci,Tshort) represents the instantaneous distance between the target with a sampling interval of T s, an azimuth angle of θ smi (m), and an azimuthal distance of R sni (n) and the satellite trajectory at the short synthetic aperture of the ith sub-aperture, an
(5) Carrying out correlation processing on a Doppler signal rd short(l;Tci of a target under the short synthetic aperture of the ith sub-aperture and a Doppler signal r short(l;m,n,Tci)rshort(l;m,n,Tci) under the short synthetic duration of the ith sub-aperture in a short synthetic aperture range to obtain a positioning result of the first grid target point:
Wherein I short(m,n;Tci) represents the target grid point positioning result obtained by rough search under the short synthetic aperture of the ith sub-aperture, which is an M s×Ns -dimensional real matrix, namely represents correlation calculation, |·| represents a modulus value,/> represents the complex conjugate of the doppler signal rd short(l;Tci) of the target under the short synthetic aperture of the ith sub-aperture.
(6) Searching the peak position of the I short(m,n;Tci) according to the positioning result of the first grid target point, and correspondingly obtaining the coarse positioning azimuth angle theta smi(msi) and the azimuth distance R sni(nsi of the first grid target point through the azimuth index m si and the azimuth distance index n si of the grid point of the position.
(7) Calculate the corresponding frequency and frequency modulation of the target at the first grid target point from the resulting azimuth θ smi(msi) and azimuth distance R sni(nsi) as follows:
Where v represents the platform operating speed and λ represents the signal carrier wavelength.
(8) And according to the frequency corresponding to the obtained target, performing down-conversion processing on the discretized signal sequence rd obtained by sampling by the signal sampling model to obtain a sampled received signal rd 1 after the down-conversion processing, wherein the following steps are performed:
rd1＝rd·exp(-j2πfdt)。
(9) And according to the frequency modulation corresponding to the obtained target, performing low-pass filtering processing on the sampling received signal rd 1 after the down-conversion processing to obtain a sampling received signal rd 2 after the filtering processing, wherein the following steps are performed:
rd2＝ifft(fft(filter,length(rd1))·fft(rd1))
wherein, fft (·) is fourier transform, ifft (·) is inverse fourier transform, |·| represents modulus, length (·) represents signal length, filter represents filter time domain expression, as follows:
filter＝cfirpm(No,[-1 -F2 -F1 F1 F2 1],@lowpass)；
Wherein cfirpm is a matlab-on-hand cfirpm function, which is used to generate a filter time domain expression ;F1＝2|Ka|Tlong/fs,F2＝3|Ka|Tlong/fs;No for the corresponding band range, which represents order, @ lowpass represents a low pass filter call function.
(10) And according to the frequency corresponding to the obtained target, performing up-conversion processing on the filtered sampling signal rd 2 to obtain an up-converted sampling signal rd 3, wherein the up-converted sampling signal rd 3 is as follows:
rd3＝rd2·exp(j2πfdt)。
(11) Taking T ci as a center, taking T long as a interception length, taking down as a downsampling multiple of a positive integer, intercepting and sampling the up-converted sampling signal rd 3 to obtain a Doppler signal of a target under a long synthetic aperture, wherein the Doppler signal is as follows:
rdlong(l;Tci,down)＝rd3(l·down),l＝Nl1,Nl1+1,…,Nl2
Where rd long(l;Tci, down) represents the Doppler signal of the target under the long synthetic aperture of the ith sub-aperture, which is a1× (N l2-Nl1 +1) -dimensional complex matrix, i.e., Nl1＝round(Tli1fs/down) represents the start sampling point of the truncated sampling signal of the ith sub-aperture under the long synthetic aperture, N l2＝round(Tli2fs/down) represents the end sampling point of the truncated sampling signal of the ith sub-aperture under the long synthetic aperture, round (·) represents the nearest integer,/> represents the time start point of the truncated sampling signal, and/> represents the time end point of the truncated sampling signal, then the range of the Doppler signal of the target under the ith sub-aperture under the long synthetic aperture is:
tli(l;Tci,Tlong,down)＝t(l·Ts·down),l＝Nl1,Nl1+1,…,Nl2.
(12) Azimuth angle theta smi(msi of the first mesh target point obtained by the rough search and azimuth distance R sni(nsi) are used as search centers of the fine search, and fine meshing subdivision based on azimuth angles and azimuth distances (namely, the distance between the sub-aperture center and the target) is performed on a search area near the center, as follows:
azimuth angle subdivision is:
Wherein θ lmi (M) represents azimuth grid points obtained by fine meshing subdivision under the ith sub-aperture, which is an M l ×1-dimensional real matrix, i.e., θli is an azimuth subdivision range; m l is the number of grid cells over the total azimuth, and θ li＝Mldθli,dθli is the azimuth split interval.
The dissection of the azimuthal distance is as follows:
Wherein R lni (N) represents an azimuthal distance grid point obtained by fine meshing subdivision under the ith sub-aperture, which is an N l ×1-dimensional real matrix, i.e., Rli is an azimuthal distance subdivision range; n l is the grid cell number of the total azimuthal distance, and R li＝NldRli,dRli is the azimuthal distance split interval.
(13) Taking a grid point with an azimuth angle of theta lmi and an azimuth distance of R lni as a target point, namely a second grid target point, referring to the Doppler received signal acquisition flow in step 101, and combining the platform track to obtain a Doppler signal R long of the grid target point in a long synthesis duration, wherein the Doppler signal R long(l;m,n,Tci is a demodulation Doppler signal R long(l;m,n,Tci under the long synthesis duration, and the demodulation effect is considered, as follows:
wherein R (l; m, n, T ci,Tlong, down) represents the instantaneous distance between the target with the sampling interval of Down.T s, the azimuth angle being θ lmi (m), the azimuthal distance being R lni (n), and the satellite trajectory, under the long synthetic aperture of the ith sub-aperture, and:
where t li(l;Tci,Tlong, down) represents the doppler received signal interception time range for the i-th sub-aperture under a long synthetic aperture.
(14) And performing correlation processing on the Doppler signals rd long(l;Tci and down) intercepted under the long synthetic aperture and the de-modulated Doppler signals r long(l;m,n,Tci and down) under the long synthetic duration within the range of the long synthetic aperture to obtain a positioning result of the second grid target point, wherein the positioning result is as follows:
Wherein represents the second mesh target point location result under the i-th sub-aperture under the long synthetic aperture, which is an M l×Nl -dimensional real matrix,/> represents the correlation calculation, |·| represents the modulus value,/> represents the complex conjugate of the doppler signal rd long(l;Tci, down) representing the target under the i-th sub-aperture under the long synthetic aperture.
(15) Searching for the peak position of I long(m,n;Tci, down according to the positioning result of the second mesh target point, and obtaining the azimuth angle phi i, i=1, 2, …, and the estimated value phi i of I of the target under the ith sub-aperture by the azimuth angle index m li (the azimuth distance index is n li) of the mesh point of the position, as follows:
φi＝θlmi(mli)
Step 103: and obtaining the distance direction distance and the azimuth direction distance of the radiation source target by a least square method according to the obtained azimuth angle estimated values of the target under a plurality of sub-apertures with different central aperture positions.
Further, in some embodiments, step 103 includes:
Referring to fig. 3, based on the azimuth angle estimated values of the target under the plurality of sub-apertures with different central aperture positions, a system of equations R for solving the position of the radiation source target with a distance R, a z, and a 1、R2、…、Ri、…、RI is established according to the geometrical relationship between different distances and azimuth angles, as follows:
Wherein the sub-aperture center distance L i＝v·Lci,Ri is the distance between the sub-aperture center and the target, i.e. the azimuthal distance, i=1, 2, …, I, Φ i, i=1, 2, …, I denotes the target azimuth.
The above equation set may be expressed as:
Ax＝b
Wherein the method comprises the steps of
Solving the equation set by a least square method to obtain:
x＝(A*A)\(A*b)
Wherein a * represents the conjugate transpose of matrix a, thereby obtaining the positioning position of the target with the range direction distance R and the azimuth direction distance a s: a z =x (1), r=x (2), where x (1) represents a first element of the solution vector x of the set of equations and x (2) represents a second element of the solution vector x of the set of equations.
The positioning effect of the present invention is further illustrated below with reference to specific embodiments.
Example 1
FIG. 4 is a schematic diagram of a simulation positioning scenario according to an embodiment of the present invention, where simulation parameters set in the embodiment include:
The platform data are generated by MATLAB, P is the central position of a scene, T is the target position, the height of the platform at A is 371km, the included angle between an AP and a yoz plane is 70 degrees, the distance between the AP and the AP is 1200km, the height of the platform at B is 357km, the included angle between BP and a yoz plane is 68 degrees, the platform flies at a constant speed of 3000m/s from A to B, the time is 0 to 42.92s, and the T coordinate position of a radiation source target is: r=303636.02 m, a z = 1146263.59m.
Echo signals are generated in MATLAB by using platform data, and the carrier frequency of the signals is: 7.2445GHz; code rate: 200bound/s; signal-to-noise ratio: 5dB; the sampling rate is 2KHz.
During the positioning process:
the synthesis duration of the rough search is 0.1s, the azimuth search range is 5 degrees, and the azimuth search interval is 2e-3 degrees; the distance search range is 100km, spaced 25km apart.
The fine search synthesis time length is 1s, the azimuth search range is 2e-2 degrees, and the azimuth search interval is 1e-6 degrees; the distance search range is 100km, spaced 25km apart.
The examples include two sets of comparative experiments with different aperture numbers, including:
(1) Group A: the aperture number is 2, and the center moment is T c1＝5,Tc1 =10;
(2) Group B: the aperture number is 21, and the center time is T ci =5+ (i-1)/4, i=1, 2, …,21.
Fig. 5 is a schematic diagram of a result of an azimuth positioning error of the group a, fig. 6 is a schematic diagram of a result of a distance positioning error of the group a, fig. 7 is a schematic diagram of a result of an azimuth positioning error of the group B, and fig. 8 is a schematic diagram of a result of a distance positioning error of the group B. The calculation can be obtained by: under 2 sub-apertures, the azimuth positioning deviation is 118.8m, the standard deviation is 516.1m, the distance deviation is 31.9m, the standard deviation is 139.4m, and the average error is 442m; under 21 sub-apertures, the azimuth positioning deviation is 85.9m, the standard deviation is 228.9m, the distance deviation is 22.9m, the standard deviation is 61.8m, and the average error is 204m.
The above examples are only preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples. All technical schemes belonging to the concept of the invention belong to the protection scope of the invention. It should be noted that modifications and adaptations to the present invention may occur to one skilled in the art without departing from the principles of the present invention and are intended to be within the scope of the present invention.
Claims (7)
1. A method for positioning a radiation source based on multi-aperture cross positioning, comprising:
Step 101: performing down-conversion and de-modulation processing on a radiation source target signal received by a receiver, namely a received signal, so as to obtain a Doppler received signal of the radiation source target;
Step 102: sampling Doppler receiving signals of the radiation source targets according to a signal sampling model, intercepting and searching the obtained sampling signals based on a searching model with multiple synthetic apertures, obtaining azimuth angle estimated values of the targets under multiple sub apertures with different central aperture positions through a back projection algorithm in searching, and constructing the searching model based on a searching strategy which is sequentially carried out by coarse searching and fine searching;
Step 103: obtaining the distance and azimuth distance of the radiation source target by a least square method according to the azimuth angle estimated values of the target under a plurality of sub-apertures with different central aperture positions;
the search model is constructed as follows:
The sub-apertures participating in the search comprise 1 st, 2 nd, … th, I th and … th I-th sub-apertures, the central moment positions of the corresponding sub-apertures are T ci, i=1, 2, …, I, the central space positions of the corresponding sub-apertures are L i＝vTci, v is the movement speed of a platform, coarse search and fine search for targets are sequentially carried out under the aperture arrays of the plurality of sub-apertures to obtain azimuth angles phi i of any I-th sub-aperture and the targets, wherein the aperture search duration of the coarse search is T short, the aperture search duration of the fine search is T long,Tlong＞Tshort, and the search center of the fine search is the initial positioning position of the targets obtained through the coarse search.
2. The method of claim 1, wherein the signal sampling model is set as follows:
rd(l)＝r2(lTs),l＝0,1,…,L-1
Wherein, rd () represents a discretized signal sequence obtained after sampling, which is a 1×l-dimensional complex matrix, that is, rd e C 1×L; l represents the first sampling point signal of the one-dimensional vector, and L represents the number of signal sampling points; Represents a signal sampling time interval, where f s represents a sampling frequency, and the corresponding signal sampling time range is t=lt s, l=0, 1, …, L-1.
3. The method according to claim 1, wherein in step 101, the obtaining of the doppler received signal of the radiation source object comprises:
(1) Setting related parameters of a radiation source, which specifically comprises: setting a radiation source signal modulation mode as Binary Phase Shift Keying (BPSK), wherein carrier frequencies are f c, the radiation source signal is s (t) =g (t) exp (j 2 pi f c t), t represents time, and g (t) is a baseband code element signal of the radiation source signal;
(2) Setting scene and platform receiver parameters, specifically comprising: under a rectangular coordinate system, the platform moves linearly at a constant speed v, the motion track is [ x (t), y (t), z (t) ], the speed vector is [ v x,vy,vz ], the radiation source target radiates electromagnetic signals around the earth surface, and the corresponding coordinates are [ x 0,y0, 0];
(3) According to the settings of (1) and (2), a radiation source target signal received by an onboard receiver, namely a received signal r (t), is obtained as follows:
Where a represents the intensity of the received signal, w (t) is zero mean, variance is sigma 2 gaussian white noise, c represents the speed of light, represents the instantaneous distance of the radiation source target to the receiver;
(4) And performing down-conversion processing on the received signal r (t) according to the signal carrier frequency to obtain a down-conversion processed signal r 1 (t), wherein the down-conversion processing signal r 1 (t) is as follows:
Wherein w 1(t)＝w(t)exp(-j2πfc t) represents the down-converted interference signal, represents the baseband symbol signal of the radiation source signal at/> time;
(5) Square-de-modulating the down-converted processed signal r 1 (t) to obtain a Doppler received signal r 2 (t) of the radiation source target:
Wherein, C is a normal complex number, represents the interference signal after demodulation.
4. The method of claim 1, wherein the step 102 comprises:
sampling the Doppler received signal according to the signal sampling model to obtain a discretized sampled received signal;
Intercepting and sampling the discretized sampling received signal according to the coarse search aperture time length T short to obtain a target Doppler signal under a short synthetic aperture;
Performing first meshing subdivision according to azimuth angles and distances in azimuth angles of a search area for performing target search, namely coarse meshing subdivision;
Taking grid points obtained by coarse meshing subdivision as a first target point, and obtaining a de-modulated Doppler signal of the first target point, namely a de-modulated Doppler signal under short synthesis duration;
performing correlation processing on the target Doppler signal under the short synthetic aperture and the de-modulated Doppler signal under the short synthetic duration within a short synthetic aperture range to obtain a positioning result of the first target point;
searching the peak position of the positioning result under coarse gridding sectioning according to the positioning result of the first target point, and obtaining the positioning position of the first target point under coarse searching according to the first azimuth index and the distance index in the first azimuth direction which are correspondingly obtained, wherein the positioning position comprises a coarse first azimuth and the distance in the first azimuth direction;
obtaining a frequency and a tuning frequency corresponding to the target according to the first azimuth angle and the distance calculation in the first azimuth angle direction;
performing down-conversion processing on the discretized sampling received signal according to the frequency corresponding to the target to obtain a down-converted sampling received signal;
carrying out low-pass filtering treatment on the sampling receiving signal after the down-conversion treatment according to the frequency modulation to obtain a sampling receiving signal after the filtering treatment;
Performing up-conversion processing on the filtered sampling received signal according to the frequency corresponding to the target to obtain an up-converted sampling signal;
Intercepting and sampling the up-converted sampling signal according to the finely searched searching aperture duration T long to obtain a target Doppler signal under a long synthetic aperture;
taking the positioning position of the first target point under the rough search as a center, and performing second meshing subdivision on a search area for performing target search according to the azimuth angle and the distance in the azimuth direction, namely fine meshing subdivision;
Taking grid points obtained by fine meshing subdivision as a second target point, and obtaining a de-modulated Doppler signal of the second target point, namely a de-modulated Doppler signal under long synthesis duration;
performing correlation processing on the target Doppler signal under the long synthetic aperture and the de-modulated Doppler signal under the long synthetic duration within the range of the long synthetic aperture to obtain a positioning result of the second target point;
Searching the peak position of the positioning result under the fine grid segmentation according to the positioning result of the second target point, and obtaining the azimuth angle of the second target point under the fine search, namely the azimuth angle estimated value, according to the second azimuth angle index and the distance index in the second azimuth angle direction which are correspondingly obtained;
wherein the distance in the azimuth direction is the distance between the sub-aperture center and the target.
5. The method of claim 4, wherein the step 102 specifically comprises:
(1) Based on the search model, taking the central moment position T ci of the sub-aperture as the center, taking T short as the interception length, intercepting the discretized signal rd obtained by sampling the signal sampling model to obtain Doppler signals of the target under the short synthetic aperture, wherein the Doppler signals are as follows:
rdshort(l;Tci)＝rd(l),l＝Ns1,Ns1+1,…,Ns2
Where rd short represents the Doppler signal of the target under the short synthetic aperture of the ith sub-aperture, which is a1× (N s2-Ns1 +1) -dimensional complex matrix, i.e., Ns1＝round(Tsi1fs) represents the start sampling point of the truncated signal rd of the ith sub-aperture under short synthetic aperture truncation, N s2＝round(Tsi2fs) represents the end sampling point of the truncated signal rd of the ith sub-aperture under short synthetic aperture truncation, round (·) represents the nearest rounding,/> represents the time starting point of the truncated signal,/> represents the time ending point of the truncated signal, i.e., the Doppler signal truncated time range tsi(l;Tci,Tshort)＝t(lTs),l＝Ns1,Ns1+1,…,Ns2,fs of the ith sub-aperture represents the sampling frequency under short synthetic aperture truncation, represents the signal sampling time interval, and l represents the signal of the first sampling point;
(2) Setting the central position coordinates of the search area as [ X 0,Y0, 0], and calculating a squint angle theta ci and a squint distance R ci corresponding to the central position of the search area by combining the central position coordinates of the synthetic aperture [ X ci,yci,zci ] and a velocity vector [ v x,vy,vz ], wherein the squint angle theta ci and the squint distance R ci are as follows:
(3) Taking the squint angle theta ci and the squint distance R ci as the center, carrying out coarse meshing subdivision of the azimuth angle and the distance in the azimuth direction, namely the azimuth distance,
Wherein, coarse meshing subdivision of azimuth angle is as follows:
represents azimuth grid points obtained by coarse meshing subdivision under the ith sub-aperture, and the azimuth grid points are M s multiplied by 1-dimensional real matrices; θ si is the azimuth split range; m s is the grid cell number over the total azimuth, and θ si＝Msdθsi,dθsi is the azimuth split interval; m represents an mth azimuth grid cell;
coarse meshing subdivision of azimuth distance is as follows:
represents azimuth distance grid points obtained by coarse meshing dissection under the ith sub-aperture, and the azimuth distance grid points are N s multiplied by 1-dimensional real matrices; r si is the azimuth distance subdivision range; n s is the total number of distance grid cells in azimuth, and R si＝NsdRsi,dRsi is the distance subdivision interval in azimuth; n represents the nth range grid cell in azimuth;
(4) Taking grid points with an azimuth angle of theta smi,m＝1,…,Ms and an azimuth distance of R sni,n＝1,…,Ns as target points, namely a first target point, and combining the motion track of a platform to obtain Doppler signals R short(l;m,n,Tci under the short synthesis duration of the ith sub-aperture considering the de-modulation effect, wherein the Doppler signals R short(l;m,n,Tci are as follows:
Wherein f c represents the carrier frequency, R (l; m, n, T ci,Tshort) represents the instantaneous distance between the target with a sampling interval T s of which the azimuth angle is theta smi (m) and the azimuth distance is R sni (n) and the satellite trajectory under the short synthetic aperture of the ith sub-aperture, and
Wherein, t si(l;Tci,Tshort) represents the Doppler signal interception time range of the ith sub-aperture under short synthetic aperture interception;
(5) And carrying out correlation processing on the Doppler signal rd short(l;Tci of the target under the short synthetic aperture of the ith sub-aperture and the Doppler signal r short(l;m,n,Tci) under the short synthetic duration of the ith sub-aperture in a short synthetic aperture range to obtain a positioning result of the first target point, wherein the positioning result is as follows:
wherein I short(m,n;Tci) represents the target grid point positioning result obtained by rough search under the short synthetic aperture of the ith sub-aperture, which is an M s×Ns -dimensional real matrix, namely represents correlation calculation, |·| represents a modulus value,/> represents the complex conjugate of the doppler signal rd short(l;Tci) of the target under the short synthetic aperture of the ith sub-aperture;
(6) Searching the peak position of I short(m,n;Tci) according to the positioning result of the first target point, and correspondingly obtaining the coarse positioning azimuth angle theta smi(msi) and the azimuth distance R sni(nsi of the first target point through the azimuth index m si and the azimuth distance index n si of the grid point of the position;
(7) From the resulting azimuth angle θ smi(msi) and azimuth distance R sni(nsi), a frequency f d corresponding to the target at the first target point and a frequency modulation K a are calculated as follows:
Wherein v represents the platform running speed, and lambda represents the signal carrier wavelength;
(8) According to the frequency corresponding to the obtained target, performing down-conversion processing on the discretized signal sequence rd obtained by sampling by the signal sampling model to obtain a sampled received signal rd 1 after the down-conversion processing, wherein the following steps are performed:
rd1＝rd·exp(-j2πfdt)；
(9) And according to the frequency modulation corresponding to the obtained target, performing low-pass filtering processing on the sampling received signal rd 1 after the down-conversion processing to obtain a sampling received signal rd 2 after the filtering processing, wherein the following steps are performed:
rd2＝ifft(|fft(filter,length(rd1))|·fft(rd1))
wherein, fft (·) is fourier transform, ifft (·) is inverse fourier transform, |·| represents modulus, length (·) represents signal length, filter represents filter time domain expression, as follows:
filter＝cfirpm(No,[-1 -F2 -F1 F1 F2 1]，@lowpass)；
Wherein cfirpm represents the order for function ;F1＝2|Ka|Tlong/fs,F2＝3|Ka|Tlong/fs;No used to generate the filter time domain expression for the corresponding band range, @ lowpass represents the low pass filter call function;
(10) And according to the frequency corresponding to the obtained target, performing up-conversion processing on the filtered sampling received signal rd 2 to obtain an up-converted sampling signal rd 3, wherein the up-converted sampling signal rd 3 is as follows:
rd3＝rd2·exp(j2πfdt)；
(11) Taking T ci as a center, taking T long as a interception length, taking down as a downsampling multiple of a positive integer, intercepting and sampling the up-converted sampling signal rd 3 to obtain a target Doppler signal rd long(l;Tci under a long synthetic aperture, and determining the following steps:
rdlong(l;Tci,down)＝rd3(l·down),l＝Nl1,Nl1+1,…,Nl2
where rd long(l;Tci, down) represents a target Doppler signal obtained by downsampling the long synthetic aperture of the ith sub-aperture by 1× (N l2-Nl1 +1) dimensional complex matrix, i.e., Nl1＝round(Tli1fs/down) represents a start sampling point of downsampling signal of the ith sub-aperture truncated by the long synthetic aperture, N l2＝round(Tli2fs/down) represents a stop sampling point of downsampling signal of the ith sub-aperture truncated by the long synthetic aperture, round (·) represents a nearest integer,/> represents a time start point of downsampling signal of the truncated down times,/> represents a time end point of downsampling signal of the truncated down times, and the interception time range of Doppler signal of the target under the ith sub-aperture is the long synthetic aperture ：tli(l;Tci,Tlong,down)＝t(l·Ts·down),l＝Nl1,Nl1+1,…,Nl2;
(12) Azimuth angle theta smi(msi) and azimuth distance R sni(nsi) of the first target point obtained by the rough search are used as search centers of the fine search, and fine meshing subdivision based on azimuth angles and azimuth distances is performed on a search area near the center, wherein the fine meshing subdivision is as follows:
azimuth angle subdivision is:
Wherein θ lmi (M) represents azimuth grid points obtained by fine meshing subdivision under the ith sub-aperture, which is an M l ×1-dimensional real matrix, i.e., θli is an azimuth subdivision range; m l is the grid cell number over the total azimuth, and θ li＝Mldθli,dθli is the azimuth split interval;
The azimuthal distance is split as follows:
Wherein R lni (N) represents an azimuthal distance grid point obtained by fine meshing subdivision under the ith sub-aperture, which is an N l ×1-dimensional real matrix, i.e., Rli is an azimuthal distance subdivision range; n l is the grid cell number of the total azimuth distance, and R li＝NldRli,dRli is the azimuth distance subdivision interval;
(13) Taking grid points with an azimuth angle of theta lmi and an azimuth distance of R lni as target points, namely second target points, and combining the platform track to obtain Doppler signals R long, which take the effect of de-modulation into account, of the second target points in long synthesis duration, namely de-modulated Doppler signals R long(l;m,n,Tci and down in the long synthesis duration), wherein the following steps are performed:
wherein R (l; m, n, T ci,Tlong, down) represents the instantaneous distance between the target with the sampling interval of Down.T s, the azimuth angle being θ lmi (m), the azimuthal distance being R lni (n), and the satellite trajectory, under the long synthetic aperture of the ith sub-aperture, and:
Wherein, t li(l;Tci,Tlong, down) represents the Doppler received signal interception time range of the ith sub-aperture under the long synthetic aperture;
(14) And performing correlation processing on the target Doppler signals rd long(l;Tci and down) under the long synthetic aperture and the de-modulated Doppler signals r long(l;m,n,Tci and down) under the long synthetic duration within the range of the long synthetic aperture to obtain a positioning result of the second target point, wherein the positioning result is as follows:
Wherein represents the second target point positioning result under the i-th sub-aperture under the long synthetic aperture, which is a M l×Nl -dimensional real matrix,/> represents the correlation calculation, |·| represents the modulus value, represents the complex conjugate of the target doppler signal rd long(l;Tci, down) under the i-th sub-aperture under the long synthetic aperture;
(15) Searching for the peak position of I long(m,n;Tci, down) according to the positioning result of the second target point, and obtaining the azimuth angle phi i, i=1, 2, …, the estimated value phi i of the target under the ith sub-aperture by the azimuth index m li of the grid point of the position, as follows:
φi＝θlmi(mli)。
6. the method of claim 1, wherein the step 103 comprises:
Based on the obtained azimuth angle estimated values of the targets under the plurality of sub-apertures with different central aperture positions, according to the geometrical relationship between different distances and azimuth angles, a system of equations R for solving the position of the radiation source target with the distance R, the azimuth distance A z and the distance R 1、R2、…、Ri、…、RI in the azimuth direction is established, wherein the system of equations R is as follows:
Wherein the sub-aperture center distance L i＝v·Lci,Ri is the distance between the sub-aperture center and the target, i.e. the distance in the azimuth direction, i=1, 2, …, I, Φ i, i=1, 2, …, I represents the target azimuth;
Solving the equation set through a least square method to obtain the distance R and the azimuth distance A s of the target.
7. The method of claim 6, wherein the target is solved for a range distance R and a bearing distance a z as follows:
Az＝x(1)，R＝x(2)，
x (1), x (2) represent the first row element and the second row element of the solution matrix x of the following system of equations:
x= (a *A)\(A* b), wherein:
a * represents the conjugate transpose of matrix a.
Priority Applications (1)
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