CN110275165B - Equivalent phase center and accumulation time optimization method for formation GEO SAR - Google Patents

Equivalent phase center and accumulation time optimization method for formation GEO SAR Download PDF

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CN110275165B
CN110275165B CN201910377044.9A CN201910377044A CN110275165B CN 110275165 B CN110275165 B CN 110275165B CN 201910377044 A CN201910377044 A CN 201910377044A CN 110275165 B CN110275165 B CN 110275165B
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胡程
董锡超
陈志扬
龙腾
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
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Abstract

The invention discloses an equivalent phase center and accumulation time optimization method of formation GEO SAR, which adopts the criterion of optimizing the distance between non-zero phase centers, thereby being capable of obtaining the uniform optimization result of the phase center of the formation GEO SAR and realizing the satellite orbit root design by combining with the resolution requirement. The invention can obtain the best quality imaging result with the lowest grating lobe because the ground grating lobe position is accurately calculated and the best accumulation time for inhibiting the grating lobe is designed.

Description

Equivalent phase center and accumulation time optimization method for formation GEO SAR
Technical Field
The invention belongs to the technical field of synthetic aperture radars, and particularly relates to an equivalent phase center and accumulation time optimization method for a formation GEO SAR.
Background
A Synthetic Aperture Radar (SAR) is an all-weather all-time high-resolution microwave remote sensing imaging radar and can be installed on flight platforms such as airplanes, satellites and missiles. Since the invention in the 50 s of the last century, the method has been widely applied to various fields, such as disaster control, vegetation analysis, microwave remote sensing and the like. Geosynchronous orbit synthetic aperture radar (GEO SAR) is a SAR satellite operating in a 36000km high geosynchronous orbit. Compared with a low-orbit SAR (LEO SAR, the orbit height is lower than 1000km), the GEO SAR has the characteristics of large imaging range, short revisit time and the like, and is a research hotspot at home and abroad at present.
Formation of a GEO SAR using multiple satellites transmitting and receiving signals simultaneously forms multiple phase centers, which reduces the accumulation time and transmit power relative to a single-satellite GEO SAR. However, the formation GEO SAR system parameters are many, the degree of freedom of the satellite orbit element design is large, and the relationship between the system performance and the system parameters is complex, especially the resolution. Therefore, it is very difficult to design an effective number of satellite orbits according to the required resolution. The existing literature is mostly based on a numerical simulation method for calculating the resolution of the formation SAR, and the number of satellite orbits cannot be designed according to the required resolution; a few analytical design methods only consider front side view and are not applicable to GEO SAR. In addition, in the actual work of the satellite, the orbit is difficult to maintain in an ideal state, and the occurrence of an orbit crossing baseline is difficult to avoid, so that an imaging result has obvious grating lobes. Therefore, for a satellite configuration with a cross-track baseline condition, a reasonable integration time needs to be designed to suppress grating lobes. This is not mentioned in the research literature of existing formation SAR.
Disclosure of Invention
In view of this, the present invention provides an equivalent phase center and accumulation time optimization method for a formation GEO SAR, which can design the number of orbits of each satellite according to the resolution requirement, and design an ideal accumulation time by combining the distance in the actual motion of the satellite to suppress the grating lobe, thereby obtaining the optimal imaging quality.
An equivalent phase center optimization method for a formation GEO SAR comprises the following steps:
step 1, determining the relative position of the satellites of the formation GEO SAR by using a numerical optimization method based on the maximized phase center uniformity, and specifically comprising the following steps:
step 11, assuming that there are N satellites in total, the position of the nth satellite is thetanN is 1,2, …, N, and the positions of the head and tail satellites in the formation are respectively 0 and 1, namely theta1＝0，θ N1 is ═ 1; then [0,1 ] is mixed]The interval value domain is uniformly discretized, and the interval division number is set to be K, namely, the interval value domain is in [0,1 ]]Taking K numbers at equal intervals; k is at least 100;
step 12, from [0,1 ] except for 0 and 1]The number of K middle pairs theta of interval value domain division2～θN-1Arbitrarily take values in the order of numbering, i.e. 0 ═ θ1<…<θn′<…<θNConstitute a satellite position sequence { theta ═ 1n}; wherein n ═2,3,...,N-1；
Step 13, calculating the phase center position between every two satellites and arranging the phase center positions in ascending order to obtain { phi [ ]k＝(θm+θn)/2}ASCWherein the subscript ASC indicates an ascending order; m is 1,2, …, N; then, phase center distance between every two satellites is calculated according to the phase center position of each satellite; eliminating zero values in the phase center spacing, and taking the difference between the maximum spacing and the minimum spacing calculated in the rest spacing as a cost function;
step 14, according to the method of step 12, continuously making theta2～θN-1Taking values until all the satellite position sequences are traversed; after each value taking, executing the step 13 to obtain a cost function; taking the satellite position sequence with the minimum cost function as a final satellite position optimization result;
step 2, calculating the total length of the phase center array, and determining the distance between each satellite and the reference satellite by combining the relative position of the reference satellite obtained in the step 1, wherein the specific steps are as follows:
step 21, determining the central time of the aperture of the reference satellite, and calculating the slant range vector of the reference satellite at the central time of the aperture
Figure GDA0002833246860000021
And the reference satellite velocity under the geocentric geostationary coordinate system
Figure GDA0002833246860000022
Step 22, obtaining the satellite velocity ground component and the ground distance direction, specifically:
first calculating the unit vector of the slope distance
Figure GDA0002833246860000023
Wherein
Figure GDA0002833246860000024
Obtaining a normal vector of a scene plane according to a scene center position
Figure GDA0002833246860000025
Then respectively calculate
Figure GDA0002833246860000026
Projection matrix being a normal vector
Figure GDA0002833246860000027
Wherein I is an identity matrix; finally, calculating the direction of the ground distance
Figure GDA0002833246860000028
And the component of velocity
Figure GDA0002833246860000029
Step 23, solving an included angle between the ground distance direction and the velocity ground component to obtain a two-dimensional resolution included angle, and obtaining the total length of the phase center array by combining resolution requirements, specifically:
the included angle of the ground distance direction and the speed ground component is
Figure GDA00028332468600000210
Wherein
Figure GDA00028332468600000211
The angle is also the included angle of the ground two-dimensional resolution; assuming that the resolution design requirement is rho, the total length of the array is calculated according to the following formula:
Figure GDA00028332468600000212
wherein M represents the number of phase centers, and lambda is the signal wavelength;
and step 24, combining the relative positions of the satellites obtained in the step 1, and calculating the distance between the kth satellite and the reference satellite in the following way:
Figure GDA0002833246860000031
and 25, calculating to obtain the equivalent phase center according to the distance between the satellite and the reference satellite.
Preferably, in the step 14, if there are multiple sets of cost functions that are the same as the minimum, the set with the largest number of spacings is taken as the final satellite position optimization result.
An accumulation time optimization method for formation GEO SAR comprises the following steps:
step 1, determining the relative satellite position of a formation GEO SAR by using a numerical optimization method based on the maximized phase center uniformity specifically comprises the following steps:
step 11, assuming that there are N satellites in total, the position of the nth satellite is thetanN is 1,2, …, N, and the positions of the head and tail satellites in the formation are respectively 0 and 1, namely theta1＝0，θ N1 is ═ 1; then [0,1 ] is mixed]The interval value domain is uniformly discretized, and the interval division number is set to be K, namely, the interval value domain is in [0,1 ]]Taking K numbers at equal intervals; k is at least 100;
step 12, from [0,1 ] except for 0 and 1]The number of K middle pairs theta of interval value domain division2～θN-1Arbitrarily take values in the order of numbering, i.e. 0 ═ θ1<…<θn′<…<θNConstitute a satellite position sequence { theta ═ 1n}; wherein N' is 2, 3.., N-1;
step 13, calculating the phase center position between every two satellites and arranging the phase center positions in ascending order to obtain { phi [ ]k＝(θm+θn)/2}ASCWherein the subscript ASC indicates an ascending order; m is 1,2, …, N; then, phase center distance between every two satellites is calculated according to the phase center position of each satellite; eliminating zero values in the phase center spacing, and taking the difference between the maximum spacing and the minimum spacing calculated in the rest spacing as a cost function;
step 14, according to the method of step 12, continuously making theta2～θN-1Taking values until all the satellite position sequences are traversed; after each value taking, executing the step 13 to obtain a cost function; taking the satellite position sequence with the minimum cost function as a final satellite position optimization result;
step 2, calculating the total length of the phase center array, and determining the distance between each satellite and the reference satellite by combining the relative position of the reference satellite obtained in the step 1, wherein the specific steps are as follows:
step 21, determining the central time of the aperture of the reference satellite, and calculating the slant range vector of the reference satellite at the central time of the aperture
Figure GDA0002833246860000032
And the reference satellite velocity under the geocentric geostationary coordinate system
Figure GDA0002833246860000033
Step 22, obtaining the satellite velocity ground component and the ground distance direction, specifically:
first calculating the unit vector of the slope distance
Figure GDA0002833246860000041
Wherein
Figure GDA0002833246860000042
Obtaining a normal vector of a scene plane according to a scene center position
Figure GDA0002833246860000043
Then respectively calculate
Figure GDA0002833246860000044
Projection matrix being a normal vector
Figure GDA0002833246860000045
Wherein I is an identity matrix; finally, calculating the direction of the ground distance
Figure GDA0002833246860000046
And the component of velocity
Figure GDA0002833246860000047
Step 23, solving an included angle between the ground distance direction and the velocity ground component to obtain a two-dimensional resolution included angle, and obtaining the total length of the phase center array by combining resolution requirements, specifically:
the included angle of the ground distance direction and the speed ground component is
Figure GDA0002833246860000048
Wherein
Figure GDA0002833246860000049
The angle is also the included angle of the ground two-dimensional resolution; assuming that the resolution design requirement is rho, the total length of the array is calculated according to the following formula:
Figure GDA00028332468600000410
wherein M represents the number of phase centers, and lambda is the signal wavelength;
and step 24, combining the relative positions of the satellites obtained in the step 1, and calculating the distance between the nth satellite and the reference satellite in the following way:
Figure GDA00028332468600000411
step 3, based on the principle that the satellite trajectories under the geocentric geostationary coordinate system are consistent, calculating the relative orbital element of the satellite according to the satellite distance obtained in the step 2, specifically:
step 31, firstly, calculating the time difference of the passing place of the nth satellite relative to the reference satellite as Δ tn＝ΔdnV, wherein
Figure GDA00028332468600000412
Then, the difference between the mean and the near point angles of the nth satellite relative to the reference satellite is calculated to be delta Mn＝ωsΔtnWherein ω issIs the angular velocity of the satellite; finally, calculating the difference delta omega between the ascension points of the nth satellite relative to the reference satelliten＝-ωEΔtnWherein ω isEAngular velocity of the earth's rotation;
step 32, obtaining the difference Δ u between the true anomaly from the difference between the mean anomaly and the true anomaly according to the relationship between the mean anomaly and the true anomaly of the satelliten：
Figure GDA00028332468600000413
Wherein e is the eccentricity of the satellite, urefIs the current true near point angle of the reference satellite; the true anomaly angle of the nth satellite is un＝Δun+uref；
Step 4, based on the grating lobe minimization criterion, calculating the optimal accumulation time according to the actual position of the satellite, specifically:
step 41, measuring the total length of the array according to the satellite positioning, and assuming the measured total length of the array as a vector in consideration of the size and the direction
Figure GDA0002833246860000051
Computing an array pitch vector of
Figure GDA0002833246860000052
The ground component of the array pitch vector is calculated in the following way:
Figure GDA0002833246860000053
step 42, first calculate the direction of the ground component of the array pitch vector
Figure GDA0002833246860000054
Then obtaining the included angle between the ground component of the array spacing vector and the ground spacing direction
Figure GDA0002833246860000055
The final optimal accumulation time calculation formula is:
Figure GDA0002833246860000056
preferably, in the step 14, if there are multiple sets of cost functions that are the same as the minimum, the set with the largest number of spacings is taken as the final satellite position optimization result.
The invention has the following beneficial effects:
the invention adopts the criterion of optimizing the distance between the nonzero phase centers, thereby being capable of obtaining the uniform optimization result of the formation GEO SAR phase centers and realizing the design of the satellite orbit root by combining the requirement of resolution ratio. The invention can obtain the best quality imaging result with the lowest grating lobe because the ground grating lobe position is accurately calculated and the best accumulation time for inhibiting the grating lobe is designed.
Drawings
FIG. 1 is a schematic diagram of the geometry of satellites in a formation GEO SAR;
FIG. 2 is a schematic diagram of phase center array grating lobes in the equivalent phase center and accumulation time optimization method of the formation GEO SAR of the present invention;
FIG. 3 is a schematic diagram of a final grating lobe in the equivalent phase center and accumulation time optimization method of the formation GEO SAR of the present invention;
FIG. 4 is a schematic diagram of the satellite relative position optimization result of the equivalent phase center and accumulation time optimization method of the formation GEO SAR of the present invention;
FIG. 5 is a schematic diagram of the phase center position optimization result of the equivalent phase center and accumulation time optimization method of the formation GEO SAR of the present invention;
FIG. 6 is a schematic diagram of a phase center distance normalization position optimization result of the equivalent phase center and accumulation time optimization method of the formation GEO SAR of the present invention;
FIG. 7 is a schematic diagram of a point target imaging result obtained by the number of orbits and accumulation time obtained by the equivalent phase center and accumulation time optimization method of the formation GEO SAR of the present invention;
fig. 8(a), 8(b) and 8(c) are schematic azimuthal cross-sectional views of the point target imaging result of the equivalent phase center and accumulation time optimization method of the formation GEO SAR of the present invention at the accumulation times of 182s, 185s and 188s, respectively.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention discloses an equivalent phase center optimization method of a formation GEO SAR, which comprises the following steps:
step 1, determining the relative position of the satellites of the formation GEO SAR by using a numerical optimization method based on the maximized phase center uniformity, and specifically comprising the following steps:
step 11, assuming that there are N satellites in total, the position of the nth satellite is thetanN is 1,2, …, N, and the positions of the head and tail satellites in the formation are normalized, namely, the values are 0 and 1 respectively, namely theta1＝0，θ N1 is ═ 1; then [0,1 ] is mixed]The interval value domain is uniformly discretized, and the interval division number is set to be K, namely, the interval value domain is in [0,1 ]]Taking K numbers at equal intervals; to ensure the precision, K is at least 100;
step 12, from [0,1 ] discretized uniformly except for 0 and 1]Interval value range pair theta2～θN-1Arbitrarily take values in the order of numbering, i.e. 0 ═ θ1<…<θn<…<θNConstitute a satellite position sequence { theta ═ 1n}；
Step 13, calculating the position of the phase center and arranging the phase center in ascending order to obtain { phik＝(θm+θn)/2}ASCWherein the subscript ASC indicates an ascending order; m is 1,2, …, N; then, calculating the phase center distance according to the phase center position of each satellite; eliminating zero values in the phase center spacing, and calculating the difference between the maximum spacing and the minimum spacing in the rest spacings as a cost function; wherein the set of non-zero phase center spacings is { Δ φ'k}＝{φk-φk-1|φk>φk-1Is expressed as g-max [. DELTA.. phi.'k}-min{Δφ′k}；
Step 14, according to step 12, continuously theta2～θN-1Taking values until all the satellite position sequences are traversed; after each value taking, step 13 is executed to replace the satellite position sequence with the minimum cost function as a final optimization result; and if the cost functions of the multiple groups are the minimum, taking the group with the maximum number of non-zero normalized intervals. Assuming that the number of reserved phase centers is M, the position of the reference satellite is also the position of the middle phase center, and is recorded as
Figure GDA0002833246860000061
The final phase center is uniform since zero spacing is eliminated.
The above optimization process can be expressed as:
Figure GDA0002833246860000062
step 2, calculating the total length of the phase center array by using a resolution formula according to the resolution requirement, and determining the distance between each satellite and a reference satellite (namely a central satellite) by combining the relative positions of the satellites obtained in the step 1, wherein the method specifically comprises the following steps:
step 21, determining a reference satellite aperture center time, and calculating a satellite slant range vector of the aperture center time and a satellite velocity under a geocentric geostationary coordinate system (abbreviated as "geostationary system"), specifically:
determining the position of the central point of the scene according to the beam direction and the downward view angle of the reference satellite by taking the middle satellite as the reference satellite and the reference satellite over the equator as the aperture central time, and calculating the slope vector according to the position of the scene and the satellite position
Figure GDA0002833246860000071
Then calculating the speed of the satellite under the earth fixation system according to the orbital element number of the satellite
Figure GDA0002833246860000072
The calculation method is shown in the reference: "Piakai, satellite navigation principle and system" of Sichuan electronic technology university Press, 2011 ".
Step 22, projecting the slant range vector and the satellite earth center earth fixation system speed respectively to obtain a satellite speed earth component and an earth range direction:
as shown in FIG. 1, the unit vector of the slope distance is calculated first
Figure GDA0002833246860000073
Wherein
Figure GDA0002833246860000074
Obtaining a normal vector of a scene plane according to a scene center position
Figure GDA0002833246860000075
Then respectively calculate
Figure GDA0002833246860000076
Projection matrix being a normal vector
Figure GDA0002833246860000077
Where I is the identity matrix. Finally, calculating the direction of the ground distance
Figure GDA0002833246860000078
And the component of velocity
Figure GDA0002833246860000079
Step 23, solving an included angle between the ground distance direction and the velocity ground component to obtain a two-dimensional resolution included angle, and obtaining the total length of the phase center array by combining resolution requirements:
the included angle between the ground distance direction and the speed ground component can be calculated as
Figure GDA00028332468600000710
Wherein
Figure GDA00028332468600000711
The angle is also the included angle of the ground two-dimensional resolution; assuming that the resolution design requirement is rho, the total length of the array is calculated according to the following formula
Figure GDA00028332468600000712
Where λ is the signal wavelength. The derivation process of equation (2) is: considering that the motion of the satellite also contributes a certain synthetic aperture, the resolution is determined by the total length of the array and the motion of the satellite. The moving distance of the satellite is the phase center distance, so the full aperture LsEqual to head-to-tail satellite interval dsPlus the phase center spacing dsL (M-1), i.e. Ls＝ds+ds/(M-1)＝Mds/(M-1). In addition, the resolution is expressed by
Figure GDA00028332468600000713
From this, equation (2) can be obtained.
Step 24, since the satellite positions are normalized, combining the relative satellite positions obtained in step 1, the distance between the nth satellite and the reference satellite is calculated as follows:
Figure GDA00028332468600000714
and 25, calculating to obtain an equivalent phase center according to the distance between the satellite and the reference satellite.
On the basis of the equivalent phase center optimization method of the formation GEO SAR, the invention also provides an accumulation time optimization method of the formation GEO SAR, which specifically comprises the following steps:
step 3, based on the principle that the satellite trajectories under the geocentric geostationary coordinate system are consistent, calculating the relative orbital element of the satellite according to the satellite distance obtained in the step 2, specifically:
step 31, calculating the time difference between the passing near point of each satellite and the reference satellite according to the earth-fixed system velocity and the distance of the satellite, further obtaining the difference between the mean angle of the near points and the difference between the ascent point and the ascent point of each satellite, and finally obtaining the ascent point and the ascent point of each satellite. Firstly, the time difference of the passing near place of the nth satellite relative to the reference satellite is calculated to be delta tn＝ΔdnV, wherein
Figure GDA0002833246860000081
Then, the difference between the mean and the near point angles of the nth satellite relative to the reference satellite is calculated to be delta Mn＝ωsΔtnWherein ω issIs the angular velocity of the satellite. Finally, calculating the difference delta omega between the ascension points of the nth satellite relative to the reference satelliten＝-ωEΔtnWherein ω isEIs the angular velocity of the earth's rotation.
The difference between the mean anomaly and the rising point declination is derived as follows: the main application of formation GEO SAR is federationImaging and thus the formation ideally should have no cross-track baselines. To achieve this, it is necessary to coincide the earth fixation loci of the respective satellites. Firstly, the other satellites have the same semimajor axis, eccentricity, inclination and argument of the perigee as the reference satellite, so as to ensure that the tracks of the satellites under the geocentric geostationary coordinate system have the same shape. The remaining two orbital elements, the ascension at the ascending crossing point, are different from the true periapical angle. In order to make the geocentric-geostationary coordinate system trajectories of the satellites coincide, the longitude of the elevation point of each satellite needs to be equal. The distance between the nth satellite and the reference satellite is delta dnSo that the difference between the time of the passing-by points is Δ tn＝Δdn/v，ΔtnAnd is also the difference in the time to cross the crossover point. So that the difference between the mean and the approximate point angle is Δ Mn＝ωsΔtn. Within the difference of the time of crossing the ascent intersection, the earth rotates. In order to make the elevation point longitude of the satellite the same, the difference between the elevation point right ascension of the satellite needs to compensate the angle of the earth rotation within the difference between the satellite crossing the elevation point time. So that the difference between the ascension points and the right ascension paths is Δ Ωn＝-ωEΔtn. Therefore, the right ascension of the satellite n is omegan＝ΔΩn+Ωref。
And step 32, obtaining the difference of the true near point angles according to the relation between the satellite mean near point angles and the true near point angles and finally obtaining the true near point angles of the satellites. Is calculated by the formula
Figure GDA0002833246860000082
Wherein e is the eccentricity of the satellite, urefReference is made to the current true anomaly of the satellite. The true anomaly of satellite n is therefore un＝Δun+uref。
The derivation process of equation (4) is as follows: according to the reference: "Piezing, satellite navigation principle and system" from Sichuan electronic science and technology university Press, 2011 ", the relationship between the satellite near point angle E and the mean near point angle M is E ═ M + sinE, and the relationship between the true near point angle u and the mean near point angle is
Figure GDA0002833246860000091
Considering the formation SAR of the common imaging, the satellite spacing is small, so that the mean, partial and true paraxial point angles of the satellites can be considered to be uniformly distributed. To obtain the relationship between the difference between the mean-near-point angle and the difference between the true-near-point angle, we derive the derivative of the mean-near-point angle with respect to the true-near-point angle, yielding:
Figure GDA0002833246860000092
further based on the relationship between the true and the off-near point angles, 1-ecosE ═ 1-e can be obtained2) /(1+ ecosu), therefore
Figure GDA0002833246860000093
The formula (4) can be obtained from the above formula.
Step 4, based on the grating lobe minimization criterion, calculating the optimal accumulation time according to the actual position of the satellite, specifically:
step 41, measuring the total length and direction of the array in actual operation of the satellite, thereby calculating the array distance of the phase center, projecting the array distance to the ground, and obtaining the ground component of the array distance:
measuring the total length of the array according to satellite positioning, and considering the size and the direction, assuming that the measured total length of the array is a vector
Figure GDA0002833246860000094
Computing an array pitch vector of
Figure GDA0002833246860000095
The array ground component is calculated in the manner of
Figure GDA0002833246860000096
Step 42, calculating the included angle between the array spacing vector ground component and the ground spacing direction, and finally calculating the maximum of the suppressed grating lobeGood accumulation time. The direction of the ground component of the array pitch vector is calculated first
Figure GDA0002833246860000097
Then obtaining the included angle between the ground component of the array spacing vector and the ground spacing direction
Figure GDA0002833246860000098
The final optimal accumulation time calculation formula is:
Figure GDA0002833246860000099
the optimal accumulation time is derived as follows.
As shown in fig. 2, the grating lobes caused by the array are strip-shaped. Since the SAR signal propagation path is a double-pass skew, the array width is
Figure GDA00028332468600000910
The resulting array gives rise to grating lobes of width
Figure GDA00028332468600000911
In the direction of
Figure GDA00028332468600000912
In addition, the output result of the matched filtering of the emission bandwidth is a strip-shaped sinc (·) function on the ground, and the final grating lobe is obtained after the multiplication of the output result and the array-caused grating lobe
Figure GDA00028332468600000913
As shown in figure 3 of the drawings,
Figure GDA00028332468600000914
and
Figure GDA00028332468600000915
the vertical direction is perpendicular to the horizontal direction,
Figure GDA00028332468600000916
and
Figure GDA00028332468600000917
and is vertical.
Figure GDA00028332468600000918
And
Figure GDA00028332468600000919
are respectively a right-angle side and a hypotenuse side of a right-angled triangle which is formed by stretching
Figure GDA0002833246860000101
The final calculation formula of the position vector of the first grating lobe is thus
Figure GDA0002833246860000102
The projection of the satellite motion distance on the ground is
Figure GDA0002833246860000103
In the direction of
Figure GDA0002833246860000104
The aperture formed by the satellite motion forms a sinc (·) function on the ground, and the first zero depth position in the direction of the grating lobe is
Figure GDA0002833246860000105
Order to
Figure GDA0002833246860000106
The optimal accumulation time T can be obtainedsThe calculation formula of (c) is shown in formula (8).
Example (b):
the present invention is discussed in detail below in conjunction with fig. 1-8. In the invention, the requirement of resolution, the orbital element number of the reference satellite and the aperture center position of the reference satellite are input by a user.
In this example, the relevant parameters are shown in table 1, where satellite 2 is the reference satellite.
TABLE 1
Figure GDA0002833246860000107
Figure GDA0002833246860000111
The equivalent phase center and accumulation time optimization method of the formation GEO SAR specifically comprises the following steps:
step 1, determining the relative position of a satellite by using a numerical optimization method based on the maximized phase center uniformity.
Step 11, normalizing the head and tail satellite positions, namely, respectively taking the values as 0 and 1, and then taking the value of [0,1]The interval is evenly discretized. End-to-end satellite position normalization, theta1＝0、θ 31. Discretizing according to the interval division number K of 200 to obtain 1/200,2/200, … and 199/200.
And step 12, taking different values from the discretization value domain by the rest satellites in an orderly manner as the positions of all the satellites, and taking the mean value of every two satellite positions to obtain the phase center position and ordering the phase center position. Since there are only 3 satellites, only the position of the 2 nd satellite needs to be optimized. Assume the current theta 21/200, the phase center position is obtained as (θ)1+θ1)/2、(θ1+θ2)/2、(θ1+θ3)/2、(θ2+θ2)/2、(θ2+θ3)/2、(θ3+θ3) 2, i.e. 0, 1/400, 200/400, 2/400, 201/400, 1. The phase centers are sorted in ascending order to give 0, 1/400, 2/400, 200/400, 201/400, 1.
And step 13, calculating the phase center distance, reserving a non-zero value and calculating the difference between the maximum distance and the minimum distance as a cost function. Subtracting adjacent phase centers results in phase center spacings of 1/400, 1/400, 198/400, 1/400 and 199/400, so that the difference between the maximum spacing and the minimum spacing is 199/400-1/400-198/400, which is the value of the cost function in the present sequence of satellite positions { θ }nThe specific value at the time of taking the value.
And step 14, traversing all the satellite position sequences, and circularly operating the step 12 and the step 13 to replace the satellite position sequence with the minimum cost function as a final optimization result, wherein if a plurality of groups of cost functions are the minimum, one group with the maximum number of non-zero normalized intervals is selected. Traverse of theta2After taking value, we are at theta2The minimum cost function is obtained at 100/200, so the final satellite position sequence is {0,1/2,1}, the reference satellite is 1/2, and the obtained phase center number M is 5.
Fig. 4 shows the normalized positions of the optimized satellites, which are uniformly arranged. Fig. 5 shows the ascending order of the normalized positions of the phase centers, and it can be seen that there is one phase center that is repeated and the remaining phase centers are on a straight line. Fig. 6 shows the normalized spacing of the phase centers, and it can be seen that the spacing of the remaining phase centers is identical except for the repeated phase centers.
And 2, calculating the total length of the phase center array by using a resolution formula according to the resolution requirement, and determining the distance between each satellite and a reference satellite (namely a central satellite) by combining the relative positions of the satellites obtained in the step 1.
And step 21, calculating the slant range vector of the reference satellite aperture center moment and the speed under the earth fixation system. Obtaining the scene center coordinate of
Figure GDA0002833246860000121
The satellite position is
Figure GDA0002833246860000122
Thus the vector of the skew
Figure GDA0002833246860000123
Obtaining the speed under the earth's fixation
Figure GDA0002833246860000124
And step 22, projecting the unit slant range vector and the earth-centered earth-fixed system speed of the satellite respectively to obtain earth range direction and speed earth components.Length of skew
Figure GDA0002833246860000125
Unit slope distance vector
Figure GDA0002833246860000126
Scene normal vector
Figure GDA0002833246860000127
To be provided with
Figure GDA0002833246860000128
Projection matrix being a normal vector
Figure GDA0002833246860000129
Figure GDA00028332468600001210
Are respectively as
Figure GDA00028332468600001211
Finally, calculating the direction of the ground distance
Figure GDA00028332468600001212
Component of velocity
Figure GDA00028332468600001213
And step 23, solving an included angle between the ground distance direction and the speed ground component to obtain a two-dimensional resolution included angle, and obtaining the total length of the phase center array by combining resolution requirements. Calculating the direction of the component of the velocity as
Figure GDA00028332468600001214
Thereby obtaining the included angle of resolution
Figure GDA00028332468600001215
Thereby obtaining the total length d of the array according to the formula (2)s＝622.6km。
Step 24, combining the satellite obtained in the step 1The relative position determines the range of each satellite relative to a reference satellite. Because the 2 nd satellite is the reference satellite, we need to calculate the distances between the 1 st and 3 rd satellites relative to the reference satellite.
Figure GDA00028332468600001216
And 3, calculating the relative orbit number of the satellite according to the satellite space obtained in the step 2 on the basis of the principle that the satellite tracks under the geocentric geostationary coordinate system are consistent.
Step 31, calculating the time difference between the passing near point of each satellite and the reference satellite according to the earth-fixed system velocity and the distance of the satellite, and further obtaining the difference between the mean-near point angle and the rising-crossing declination. In GEO SAR ωs＝ω E2 pi/86400 rad/s. Magnitude of earth-fixing system velocity
Figure GDA0002833246860000131
The difference between the 1 st satellite and the reference satellite in the past-close-in time is Δ t1＝Δd1V-364 s, the difference between the mean and the anomaly Δ M1＝ωsΔt1Is-1.517 deg., and the difference between the ascension points is delta omega1＝-ωEΔt11.517 °, therefore, the right ascension at the intersection point is Ω1＝ΔΩ1+Ωref298.843. The 3 rd satellite ascent point declination is 295.809 ° by the same principle.
And step 32, obtaining the difference of the true proximal angles from the difference of the mean proximal angles according to the relation between the mean proximal angles and the true proximal angles. In this example, the eccentricity e is equal to 0, so that the difference Δ u between the true paraxial points can be obtained according to the formula (4)1＝ΔM1At-1.517 °, satellite 1 true anomaly is 358.483 °, and similarly satellite 3 true anomaly is 1.517 °.
We use the obtained satellite orbit number to perform point target BP imaging simulation, and since there are only 1 phase centers between adjacent satellites, the accumulation time is 364/2 ═ 182 s. Fig. 7 shows the BP imaging results obtained using table 2 and the theoretically obtained accumulation times. The resolution in the X direction is evaluated to be 4.4m, the result of 60MHz bandwidth is met, the resolution in the Y direction is evaluated to be 5.05m, and the design requirement of the resolution is met.
And 4, calculating the optimal accumulation time according to the actual position of the satellite based on the grating lobe minimization criterion.
And step 41, measuring the total length and the direction of the array in actual operation of the satellite, thereby calculating the array distance of the phase center, and projecting the array distance to the ground to obtain the ground component of the array distance. Here we simulated the actual situation by generating an array with a cross-rail baseline with the ascending cross-declination with a deviation in table 1. The total array length can be obtained according to the parameters in Table 1
Figure GDA0002833246860000132
Thus array pitch vector
Figure GDA0002833246860000133
Thereby obtaining the array ground component of
Figure GDA0002833246860000134
And 42, calculating an included angle between the ground component of the array spacing and the ground distance, and finally calculating the optimal accumulation time of the suppressed grating lobes. Direction of ground component of array pitch
Figure GDA0002833246860000135
Therefore, the rest of the ground distance forms an included angle
Figure GDA0002833246860000136
The optimal accumulation time is finally obtained as 184.76 ≈ 185 s.
Fig. 8(a), (b), and (c) are azimuthal cross-sectional views of accumulation times of 182s, 185s, and 188s, respectively, and it can be seen that the azimuthal cross-sectional grating lobe is the lowest when the accumulation time is 185s, explaining the effectiveness of the optimal accumulation time calculation method.
According to simulation results, the equivalent phase center and accumulation time optimization design method of the formation GEO SAR can be used for designing the number of satellite orbits, and the optimal accumulation time can be designed to inhibit grating lobes.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. An equivalent phase center optimization method for a formation GEO SAR is characterized by comprising the following steps:
step 1, determining the relative position of the satellites of the formation GEO SAR by using a numerical optimization method based on the maximized phase center uniformity, and specifically comprising the following steps:
step 11, assuming that there are N satellites in total, the position of the nth satellite is thetanN is 1,2, …, N, and the positions of the head and tail satellites in the formation are respectively 0 and 1, namely theta1＝0，θN1 is ═ 1; then [0,1 ] is mixed]The interval value domain is uniformly discretized, and the interval division number is set to be K, namely, the interval value domain is in [0,1 ]]Taking K numbers at equal intervals; k is at least 100;
step 12, from [0,1 ] except for 0 and 1]The number of K middle pairs theta of interval value domain division2～θN-1Arbitrarily take values in the order of numbering, i.e. 0 ═ θ1＜…＜θn′＜…＜θNConstitute a satellite position sequence { theta ═ 1n}; wherein N' is 2, 3.., N-1;
step 13, calculating the phase center position between every two satellites and arranging the phase center positions in ascending order to obtain { phi [ ]k＝(θm+θn)/2}ASCWherein the subscript ASC indicates an ascending order; m is 1,2, …, N; then, phase center distance between every two satellites is calculated according to the phase center position of each satellite; eliminating zero values in the phase center spacing, and taking the difference between the maximum spacing and the minimum spacing as a cost function in the rest spacing;
step 14, according to the method of step 12, continuously making theta2～θN-1Taking values until all the satellite position sequences are traversed; after each value taking, executing the step 13 to obtain a cost function; taking the satellite position sequence with the minimum cost function as a final satellite position optimization result;
step 2, calculating the total length of the phase center array, and determining the distance between each satellite and the reference satellite by combining the relative positions of the satellites obtained in the step 1, wherein the specific steps are as follows:
step 21, determining the central time of the aperture of the reference satellite by taking the intermediate satellite as the reference satellite, and calculating the slant range vector of the reference satellite at the central time of the aperture
Figure FDA0002885668090000011
And the reference satellite velocity under the geocentric geostationary coordinate system
Figure FDA0002885668090000012
Step 22, obtaining the satellite velocity ground component and the ground distance direction, specifically:
first calculating the unit vector of the slope distance
Figure FDA0002885668090000013
Wherein
Figure FDA0002885668090000014
Obtaining a normal vector of a scene plane according to a scene center position
Figure FDA0002885668090000015
Then respectively calculate
Figure FDA0002885668090000016
Projection matrix being a normal vector
Figure FDA0002885668090000017
Wherein I is an identity matrix; finally, calculating the direction of the ground distance
Figure FDA0002885668090000018
And the component of velocity
Figure FDA0002885668090000019
Step 23, solving an included angle between the ground distance direction and the velocity ground component to obtain a two-dimensional resolution included angle, and obtaining the total length of the phase center array by combining resolution requirements, specifically:
the included angle of the ground distance direction and the speed ground component is
Figure FDA00028856680900000110
Wherein
Figure FDA00028856680900000111
The angle is also the included angle of the ground two-dimensional resolution; assuming that the resolution design requirement is rho, the total length of the array is calculated according to the following formula:
Figure FDA0002885668090000021
wherein M represents the number of phase centers, and lambda is the signal wavelength;
and step 24, combining the relative positions of the satellites obtained in the step 1, and calculating the distance between the nth satellite and the reference satellite in the following way:
Figure FDA0002885668090000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002885668090000023
is a reference satellite position;
and 25, calculating to obtain the equivalent phase center according to the distance between the satellite and the reference satellite.
2. The equivalent phase center optimization method of formation GEO SAR of claim 1, wherein in said step 14, if there are multiple sets of cost functions that are the same as the minimum, the set with the largest number of spacings is taken as the final optimization result of satellite position.
3. An accumulation time optimization method for formation GEO SAR is characterized by comprising the following steps:
step 1, determining the relative position of the satellites of the formation GEO SAR by using a numerical optimization method based on the maximized phase center uniformity, and specifically comprising the following steps:
step 11, assuming that there are N satellites in total, the position of the nth satellite is thetanN is 1,2, …, N, and the positions of the head and tail satellites in the formation are respectively 0 and 1, namely theta1＝0，θN1 is ═ 1; then [0,1 ] is mixed]The interval value domain is uniformly discretized, and the interval division number is set to be K, namely, the interval value domain is in [0,1 ]]Taking K numbers at equal intervals; k is at least 100;
step 12, from [0,1 ] except for 0 and 1]The number of K middle pairs theta of interval value domain division2～θN-1Arbitrarily take values in the order of numbering, i.e. 0 ═ θ1＜…＜θn′＜…＜θNConstitute a satellite position sequence { theta ═ 1n}; wherein N' is 2, 3.., N-1;
step 13, calculating the phase center position between every two satellites and arranging the phase center positions in ascending order to obtain { phi [ ]k＝(θm+θn)/2}ASCWherein the subscript ASC indicates an ascending order; m is 1,2, …, N; then, phase center distance between every two satellites is calculated according to the phase center position of each satellite; eliminating zero values in the phase center spacing, and taking the difference between the maximum spacing and the minimum spacing as a cost function in the rest spacing;
step 14, according to the method of step 12, continuously making theta2～θN-1Taking values until all the satellite position sequences are traversed; after each value taking, executing the step 13 to obtain a cost function; taking the satellite position sequence with the minimum cost function as a final satellite position optimization result;
step 2, calculating the total length of the phase center array, and determining the distance between each satellite and the reference satellite by combining the relative positions of the satellites obtained in the step 1, wherein the method specifically comprises the following steps:
step 21, determining the central time of the aperture of the reference satellite by taking the intermediate satellite as the reference satellite, and calculating the slant range vector of the reference satellite at the central time of the aperture
Figure FDA0002885668090000031
And the reference satellite velocity under the geocentric geostationary coordinate system
Figure FDA0002885668090000032
Step 22, obtaining the satellite velocity ground component and the ground distance direction, specifically:
first calculating the unit vector of the slope distance
Figure FDA0002885668090000033
Wherein
Figure FDA0002885668090000034
Obtaining a normal vector of a scene plane according to a scene center position
Figure FDA0002885668090000035
Then respectively calculate
Figure FDA0002885668090000036
Projection matrix being a normal vector
Figure FDA0002885668090000037
Wherein I is an identity matrix; finally, calculating the direction of the ground distance
Figure FDA0002885668090000038
And the component of velocity
Figure FDA0002885668090000039
Step 23, solving an included angle between the ground distance direction and the velocity ground component to obtain a two-dimensional resolution included angle, and obtaining the total length of the phase center array by combining resolution requirements, specifically:
the included angle of the ground distance direction and the speed ground component is
Figure FDA00028856680900000310
Wherein
Figure FDA00028856680900000311
The angle is also the included angle of the ground two-dimensional resolution; assuming that the resolution design requirement is rho, the total length of the array is calculated according to the following formula:
Figure FDA00028856680900000312
wherein M represents the number of phase centers, and lambda is the signal wavelength;
and step 24, combining the relative positions of the satellites obtained in the step 1, and calculating the distance between the nth satellite and the reference satellite in the following way:
Figure FDA00028856680900000313
in the formula (I), the compound is shown in the specification,
Figure FDA00028856680900000314
is a reference satellite position;
step 3, based on the principle that the satellite trajectories under the geocentric geostationary coordinate system are consistent, calculating the relative orbital element of the satellite according to the satellite distance obtained in the step 2, specifically:
step 31, firstly, calculating the time difference of the passing place of the nth satellite relative to the reference satellite as Δ tn＝ΔdnV, wherein
Figure FDA00028856680900000315
Then, the difference between the mean and the near point angles of the nth satellite relative to the reference satellite is calculated to be delta Mn＝ωsΔtnWherein ω issIs the angular velocity of the satellite; finally, calculating the difference delta omega between the ascension points of the nth satellite relative to the reference satelliten＝-ωEΔtnWherein ω isEAngular velocity of the earth's rotation;
step 32, according to the relation between the satellite mean-near point angle and the true-near point angle, the mean-near pointThe difference between the angles is obtained as the difference between the true proximal angles Deltaun：
Figure FDA0002885668090000041
Wherein e is the eccentricity of the satellite, urefIs the current true near point angle of the reference satellite; the true anomaly angle of the nth satellite is un＝Δun+uref；
Step 4, based on the grating lobe minimization criterion, calculating the optimal accumulation time according to the actual position of the satellite, specifically:
step 41, measuring the total length of the array according to the satellite positioning, and assuming the measured total length of the array as a vector in consideration of the size and the direction
Figure FDA0002885668090000042
Computing an array pitch vector of
Figure FDA0002885668090000043
The ground component of the array pitch vector is calculated in the following way:
Figure FDA0002885668090000044
step 42, first calculate the direction of the ground component of the array pitch vector
Figure FDA0002885668090000045
Then obtaining the included angle between the ground component of the array spacing vector and the ground spacing direction
Figure FDA0002885668090000046
The final optimal accumulation time calculation formula is:
Figure FDA0002885668090000047
4. the method for optimizing accumulation time of formation GEO SAR of claim 3, wherein in said step 14, if there are multiple sets of cost functions that are the same as the minimum, the set with the largest number of spacings is taken as the final optimization result of satellite position.
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101520511A (en) * 2009-03-13 2009-09-02 北京航空航天大学 Method for formation configuration of distributed satellites with synthetic aperture radars
CN101566689A (en) * 2009-06-10 2009-10-28 电子科技大学 Method for eliminating grating lobes of three-dimensional synthetic aperture radar image
CN102508243A (en) * 2011-10-21 2012-06-20 北京理工大学 Beam position design method of inclined geosynchronous orbit synthetic aperture radar
CN103116161A (en) * 2013-01-25 2013-05-22 北京理工大学 SAR (synthetic aperture radar) forest secondary scattering effective path calculating method based on rugged topography
CN103630897A (en) * 2012-08-28 2014-03-12 中国科学院电子学研究所 Multichannel synthetic aperture radar imaging method
CN108020834A (en) * 2017-11-14 2018-05-11 石家庄铁道大学 Based on moving target detecting method, device and the electronic equipment for improving EDPCA
CN108627831A (en) * 2018-05-11 2018-10-09 西安空间无线电技术研究所 High rail Satellite Targets ISAR imaging methods in a kind of ultralow signal-to-noise ratio

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101520511A (en) * 2009-03-13 2009-09-02 北京航空航天大学 Method for formation configuration of distributed satellites with synthetic aperture radars
CN101566689A (en) * 2009-06-10 2009-10-28 电子科技大学 Method for eliminating grating lobes of three-dimensional synthetic aperture radar image
CN102508243A (en) * 2011-10-21 2012-06-20 北京理工大学 Beam position design method of inclined geosynchronous orbit synthetic aperture radar
CN103630897A (en) * 2012-08-28 2014-03-12 中国科学院电子学研究所 Multichannel synthetic aperture radar imaging method
CN103116161A (en) * 2013-01-25 2013-05-22 北京理工大学 SAR (synthetic aperture radar) forest secondary scattering effective path calculating method based on rugged topography
CN108020834A (en) * 2017-11-14 2018-05-11 石家庄铁道大学 Based on moving target detecting method, device and the electronic equipment for improving EDPCA
CN108627831A (en) * 2018-05-11 2018-10-09 西安空间无线电技术研究所 High rail Satellite Targets ISAR imaging methods in a kind of ultralow signal-to-noise ratio

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
Andrea Monti Guarnieri, et al.Advanced Radar Geosynchronous Observation System: ARGOS.《IEEE GEOSCIENCE AND REMOTE SENSING LETTERS》.2015, *
Zhao Bingji ,et al.An Integration Time optimization Approach for Geo-SAR.《IGARSS 2016》.2016, *
孙稚超.基于GEO辐射源的星机SAR成像理论与方法研究.《中国博士学位论文全文数据库 信息科技辑》.2018, *
陈志扬, 等.一种中等倾角的GEO SAR编队卫星群方案.《中国电子学会》.2017, *

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