CN103762412A - Onboard downward-looking 3D SAR sparse array antenna laying method - Google Patents

Abstract

The invention provides an onboard downward-looking 3D SAR sparse array antenna laying method. The method aims to solve the problems that according to onboard 3D SAR system antenna laying, a platform installation space is limited and a design method is complicated; according to the flight height of an aerial carrier, an observation area maximum height change range function, a radar system work wavelength and a resolution ratio in the array direction, antenna laying design is carried out. The method is simple in operation, free of complicated computation and capable of guaranteeing that a grating lobe of a target response function in the array direction of a system is controlled to be at a reasonable level.

Description

Airborne downward-looking3D SAR sparse array antenna layout method

Technical Field

The invention relates to an airborne downward-looking3D SAR sparse array antenna layout method.

Background

An airborne downward-looking array 3D SAR (Three-Dimensional Synthetic Aperture Radar, 3D SAR for short) realizes resolution by means of pulse compression in the wave propagation direction by observing a machine bottom area; the aperture synthesis is realized by means of the motion of the airborne platform in the track direction, and further the track direction resolution is realized; in the array direction, aperture synthesis is realized by arranging sparse array antennas along the wings and ventral of the aircraft, and thus, array direction resolution is realized (see non-patent documents 1 and 2).

If a large number of antenna subarrays are arranged uniformly along the wing and the belly, the aerodynamic performance of the aircraft and the like are greatly influenced on the one hand. On the other hand, uniformly arranging a large number of array elements also increases system cost and system complexity. In response to these problems, the skilled person has conducted a lot of research work on how to perform array-to-antenna sub-array layout, and for example, the following methods are disclosed in non-patent documents 3, 4, and 5. M multiplied by N equivalent phase centers are virtualized by M transmitting antenna units and N receiving antenna units, and the distance between the phase centers needs to be smaller than a half wavelength. However, the above method needs to use the antenna array element as an omnidirectional antenna as a premise, that is, all targets that can be observed by the array can be covered.

However, in actual observation, due to limitations of a system signal-to-noise ratio, a resolution, and the like, an array-to-observation range of the system is always limited to a certain observation range, not an array-to ± 90 °.

In addition, in the layout of the antenna subarrays, the actual size of the antenna array, the antenna installation space on the flight platform, and the layout relationship among the antenna subarrays are not considered, and the situation that the antennas are staggered in the track direction, especially the overlapping layout of part of the transmitting antennas and the receiving antennas is not beneficial to the system implementation, and the flexible installation of the antennas on the flight platform is not beneficial.

Furthermore, in prior art antenna layouts, the target elevation range effect has not been considered in the array element layout. Furthermore, it is also necessary to ensure that the grating lobe control of the system array to the response function is at a reasonable level.

Non-patent documents:

non-patent document 1: klare.a newwairborn rad for3D imaging-simulation study of art ino. eusar Dresden, Germany, 2006; w.m, e.j, e.a. pets o.an air airborne for the same dimensional imaging and optimization and status of artino.

Non-patent document 2: du, Y.P.Wang, W.hong, et al.A. Three-Dimensional transmission chemistry for down-pointing-viewing 3D-SAR with single-transmitting and multiple-receiving linear array antenna.

Non-patent document 3: klare, D.Cerutti-Maori, A.Brenner, J.Ender.image quality analysis of the ventilating space MIMO antenna array of the airframe 3D imaging radar ARTINO.2007.

Non-patent document 4: m.weiss, o.peters, j.end.a three-dimensional SAR system on an uav.igarss2007, Barcelona, Spain, 2008: 5315-5318.

Non-patent document 5: pengzhiming, Wanyanping, Tan Weixian, and the like, an airborne downward-looking MIMO3D-SAR three-dimensional imaging algorithm based on a cross-course sparse array, an electronic and information declaration, 2012 and 34 (4): 943-949.

The invention content is as follows:

technical problem to be solved

Aiming at the problems in the prior art, the invention provides an airborne downward-looking3D SAR sparse array antenna layout method, which solves the problems of complex design method of array-to-antenna layout, limited antenna layout space and the like in airborne downward-looking3D SAR imaging, particularly can carry out array-to-antenna layout design according to the system array directional resolution and the observation range, and can ensure that the grating lobe control of the system array to the response function is at a reasonable level.

(II) technical scheme

In order to achieve the above object, the invention provides an airborne downward-looking3D SAR sparse array antenna layout method, which comprises the following steps:

step S1, determining the azimuth dimension of the array antenna, the layout length of the array antenna and the half beam width of the array antenna unit according to the flight altitude of the aircraft, the maximum altitude variation range function of an observation area, the working wavelength of the radar system, the azimuth resolution and the array resolution which are taken as parameters of the airborne downward-looking3D SAR system;

step S2, determining the array direction size of the transmitting antenna unit, the distance between the transmitting antenna units and the array direction size of the receiving antenna unit based on the array direction antenna layout length and the array antenna unit half beam width;

step S3, calculating the number of transmitting antenna units, the number of receiving antenna units, the spacing of receiving antenna units, the distribution of the geometric center positions of transmitting antennas and the distribution of the geometric center positions of receiving antenna units according to the array-to-antenna layout length and the spacing of the transmitting antenna units;

step S4, establishing array-direction sampling point position coordinates according to the flight height of the aerial carrier and the half beam width of the array-direction antenna unit, and determining an array-direction response function f { X (k) -x) of a system airborne point target by using the array-direction sampling point position coordinates, the flight height of the aerial carrier and the working wavelength of the radar system₀Array-wise response function of extreme edge target of observation area <math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> <mo>;</mo> </mrow></math>

Step S5, under the system, the array directional response function f { X (k) -x of the point target₀Array directional response function of the most marginal target of the observation area <math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> </mrow></math> The grating lobe is positioned in the system imaging observation area +/-q_LBesides, and

then, step S6 is executed, the array directional response function f { X (k) -x of the target under the system is₀Array directional response function of the most marginal target of the observation area <math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> </mrow></math> The grating lobe of (2) falls in the system imaging observation area + -q_LIn or on

Then, the number of the receiving antenna units is increased by one, and the process returns to step S3, where H is the flying height of the carrier and L is the flying height of the carrier_eFor array-wise antenna layout the effective aperture length, l_cFor the operating wavelength of the radar system, r_LThe array directional resolution;

step S6, outputting the array antenna direction size L_AThe array directional size of the transmitting antenna units, the number of the transmitting antenna units, the distribution of the geometric center positions of the transmitting antennas, the array directional size of the transmitting antenna units, the number of the receiving antenna units and the distribution of the geometric center positions of the receiving antenna units; and

step S7, performing layout of the airborne downward-looking 3DSAR sparse array antenna according to the layout parameters output in the step S6.

(III) effects of the invention

According to the invention, the radar system index and the actual observation range are taken as input, the actual antenna array dimension, the antenna installation space on the flight platform and the antenna subarray layout relation are considered, the situation that the conventional antenna is staggered and arranged in the front and back directions of the track direction is solved, particularly the overlapping layout of part of the transmitting antenna and the receiving antenna is realized, and the flexible installation of the antenna on the flight platform is facilitated; in addition, the influence of the target elevation range is considered in the array element layout, and compared with the prior art, the method is simple to operate, does not need complex calculation, and can be effectively applied to radar system design.

Drawings

Fig. 1 is a flowchart illustrating an airborne look-down 3D SAR sparse array antenna layout method in an embodiment of the present invention.

Fig. 2 shows a procedure for antenna layout based on antenna layout parameters determined in an embodiment of the present invention.

Fig. 3 is a schematic diagram illustrating antenna layout based on the determined antenna layout parameters in the embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.

It should be noted that in the drawings or the description, the same reference numerals are used for similar or identical parts. Implementations not depicted or described in the drawings are of a form known to those of ordinary skill in the art. Additionally, while exemplifications of parameters including particular values may be provided herein, it is to be understood that the parameters need not be exactly equal to the respective values, but may be approximated to the respective values within acceptable error margins or design constraints. In addition, directional terms such as "upper", "lower", "front", "rear", "left", "right", and the like, referred to in the following embodiments, are directions only referring to the drawings. Accordingly, the directional terminology is used for purposes of illustration and is in no way limiting.

In one exemplary embodiment of the invention, an airborne look-down 3D SAR sparse array antenna layout method is provided. Fig. 1 shows a flowchart of an airborne look-down 3D SAR sparse array antenna layout method in an embodiment of the present invention. As shown in fig. 1, the method for laying out an airborne downward-looking3D SAR sparse array antenna according to the present embodiment includes:

step S1: according to the flight height H of the airborne machine and the maximum height variation range function H of an observation area as the parameters of the airborne downward-looking3D SAR system_T(x) Working wavelength l of radar system_cAzimuthal resolution r_AAnd array-wise resolution r_LCalculating the azimuth dimension L of the array antenna_AArray-to-antenna layout length L and array antenna element half-beam width q_L；

Where x represents an array-to-target position variable, and x ═ H-H_T(x)]×tan(θ_x)，θ_x∈[-θ_L，+θ_L]The parameters of the airborne downward-looking3D SAR system mainly comprise the flying height H of the airborne aircraft and the maximum height variation range function H of an observation area_T(x) Working wavelength l of radar system_cAnd array-wise resolution r_L；

Step S2: according to the length L of the array-oriented antenna layout and the half beam width q of the array antenna unit_LCalculating directional size l of transmitting antenna unit array_TThe distance Dl between the transmitting antenna units_TThe array dimension l of the receiving antenna unit_R：

$l_T=\frac{l_c}{\tan \left({2q}_L\right)}{K}_b;$

${\mathrm{Dl}}_T=\frac{l_c}{\tan \left({2q}_L\right)}{K}_b;$

$l_R=\frac{l_c}{\tan \left({2q}_L\right)}{K}_b;$

Wherein, K_bAs a function of the beam width factor, the current distribution over the antenna aperture, usually K_b＝0.886；

Step S3: according to the length L of the array-oriented antenna layout and the interval Dl of the transmitting antenna units_TCalculating the number M of transmitting antenna units, the number N of receiving antenna units and the distance Dl between the receiving antenna units_RDistribution L of geometric center positions of transmitting antennas_Tx(M), M1, 2, M and distribution L of geometric center positions of the receiving antenna elements_Rx(n)，n＝1，2，...，N；

Step S4: according to the distribution L of the geometric center positions of the antenna units_xHalf-wave beam width q of array antenna unit_LAnd radar system operating wavelength l_cLower point target f of computer systemX(k)-x₀Array-wise response function of extreme edge target of observation area <math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> <mo>,</mo> </mrow></math> Wherein,

is corresponding to q_LTarget position coordinates of time, x_nRepresenting the position coordinates of the under-machine point target, X (k) being the position coordinates of the array-wise sampling points, and the array-wise coordinates of the under-machine point target being

Also equal to the array towards the center of the antenna layout;

step S5: in the array-wise response function f { X (k) -x₀And <math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> </mrow></math> the grating lobe is positioned in the system imaging observation area +/-q_LBesides, andin which L is_eFor array-wise antenna layout the effective aperture length, l_cFor the operating wavelength of the radar system, r_LFor array-directional resolution, H is the carrier flight height,

is corresponding to q_LThe target position coordinates of time, then step S6 is executed; in an array-wise response function f { X { (k) -X₀And <math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> </mrow></math> the grating lobe is positioned in the system imaging observation area +/-q_LIn or on

In which

Is corresponding to q_LThe current target position coordinates are obtained by adding 1 to the number N of receiving antenna elements, and the process returns to step S3;

step S6: outputting airborne downward-looking3D SAR sparse array antenna layout parameters including array antenna direction size L_AArray dimension l of transmitting antenna element_TNumber of transmitting antenna units M, distribution of geometric center positions of transmitting antennas L_Tx(M), M1, 2.. M, dimension l of the array of receiving antenna elements_RThe number N of receiving antenna units and the distribution L of the geometric center positions of the receiving antenna units_Rx(n)，n＝1，2，...，N。

Step S7: and according to the layout parameters of the airborne downward-looking3D SAR sparse array antenna output in the step S6, carrying out layout of the airborne downward-looking3D SAR sparse array antenna.

In addition, the step S1 includes the following steps:

step S11: according to the flying height H of the carrier and the working wavelength l of the radar system_cAzimuthal resolution r_AAnd array-wise resolution r_LCalculating the azimuth dimension L of the array antenna_AAnd array-to-antenna layout length L:

$L=\frac{l_{c}H}{{2r}_L}$

$L_A=\frac{l_{c}H}{{2r}_A}$

the azimuth dimension of the array antenna comprises the azimuth dimension of a transmitting antenna unit and the azimuth dimension of a receiving antenna unit, the azimuth dimensions of the two antennas are equal, and both the azimuth dimensions are L_A。

Step S12: according to the flying height H of the carrier and the maximum height variation range function H of an observation area_T(x) Working wavelength l of radar system_cAnd array-wise imaging width W_LCalculating half-wave beam width q of array antenna unit_L：

<math><mrow> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>=</mo> <mi>max</mi> <mo>{</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>W</mi> <mi>L</mi> </msub> <mrow> <mn>2</mn> <mi>H</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <mi>x</mi> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>H</mi> <mo>-</mo> <mi>max</mi> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>}</mo> </mrow></math>

Where x represents an array-to-target position variable, and x is H × tan (θ)_x)，θ_x∈[-θ_L，+θ_L]， Is corresponding to q_LMax represents taking the maximum value.

In addition, the step S3 includes the following steps:

step S31: if step S5 has been executed, go to step S32; if step S5 has not been executed, the antenna layout length L and the transmitting antenna unit spacing Dl are determined according to the array_TCalculating the number M of transmitting antenna units and the number N of receiving antenna units:

wherein a represents a variable of the number of transmitting antenna elements, b represents a variable of the number of receiving antenna elements, Δ l_TThe transmit antenna element spacing is shown as,

the function of rounding up is represented by,representing a lower integer, M and N are respectively positive integers, and min (2a + b) represents taking a minimum value of (2a + b);

step S32: according to the number M of transmitting antenna units, the number N of receiving antenna units and the distance Dl between the transmitting antenna units_TCalculating the distance Dl between the receiving antenna units_R：

${\mathrm{Dl}}_R=\frac{{\mathrm{Dl}}_T}{2}M$

Step S33: according to the transmitting antennaNumber of elements M, number of receiving antenna elements N, and distance between transmitting antenna elements Dl_TAnd the receiving antenna unit interval Dl_RGeometric center position distribution L of downward-looking transmitting antenna on computer_Tx(M), M1, 2, M and distribution L of geometric center positions of the receiving antenna elements_Rx(n)，n＝1，2，...，N：

<math><mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>L</mi> <mi>Rx</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&Delta;l</mi> <mi>R</mi> </msub> <mo>&times;</mo> <mi>n</mi> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>Tx</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>L</mi> <mi>Rx</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mrow> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mi>&Delta;l</mi> </mrow> <mi>T</mi> </msub> <mo>&times;</mo> <mi>m</mi> <mo>;</mo> <mi>m</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mfrac> <mi>M</mi> <mn>2</mn> </mfrac> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>Rx</mi> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&Delta;l</mi> <mi>T</mi> </msub> <mo>&times;</mo> <mrow> <mo>(</mo> <mi>m</mi> <mo>-</mo> <mfrac> <mi>M</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <mi>m</mi> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mi>M</mi> <mn>2</mn> </mfrac> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>;</mo> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced></math>

Wherein Dl is_RFor receiving the antenna element spacing, Dl_TIs the transmit antenna element spacing.

Step S34: l obtained according to step S33_Rx(n) and L_Tx(m) generating an array-to-antenna layout effective aperture length L_eAnd a virtual equivalent phase center L_TRx(q)，q＝1，L，MN：

$L_e=\frac{L_{\mathrm{Tx}}\left(M\right)+L_{\mathrm{Rx}}\left(N\right)}{2}-\frac{L_{\mathrm{Tx}}\left(1\right)+L_{\mathrm{Rx}}\left(1\right)}{2};$

for n＝1∶N，

for m＝1∶M，

<math><mrow> <msub> <mi>L</mi> <mi>TRx</mi> </msub> <mo>[</mo> <mi>q</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <mi>N</mi> <mo>+</mo> <mi>m</mi> <mo>]</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>L</mi> <mi>Rx</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>L</mi> <mi>Tx</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow></math>

end；

end；

L_Rx(n) and L_TxAnd (m) performing antenna phase center equivalence in a circulating mode between every two antennas to obtain equivalent phase centers of MN antennas.

In addition, the step S4 includes the following steps:

step S41: according to the flying height H of the carrier and the half-wave beam width q of the array antenna unit_LEstablishing position coordinates of array-oriented sampling points

Wherein,

and

respectively representing upper and lower rounded, Dl_TIn order to transmit the antenna element spacing,

for array-to-antenna layout center, q_LHalf-wave beam width of the array-directional antenna unit;

step S42: according to the flying height H of the carrier and the working wavelength l of the radar system_cAnd determining an array-oriented response function f { X (k) -x of an off-machine point target of the system according to the position coordinates X (k) of the array-oriented sampling points₀Array-wise response function of extreme edge target of observation area <math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> <mo>:</mo> </mrow></math>

<math><mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>}</mo> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>MN</mi> </munderover> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&times;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>+</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <msub> <mi>L</mi> <mi>TRx</mi> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced></math>

<math><mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>}</mo> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>MN</mi> </munderover> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&times;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>+</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <msub> <mi>L</mi> <mi>TRx</mi> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced></math>

Wherein x is₁Indicating the array to target location coordinates, L_TRx(q) is the virtual equivalent phase center q 1, L, MN, $f\{X\left(k\right)-x_0\}=f\{X\left(k\right)-x_1\}{|}_{x_1=x_0},$

<math><mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> <mo>=</mo> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>}</mo> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> </mrow> </msub> <mo>.</mo> </mrow></math>

fig. 2 shows the steps for performing an onboard look-down 3D SAR sparse array antenna layout based on the antenna layout parameters determined in the above-described embodiment of the present invention. Fig. 3 shows a schematic diagram of antenna layout based on antenna layout parameters determined in an embodiment of the invention.

Calculating the array dimension l of the transmitting antenna unit by the method_TNumber of transmitting antenna units M, distribution of geometric center positions of transmitting antennas L_Tx(M), M1, 2.. M, dimension l of the array of receiving antenna elements_RThe number N of receiving antenna units and the distribution L of the geometric center positions of the receiving antenna units_Rx(N), N is 1, 2.., N, and the step S7 further includes the following steps:

step S71: determining an antenna layout parameter list, wherein the determined antenna layout parameter list is shown in table 1;

TABLE 1

Array antenna layout parameters	Symbol
		Array antenna azimuth dimension	LA
Array dimension of transmitting antenna unit	lT
		Number of transmitting antenna elements	M
Distribution of geometrical center positions of transmitting antennas	LTx(m)
		Receiving antenna sheetDimension of element array	lR
Number of receiving antenna units	N
		Distribution of geometric center positions of receiving antenna elements	LRx(n)

Step S72: determining antenna layout marking points according to the antenna layout parameter list, selecting a platform to be laid out, and distributing L according to the geometric center position of a transmitting antenna_Tx(M) determining transmitting antenna mark points which can be distributed by the platform, and marking the transmitting antenna mark points as PosT (mt), wherein mt is 1_Rx(N) determining receiving antenna marking points which can be laid out by a platform, and marking the receiving antenna marking points as PosR (nr), wherein nr is 1.

Step S73: the transmitting antenna and the receiving antenna are arranged, the transmitting antenna marking points PosT and the receiving antenna marking points PosR can be arranged according to the platform, and the transmitting antenna and the receiving antenna are respectively arranged according to the principle that the geometric center coincides with the marking points.

The embodiment of the invention is explained above, and the on-board look-down 3D SAR sparse array antenna layout method is based on radar system indexes and actual observation ranges, and takes into consideration the actual antenna array dimension, the antenna installation space on the flight platform, and the layout relationship between antenna subarrays, so that the situation that the conventional antenna is staggered and arranged in the front-back direction of the track can be solved, especially the overlapping layout of part of transmitting antennas and receiving antennas equivalent antennas is avoided, and the flexible installation of the antenna on the flight platform is facilitated.

The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. An airborne look-down 3D SAR sparse array antenna layout method is characterized by comprising the following steps:

step S1, determining the azimuth dimension of the array antenna, the layout length of the array antenna and the half beam width of the array antenna unit according to the flight altitude of the aircraft, the maximum altitude variation range function of an observation area, the working wavelength of the radar system, the azimuth resolution and the array resolution which are taken as parameters of the airborne downward-looking3D SAR system;

step S2, determining the array direction size of the transmitting antenna unit, the distance between the transmitting antenna units and the array direction size of the receiving antenna unit based on the array direction antenna layout length and the array antenna unit half beam width;

step S3, calculating the number of transmitting antenna units, the number of receiving antenna units, the spacing of receiving antenna units, the distribution of the geometric center positions of transmitting antennas and the distribution of the geometric center positions of receiving antenna units according to the array-to-antenna layout length and the spacing of the transmitting antenna units;

step S4, establishing array-direction sampling point position coordinates according to the flight height of the aerial carrier and the half beam width of the array-direction antenna unit, and determining an array-direction response function f { X (k) -x) of a system airborne point target by using the array-direction sampling point position coordinates, the flight height of the aerial carrier and the working wavelength of the radar system₀Array-wise response function of extreme edge target of observation area

<math> <mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> <mo>;</mo> </mrow> </math>

Step S5, under the system, the array directional response function f { X (k) -x of the point target₀Array directional response function of the most marginal target of the observation area <math> <mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> <mo>;</mo> </mrow> </math> The grating lobe is positioned in the system imaging observation area +/-q_LBesides, and

then, step S6 is executed, the array directional response function f { X (k) -x of the target under the system is₀Array directional response function of the most marginal target of the observation area <math> <mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> </mrow> </math> The grating lobe of (2) falls in the system imaging observation area + -q_LIn or on

Then, the number of the receiving antenna units is increased by one, and the process returns to step S3, where H is the flying height of the carrier and L is the flying height of the carrier_eFor array-wise antenna layout the effective aperture length, l_cFor the operating wavelength of the radar system, r_LThe array directional resolution;

step S6, outputting the directional size of the transmitting antenna element array, the number of transmitting antenna elements, the distribution of the geometric center positions of the transmitting antennas, the directional size of the receiving antenna element array, the number of receiving antenna elements, and the distribution of the geometric center positions of the receiving antenna elements;

step S7, performing layout of the airborne downward-looking 3DSAR sparse array antenna according to the layout parameters output in the step S6.

2. The method of claim 1, wherein the method comprises the steps of,

in the step S1, in the above step,

setting the flying height of the carrier to be H and the working wavelength of the radar system to be l_cSetting the array-directional resolution to r_LSetting the azimuth resolution as r_ASetting the azimuth dimension of the array antenna to L_AWhen the length of the array antenna layout is set to L,

$L=\frac{l_{c}H}{{2r}_L}$

$L_A=\frac{l_{c}H}{{2r}_A}$

setting the function of the maximum height variation range of the observation area as h_T(x) Setting the imaging width of the array to be W_LSetting the half-wave beam width of the array to the antenna unit as q_LWhen the temperature of the water is higher than the set temperature,

<math> <mrow> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>=</mo> <mi>max</mi> <mo>{</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <mi>W</mi> <mrow> <mn>2</mn> <mi>H</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <mi>x</mi> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>H</mi> <mo>-</mo> <mi>max</mi> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>}</mo> <mo>,</mo> </mrow> </math>

where x represents an array-to-target position variable, and x is H × tan (θ)_x)，θ_x∈[-θ_L，+θ_L]，Is corresponding to q_LThe target position coordinates of (2).

3. The method of airborne look-down 3D SAR sparse array antenna placement of claim 1,

in the step S2, the radar system operating wavelength is set to l_cSetting the half beam width of the array antenna unit as q_LSetting the array of transmit antenna elements to a dimension of/_TSetting the transmitting antenna unit spacing to Dl_TSetting the array dimension of the receiving antenna unit to be l_RWhen the temperature of the water is higher than the set temperature,

$l_T=\frac{l_c}{\tan \left({2q}_L\right)}{K}_b;{\mathrm{Dl}}_T=l_T;l_R=\frac{l_c}{\tan \left({2q}_L\right)}{K}_b;$

wherein, K_bSetting K for the beam width factor in relation to the current distribution over the antenna aperture_b＝0.886。

4. The method of claim 1, wherein the method comprises the steps of,

the step S3 further includes:

step S31, if step S5 has been executed, go to step S32; if step S5 has not been executed, according to the array-to-antenna layout length and the transmitting antenna unit spacing Dl_TDetermining the number of transmit antenna elements and the number of receive antenna elements,

setting the array-to-antenna layout length as L and the transmitting antenna unit spacing as Dl_TWhen the number of the transmitting antenna units is set as M and the number of the receiving antenna units is set as N,

wherein a represents a variable of the number of transmitting antenna elements, b represents a variable of the number of receiving antenna elements, Al_TThe transmit antenna element spacing is shown as,

the function of rounding up is represented by,representing a lower integer, M and N are respectively positive integers, and min (2a + b) represents taking a minimum value of (2a + b);

step S32, using the number of the transmitting antenna units and the transmitting antenna unit spacing in the step S31 to determine the receiving antenna unit spacing, setting the receiving antenna unit spacing to Dl_RWhen the temperature of the water is higher than the set temperature,

${\mathrm{Dl}}_R=\frac{{\mathrm{Dl}}_T}{2}M,$

wherein Dl is_TThe distance between the transmitting antenna units is defined, and M is the number of the transmitting antenna units;

step S33, determining the distribution L of the geometric center position of the transmitting antenna according to the number of the transmitting antenna units, the number of the receiving antenna units, the distance between the transmitting antenna units and the distance between the receiving antenna units_Tx(m)L_Tx(M), M1, 2, M and distribution L of geometric center positions of the receiving antenna elements_Rx(n)L_Rx(n)，n＝1，2，...，N，

<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>L</mi> <mi>Rx</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&Delta;l</mi> <mi>R</mi> </msub> <mo>&times;</mo> <mi>n</mi> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>Tx</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>L</mi> <mi>Rx</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&Delta;l</mi> <mi>T</mi> </msub> <mo>&times;</mo> <mi>m</mi> <mo>;</mo> <mi>m</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mfrac> <mi>M</mi> <mn>2</mn> </mfrac> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>Rx</mi> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&Delta;l</mi> <mi>T</mi> </msub> <mo>&times;</mo> <mrow> <mo>(</mo> <mi>m</mi> <mo>-</mo> <mfrac> <mi>M</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> <mi>m</mi> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mi>M</mi> <mn>2</mn> </mfrac> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>;</mo> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

Wherein M is the number of the transmitting antenna units, N is the number of the receiving antenna units, Dl_TFor transmitting antenna element spacing, Dl_RIs the receive antenna element spacing.

5. The method of claim 4, wherein the method comprises the steps of,

using the distribution L of the geometric center positions of the receiving antenna elements_Rx(n) and the distribution L of the geometrical center positions of the transmitting antennas_Tx(m) generating an effective aperture length and a virtual equivalent phase center of an array-to-antenna layout, wherein the geometric center positions of the receiving antenna units are distributed in L_Rx(n) and the distribution L of the geometrical center positions of the transmitting antennas_TxAnd (m) performing antenna phase center equivalence in a circulating mode between every two antennas to obtain equivalent phase centers of MN antennas.

6. The method of claim 1, wherein the method comprises the steps of,

in step S4, when the array-directional sampling point position coordinates are set to x (k),

<math> <mrow> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <msub> <mi>&Delta;l</mi> <mi>T</mi> </msub> <mn>2</mn> </mfrac> <mo>&times;</mo> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mo>-</mo> <mi>K</mi> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mn>0,1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> <mo>,</mo> </mrow> </math>

wherein,

and

respectively representing an upper rounding function and a lower rounding function,representing the array towards the center of the antenna layout, Dl_TFor transmitting antenna element spacing, q_LHalf-wave beam width of the array-directional antenna unit;

calculating an array directional response function f { X (k) -x of the system under-machine point target by using the array directional sampling point position coordinates X (k)₀Array directional response function of the most marginal target of the observation area <math> <mrow> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> <mo>}</mo> </mrow> </math> When the temperature of the water is higher than the set temperature,

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>}</mo> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>MN</mi> </munderover> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>exp</mi> <mrow> <mo>(</mo> <mi></mi> <mo>-</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&times;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>+</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <msub> <mi>L</mi> <mi>TRx</mi> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>f</mi> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>}</mo> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>{</mo> <mo>[</mo> <mi>H</mi> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>&times;</mo> <mi>tan</mi> <mrow> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>}</mo> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>MN</mi> </munderover> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <mi>X</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&times;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>+</mo> <mi>j</mi> <mn>4</mn> <mi>&pi;</mi> <mfrac> <msqrt> <msup> <mrow> <mo>[</mo> <msub> <mi>L</mi> <mi>TRx</mi> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>[</mo> <mi>H</mi> <mo>-</mo> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </msqrt> <msub> <mi>&lambda;</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

wherein H is the flying height of the carrier, l_cFor the operating wavelength, x, of the radar system₁The target array position coordinates.

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