CN107179537A - A kind of distributive array SAR phase center calibrating methods based on Orthogonal Subspaces principle - Google Patents

A kind of distributive array SAR phase center calibrating methods based on Orthogonal Subspaces principle Download PDF

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CN107179537A
CN107179537A CN201710431974.9A CN201710431974A CN107179537A CN 107179537 A CN107179537 A CN 107179537A CN 201710431974 A CN201710431974 A CN 201710431974A CN 107179537 A CN107179537 A CN 107179537A
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msub
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CN201710431974.9A
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刘志铭
楼良盛
牛瑞
梁兴东
卜运成
王宇
陈刚
高力
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中国人民解放军61540部队
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques

Abstract

The invention discloses a kind of distributive array synthetic aperture radar phase center calibrating method based on Orthogonal Subspaces principle, implementation step is:(1) the noise subspace U of radar array output data is obtained according to multiple signal classification algorithm principleN;(2) the instantaneous direction of arrival of calibration source is obtained by airborne positioning and orientation systematic survey apparatus measuring value;(3) ideal array parameter computing array flow pattern is used, with reference to noise subspace and instantaneous DOA estimates computer azimuth angle information matrix P, B;(4) by matrix P, B carries out optimization computation, returns to the deviation δ of phase centre location and ideal position estimate, then by plus position deviation δ being to obtain phase centre location estimation by ideal position.The present invention can be calibrated accurately distributive array SAR system phase center, and the demarcation of all phase centre locations is once completed, the efficiency and precision of phase centre location calibration can be significantly improved, and then improves reconstruction accuracy and elevation to super-resolution performance.

Description

A kind of distributive array SAR phase centers calibration based on Orthogonal Subspaces principle Method

Technical field

The present invention relates to a kind of distributive array synthetic aperture radar phase center calibration based on Orthogonal Subspaces principle Method, belongs to SAR signal processing technical field, the phase available for distributive array polarization sensitive synthetic aperture radar system Calibrate center.

Background technology

Phase center calibration is synthetic aperture radar (Synthetic Aperture Radar, SAR) Data processing One key technology.Each passage in multi-channel system is due to by the factor shadow such as alignment error, baseline shock, phase center be equivalent Ring and deviate ideal position, it is necessary to preceding in actual phase in SAR three-dimensional imagings and resolution using phase center calibration technology Heart position is demarcated, so as to obtain actual phase centre location, obtains accurate three-dimensional reconstruction result.At present in SAR necks Domain, the orientation multi-channel system detected for moving-target is relatively common, and its corresponding calibration research is also more, such as using many The fuzzy phase centre location calibrations for carrying out orientation multichannel of Pu Le.But array three-dimensional be imaged etc. application in need across The multichannel in course.

Across in the calibration of course multichannel research, most study is binary channels interference synthetic aperture radar (Interferometry Synthetic Aperture Radar, InSAR) is calibrated, and it mainly has two class methods.First kind side Method is the interference calibration based on phasing, and the basic thought of this method is to miss all parameter error reduction to interferometric phase In difference, therefore application is simpler, but due to being phase error by all error reduction, therefore specifically can not understand in phase The deviation of heart position and other interferometric parameter deviations;Equations of The Second Kind method is the interference calibration based on Sensitivity equation, such method All kinds of interferometric parameters, such as baseline length, baseline angle and interferometric phase deviation can be estimated, it is available by simply converting The estimation of phase centre location, but for being calibrated for multichannel phase center, such method can only once determine two The position of passage, efficiency is low, and the calibration precision of more different baseline length is different, causes each phase centre location to be determined Target precision is inconsistent.

The content of the invention

In view of existing methods limitation, the present invention proposes a kind of distributive array SAR based on Orthogonal Subspaces principle Phase center calibrating method.The general principle of this method is:In multiple signal classification (Multiple signal Classification, MUSIC) noise subspace obtained in algorithm is orthogonal with array manifold, and noise subspace can be utilized The data of array received are solved, and array manifold be by phase center and direction of arrival (Direction Of Arrival, DOA) uniquely determine, therefore the orthogonality of noise subspace and array manifold, using phase center as unknown quantity, structure can be utilized Minimum cost function is built to calibrate phase centre location.

According to the distributive array SAR phase center calibrating methods proposed by the present invention based on Orthogonal Subspaces principle, bag Include following steps:

1) the noise subspace U of radar array output data is obtained according to MUSIC algorithm principlesN

2) surveyed by airborne positioning and orientation system (Positioning and Orientation System, POS) measuring instrument Value obtains calibration source DOA;

3) ideal array parameter computing array flow pattern is used, with reference to noise subspace and DOA estimate computer azimuth angles Information matrix P, B;

4) by matrix P, B carries out optimization computation, returns to the deviation δ of phase centre location and ideal position estimate, Again by by ideal position plus position deviation δ be obtain phase centre location estimate.

Further, step 1 of the present invention) detailed process be:

Signal X 1a) received to array seeks covariance matrix Rxx, and it can be byEstimation, wherein L tables Show fast umber of beats, XlL-th of signal is represented,Represent XlConjugate transposition.

Eigenvalues Decomposition 1b) is carried out to Rxx, the corresponding characteristic vector of less M characteristic value is constituted into matrix UN.Wherein M is information source number.

Further, step 3 of the present invention) detailed process be:

3a) array manifold under ideal array parameter is calculated using following formula:

Wherein (xn0,yn0,zn0), n=1,2 ... N is the ideal three-dimensional coordinate of each phase center, θiiRespectively i-th The azimuth of individual information source and the angle of pitch, are shown in that Fig. 2, λ represent radar operation wavelength, []HRepresent conjugate transposition, []TRepresent to turn Put.

3b) construction orientation angles information matrix P, B:

Wherein

Further, step 4 of the present invention) detailed process be:

4a) construction minimizes function

Obtain phase centre location deviationWherein real () represents realistic portion behaviour Make;

4b) calculate phase centre location estimateWherein xyz0For the ideal of phase centre location vector Value.

The beneficial effects of the invention are as follows:A kind of distributive array SAR based on Orthogonal Subspaces principle of the present invention Phase center calibrating method, accurately can be calibrated distributive array SAR system phase center, and in all phases The demarcation of heart position is once completed, it is not necessary to two-by-two mutually calibration, can significantly improve phase centre location calibration efficiency and Precision, and then reconstruction accuracy and elevation are improved to super-resolution performance.

Brief description of the drawings

Fig. 1 is the flow chart of the specific embodiment of the invention.

Fig. 2 is a kind of data acquisition schematic diagram of distributed SAR system.

Fig. 3 is matrix P amplitude expression figure.

Fig. 4 is matrix P phase meter diagram.

Fig. 5 is the amplitude expression figure of matrix B.

Fig. 6 is the phase meter diagram of matrix B.

Fig. 7 is the ideal value and estimate comparison diagram of phase center x coordinate.

Fig. 8 is the ideal value and estimate comparison diagram of phase center y-coordinate.

Fig. 9 is the ideal value and estimate comparison diagram of phase center z coordinate.

Figure 10 is the ideal value and estimate deviation map of phase center x coordinate.

Figure 11 is the ideal value and estimate deviation map of phase center y-coordinate.

Figure 12 is the ideal value and estimate deviation map of phase center z coordinate.

Specific embodiment

One phase center is along course distribution is cut, and number of active lanes is 16, and information source number obtains schematic diagram such as 4 SAR data Fig. 2, platform flies in the x-direction, and left wing is designated as y to cut course, and elevation constitutes right-handed coordinate system to z and x and y.In order to verify this The algorithm proposed is invented, one group of simulation result is given, its parameter is shown in Table 1.

The simulation parameter of table 1

Phase center scaling experiment is carried out to the analogue system using method proposed by the present invention.Its implementing procedure such as Fig. 1 Shown, it is concretely comprised the following steps:

Step 1:The noise subspace U of radar array output data is obtained according to MUSIC algorithm principlesN

The detailed process of the step is:

Signal X 1a) received to array seeks covariance matrix Rxx, and it can be byEstimation, wherein L tables Show fast umber of beats, XlL-th of signal is represented,Represent XlConjugate transposition.

L=3 in this example, trying to achieve covariance matrix Rxx (16 × 16 matrixes) is:

Sequence number 1 2 3 …… 14 15 16 1 3.9973+0.0000i 0.0187-1.1731i -0.7408-1.3710i …… 1.2498+1.2178i -0.6833-1.6531i 0.0699+0.2248i 2 0.0187+1.1731i 3.9066+0.0000i 0.3840-1.1876i …… 1.2577-0.4313i 1.3551+1.2436i -0.1578-1.8991i 3 -0.7408+1.3710i 0.3840+1.1876i 3.9616+0.0000i …… 1.0893+0.0816i 1.2918-0.7244i 1.0953+1.3633i 4 0.6376+1.7695i -0.5775+1.3296i -0.0432+1.0660i …… -0.8388+3.6819i 1.2245+0.4998i 1.3018-0.2146i …… …… …… …… …… …… …… …… 13 1.0973+0.6106i 1.0868-0.2348i -0.2374-3.9069i …… 0.2160-1.2245i -0.8823-1.5139i 1.0851-1.5395i 14 1.2498-1.2178i 1.2577+0.4313i 1.0893-0.0816i …… 3.8114+0.0000i 0.3226-1.2778i -0.3269-1.4062i 15 -0.6833+1.6531i 1.3551-1.2436i 1.2918+0.7244i …… 0.3226+1.2778i 4.0939+0.0000i 0.2476-1.1275i 16 0.0699-0.2248i -0.1578+1.8991i 1.0953-1.3633i …… -0.3269+1.4062i 0.2476+1.1275i 3.9331+0.0000i

Eigenvalues Decomposition 1b) is carried out to Rxx, the corresponding characteristic vector of less M characteristic value is constituted into matrix UN.Wherein M is information source number.M=4 in this example, the matrix U tried to achieveN(12 × 16 matrixes) are:

Sequence number 1 2 3 …… 10 11 12 1 0.1136-0.0405i -0.0397-0.0979i 0.0253-0.4628i …… 0.1767+0.0606i -0.2086-0.1628i 0.2027-0.0168i 2 -0.0385+0.2086i -0.0162+0.1971i -0.0173+0.0172i …… 0.0745-0.1485i 0.1875+0.2089i -0.0120-0.0084i 3 0.2062-0.1743i -0.1281+0.1481i -0.0572+0.0972i …… -0.3627+0.1847i 0.0428-0.2533i -0.1223-0.0452i 4 0.0599+0.1042i -0.0462+0.3128i 0.0262+0.2989i …… 0.1940-0.1071i 0.3072+0.0238i 0.0947+0.2748i …… …… …… …… …… …… …… …… 13 -0.2183+0.1086i -0.1418-0.2242i 0.1032-0.1741i …… -0.2358-0.3608i 0.0693+0.0124i -0.1703+0.0447i 14 0.0523+0.2016i -0.3184+0.0260i -0.0082+0.0536i …… 0.1631+0.0855i -0.0411+0.0138i 0.0092+0.0083i 15 0.0635+0.1524i -0.1455+0.0496i -0.1468+0.1036i …… 0.2636-0.0521i -0.1889-0.2447i -0.2957-0.2840i 16 -0.1500-0.0000i 0.5266+0.0000i -0.2666+0.0000i …… 0.0596+0.0000i -0.1252+0.0000i -0.0994+0.0000i

Step 2:Calibration source DOA is obtained by airborne POS measurement apparatus measuring values;

θmeasure=[- 40-20 25 45], φmeasure=[30 60 30 60]

Step 3:Using ideal array parameter computing array flow pattern, with reference to noise subspace and DOA estimate computer azimuths Angle information matrix P, B;

The detailed process of the step is:

3a) array manifold under ideal array parameter is calculated using following formula:

Wherein (xn0,yn0,zn0), n=1,2 ... N is the ideal three-dimensional coordinate of each phase center, θiiRespectively i-th The azimuth of individual information source and the angle of pitch, λ represent radar operation wavelength, []HRepresent conjugate transposition, []TRepresent transposition.

3b) construction orientation angles information matrix P, B:

Wherein

Step 3 show that orientation angles information matrix P, B are vector sum (N-M) M × (N-M) M of (N-M) M × 1 respectively Matrix (in this example be respectively 48 × 1 and 48 × 48 matrixes).It is represented in the form of amplitude and phase as Fig. 3, Fig. 4, Fig. 5, Fig. 6.

Step 4:Optimization computation is carried out by matrix P, B, the deviation δ of phase centre location and ideal position estimation is returned Value, then by by ideal position plus position deviation δ be obtain phase centre location estimation.

The detailed process of the step is:

4a) construction minimizes function

Obtain phase centre location deviation

4b) calculate phase centre location estimateWherein xyz0For the ideal value of phase centre location.

The result of calculation such as Fig. 7 (deviation between the actual value and estimate of each phase center x coordinate) of step 4, Fig. 8 (deviation between the actual value and estimate of each phase center y-coordinate) and Fig. 9 (actual value of each phase center z coordinate and estimate Deviation between evaluation) shown in.

From the point of view of the calibration results, the x of each phase center, y, z three-dimensional coordinates estimation are very accurate.Each phase center Position xyz coordinates estimate and the deviation of actual value are represented to see Figure 10, Figure 11, Figure 12 respectively with numerical value, from figure Estimate and actual value very close to.It calibrates mean square error MSE (Mean Square Error)Equal to 0.039mm.

Found by the result of embodiment, a kind of distributive array SAR based on Orthogonal Subspaces principle proposed by the present invention Phase center calibrating method, accurately can be calibrated distributive array SAR system phase center, and in all phases The demarcation of heart position is once completed, it is not necessary to mutually calibration two-by-two, greatly improves efficiency, it is ensured that precision.

The embodiment of the present invention is described above in association with accompanying drawing, but these explanations can not be understood to limitation The scope of the present invention, protection scope of the present invention is limited by appended claims, any in the claims in the present invention base Change on plinth is all protection scope of the present invention.

Claims (4)

1. the distributive array synthetic aperture radar phase center calibrating method based on Orthogonal Subspaces principle, it is characterised in that This method comprises the following steps:
1) radar is obtained according to multiple signal classification (Multiple signal classification, MUSIC) algorithm principle The noise subspace U of array output dataN
2) apparatus measuring value is measured by airborne positioning and orientation system (Positioning and Orientation System, POS) Obtain calibration source direction of arrival (Direction Of Arrival, DOA);
3) ideal array parameter computing array flow pattern is used, with reference to noise subspace and DOA estimate computer azimuth angle information Matrix P, B;
4) by matrix P, B carries out optimization computation, returns to the deviation δ of phase centre location and ideal position estimate, then leads to Cross by ideal position plus position deviation δ obtain phase centre location estimation.
2. the distributive array SAR phase center calibrating methods based on Orthogonal Subspaces principle according to claim 1, It is characterized in that the step 1) detailed process be:
Signal X 2a) received to array seeks covariance matrix Rxx, and it can be byEstimation, wherein L represents fast Umber of beats, XiRepresent i-th of signal, Xi HRepresent the conjugate transposition of i-th of signal;
Eigenvalues Decomposition 2b) is carried out to Rxx, the corresponding characteristic vector of less M characteristic value is constituted into matrix UN.Wherein M is letter Source number.
3. the distributive array SAR phase center calibrating methods based on Orthogonal Subspaces principle according to claim 1, It is characterized in that the step 3) detailed process be:
3a) array manifold under ideal array parameter is calculated using following formula:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>exp</mi> <mo>{</mo> <mi>j</mi> <mfrac> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>sin&amp;phi;</mi> <mi>i</mi> </msub> <msub> <mi>cos&amp;theta;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <mi>n</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>sin&amp;phi;</mi> <mi>i</mi> </msub> <msub> <mi>sin&amp;theta;</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>n</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>cos&amp;phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <mi>exp</mi> <mo>{</mo> <mi>j</mi> <mfrac> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>N</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>sin&amp;phi;</mi> <mi>i</mi> </msub> <msub> <mi>cos&amp;theta;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <mi>N</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>sin&amp;phi;</mi> <mi>i</mi> </msub> <msub> <mi>sin&amp;theta;</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>N</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>cos&amp;phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>}</mo> <msup> <mo>&amp;rsqb;</mo> <mi>H</mi> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein (xn0,yn0,zn0), n=1,2 ... N is the ideal three-dimensional coordinate of each phase center, θiiRespectively i-th letter The azimuth in source and the angle of pitch, λ represent radar operation wavelength, []HRepresent conjugate transposition, []TRepresent transposition;
3b) construction orientation angles information matrix P, B:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>P</mi> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>P</mi> <mn>1</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>P</mi> <mn>1</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msubsup> <mi>P</mi> <mi>M</mi> <mi>T</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>U</mi> <mi>N</mi> <mi>H</mi> </msubsup> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>B</mi> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>B</mi> <mn>1</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>B</mi> <mn>2</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msubsup> <mi>B</mi> <mi>M</mi> <mi>T</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> <msub> <mi>B</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>U</mi> <mi>N</mi> <mi>H</mi> </msubsup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>j</mi> <mfrac> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mrow> <mo>{</mo> <mrow> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mi>j</mi> <mfrac> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mrow> <mo>{</mo> <mrow> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mi>j</mi> <mfrac> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mrow> <mo>{</mo> <mrow> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
4. the distributive array SAR phase center calibrating methods based on Orthogonal Subspaces principle according to claim 1, It is characterized in that the step 4) detailed process be:
4a) construction minimizes function
<mrow> <mover> <mi>&amp;delta;</mi> <mo>^</mo> </mover> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>&amp;delta;</mi> </munder> <mo>|</mo> <mo>|</mo> <mi>P</mi> <mo>+</mo> <mi>B</mi> <mi>&amp;delta;</mi> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Obtain phase centre location deviationWherein real () represents realistic portion's operation;
4b) calculate phase centre location estimateWherein xyz0For the ideal of phase centre location vector Value.
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