CN102253374A - Method for calibrating compact polarimetric SAR (Synthetic Aperture Radar) in long wave-length spaceborne pi/4 mode - Google Patents

Abstract

The invention discloses a method for calibrating a compact polarimetric SAR (Synthetic Aperture Radar) in a long wave-length spaceborne pi/4 mode. The method comprises the following steps: 1, acquiring an estimation value of the degree of unbalancedness of a transmission channel; 2, acquiring an estimation value of a channel crosstalk coefficient of a vertical-launching horizontal-receiving component; 3, acquiring an estimation value of a Faraday rotation angle; 4, acquiring an estimation value of an unambiguous Faraday rotation angle by utilizing TEC (Total Electron Content) data provided by a global navigation satellite system; 5, acquiring an estimation value of the degree of unbalancedness of a receiving channel; and 6, acquiring an estimation value of a channel crosstalk coefficient of a horizontal-launching vertical-receiving component. By utilizing the method, accurate calibration still can be performed without scaler errors or system noise, and high-precision calibration can still be performed when the scaler errors and system noise exist. The method provided by the invention has important application value in processing the compact polarimetric SAR data in the long wave-length spaceborne pi/4 mode represented by a P wave band.

Description

The spaceborne π of a kind of long wavelength/4 patterns are condensed the calibrating method of polarization SAR

Technical field

The present invention relates to the spaceborne π of a kind of long wavelength/4 patterns and condense the calibrating method of polarimetric synthetic aperture radar (SAR), belong to the signal processing technology field.

Background technology

European Space Agency (ESA) proposes pattern-band " biomass " in the near future and (BIOMASS) plans, a spaceborne pattern-band SAR satellite will be developed and launch to plan, be intended to utilize spaceborne long wavelength's synthetic-aperture radar that surface vegetation is surveyed, and then the carbon cycle of inverting land, for providing technology, the research around global warming supports with theoretical.This plan has very important scientific meaning and using value, also is in technology exploration and demonstration stage at present.Forest biomass observation SAR becomes one of current international research forward position hot subject, and long wavelength's satellite-borne SAR has great potential aspect the inverting top biomass, caused the great attention of each main scientific and technological power in the world in recent years.

The Polarization scattering information on the face of land can be the inverting forest biomass important information is provided.Than common single polarization, complete polarization SAR can obtain the interchannel abundanter target information of different polarization, have significant advantage, but it is difficult to realize that the wide swath of single polarization SAR is wide.For head it off, the foreign scholar has proposed to condense the polarization SAR mode of operation in recent years, this mode of operation can reach the observation bandwidth of conventional single polarization pattern, and can receive four POLARIZATION CHANNEL information that the polarization data inversion goes out the complete polarization pattern by vertical and level.

A kind of polarization SAR mode of operation of condensing is π/4 patterns, and the linear hybrid polarized signal of its emission vertical polarization+horizontal polarization (H+V, 45 ° linear polarization) receives level and vertical signals having linear polarisation simultaneously respectively.Simultaneously, the spaceborne π of long wavelength's (especially pattern-band)/4 patterns are condensed the polarization SAR system and can be subjected to ionospheric having a strong impact on, and make the polarization plane of SAR signal rotate, and finally cause the SAR image can not correctly reflect the polarization scattering characteristics of face of land target.

Summary of the invention

The present invention proposes the spaceborne π of a kind of long wavelength/4 patterns and condense the calibrating method of polarization SAR, this method is the new method that the spaceborne π of a kind of long wavelength of being applicable to/4 patterns are condensed the polarization SAR calibration based on the total amount of electrons of high precision Global Ionospheric (TEC) Monitoring Data and the 10th generation international geomagnetic reference field model (IGRF10) that four initiatively polarize scaler and GPS (Global Position System) (GNSS) provide.

The spaceborne π of a kind of long wavelength/4 patterns are condensed the calibrating method of polarization SAR, comprise following step:

Step 1: the estimated value of obtaining the transmission channel degree of unbalancedness;

Step 2: obtain the estimated value that the Vertical Launch level receives the channels crosstalk coefficient of component;

Step 3: the estimated value of obtaining faraday's rotation angle;

Step 4: the TEC data of utilizing GPS (Global Position System) to provide are obtained does not have fuzzy faraday's rotation angle estimated value;

Step 5: the estimated value of obtaining the receiving cable degree of unbalancedness;

Step 6: the estimated value of obtaining the channels crosstalk coefficient of level emission vertical junction contracture amount.

The invention has the advantages that:

(1) the method treatment scheme of the present invention's proposition is simple;

(2) the present invention can not calibrate when having scaler error and system noise accurately, still can carry out high-precision calibration when having scaler error and system noise.

(3) method that proposes of the present invention is to being that the spaceborne π of long wavelength/4 patterns of representative are condensed the polarization SAR data processing and had important application with the pattern-band.

Description of drawings

Fig. 1 is a method flow diagram of the present invention;

Fig. 2 is the amplitude Estimation result curve of the present invention's transmission channel degree of unbalancedness when not having scaler error and system noise;

Fig. 3 is the phase estimation result curve of the present invention's transmission channel degree of unbalancedness when not having scaler error and system noise;

Fig. 4 is the amplitude Estimation result curve that the present invention's Vertical Launch level when not having scaler error and system noise receives the channels crosstalk coefficient of component;

Fig. 5 is the phase estimation result curve that the present invention's Vertical Launch level when not having scaler error and system noise receives the channels crosstalk coefficient of component;

Fig. 6 is the estimated result curve of the present invention's faraday's rotation angle when not having scaler error and system noise;

Fig. 7 is the amplitude Estimation result curve of the present invention's receiving cable degree of unbalancedness when not having scaler error and system noise;

Fig. 8 is the phase estimation result curve of the present invention's receiving cable degree of unbalancedness when not having scaler error and system noise;

Fig. 9 is the amplitude Estimation result curve of the present invention's channels crosstalk coefficient of level emission vertical junction contracture amount when not having scaler error and system noise;

Figure 10 is the phase estimation result curve of the present invention's channels crosstalk coefficient of level emission vertical junction contracture amount when not having scaler error and system noise;

Figure 11 is the amplitude Estimation result curve of the present invention's transmission channel degree of unbalancedness under certain scaler error and system noise condition;

Figure 12 is the phase estimation result curve of the present invention's transmission channel degree of unbalancedness under certain scaler error and system noise condition;

Figure 13 is the present invention flushes the channels crosstalk coefficient of contracture amount at certain scaler error and the sagging straight hair jetting of system noise condition an amplitude Estimation result curve;

Figure 14 is the present invention flushes the channels crosstalk coefficient of contracture amount at certain scaler error and the sagging straight hair jetting of system noise condition a phase estimation result curve;

Figure 15 is the estimated result curve of the present invention's faraday's rotation angle under certain scaler error and system noise condition;

Figure 16 is the amplitude Estimation result curve of the present invention's receiving cable degree of unbalancedness under certain scaler error and system noise condition;

Figure 17 is the phase estimation result curve of the present invention's receiving cable degree of unbalancedness under certain scaler error and system noise condition;

Figure 18 is the amplitude Estimation result curve of the present invention's channels crosstalk coefficient of level emission vertical junction contracture amount under certain scaler error and system noise condition;

Figure 19 is the phase estimation result curve of the present invention's channels crosstalk coefficient of level emission vertical junction contracture amount under certain scaler error and system noise condition;

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention is based on π/4 patterns and condense the error model of polarization SAR, as the formula (1):

$\left[\begin{array}{c}{M}_{\mathrm{EH}}\\ M_{\mathrm{EV}}\end{array}\right]=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& {\mathrm{\&delta;}}_2\\ {\mathrm{\&delta;}}_1& {\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000056436530000021.png,HDA0000056436530000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\end{array}\right]\&CenterDot;\left[\begin{array}{cc}\cos \mathrm{\&Omega;}& \sin \mathrm{\&Omega;}\\ -\sin \mathrm{\&Omega;}& \cos \mathrm{\&Omega;}\end{array}\right]\&CenterDot;\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\cos \mathrm{\&Omega;}+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\sin \mathrm{\&Omega;}\\ -\sin \mathrm{\&Omega;}{+\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\cos \mathrm{\&Omega;}\end{array}\right]---\left(1\right)$

In the formula, M _EVAnd M _EHExpression is measured the reception vertical polarization component of Scattering of Vector and is received horizontal polarization component, S respectively _HH, S _HV, S _VH, S _VVThe scattering matrix of the matrix representation target that constitutes, emission level polarizes and receives the horizontal polarization component, launches vertical polarization and receives horizontal polarization component, emission level polarization reception vertical polarization component, emission vertical polarization reception vertical polarization component in the representing matrix respectively.Ω represents faraday's rotation angle, f ₁Expression receiving cable degree of unbalancedness, f ₂Expression transmission channel degree of unbalancedness, δ ₁The channels crosstalk coefficient of expression level emission vertical junction contracture amount, δ ₂Expression Vertical Launch level receives the channels crosstalk coefficient of component.

Four scaler that initiatively polarize that the present invention is based on are expressed as X, Y, A and B, and its scattering matrix is respectively:

$S_X=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 1& 0\end{array}\right]$

$S_Y=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]$

$S_A=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$

$S_B=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]---\left(3\right)$

The spaceborne π of a kind of long wavelength of the present invention/4 patterns are condensed the calibrating method of polarization SAR, and method flow specifically comprises following step as shown in Figure 1.

Step 1: the estimated value of obtaining the transmission channel degree of unbalancedness

Estimated value according to formula (3) and formula (4) calculating receiving cable degree of unbalancedness

In the formula, | x| is the modular arithmetic of getting plural x, and:

$\left\{\begin{array}{c}{x}_1=\frac{1}{2}[(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)+\sqrt{{(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)}^2-4(1-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}]\\ x_2=\frac{1}{2}[(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)-\sqrt{{(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)}^2-4(1-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}]\end{array}\right.---\left(4\right)$

In the formula:

The level of the scaler X Scattering of Vector that expression measures receives component,

The level of the scaler Y Scattering of Vector that expression measures receives component,

The level of the scaler A Scattering of Vector that expression measures receives component,

The level of the scaler B Scattering of Vector that expression measures receives component.

Step 2: obtain the estimated value that the Vertical Launch level receives the channels crosstalk coefficient of component

Calculate the estimated value that the Vertical Launch level receives the channels crosstalk coefficient of component according to formula (5)

${\widehat{\mathrm{\&delta;}}}_2=M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y-{\hat{f}}_2---\left(\text{5}\right)$

Step 3: the estimated value of obtaining faraday's rotation angle

Estimated value according to formula (6) and formula (7) calculating faraday rotation angle

${\widehat{\mathrm{\&Omega;}}}_F=\frac{1}{2}\arg (\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\widehat{\mathrm{\&Omega;}}}_F+j\sin 2{\widehat{\mathrm{\&Omega;}}}_F)---\left(6\right)$

In the formula, the argument computing of arg (x) for getting plural x, and

$\left\{\begin{array}{c}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\widehat{\mathrm{\&Omega;}}}_F=\mathrm{real}\left[\frac{(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)(2-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)-(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)(2{\hat{f}}_2-M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}{{(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}^2+{(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}^2}\right]\\ \sin 2{\widehat{\mathrm{\&Omega;}}}_F=\mathrm{real}\left[\frac{(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)(2-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)+(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)(2{\hat{f}}_2-M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}{{(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}^2+{(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}^2}\right]\end{array}\right.---\left(7\right)$

In the formula, the real part computing of real (x) for getting plural x.

Step 4: the TEC data of utilizing GPS (Global Position System) to provide are obtained does not have fuzzy faraday's rotation angle estimated value

For faraday's rotation angle estimated value to trying to achieve in the step 3

Angle fuzzy revise fully, the ionized layer TEC observation data of utilizing Global Navigation Satellite System (GNSS) to provide, and, try to achieve the guestimate value of faraday's rotation angle according to formula (8) in conjunction with the 10th generation international geomagnetic reference field model (IGRF10) earth magnetism computation model

${\widehat{\mathrm{\&Omega;}}}_{\mathrm{GNSS}}\&ap;\frac{\mathrm{<figure-callout\; id="0"\; label="K\; f"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">K</figure-callout>}}{f_{}^{}}\&CenterDot;{[B\cos \mathrm{\&psi;}\&CenterDot;\sec \mathrm{\&theta;}]}_{400}\&CenterDot;\mathrm{TEC}---\left(8\right)$

In the formula, f ₀The frequency of operation of expression SAR system, unit is Hz, K is a constant 2.365 * 10 ⁴Am ²/ kg, B represents earth magnetic field intensity, unit is Wb/m ², θ represents the visual angle of borne SAR, and ψ represents the angle of magnetic field of the earth direction and the radar electromagnetic wave direction of propagation (being the controlling antenna wave beam to point direction), and TEC is perpendicular to the ionosphere total electron content on the direction of ground, and unit is TECU, 1TECU=10 ¹⁶m ^-2The magnetic field of the earth factor [Bcos ψ sec θ] ₄₀₀On 400 kilometers height, calculate.

Employing formula (9) is obtained and is not had fuzzy faraday's rotation angle estimated value the ambiguity solution that carries out of faraday's rotation angle estimated value

$\widehat{\mathrm{\&Omega;}}={\widehat{\mathrm{\&Omega;}}}_F+\mathrm{round}\left(\frac{{\widehat{\mathrm{\&Omega;}}}_{\mathrm{GNSS}}-{\widehat{\mathrm{\&Omega;}}}_F}{\mathrm{\&pi;}/2}\right)\&CenterDot;\frac{\mathrm{\&pi;}}{2}---\left(9\right)$

In the formula, round (x) is for getting the immediate round values with x.

Step 5: the estimated value of obtaining the receiving cable degree of unbalancedness

Calculate the estimated value of receiving cable degree of unbalancedness according to formula (10)

${\hat{f}}_1=\frac{1}{2}[(M_{\mathrm{EV}}^X-M_{\mathrm{EV}}^Y)\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">cos</figure-callout>}2\widehat{\mathrm{\&Omega;}}-(M_{\mathrm{EV}}^A+M_{\mathrm{EV}}^B)\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">sin</figure-callout>}2\widehat{\mathrm{\&Omega;}}+(M_{\mathrm{EV}}^X+M_{\mathrm{EV}}^Y)]---\left(10\right)$

In the formula:

The vertical junction contracture amount of the scaler X Scattering of Vector that expression measures,

The vertical junction contracture amount of the scaler Y Scattering of Vector that expression measures, The vertical junction contracture amount of the scaler A Scattering of Vector that expression measures,

The vertical junction contracture amount of the scaler B Scattering of Vector that expression measures.

Step 6: the estimated value of obtaining the channels crosstalk coefficient of level emission vertical junction contracture amount

Launch the estimated value of the channels crosstalk coefficient of vertical junction contracture amount according to formula (11) calculated level

${\widehat{\mathrm{\&delta;}}}_1=\frac{1}{2}[(M_{\mathrm{EV}}^X-M_{\mathrm{EV}}^Y)\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">sin</figure-callout>}2\widehat{\mathrm{\&Omega;}}+(M_{\mathrm{EV}}^A+M_{\mathrm{EV}}^B)\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">cos</figure-callout>}2\widehat{\mathrm{\&Omega;}}+(M_{\mathrm{EV}}^A-M_{\mathrm{EV}}^B)]---\left(11\right)$

Through above six steps, finished the estimation of estimation, emission and receiving cable degree of unbalancedness error to faraday's rotation angle, and the estimation of channels crosstalk coefficient, finish π/4 patterns and condense polarization SAR calibration processing, realize calibration.

Embodiment:

The method that the present invention proposes has been carried out the emulation experiment checking.Simulating, verifying is divided into two parts, and first does not consider scaler error and system noise, has verified the present invention precise calibration result with this understanding; Second portion is considered the existence of scaler error and system noise in the actual conditions simultaneously, has verified that the present invention still has high-precision calibration result under certain scaler error and system noise.

First: do not consider scaler error and system noise

With given parameter, comprise faraday's rotation angle Ω in the emulation experiment, transmission channel degree of unbalancedness f ₂, receiving cable degree of unbalancedness f ₁, linear polarization receiving cable crosstalk coefficient δ ₁And δ ₂, and the scattering matrix of four scaler is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler in the formula (2), is expressed as respectively

Calibrate processing according to step 1 to step 6 then, be specially:

1.1 suppose the amplitude of transmission channel degree of unbalancedness | f ₂| begin to increase to 3dB from-3dB, dummy spacings is 0.1dB, carries out 61 emulation altogether.For making emulation have more generality, make the phase place arg (f of transmission channel degree of unbalancedness ₂) evenly distribute in [180 °, 180 °] (promptly in emulation each time, in this interval, get a value at random, and it being identical to get the possibility of any one value in this interval), make the amplitude of receiving cable degree of unbalancedness simultaneously | f ₁| in [3,3] dB, evenly distribute, make the phase place arg (f of receiving cable degree of unbalancedness ₁) in [180 °, 180 °], evenly distribute, make the amplitude of channels crosstalk coefficient | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute the phase place arg (δ of channels crosstalk coefficient ₁) and arg (δ ₂) in [180 °, 180 °], evenly distribute.Simultaneously, faraday's rotation angle Ω is evenly distributed in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1.At last with 61 | f ₂| estimated result be presented among Fig. 2 with the form of curve.

1.2 suppose the phase place arg (f of transmission channel degree of unbalancedness ₂) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, carries out 61 emulation altogether.Equally, make | f ₁| with | f ₂| in [3,3] dB, evenly distribute arg (f ₁) in [180 °, 180 °], evenly distribute, | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₁) and arg (δ ₂) in [180 °, 180 °], evenly distribute, Ω evenly distributes in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1.At last with 61 arg (f ₂) estimated result be presented among Fig. 3 with the form of curve.

Receive the amplitude of the channels crosstalk coefficient of component 1.3 suppose the Vertical Launch level | δ ₂| begin to increase to-10dB from-40dB, dummy spacings is 0.5dB, carries out 61 emulation altogether.Equally, make | f ₁| and | f ₂| in [3,3] dB, evenly distribute arg (f ₁) and arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₁| in [40 ,-10] dB, evenly distribute arg (δ ₁) and arg (δ ₂) in [180 °, 180 °], evenly distribute, Ω evenly distributes in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1, step 2.At last with 61 | δ ₂| estimated result be presented among Fig. 4 with the form of curve.

Receive the phase place arg (δ of the channels crosstalk coefficient of component 1.4 suppose the Vertical Launch level ₂) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, carries out 61 emulation altogether.Equally, make | f ₁| with | f ₂| in [3,3] dB, evenly distribute arg (f ₁) and arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₁) in [180 °, 180 °], evenly distribute, Ω evenly distributes in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1, step 2.At last with 61 arg (δ ₂) estimated result be presented among Fig. 5 with the form of curve.

1.5 establishing polarization SAR system works frequency is f ₀=4.35 * 10 ⁸Hz, the radar antenna visual angle is θ=23 °, constant K=2.365 * 10 ⁴Am ²/ kg.If it is on January 1st, 2008 that the SAR satellite obtains the date of data, the imaging observation zone is positioned at 0 °, and 75 ° of north latitude in above-mentioned parameter substitution IGRF10 earth magnetism computation model, can be B=4.583 * 10 in the hope of the earth magnetic field intensity on the 400 kilometers height in ground ^-5Wb/m ², angle ψ=9.28 of the magnetic direction and the radar electromagnetic wave direction of propagation °.According to CODE/GIM TEC data, TEC=9.4TECU is arranged, the formula in the substitution step 4 (8) is tried to achieve

These data can be used for the calibration of actual SAR data and handle.Consider the random meausrement error of CODE/GIM ionized layer TEC existence ± 5TECU, then can calculate faraday's rotation angle estimation error of measuring error introducing thus according to formula (8)

Formula (9) can be used for ambiguity solution as can be known, so CODE/GIM ionized layer TEC measuring error does not have influence to this ambiguity solution method.

During emulation, suppose that faraday's rotation angle Ω increases to 360 ° since 0 °, dummy spacings is 6 °, carries out 61 emulation altogether.Equally, make | f ₁| with | f ₂| in [3,3] dB, evenly distribute arg (f ₁) and arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₁) and arg (δ ₂) in [π, π], evenly distribute.In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1, step 3 and step 4.At last the estimated result of 61 the faraday's rotation angle form with curve is presented among Fig. 6.

1.6 suppose the amplitude of receiving cable degree of unbalancedness | f ₁| begin to increase to 3dB from-3dB, dummy spacings is 0.1dB, carries out 61 emulation altogether.Equally, make | f ₂| in [3,3] dB, evenly distribute arg (f ₁) and arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₁) and arg (δ ₂) in [180 °, 180 °], evenly distribute, Ω evenly distributes in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1, step 3, step 4 and step 5.At last with 61 | f ₁| estimated result be presented among Fig. 7 with the form of curve.

1.7 suppose the phase place arg (f of receiving cable degree of unbalancedness ₁) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, carries out 61 emulation altogether.Equally, make | f ₂| with | f ₁| in [3,3] dB, evenly distribute arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₁) and arg (δ ₂) in [180 °, 180 °], evenly distribute, Ω evenly distributes in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1, step 3, step 4 and step 5.At last with 61 arg (f ₁) estimated result be presented among Fig. 8 with the form of curve.

1.8 suppose the amplitude of the channels crosstalk coefficient of level emission vertical junction contracture amount | δ ₁| begin to increase to-10dB from-40dB, dummy spacings is 0.5dB, carries out 61 emulation altogether.Equally, make | f ₁| and | f ₂| in [3,3] dB, evenly distribute arg (f ₁) and arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₁) and arg (δ ₂) in [180 °, 180 °], evenly distribute, Ω evenly distributes in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1, step 3, step 4 and step 6.At last with 61 | δ ₁| estimated result be presented among Fig. 9 with the form of curve.

1.9 suppose the phase place arg (δ of the channels crosstalk coefficient of level emission vertical junction contracture amount ₁) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, carries out 61 emulation altogether.Equally, make | f ₁| with | f ₂| in [3,3] dB, evenly distribute arg (f ₁) and arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₂) in [180 °, 180 °], evenly distribute, Ω evenly distributes in [0 °, 360 °].In emulation each time, the scattering matrix of four scaler in the formula (2) is distinguished the component that substitution formula (1) is tried to achieve the measurement Scattering of Vector of four scaler, carry out simulation calculation according to step 1, step 3, step 4 and step 6.At last with 61 arg (δ ₁) estimated result be presented among Figure 10 with the form of curve.

Second portion: consider scaler error and system noise

In the reality, scaler all is imperfect (factors such as imperfect structure, antenna direction), with calibration error regard as even polarization noise (Average Polarimetric Noise, APN), the error model of the used four kinds of scaler of the present invention is provided by following formula:

$S_X^{\&prime;}=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\&delta;}}_X& {\mathrm{\&delta;}}_{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">X</figure-callout>}}^2\\ 1& {\mathrm{\&delta;}}_X\end{array}\right]$

$S_Y^{\&prime;}=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HDA0000056436530000021.png,HDA0000056436530000031.png"\; state="\{\{state\}\}">X</figure-callout>}}& 1\\ {\mathrm{\&delta;}}_{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">Y</figure-callout>}}^2& {\mathrm{\&delta;}}_Y\end{array}\right]$

$S_A^{\&prime;}=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}1& {\mathrm{\&delta;}}_A\\ {\mathrm{\&delta;}}_A& {\mathrm{\&delta;}}_A^2\end{array}\right]$

$S_B^{\&prime;}=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">B</figure-callout>}}^2& {\mathrm{\&delta;}}_B\\ {\mathrm{\&delta;}}_B& 1\end{array}\right]---\left(12\right)$

In the formula, δ _A, δ _B, δ _XAnd δ _YRepresent the error (APN) of each scaler, be plural form.In the emulation of this part, suppose | δ _A|=| δ _B|=| δ _X|=| δ _Y|=APN=-42dB, and hypothesis phase place arg (δ _A), arg (δ _B), arg (δ _X) and arg (δ _Y) in [180 °, 180 °], evenly distribute.

Simultaneously, system noise is measured with signal to noise ratio (snr).This moment, π/4 patterns were condensed the error model of polarization, and promptly formula (1) should be rewritten as:

$\left[\begin{array}{c}{M}_{\mathrm{EH}}\\ M_{\mathrm{EV}}\end{array}\right]=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& {\mathrm{\&delta;}}_2\\ {\mathrm{\&delta;}}_1& {\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000056436530000021.png,HDA0000056436530000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\end{array}\right]\&CenterDot;\left[\begin{array}{cc}\cos \mathrm{\&Omega;}& \sin \mathrm{\&Omega;}\\ -\sin \mathrm{\&Omega;}& \cos \mathrm{\&Omega;}\end{array}\right]\&CenterDot;\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\cos \mathrm{\&Omega;}+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\sin \mathrm{\&Omega;}\\ -\sin \mathrm{\&Omega;}{+\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000056436530000021.png,HDA0000056436530000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\cos \mathrm{\&Omega;}\end{array}\right]+\left[\begin{array}{c}{N}_H\\ N_V\end{array}\right]---\left(13\right)$

In the formula, N _H, N _VFor measuring the additivity complex noise in the matrix.In the emulation of this part, suppose phase place arg (N _H) and arg (N _V) in [180 °, 180 °], evenly distribute, and supposing the system signal to noise ratio snr=50dB.

In the emulation of this part,, comprise faraday's rotation angle Ω, transmission channel degree of unbalancedness f earlier according to given parameter ₂, receiving cable degree of unbalancedness f ₁, linear polarization receiving cable crosstalk coefficient δ ₁And δ ₂, press formula (12), formula (1) and following formula:

$\left\{\begin{array}{c}{N}_H=-50\mathrm{dB}\&CenterDot;\left|M_{\mathrm{EH}}\right|\&CenterDot;e^{j\&CenterDot;\arg \left(N_H\right)}\\ N_V=-50\mathrm{dB}\&CenterDot;\left|M_{\mathrm{EV}}\right|\&CenterDot;e^{j\&CenterDot;\arg \left(N_V\right)}\end{array}\right.---\left(14\right)$

Obtain

(representing respectively to measure additivity complex noise on vector) by each scaler that is added in that following formula is determined.Error model with four scaler scattering matrixes in the formula (12) reaches then

Substitution formula (13) is tried to achieve the component of the measurement Scattering of Vector of four scaler, is expressed as respectively

Calibrate processing according to step 1 to step 6 at last, be specially:

2.1 suppose the amplitude of transmission channel degree of unbalancedness | f ₂| begin to increase to 3dB from-3dB, dummy spacings is 0.1dB, and other parameters are carried out 61 emulation altogether with 1.1.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1 then.At last with 61 | f ₂| estimated result be presented among Figure 11 with the form of curve.

2.2 suppose the phase place arg (f of transmission channel degree of unbalancedness ₂) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, other parameters are carried out 61 emulation altogether with 1.2.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1 then.At last with 61 arg (f ₂) estimated result be presented among Figure 12 with the form of curve.

Receive the amplitude of the channels crosstalk coefficient of component 2.3 suppose the Vertical Launch level | δ ₂| begin to increase to-10dB from-40dB, dummy spacings is 0.5dB, and other parameters are carried out 61 emulation altogether with 1.3.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1, step 2 then.At last with 61 | δ ₂| estimated result be presented among Figure 13 with the form of curve.

Receive the phase place arg (δ of the channels crosstalk coefficient of component 2.4 suppose the Vertical Launch level ₂) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, other parameters are carried out 61 emulation altogether with 1.4.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1, step 2 then.At last with 61 arg (δ ₂) estimated result be presented among Figure 14 with the form of curve.

Increase to 360 ° 2.5 suppose faraday's rotation angle Ω since 0 °, dummy spacings is 6 °, and other parameters are carried out 61 emulation altogether with 1.5.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1, step 3 and step 4 then.At last the estimated result of 61 the faraday's rotation angle form with curve is presented among Figure 15.

2.6 suppose the amplitude of receiving cable degree of unbalancedness | f ₁| begin to increase to 3dB from-3dB, dummy spacings is 0.1dB, and other parameters are carried out 61 emulation altogether with 1.6.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1, step 3, step 4 and step 5 then.At last with 61 | f ₁| estimated result be presented among Figure 16 with the form of curve.

2.7 suppose the phase place arg (f of receiving cable degree of unbalancedness ₁) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, other parameters are carried out 61 emulation altogether with 1.7.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1, step 3, step 4 and step 5 then.At last with 61 arg (f ₁) estimated result be presented among Figure 17 with the form of curve.

2.8 suppose the amplitude of the channels crosstalk coefficient of level emission vertical junction contracture amount | δ ₁| begin to increase to-10dB from-40dB, dummy spacings is 0.5dB, and other parameters are carried out 61 emulation altogether with 1.8.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1, step 3, step 4 and step 6 then.At last with 61 | δ ₁| estimated result be presented among Figure 18 with the form of curve.

2.9 suppose the phase place arg (δ of the channels crosstalk coefficient of level emission vertical junction contracture amount ₁) beginning to increase to 180 ° from-180 °, dummy spacings is 6 °, other parameters are carried out 61 emulation altogether with 1.9.In emulation each time, obtain by formula (12), formula (1) and formula (14)

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1, step 3, step 4 and step 6 then.At last with 61 arg (δ ₁) estimated result be presented among Figure 19 with the form of curve.

2.10 carry out simulation calculation with Meng Te-Carlow method, simulation times is 100000 times.In the Meng Te that carries out-Carlow emulation, suppose | f ₁| with | f ₂| in [3,3] dB, evenly distribute arg (f ₁) and arg (f ₂) in [180 °, 180 °], evenly distribute, | δ ₁| and | δ ₂| in [40 ,-10] dB, evenly distribute arg (δ ₁) and arg (δ ₂) in [π, π], evenly distribute, Ω evenly distributes in [0 °, 360 °].Right back-pushed-type (12), formula (1) and formula (14) are obtained

The component that the error model of four scaler scattering matrixes difference substitution formula (13) is tried to achieve the measurement Scattering of Vector of four scaler in the cotype (12) carries out simulation calculation according to step 1 to step 6 again.Table 1 has provided 100000 simulation calculation results' the average of calibration error of faraday's rotation angle Ω and standard deviation, passage degree of unbalancedness f ₁And f ₂The average of amplitude calibration sum of errors phase place calibration error and standard deviation, channels crosstalk coefficient δ ₁And δ ₂The average and the standard deviation of amplitude calibration sum of errors phase place calibration error.

Table 1

The method that above-mentioned two parts emulation experiment explanation the present invention proposes is that the spaceborne π of simple, the high-precision long wavelength of a kind of treatment scheme/4 patterns are condensed the calibrating method of polarization SAR.

Claims (1)

1. the spaceborne π of long wavelength/4 patterns are condensed the calibrating method of polarization SAR, condense the error model of polarization SAR based on π/4 patterns, model as the formula (1):

$\left[\begin{array}{c}{M}_{\mathrm{EH}}\\ M_{\mathrm{EV}}\end{array}\right]=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& {\mathrm{\&delta;}}_2\\ {\mathrm{\&delta;}}_1& f_1\end{array}\right]\&CenterDot;\left[\begin{array}{cc}\cos \mathrm{\&Omega;}& \sin \mathrm{\&Omega;}\\ -\sin \mathrm{\&Omega;}& \cos \mathrm{\&Omega;}\end{array}\right]\&CenterDot;\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\cos \mathrm{\&Omega;}+f_2\sin \mathrm{\&Omega;}\\ -\sin \mathrm{\&Omega;}{+f}_2\cos \mathrm{\&Omega;}\end{array}\right]---\left(1\right)$

In the formula, M _EVAnd M _EHExpression is measured the reception vertical polarization component of Scattering of Vector and is received horizontal polarization component, S respectively _HH, S _HV, S _VH, S _VVThe scattering matrix of the matrix representation target that constitutes, emission level polarizes and receives the horizontal polarization component, launches vertical polarization and receives horizontal polarization component, emission level polarization reception vertical polarization component, emission vertical polarization reception vertical polarization component in the representing matrix respectively; Ω represents faraday's rotation angle, f ₁Expression receiving cable degree of unbalancedness, f ₂Expression transmission channel degree of unbalancedness, δ ₁The channels crosstalk coefficient of expression level emission vertical junction contracture amount, δ ₂Expression Vertical Launch level receives the channels crosstalk coefficient of component;

Four scaler that initiatively polarize are expressed as X, Y, A and B, and its scattering matrix is respectively:

$S_X=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 1& 0\end{array}\right]$

$S_Y=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]$

$S_A=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$

$S_B=\left[\begin{array}{cc}{S}_{\mathrm{HH}}& S_{\mathrm{HV}}\\ S_{\mathrm{VH}}& S_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]---\left(2\right)$

It is characterized in that, specifically comprise following step;

Step 1: the estimated value of obtaining the transmission channel degree of unbalancedness

Estimated value according to formula (3) and formula (4) calculating receiving cable degree of unbalancedness

In the formula, | x| is the modular arithmetic of getting plural x, and:

$\left\{\begin{array}{c}{x}_1=\frac{1}{2}[(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)+\sqrt{{(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)}^2-4(1-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}]\\ x_2=\frac{1}{2}[(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)-\sqrt{{(M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y)}^2-4(1-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}]\end{array}\right.---\left(4\right)$

In the formula:

The level of the scaler X Scattering of Vector that expression measures receives component,

The level of the scaler Y Scattering of Vector that expression measures receives component, The level of the scaler A Scattering of Vector that expression measures receives component,

The level of the scaler B Scattering of Vector that expression measures receives component;

Step 2: obtain the estimated value that the Vertical Launch level receives the channels crosstalk coefficient of component

Calculate the estimated value that the Vertical Launch level receives the channels crosstalk coefficient of component according to formula (5)

${\widehat{\mathrm{\&delta;}}}_2=M_{\mathrm{EH}}^X+M_{\mathrm{EH}}^Y-{\hat{f}}_2---\left(\text{5}\right)$

Step 3: the estimated value of obtaining faraday's rotation angle

Estimated value according to formula (6) and formula (7) calculating faraday rotation angle

${\widehat{\mathrm{\&Omega;}}}_F=\frac{1}{2}\arg (\cos 2{\widehat{\mathrm{\&Omega;}}}_F+j\sin 2{\widehat{\mathrm{\&Omega;}}}_F)---\left(6\right)$

In the formula, the argument computing of arg (x) for getting plural x, and

$\left\{\begin{array}{c}\cos 2{\widehat{\mathrm{\&Omega;}}}_F=\mathrm{real}\left[\frac{(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)(2-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)-(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)(2{\hat{f}}_2-M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}{{(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}^2+{(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}^2}\right]\\ \sin 2{\widehat{\mathrm{\&Omega;}}}_F=\mathrm{real}\left[\frac{(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)(2-M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)+(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)(2{\hat{f}}_2-M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}{{(M_{\mathrm{EH}}^A+M_{\mathrm{EH}}^B)}^2+{(M_{\mathrm{EH}}^X-M_{\mathrm{EH}}^Y)}^2}\right]\end{array}\right.---\left(7\right)$

In the formula, the real part computing of real (x) for getting plural x;

Step 4: the TEC data of utilizing GPS (Global Position System) to provide are obtained does not have fuzzy faraday's rotation angle estimated value

The ionized layer TEC observation data of utilizing GLONASS (Global Navigation Satellite System) to provide, and in conjunction with the 10th generation international geomagnetic reference field model earth magnetism computation model, try to achieve the guestimate value of faraday's rotation angle according to formula (8)

${\widehat{\mathrm{\&Omega;}}}_{\mathrm{GNSS}}\&ap;\frac{K}{f_0^2}\&CenterDot;{[B\cos \mathrm{\&psi;}\&CenterDot;\sec \mathrm{\&theta;}]}_{400}\&CenterDot;\mathrm{TEC}---\left(8\right)$

In the formula, f ₀The frequency of operation of expression SAR system, unit is Hz, K is a constant 2.365 * 10 ⁴Am ²/ kg, B represents earth magnetic field intensity, unit is Wb/m ², θ represents the visual angle of borne SAR, and ψ represents the angle of the magnetic field of the earth direction and the radar electromagnetic wave direction of propagation, and TEC is perpendicular to the ionosphere total electron content on the direction of ground, and unit is TECU, 1TECU=10 ¹⁶m ^-2The magnetic field of the earth factor [Bcos ψ sec θ] ₄₀₀On 400 kilometers height, calculate;

Employing formula (9) is obtained and is not had fuzzy faraday's rotation angle estimated value the ambiguity solution that carries out of faraday's rotation angle estimated value

$\widehat{\mathrm{\&Omega;}}={\widehat{\mathrm{\&Omega;}}}_F+\mathrm{round}\left(\frac{{\widehat{\mathrm{\&Omega;}}}_{\mathrm{GNSS}}-{\widehat{\mathrm{\&Omega;}}}_F}{\mathrm{\&pi;}/2}\right)\&CenterDot;\frac{\mathrm{\&pi;}}{2}---\left(9\right)$

In the formula, round (x) is for getting the immediate round values with x;

Step 5: the estimated value of obtaining the receiving cable degree of unbalancedness

Calculate the estimated value of receiving cable degree of unbalancedness according to formula (10)

${\hat{f}}_1=\frac{1}{2}[(M_{\mathrm{EV}}^X-M_{\mathrm{EV}}^Y)\cos 2\widehat{\mathrm{\&Omega;}}-(M_{\mathrm{EV}}^A+M_{\mathrm{EV}}^B)\sin 2\widehat{\mathrm{\&Omega;}}+(M_{\mathrm{EV}}^A+M_{\mathrm{EV}}^B)]---\left(10\right)$

In the formula:

The vertical junction contracture amount of the scaler X Scattering of Vector that expression measures,

The vertical junction contracture amount of the scaler Y Scattering of Vector that expression measures,

The vertical junction contracture amount of the scaler A Scattering of Vector that expression measures,

The vertical junction contracture amount of the scaler B Scattering of Vector that expression measures;

Step 6: the estimated value of obtaining the channels crosstalk coefficient of level emission vertical junction contracture amount

Launch the estimated value of the channels crosstalk coefficient of vertical junction contracture amount according to formula (11) calculated level

${\widehat{\mathrm{\&delta;}}}_1=\frac{1}{2}[(M_{\mathrm{EV}}^X-M_{\mathrm{EV}}^Y)\sin 2\widehat{\mathrm{\&Omega;}}+(M_{\mathrm{EV}}^A+M_{\mathrm{EV}}^B)\cos 2\widehat{\mathrm{\&Omega;}}+(M_{\mathrm{EV}}^A-M_{\mathrm{EV}}^B)]---\left(11\right)$

Through above six steps, finished the estimation of estimation, emission and receiving cable degree of unbalancedness error to faraday's rotation angle, and the estimation of channels crosstalk coefficient, finish π/4 patterns and condense polarization SAR calibration processing, realize calibration.

Images