CN110261853B - Calibration processing method and device for polarized synthetic aperture radar - Google Patents
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Abstract
The embodiment of the invention discloses a calibration processing method and a calibration processing device for a polarization synthetic aperture radar. The method comprises the steps of obtaining a plurality of single-view complex data, a plurality of image auxiliary data and multi-class scaler information of four channels of the polarized synthetic aperture radar, wherein the four channels are four polarized channels of hh, hv, vh and vv; establishing a polarized synthetic aperture radar calibration model according to the single-view complex data, the image auxiliary data and the multi-class calibrator information; preprocessing the model to obtain a calibration parameter matrix; establishing an error equation to solve a calibration parameter matrix based on a Newton iteration method of a least square principle, and reducing the influence of accidental error factors on the estimation of calibration parameters; when the termination condition of the scaling parameter matrix calculation is reached, the scaling parameter estimation value with reduced accidental error is obtained. The method reduces the influence of accidental error factors on the calculation of the calibration parameter matrix, obtains the calibration parameter estimated value with reduced accidental errors, can obtain a high-precision calibration processing result, and has better practicability.
Description
Technical Field
The invention relates to the field of Synthetic Aperture Radar (SAR) calibration, in particular to a calibration processing method and a calibration processing device of a polarization SAR.
Background
Synthetic Aperture Radar (SAR) realizes high-resolution microwave imaging by utilizing a synthetic aperture principle, has various characteristics of all-weather, high resolution, large breadth and the like, has the appearance of synthetic aperture radars carried by various types of platforms such as missile-borne, foundation SAR, unmanned aerial vehicle SAR, near space platform SAR, handheld equipment and the like along with the technical development, and is widely applied to the fields of military and civil use.
The performance limitation of the synthetic aperture radar system causes that the obtained polarization data information is often different from the ground feature real information to a certain extent, which greatly limits the application potential and the prospect of the polarization SAR data. The polarization SAR calibration is to solve the problem of polarization distortion between polarization channels by utilizing the mutual relation between a backscattering matrix and ground characteristic points.
However, although a better mathematical model is adopted in the point target polarization synthetic aperture radar calibration method at present, the influence of accidental error factors in the calibration parameter matrix calculation process is ignored, so that the accuracy of the calculated calibration parameter estimated value is influenced, and finally the accuracy of the calibration processing result is not high, and the practicability is poor.
Disclosure of Invention
In order to overcome at least one defect in the prior art, the invention provides a calibration processing method and a device of a polarization synthetic aperture radar.
As a first aspect of the present invention, the present invention discloses a calibration processing method for a polarization synthetic aperture radar, including:
acquiring a plurality of single-view complex data, a plurality of image auxiliary data and multi-class scaler information of four channels of a polarized synthetic aperture radar, wherein the four channels are four polarized channels of hh, hv, vh and vv;
establishing a polarized synthetic aperture radar calibration model according to the single-view complex data, the image auxiliary data and the multi-class calibrator information;
preprocessing the model to obtain a calibration parameter matrix;
establishing an error equation to solve the calibration parameter matrix based on a Newton iteration method of a least square principle, and reducing the influence of accidental error factors on the calibration parameter estimation;
and obtaining the scaling parameter estimation value with reduced accidental errors after the end condition of the scaling parameter matrix calculation is reached.
In a possible implementation, the establishing a polar synthetic aperture radar calibration model according to the plurality of single-view complex data, the plurality of image auxiliary data and the multi-class scaler information specifically includes:
extracting a theoretical polarization scattering matrix S of the polarized synthetic aperture radar according to the acquired single-view complex data, the image auxiliary data and the multi-class scaler information, wherein the theoretical polarization scattering matrix S is expressed as:
the multi-class scaler comprises a multi-class corner reflector, and theoretical polarization scattering matrixes of the various scalers are expressed as follows according to the various types of the multi-class scaler:
wherein, the i is a scaler type, the hh is a horizontal transmitting and horizontal receiving channel, the hv is a horizontal transmitting and vertical receiving channel, the vh is a vertical transmitting and horizontal receiving channel, and the vv is a vertical transmitting and vertical receiving channel;
extracting images of the multi-class scaler, and calculating the backscattering sectional areas of the multi-class corner reflectors in the images;
performing radiation correction and registration on the images of the multi-class calibrator according to the backscattering sectional areas of the multi-class corner reflectors;
establishing a calibration model of the polarized synthetic aperture radar, wherein the formula of the model is formula 1:
equation 1O is RST + N,
wherein, O is a polarization scattering matrix actually measured, S is a theoretical polarization scattering matrix, R is a receiving end distortion matrix, T is a transmitting end distortion matrix, and N is a background noise matrix;
rewriting the formula of the polarization synthetic aperture radar calibration model into a matrix form to obtain a formula 2:
equation 2
The receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements which are unknown.
In a possible implementation manner, the preprocessing the model to obtain a scaling parameter matrix specifically includes:
ignoring the background noise matrix, vectorizing the matrix form of the polarization synthetic aperture radar scaling model to obtain a vector form of the polarization synthetic aperture radar scaling model, and finishing the vector form of the polarization synthetic aperture radar scaling model to obtain a formula 3:
equation 3
Assigning values of elements of a scaling parameter matrix composed of the receiving end distortion matrix R and the transmitting end distortion matrix T to a matrix l, where the matrix l is the scaling parameter matrix, and the matrix l is expressed as formula 4:
equation 4
According to the receiving end distortion matrix R and the transmitting end distortion momentFour elements in the array T are unknown, and the theoretical scattering matrix S of the i-th type scaler is usediRespectively according to formula 3 to obtain only R in sixteen parameters of matrix lvvTvv、RhhThh、RvvTvh、RvhThh、RvvThh、RhvTvv、RhhThvAnd RhhTvvThese eight parameters correspond to the values O of the actually measured polarization scattering matrix of the i-th scaleriRegarding and being independent parameters, the remaining eight parameters are dependent parameters that can be represented by the eight independent parameters of the matrix i, which is expressed as formula 5 according to the formula 3 and the formula 4:
equation 5
According to the formula 3, the formula 4 and the formula 5, the eight non-independent parameters in the matrix l are expressed by the eight independent parameters, so that a formula 6 is obtained:
equation 6
Substituting the formulas 5 and 6 into the formula 3 to obtain a formula 7:
equation 7
In a possible implementation manner, the newton iteration method based on the least square principle establishes an error equation to solve the scaling parameter matrix, and reduces the influence of accidental error factors on the scaling parameter estimation, specifically including:
step a, the ith theoretical polarization scattering matrix SiAnd the corresponding i-th actual measurement polarization scattering matrix OiSubstituting said formula 7 to obtain formula 8:
equation 8
Wherein, OivvActual measurement values, O, representing the vertical co-polarization of the i-th type scalerihhActual measurement values, O, representing horizontal co-polarization of the i-th scalerivhRepresenting the actual measurement of cross-polarization received by the i-th scaler vertical transmission horizontal reception, OihvRepresenting the cross polarization actual measurement value of the horizontal transmission and vertical reception of the ith type scaler; sivvTheoretical value, S, representing vertical co-polarization of class i scalerihhTheoretical value, S, representing horizontal co-polarization of class i scalerivhRepresenting the theoretical value of cross-polarization, S, received horizontally by the vertical transmission of the i-th scalerihvRepresenting the theoretical value of cross polarization of horizontal transmission and vertical reception of the ith type scaler;
the i equation sets in the formula 8 are solved simultaneously to obtain the initial value l of the matrix l0The initial value l0Is formula 9:
equation 9
Wherein the content of the first and second substances,
representation matrix
Transposing;
the initial value l is measured0And the i-th theoretical polarization scattering matrix SiSubstituting said formula 7 to obtain formula 10:
equation 10
Wherein the content of the first and second substances,
polarization scattering matrix O for class i actual measurementiIs set to the initial value of (a),
representation matrix
Transposing;
step b, linearizing the formula 7, and establishing an error equation, wherein the formula of the error mode is formula 11:
formula 11V ═ B Δ l- α,
wherein V represents the difference between the actual measured value and the true value,
a matrix of coefficients is represented by a matrix of coefficients,
representing the difference between the actual measured value and the initial value, OiDenotes the actual measured value,. DELTA.l-l0Expressing the correction amount, the formula 11 is rewritten to obtain the formula 12:
equation 12
Step c, obtaining a formula 13 according to the formula 12, wherein the formula 13 is an error formula V1vv、V1hh、V1vh、V1hv、V2vv、V2hh、V2vh、V2hv、V3vv、V3hh、V3hh、V3vhThe matrix expression of (c):
equation 13
Calculating the correction quantity delta l of the matrix l according to the formula 12 to obtain a formula 14:
equation 14 Δ l ═ BTB)-1BTα，
Wherein, BTRepresents a transpose of B;
the initial value l is measured0、
And said actual measured value OiSubstituting said equation 13, we get equation 15:
equation 15
Wherein the content of the first and second substances,
representation matrix
Transposing;
d, adding the formula 9 and the formula 15 to obtain l1Equation 16:
equation 16 l1＝l0+Δl1，
Similarly, equation 17 is obtained:
equation 17 ln+1＝ln+Δln+1，
Wherein n is the number of iterations;
and e, carrying out iterative calculation on the steps a, b, c and d.
In a possible embodiment, the termination condition is that the calculation is terminated when the correction Δ l is smaller than a preset threshold, and the formula of the scaled parameter estimation is formula 18:
equation 18 l ═ l11 l22 l31 l32 l33 l41 l42 l44)。
As a second aspect of the present invention, the present invention discloses a scaling processing apparatus for a polarization synthetic aperture radar, comprising:
the system comprises an acquisition module, a calibration module and a calibration module, wherein the acquisition module is used for acquiring a plurality of single-view complex data, a plurality of image auxiliary data and multi-class calibrator information of four channels of the polarized synthetic aperture radar, and the four channels are four polarized channels of hh, hv, vh and vv;
the model establishing module is used for establishing a polarized synthetic aperture radar calibration model according to the single-view complex data, the image auxiliary data and the multi-class calibrator information;
the model preprocessing module is used for preprocessing the model to obtain a calibration parameter matrix;
the first processing module is used for establishing an error equation to solve the calibration parameter matrix based on a Newton iteration method of the least square principle, and reducing the influence of accidental error factors on the calibration parameter estimation;
and the second processing module is used for obtaining the calibration parameter estimation value with reduced accidental errors after the terminal condition of the calibration parameter matrix calculation is reached.
In a possible implementation, the establishing a polar synthetic aperture radar calibration model according to the plurality of single-view complex data, the plurality of image auxiliary data and the multi-class scaler information specifically includes:
a first processing unit, configured to extract a theoretical polarization scattering matrix S of the polar synthetic aperture radar according to the acquired single-view complex data, image auxiliary data, and multi-class scaler information, where the theoretical polarization scattering matrix S is expressed as:
the multi-class scaler comprises a multi-class corner reflector, and theoretical polarization scattering matrixes of the various scalers are expressed as follows according to the various types of the multi-class scaler:
wherein, i is a scaler type, hh is a horizontal transmitting and horizontal receiving channel, hv is a horizontal transmitting and vertical receiving channel, vh is a vertical transmitting and horizontal receiving channel, andvv is a vertical transmitting and vertical receiving channel;
the second processing unit is used for extracting the images of the multi-class scaler and calculating the backscattering sectional areas of the multi-class corner reflectors in the images;
the third processing unit is used for carrying out radiation correction and registration on the images of the multi-class scaler according to the backscattering sectional areas of the multi-class corner reflectors;
a fourth processing unit, configured to establish a calibration model of the polar synthetic aperture radar, where the formula of the model is formula 1:
equation 1O is RST + N,
wherein, O is a polarization scattering matrix actually measured, S is a theoretical polarization scattering matrix, R is a receiving end distortion matrix, T is a transmitting end distortion matrix, and N is a background noise matrix;
a fifth processing unit, configured to rewrite a formula of the calibration model of the polar synthetic aperture radar to a matrix form, to obtain a formula 2:
equation 2
The receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements which are unknown.
In a possible implementation manner, the preprocessing the model to obtain a scaling parameter matrix specifically includes:
ignoring the background noise matrix, vectorizing the matrix form of the polarization synthetic aperture radar scaling model to obtain a vector form of the polarization synthetic aperture radar scaling model, and finishing the vector form of the polarization synthetic aperture radar scaling model to obtain a formula 3:
equation 3
Assigning values of elements of a scaling parameter matrix composed of the receiving end distortion matrix R and the transmitting end distortion matrix T to a matrix l, where the matrix l is the scaling parameter matrix, and the matrix l is expressed as formula 4:
equation 4
According to the fact that the receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements and are unknown, the theoretical scattering matrix S of the i-th type scaler is usediRespectively according to formula 3 to obtain only R in sixteen parameters of matrix lvvTvv、RhhThh、RvvTvh、RvhThh、RvvThh、RhvTvv、RhhThvAnd RhhTvvThese eight parameters correspond to the values O of the actually measured polarization scattering matrix of the i-th scaleriRegarding and being independent parameters, the remaining eight parameters are dependent parameters that can be represented by the eight independent parameters of the matrix i, which is expressed as formula 5 according to the formula 3 and the formula 4:
equation 5
According to the formula 3, the formula 4 and the formula 5, the eight non-independent parameters in the matrix l are expressed by the eight independent parameters, so that a formula 6 is obtained:
equation 6
Substituting the formulas 5 and 6 into the formula 3 to obtain a formula 7:
equation 7
In a possible implementation manner, the newton iteration method based on the least square principle establishes an error equation to solve the scaling parameter matrix, and reduces the influence of accidental error factors on the scaling parameter estimation, specifically including:
step a, the ith theoretical polarization scattering matrix SiAnd the corresponding i-th actual measurement polarization scattering matrix OiSubstituting said formula 7 to obtain formula 8:
equation 8
Wherein, OivvActual measurement values, O, representing the vertical co-polarization of the i-th type scalerihhActual measurement values, O, representing horizontal co-polarization of the i-th scalerivhRepresenting the actual measurement of cross-polarization received by the i-th scaler vertical transmission horizontal reception, OihvRepresenting the cross polarization actual measurement value of the horizontal transmission and vertical reception of the ith type scaler; sivvTheoretical value, S, representing vertical co-polarization of class i scalerihhTheoretical value, S, representing horizontal co-polarization of class i scalerivhRepresenting the theoretical value of cross-polarization, S, received horizontally by the vertical transmission of the i-th scalerihvRepresenting the theoretical value of cross polarization of horizontal transmission and vertical reception of the ith type scaler;
the i equation sets in the formula 8 are solved simultaneously to obtain the initial value l of the matrix l0The initial value l0Is formula 9:
equation 9
Wherein the content of the first and second substances,
representation matrix
Transposing;
the initial value l is measured0And the i-th theoretical polarization scattering matrix SiSubstituting said formula 7 to obtain formula 10:
equation 10
Wherein the content of the first and second substances,
polarization scattering matrix O for class i actual measurementiIs set to the initial value of (a),
representation matrix
Transposing;
step b, linearizing the formula 7, and establishing an error equation, wherein the formula of the error mode is formula 11:
formula 11V ═ B Δ l- α,
wherein V represents the difference between the actual measured value and the true value,
a matrix of coefficients is represented by a matrix of coefficients,
representing the difference between the actual measured value and the initial value, OiDenotes the actual measured value,. DELTA.l-l0Expressing the correction amount, the formula 11 is rewritten to obtain the formula 12:
equation 12
Step c, obtaining a formula 13 according to the formula 12, wherein the formula 13 is an error formula V1vv、V1hh、V1vh、V1hv、V2vv、V2hh、V2vh、V2hv、V3vv、V3hh、V3hh、V3vhThe matrix expression of (c):
equation 13
Solving the correction quantity delta l of the matrix l according to the formula 13 to obtain a formula 14:
equation 14 Δ l ═ BTB)-1BTα，
Wherein, BTRepresents a transpose of B;
the initial value l is measured0、
And said actual measured value OiSubstituting said equation 13, we get equation 15:
equation 15
Wherein the content of the first and second substances,
representation matrix
Transposing;
d, adding the formula 9 and the formula 15 to obtain l1Equation 16:
equation 16 l1＝l0+Δl1，
Similarly, equation 17 is obtained:
equation 17 ln+1＝ln+Δln+1，
Wherein n is the number of iterations;
and e, carrying out iterative calculation on the steps a, b, c and d.
In a possible embodiment, the termination condition is that the calculation is terminated when the correction Δ l is smaller than a preset threshold, and the formula of the scaled parameter estimation is formula 18:
equation 18 l ═ l11 l22 l31 l32 l33 l41 l42 l44)。
The calibration processing method and the device for the polarimetric synthetic aperture radar have the following beneficial effects that:
the method comprises the steps of establishing a polarized synthetic aperture radar calibration model by obtaining a plurality of single-view complex number data, a plurality of image auxiliary data and multi-class calibrator information of four channels of the polarized synthetic aperture radar, preprocessing the model to obtain a calibration parameter matrix, establishing an error equation to solve the calibration parameter matrix based on a Newton iteration method of the least square principle, reducing the influence of accidental error factors on the estimation value of the calibration parameter, and obtaining the calibration parameter estimation value with reduced accidental errors after the termination condition of the calculation of the calibration parameter matrix is reached, so that a high-precision calibration processing result can be obtained.
Drawings
The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining and illustrating the present invention and should not be construed as limiting the scope of the present invention.
Fig. 1 is a flowchart of a calibration processing method of a polarized synthetic aperture radar according to a first embodiment of the present invention;
fig. 2 is a schematic structural diagram of a scaling processing apparatus for a polar synthetic aperture radar according to a second embodiment of the present invention.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the present invention is described in more detail below with reference to the accompanying drawings and examples.
It should be noted that: the embodiments described are some embodiments of the present invention, not all embodiments, and features in embodiments and embodiments in the present application may be combined with each other without conflict. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In this document, "first", "second", "third", "fourth", "fifth", etc. are used only for distinguishing one from another, and do not indicate their degree of importance, order, etc.
The division of the modules and units herein is only one division of logical functions, and other divisions may be possible in actual implementation, for example, a plurality of modules and/or units may be combined or integrated in another system. The modules and units described as separate parts may be physically separated or not. Therefore, some or all of the units can be selected according to actual needs to implement the scheme of the embodiment.
A first embodiment of the scaling processing method for a polar synthetic aperture radar according to the present invention is described in detail below with reference to fig. 1: the embodiment is mainly applied to the calibration processing of the polarized synthetic aperture radar.
As shown in the figure, the calibration processing method for the polar synthetic aperture radar provided in this embodiment includes:
102, establishing a polarized synthetic aperture radar calibration model according to the single-view complex data, the image auxiliary data and the multi-class calibrator information; the establishing of the calibration model of the polarized synthetic aperture radar according to the multiple single-view complex data, the multiple image auxiliary data and the multiple types of calibrator information specifically comprises:
extracting a theoretical polarization scattering matrix S of the polarized synthetic aperture radar according to the acquired single-view complex data, the image auxiliary data and the multi-class scaler information, wherein the theoretical polarization scattering matrix S is expressed as:
the multi-class scaler comprises a multi-class corner reflector, and theoretical polarization scattering matrixes of the various scalers are expressed as follows according to the various types of the multi-class scaler:
wherein, the i is a scaler type, the hh is a horizontal transmitting and horizontal receiving channel, the hv is a horizontal transmitting and vertical receiving channel, the vh is a vertical transmitting and horizontal receiving channel, and the vv is a vertical transmitting and vertical receiving channel; the multi-type corner reflectors comprise at least three types of corner reflectors, wherein the preferred three types of corner reflectors are as follows: a dihedral corner reflector, a 0 ° dihedral corner reflector, and a 45 ° dihedral corner reflector; four types of corner reflectors can be adopted, and higher accuracy can be obtained by adopting the calibration processing of the four types of corner reflectors;
extracting images of the multi-class scaler, and calculating the backscattering sectional areas of the multi-class corner reflectors in the images;
performing radiation correction and registration on the images of the multi-class calibrator according to the backscattering sectional areas of the multi-class corner reflectors; the images of the various calibrators are subjected to radiation correction according to the backscattering sectional areas of the various corner reflectors, so that the image distortion caused by radiation errors can be eliminated or corrected, the images can be better close to original scenes, and the probability of error results is reduced; the registration comprises the steps of extracting features of a plurality of images to obtain feature points, and finding matched feature point pairs by carrying out similarity measurement on the feature points; obtaining image space coordinate transformation parameters through the matched feature point pairs, and carrying out image registration according to the coordinate transformation parameters;
establishing a calibration model of the polarized synthetic aperture radar, wherein the formula of the model is formula 1:
equation 1O is RST + N,
wherein, O is a polarization scattering matrix actually measured, S is a theoretical polarization scattering matrix, R is a receiving end distortion matrix, T is a transmitting end distortion matrix, and N is a background noise matrix;
rewriting the formula of the polarization synthetic aperture radar calibration model into a matrix form to obtain a formula 2:
equation 2
The receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements which are unknown;
103, preprocessing the model to obtain a calibration parameter matrix;
104, establishing an error equation to solve the calibration parameter matrix based on a Newton iteration method of a least square principle, and reducing the influence of accidental error factors on the calibration parameter estimation;
and 105, obtaining the scaling parameter estimation value with reduced accidental errors after the termination condition of the scaling parameter matrix calculation is reached.
The least square principle is greatly influenced by measurement accidental errors, the calibration processing precision requirement is difficult to meet, the Newton iteration method has the characteristic of high convergence rate, whether the Newton iteration method converges or not and the convergence rate is related to the selection of the initial value of the Newton iteration method, and if the initial value is set artificially, the Newton iteration method can be caused to be not converged. The least square principle is combined with the Newton iteration method, namely the Newton iteration method based on the least square principle can combine the advantages of good estimation performance of the least square principle and high convergence speed of the Newton iteration method, the estimation value obtained by the least square principle is used as the initial value of the Newton iteration method for iteration calculation, the problems that the least square principle is greatly influenced by the measurement accidental errors and the Newton iteration method is sensitive to the initial value can be solved, the influence of the accidental error factors on the estimation value of the calibration parameters is reduced when the calibration parameter matrix is calculated, the calibration parameter estimation value with the reduced accidental errors is obtained, and the high-precision calibration processing result can be obtained.
In a possible implementation manner, the preprocessing the model to obtain a scaling parameter matrix specifically includes:
ignoring the background noise matrix, vectorizing the matrix form of the polarization synthetic aperture radar scaling model to obtain a vector form of the polarization synthetic aperture radar scaling model, and finishing the vector form of the polarization synthetic aperture radar scaling model to obtain a formula 3:
equation 3
The purpose of the sorting is to facilitate calculation;
obtaining polarization information from a matrix form vectorization of a polarization synthetic aperture radar calibration model;
assigning values of elements of a scaling parameter matrix composed of the receiving end distortion matrix R and the transmitting end distortion matrix T to a matrix l, where the matrix l is the scaling parameter matrix, and the matrix l is expressed as formula 4:
equation 4
According to the fact that the receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements and are unknown, the theoretical scattering matrix S of the i-th type scaler is usediRespectively according to formula 3 to obtain only R in sixteen parameters of matrix lvvTvv、RhhThh、RvvTvh、RvhThh、RvvThh、RhvTvv、RhhThvAnd RhhTvvThese eight parameters correspond to the values O of the actually measured polarization scattering matrix of the i-th scaleriRegarding and being independent parameters, the remaining eight parameters are dependent parameters that can be represented by the eight independent parameters of the matrix i, which is expressed as formula 5 according to the formula 3 and the formula 4:
equation 5
According to the formula 3, the formula 4 and the formula 5, the eight non-independent parameters in the matrix l are expressed by the eight independent parameters, so that a formula 6 is obtained:
equation 6
Substituting the formulas 5 and 6 into the formula 3 to obtain a formula 7:
equation 7
In a possible implementation manner, a newton iteration method based on the least square principle is used to establish an error equation to solve the calibration parameter matrix, so as to reduce the influence of accidental error factors on the calibration parameter estimation, which specifically includes:
step a, the ith theoretical polarization scattering matrix SiAnd the corresponding i-th actual measurement polarization scattering matrix OiSubstituting said formula 7 to obtain formula 8:
equation 8
Wherein, OivvActual measurement values, O, representing the vertical co-polarization of the i-th type scalerihhActual measurement values, O, representing horizontal co-polarization of the i-th scalerivhRepresenting the actual measurement of cross-polarization received by the i-th scaler vertical transmission horizontal reception, OihvRepresenting the cross polarization actual measurement value of the horizontal transmission and vertical reception of the ith type scaler; sivvTheoretical value, S, representing vertical co-polarization of class i scalerihhTheoretical value, S, representing horizontal co-polarization of class i scalerivhRepresenting the theoretical value of cross-polarization, S, received horizontally by the vertical transmission of the i-th scalerihvRepresenting the theoretical value of cross polarization of horizontal transmission and vertical reception of the ith type scaler;
the i equation sets in the formula 8 are solved simultaneously to obtain the initial value l of the matrix l0The initial value l0Is formula 9:
equation 9
Wherein the content of the first and second substances,
representation matrix
Transposing;
the initial value l is measured0And the i-th theoretical polarization scattering matrix SiSubstituting said formula 7 to obtain formula 10:
equation 10
Wherein the content of the first and second substances,
polarization scattering matrix O for class i actual measurementiIs set to the initial value of (a),
representation matrix
Transposing;
step b, linearizing the formula 7, and establishing an error equation, wherein the formula of the error mode is formula 11:
formula 11V ═ B Δ l- α,
wherein V represents the difference between the actual measured value and the true value,
a matrix of coefficients is represented by a matrix of coefficients,
representing the difference between the actual measured value and the initial value, OiDenotes the actual measured value,. DELTA.l-l0Expressing the correction amount, the formula 11 is rewritten to obtain the formula 12:
equation 12
Step c, obtaining a formula 13 according to the formula 12, wherein the formula 13 is an error formula V1vv、V1hh、V1vh、V1hv、V2vv、V2hh、V2vh、V2hv、V3vv、V3hh、V3hh、V3vhThe matrix expression of (c):
equation 13
Calculating the correction quantity delta l of the matrix l according to the formula 12 to obtain a formula 14:
equation 14 Δ l ═ BTB)-1BTα，
Wherein, BTRepresents a transpose of B;
the initial value l is measured0、
And said actual measured value OiSubstituting said equation 13, we get equation 15:
equation 15
Wherein the content of the first and second substances,
representation matrix
Transposing;
d, adding the formula 9 and the formula 15 to obtain l1Equation 16:
equation 16 l1＝l0+Δl1，
Similarly, equation 17 is obtained:
equation 17 ln+1＝ln+Δln+1，
Wherein n is the number of iterations;
and e, carrying out iterative calculation on the steps a, b, c and d.
In a possible embodiment, the termination condition is that the calculation is terminated when the correction Δ l is smaller than a preset threshold, and the formula of the scaled parameter estimation is formula 18:
equation 18 l ═ l11 l22 l31 l32 l33 l41 l42 l44)。
The calibration processing method for the polarimetric synthetic aperture radar disclosed by the embodiment establishes a polarimetric synthetic aperture radar calibration model by obtaining a plurality of single view complex number data, a plurality of image auxiliary data and multi-class calibrator information of four channels of the polarimetric synthetic aperture radar, preprocesses the model to obtain a calibration parameter matrix, establishes an error equation to solve the calibration parameter matrix based on a Newton iteration method of a least square principle, reduces the influence of accidental error factors on the calibration parameter estimated value, and obtains the calibration parameter estimated value with reduced accidental errors after reaching the termination condition of the calibration parameter matrix calculation, so that a high-precision calibration processing result can be obtained.
A second embodiment of the scaling processing apparatus for a polar synthetic aperture radar according to the present invention is described in detail below with reference to fig. 2: the embodiment is mainly applied to the calibration processing of the polarized synthetic aperture radar.
As shown in the figure, the scaling processing apparatus for a polar synthetic aperture radar provided in this embodiment includes:
an obtaining module 201, configured to obtain multiple single-view complex data, multiple image auxiliary data, and multiple types of scaler information for four channels of a polarization synthetic aperture radar, where the four channels are hh, hv, vh, and vv polarization channels; the multi-type calibrator information comprises at least one of type, size, posture, longitude and latitude and elevation information;
the model establishing module 202 is configured to establish a polar synthetic aperture radar calibration model according to the multiple single-view complex data, the multiple image auxiliary data, and the multiple types of calibrator information; the establishing of the calibration model of the polarized synthetic aperture radar according to the multiple single-view complex data, the multiple image auxiliary data and the multiple types of calibrator information specifically comprises:
a first processing unit, configured to extract a theoretical polarization scattering matrix S of the polar synthetic aperture radar according to the acquired single-view complex data, image auxiliary data, and multi-class scaler information, where the theoretical polarization scattering matrix S is expressed as:
the multi-class scaler comprises a multi-class corner reflector, and theoretical polarization scattering matrixes of the various scalers are expressed as follows according to the various types of the multi-class scaler:
wherein, the i is a scaler type, the hh is a horizontal transmitting and horizontal receiving channel, the hv is a horizontal transmitting and vertical receiving channel, the vh is a vertical transmitting and horizontal receiving channel, and the vv is a vertical transmitting and vertical receiving channel; the multi-type corner reflectors comprise at least three types of corner reflectors, wherein the preferred three types of corner reflectors are as follows: a dihedral corner reflector, a 0 ° dihedral corner reflector, and a 45 ° dihedral corner reflector; four types of corner reflectors can also be adopted, and the calibration processing by adopting the four types of corner reflectors can be obtainedHigh accuracy;
the second processing unit is used for extracting the images of the multi-class scaler and calculating the backscattering sectional areas of the multi-class corner reflectors in the images;
the third processing unit is used for carrying out radiation correction and registration on the images of the multi-class scaler according to the backscattering sectional areas of the multi-class corner reflectors; the images of the various calibrators are subjected to radiation correction according to the backscattering sectional areas of the various corner reflectors, so that the image distortion caused by radiation errors can be eliminated or corrected, the images can be better close to original scenes, and the probability of error results is reduced; the registration comprises the steps of extracting features of a plurality of images to obtain feature points, and finding matched feature point pairs by carrying out similarity measurement on the feature points; obtaining image space coordinate transformation parameters through the matched feature point pairs, and carrying out image registration according to the coordinate transformation parameters;
a fourth processing unit, configured to establish a calibration model of the polar synthetic aperture radar, where the formula of the model is formula 1:
equation 1O is RST + N,
wherein, O is a polarization scattering matrix actually measured, S is a theoretical polarization scattering matrix, R is a receiving end distortion matrix, T is a transmitting end distortion matrix, and N is a background noise matrix;
a fifth processing unit, configured to rewrite a formula of the calibration model of the polar synthetic aperture radar to a matrix form, to obtain a formula 2:
equation 2
The receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements which are unknown;
the model preprocessing module 203 is used for preprocessing the model to obtain a calibration parameter matrix;
the first processing module 204 is configured to establish an error equation to solve the calibration parameter matrix based on a least square principle through a newton iteration method, and reduce the influence of accidental error factors on the calibration parameter estimation;
a second processing module 205, configured to obtain an estimate of the scaled parameter with reduced accidental errors when a termination condition for the scaling parameter matrix calculation is reached.
The least square principle is greatly influenced by measurement accidental errors, the calibration processing precision requirement is difficult to meet, the Newton iteration method has the characteristic of high convergence rate, whether the Newton iteration method converges or not and the convergence rate is related to the selection of the initial value of the Newton iteration method, and if the initial value is set artificially, the Newton iteration method can be caused to be not converged. The least square principle is combined with the Newton iteration method, namely the Newton iteration method based on the least square principle can combine the advantages of good estimation performance of the least square principle and high convergence speed of the Newton iteration method, the estimation value obtained by the least square principle is used as the initial value of the Newton iteration method for iteration calculation, the problems that the least square principle is greatly influenced by the measurement accidental errors and the Newton iteration method is sensitive to the initial value can be solved, the influence of the accidental error factors on the estimation value of the calibration parameters is reduced when the calibration parameter matrix is calculated, the calibration parameter estimation value with the reduced accidental errors is obtained, and the high-precision calibration processing result can be obtained.
In a possible implementation manner, the preprocessing the model to obtain a scaling parameter matrix specifically includes:
ignoring the background noise matrix, vectorizing the matrix form of the polarization synthetic aperture radar scaling model to obtain a vector form of the polarization synthetic aperture radar scaling model, and finishing the vector form of the polarization synthetic aperture radar scaling model to obtain a formula 3:
equation 3
The purpose of the sorting is to facilitate calculation;
obtaining polarization information from a matrix form vectorization of a polarization synthetic aperture radar calibration model;
assigning values of elements of a scaling parameter matrix composed of the receiving end distortion matrix R and the transmitting end distortion matrix T to a matrix l, where the matrix l is the scaling parameter matrix, and the matrix l is expressed as formula 4:
equation 4
According to the fact that the receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements and are unknown, the theoretical scattering matrix S of the i-th type scaler is usediRespectively according to formula 3 to obtain only R in sixteen parameters of matrix lvvTvv、RhhThh、RvvTvh、RvhThh、RvvThh、RhvTvv、RhhThvAnd RhhTvvThese eight parameters correspond to the values O of the actually measured polarization scattering matrix of the i-th scaleriRegarding and being independent parameters, the remaining eight parameters are dependent parameters that can be represented by the eight independent parameters of the matrix i, which is expressed as formula 5 according to the formula 3 and the formula 4:
equation 5
According to the formula 3, the formula 4 and the formula 5, the eight non-independent parameters in the matrix l are expressed by the eight independent parameters, so that a formula 6 is obtained:
equation 6
Substituting the formulas 5 and 6 into the formula 3 to obtain a formula 7:
equation 7
In a possible implementation manner, the newton iteration method based on the least square principle establishes an error equation to solve the scaling parameter matrix, and reduces the influence of accidental error factors on the scaling parameter estimation, specifically including:
step a, the ith theoretical polarization scattering matrix SiAnd the corresponding i-th actual measurement polarization scattering matrix OiSubstituting said formula 7 to obtain formula 8:
equation 8
Wherein, OivvActual measurement values, O, representing the vertical co-polarization of the i-th type scalerihhActual measurement values, O, representing horizontal co-polarization of the i-th scalerivhRepresenting the actual measurement of cross-polarization received by the i-th scaler vertical transmission horizontal reception, OihvRepresenting the cross polarization actual measurement value of the horizontal transmission and vertical reception of the ith type scaler; sivvTheoretical value, S, representing vertical co-polarization of class i scalerihhTheoretical value, S, representing horizontal co-polarization of class i scalerivhRepresenting the theoretical value of cross-polarization, S, received horizontally by the vertical transmission of the i-th scalerihvRepresenting the theoretical value of cross polarization of horizontal transmission and vertical reception of the ith type scaler;
the i equation sets in the formula 8 are solved simultaneously to obtain the initial value l of the matrix l0The initial value l0Is formula 9:
equation 9
Wherein the content of the first and second substances,
representation matrix
Transposing;
the initial value l is measured0And class i theoryTheory polarization scattering matrix SiSubstituting said formula 7 to obtain formula 10:
equation 10
Wherein the content of the first and second substances,
polarization scattering matrix O for class i actual measurementiIs set to the initial value of (a),
representation matrix
Transposing;
step b, linearizing the formula 7, and establishing an error equation, wherein the formula of the error mode is formula 11:
formula 11V ═ B Δ l- α,
wherein V represents the difference between the actual measured value and the true value,
a matrix of coefficients is represented by a matrix of coefficients,
representing the difference between the actual measured value and the initial value, OiDenotes the actual measured value,. DELTA.l-l0Expressing the correction amount, the formula 11 is rewritten to obtain the formula 12:
equation 12
Step c, obtaining a formula 13 according to the formula 12, wherein the formula 13 is an error formula V1vv、V1hh、V1vh、V1hv、V2vv、V2hh、V2vh、V2hv、V3vv、V3hh、V3hh、V3vhThe matrix expression of (c):
equation 13
Solving the correction quantity delta l of the matrix l according to the formula 13 to obtain a formula 14:
equation 14 Δ l ═ BTB)-1BTα，
Wherein, BTRepresents a transpose of B;
the initial value l is measured0、
And said actual measured value OiSubstituting said equation 13, we get equation 15:
equation 15
Wherein the content of the first and second substances,
representation matrix
Transposing;
d, adding the formula 9 and the formula 15 to obtain l1Equation 16:
equation 16 l1＝l0+Δl1，
Similarly, equation 17 is obtained:
equation 17 ln+1＝ln+Δln+1，
Wherein n is the number of iterations;
and e, carrying out iterative calculation on the steps a, b, c and d.
In a possible embodiment, the termination condition is that the calculation is terminated when the correction Δ l is smaller than a preset threshold, and the formula of the scaled parameter estimation is formula 18:
equation 18 l ═ l11 l22 l31 l32 l33 l41 l42 l44)。
In the calibration processing apparatus for a polarization synthetic aperture radar disclosed in this embodiment, a plurality of monoscopic complex data, a plurality of image auxiliary data, and a plurality of types of calibrator information of four channels of the polarization synthetic aperture radar are obtained by an obtaining module; establishing a polarized synthetic aperture radar calibration model through a model establishing module; preprocessing the model through a model preprocessing module to obtain a calibration parameter matrix; the calibration parameter matrix is solved by establishing an error equation through a first processing module and a Newton iteration method based on the least square principle, the influence of accidental error factors on the calibration parameter estimated value is reduced, and the calibration parameter estimated value with the reduced accidental errors is obtained after the second processing module reaches the termination condition of the calibration parameter matrix calculation, so that the calibration processing result with high precision can be obtained, the practicability is good, and the calibration method is more suitably applied to the calibration of multi-platform polarization synthetic aperture radars such as airborne radars, unmanned aerial vehicles and the like which have higher requirements on the calibration processing precision.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (6)
1. A calibration processing method for a polarized synthetic aperture radar is characterized by comprising the following steps:
acquiring a plurality of single-view complex data, a plurality of image auxiliary data and multi-class scaler information of four channels of a polarized synthetic aperture radar, wherein the four channels are four polarized channels of hh, hv, vh and vv;
establishing a polarized synthetic aperture radar calibration model according to the single-view complex data, the image auxiliary data and the multi-class calibrator information;
preprocessing the model to obtain a calibration parameter matrix;
establishing an error equation to solve the calibration parameter matrix based on a Newton iteration method of a least square principle, and reducing the influence of accidental error factors on the calibration parameter estimation;
obtaining a calibration parameter estimation value with reduced accidental errors when a termination condition of the calibration parameter matrix calculation is reached;
wherein, the establishing a calibration model of the polarized synthetic aperture radar according to the multiple single-view complex data, the multiple image auxiliary data and the multiple classes of calibrator information specifically comprises:
extracting a theoretical polarization scattering matrix S of the polarized synthetic aperture radar according to the acquired single-view complex data, the image auxiliary data and the multi-class scaler information, wherein the theoretical polarization scattering matrix S is expressed as:
the multi-class scaler comprises a multi-class corner reflector, and theoretical polarization scattering matrixes of the various scalers are expressed as follows according to the various types of the multi-class scaler:
wherein, the i is a scaler type, the hh is a horizontal transmitting and horizontal receiving channel, the hv is a horizontal transmitting and vertical receiving channel, the vh is a vertical transmitting and horizontal receiving channel, and the vv is a vertical transmitting and vertical receiving channel;
extracting images of the multi-class scaler, and calculating the backscattering sectional areas of the multi-class corner reflectors in the images;
performing radiation correction and registration on the images of the multi-class calibrator according to the backscattering sectional areas of the multi-class corner reflectors;
establishing a calibration model of the polarized synthetic aperture radar, wherein the formula of the model is formula 1:
equation 1O is RST + N,
wherein, O is a polarization scattering matrix actually measured, S is a theoretical polarization scattering matrix, R is a receiving end distortion matrix, T is a transmitting end distortion matrix, and N is a background noise matrix;
rewriting the formula of the polarization synthetic aperture radar calibration model into a matrix form to obtain a formula 2:
equation 2
The receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements which are unknown;
the preprocessing the model to obtain a calibration parameter matrix specifically comprises:
ignoring the background noise matrix, vectorizing the matrix form of the polarization synthetic aperture radar scaling model to obtain a vector form of the polarization synthetic aperture radar scaling model, and finishing the vector form of the polarization synthetic aperture radar scaling model to obtain a formula 3:
equation 3
Assigning values of elements of a scaling parameter matrix composed of the receiving end distortion matrix R and the transmitting end distortion matrix T to a matrix l, where the matrix l is the scaling parameter matrix, and the matrix l is expressed as formula 4:
equation 4
According to the fact that the receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements and are unknown, the theoretical scattering matrix S of the i-th type scaler is usediRespectively according to formula 3 to obtain only R in sixteen parameters of matrix lvvTvv、RhhThh、RvvTvh、RvhThh、RvvThh、RhvTvv、RhhThvAnd RhhTvvThese eight parameters correspond to the values O of the actually measured polarization scattering matrix of the i-th scaleriRegarding and being independent parameters, the remaining eight parameters are dependent parameters that can be represented by the eight independent parameters of the matrix i, which is expressed as formula 5 according to the formula 3 and the formula 4:
equation 5
According to the formula 3, the formula 4 and the formula 5, the eight non-independent parameters in the matrix l are expressed by the eight independent parameters, so that a formula 6 is obtained:
equation 6
Substituting the formulas 5 and 6 into the formula 3 to obtain a formula 7:
equation 7
2. The method according to claim 1, wherein the newton's iteration method based on the least squares principle establishes an error equation to solve the scaling parameter matrix, and reduces the influence of accidental error factors on the scaling parameter estimation, specifically comprising:
step a, the ith theoretical polarization scattering matrix SiAnd the corresponding i-th actual measurement polarization scattering matrix OiSubstituting said formula 7 to obtain formula 8:
equation 8
Wherein, OivvActual measurement values, O, representing the vertical co-polarization of the i-th type scalerihhActual measurement values, O, representing horizontal co-polarization of the i-th scalerivhRepresenting the actual measurement of cross-polarization received by the i-th scaler vertical transmission horizontal reception, OihvRepresenting the cross polarization actual measurement value of the horizontal transmission and vertical reception of the ith type scaler; sivvTheoretical value, S, representing vertical co-polarization of class i scalerihhTheoretical value, S, representing horizontal co-polarization of class i scalerivhRepresenting the theoretical value of cross-polarization, S, received horizontally by the vertical transmission of the i-th scalerihvRepresenting the theoretical value of cross polarization of horizontal transmission and vertical reception of the ith type scaler;
the i equation sets in the formula 8 are solved simultaneously to obtain the initial value l of the matrix l0The initial value l0Is formula 9:
equation 9
Wherein the content of the first and second substances,
representation matrix
the initial value l is measured0And the i-th theoretical polarization scattering matrix SiSubstituting said formula 7 to obtain formula 10:
equation 10
Wherein the content of the first and second substances,
polarization scattering matrix O for class i actual measurementiIs set to the initial value of (a),
representation matrix
Transposing;
step b, linearizing the formula 7, and establishing an error equation, wherein the formula of the error mode is formula 11:
formula 11V ═ B Δ l- α,
wherein V represents the difference between the actual measured value and the true value,
a matrix of coefficients is represented by a matrix of coefficients,
representing the difference between the actual measured value and the initial value, OiDenotes the actual measured value,. DELTA.l-l0Expressing the correction amount, the formula 11 is rewritten to obtain the formula 12:
equation 12
Step c, obtaining a formula 13 according to the formula 12, wherein the formula 13 is an error formula V1vv、V1hh、V1vh、V1hv、V2vv、V2hh、V2vh、V2hv、V3vv、V3hh、V3hh、V3vhThe matrix expression of (c):
equation 13
Calculating the correction quantity delta l of the matrix l according to the formula 12 to obtain a formula 14:
equation 14 Δl＝(BTB)-1BTα，
Wherein, BTRepresents a transpose of B;
the initial value l is measured0、
And said actual measured value OiSubstituting said equation 13, we get equation 15:
equation 15
Wherein the content of the first and second substances,
representation matrix
d, adding the formula 9 and the formula 15 to obtain l1Equation 16:
equation 16 l1＝l0+Δl1，
Similarly, equation 17 is obtained:
equation 17 ln+1＝ln+Δln+1，
Wherein n is the number of iterations;
and e, carrying out iterative calculation on the steps a, b, c and d.
3. The method according to claim 2, wherein the termination condition is that the solution is terminated when the correction amount Δ l is smaller than a preset threshold, and the formula of the scaled parameter estimation is formula 18:
equation 18 l ═ l11 l22 l31 l32 l33 l41 l42 l44)。
4. A scaling apparatus for a polarimetric synthetic aperture radar, comprising:
the system comprises an acquisition module, a calibration module and a calibration module, wherein the acquisition module is used for acquiring a plurality of single-view complex data, a plurality of image auxiliary data and multi-class calibrator information of four channels of the polarized synthetic aperture radar, and the four channels are four polarized channels of hh, hv, vh and vv;
the model establishing module is used for establishing a polarized synthetic aperture radar calibration model according to the single-view complex data, the image auxiliary data and the multi-class calibrator information;
the model preprocessing module is used for preprocessing the model to obtain a calibration parameter matrix;
the first processing module is used for establishing an error equation to solve the calibration parameter matrix based on a Newton iteration method of the least square principle, and reducing the influence of accidental error factors on the calibration parameter estimation;
the second processing module is used for obtaining the calibration parameter estimation value with reduced accidental errors after the termination condition of the calibration parameter matrix calculation is reached;
wherein, the establishing a calibration model of the polarized synthetic aperture radar according to the multiple single-view complex data, the multiple image auxiliary data and the multiple classes of calibrator information specifically comprises:
a first processing unit, configured to extract a theoretical polarization scattering matrix S of the polar synthetic aperture radar according to the acquired single-view complex data, image auxiliary data, and multi-class scaler information, where the theoretical polarization scattering matrix S is expressed as:
the multi-class scaler comprises a multi-class corner reflector, and theoretical polarization scattering matrixes of the various scalers are expressed as follows according to the various types of the multi-class scaler:
the second processing unit is used for extracting the images of the multi-class scaler and calculating the backscattering sectional areas of the multi-class corner reflectors in the images;
the third processing unit is used for carrying out radiation correction and registration on the images of the multi-class scaler according to the backscattering sectional areas of the multi-class corner reflectors;
a fourth processing unit, configured to establish a calibration model of the polar synthetic aperture radar, where the formula of the model is formula 1:
equation 1O is RST + N,
wherein, O is a polarization scattering matrix actually measured, S is a theoretical polarization scattering matrix, R is a receiving end distortion matrix, T is a transmitting end distortion matrix, and N is a background noise matrix;
a fifth processing unit, configured to rewrite a formula of the calibration model of the polar synthetic aperture radar to a matrix form, to obtain a formula 2:
equation 2
The receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements which are unknown;
the preprocessing the model to obtain a calibration parameter matrix specifically comprises:
ignoring the background noise matrix, vectorizing the matrix form of the polarization synthetic aperture radar scaling model to obtain a vector form of the polarization synthetic aperture radar scaling model, and finishing the vector form of the polarization synthetic aperture radar scaling model to obtain a formula 3:
equation 3
Assigning values of elements of a scaling parameter matrix composed of the receiving end distortion matrix R and the transmitting end distortion matrix T to a matrix l, where the matrix l is the scaling parameter matrix, and the matrix l is expressed as formula 4:
equation 4
According to the fact that the receiving end distortion matrix R and the transmitting end distortion matrix T respectively have four elements and are unknown, the theoretical scattering matrix S of the i-th type scaler is usediRespectively according to formula 3 to obtain only R in sixteen parameters of matrix lvvTvv、RhhThh、RvvTvh、RvhThh、RvvThh、RhvTvv、RhhThvAnd RhhTvvThese eight parameters correspond to the values O of the actually measured polarization scattering matrix of the i-th scaleriRegarding and being independent parameters, the remaining eight parameters are dependent parameters that can be represented by the eight independent parameters of the matrix i, which is expressed as formula 5 according to the formula 3 and the formula 4:
equation 5
According to the formula 3, the formula 4 and the formula 5, the eight non-independent parameters in the matrix l are expressed by the eight independent parameters, so that a formula 6 is obtained:
equation 6
Substituting the formulas 5 and 6 into the formula 3 to obtain a formula 7:
equation 7
5. The apparatus according to claim 4, wherein the Newton's iteration method based on the least squares principle establishes an error equation to solve the scaling parameter matrix, and reduces the influence of accidental error factors on the scaling parameter estimation, specifically comprising:
step a, the ith theoretical polarization scattering matrix SiAnd the corresponding i-th actual measurement polarization scattering matrix OiSubstituting said formula 7 to obtain formula 8:
equation 8
Wherein, OivvActual measurement values, O, representing the vertical co-polarization of the i-th type scalerihhActual measurement values, O, representing horizontal co-polarization of the i-th scalerivhRepresenting the actual measurement of cross-polarization received by the i-th scaler vertical transmission horizontal reception, OihvRepresenting the cross polarization actual measurement value of the horizontal transmission and vertical reception of the ith type scaler; sivvTheoretical value, S, representing vertical co-polarization of class i scalerihhTheoretical value, S, representing horizontal co-polarization of class i scalerivhRepresenting the theoretical value of cross-polarization, S, received horizontally by the vertical transmission of the i-th scalerihvRepresenting the theoretical value of cross polarization of horizontal transmission and vertical reception of the ith type scaler;
the i equation sets in the formula 8 are solved simultaneously to obtain the initial value l of the matrix l0The initial value l0Is formula 9:
equation 9
Wherein the content of the first and second substances,
representation matrix
the initial value l is measured0And the i-th theoretical polarization scattering matrix SiSubstituting said formula 7 to obtain formula 10:
equation 10
Wherein the content of the first and second substances,
polarization scattering matrix O for class i actual measurementiIs set to the initial value of (a),
representation matrix
Transposing;
step b, linearizing the formula 7, and establishing an error equation, wherein the formula of the error mode is formula 11:
formula 11V ═ B Δ l- α,
wherein V represents the difference between the actual measured value and the true value,
a matrix of coefficients is represented by a matrix of coefficients,
representing the difference between the actual measured value and the initial value, OiDenotes the actual measured value,. DELTA.l-l0Expressing the correction amount, the formula 11 is rewritten to obtain the formula 12:
equation 12
Step c, obtaining a formula 13 according to the formula 12, wherein the formula 13 is an error formula V1vv、V1hh、V1vh、V1hv、V2vv、V2hh、V2vh、V2hv、V3vv、V3hh、V3hh、V3vhThe matrix expression of (c):
equation 13
Solving the correction quantity delta l of the matrix l according to the formula 13 to obtain a formula 14:
equation 14 Δ l ═ BTB)-1BTα，
Wherein, BTRepresents a transpose of B;
the initial value l is measured0、
And said actual measured value OiSubstituting said equation 13, we get equation 15:
equation 15
Wherein the content of the first and second substances,
representation matrix
d, adding the formula 9 and the formula 15 to obtain l1Equation 16:
equation 16 l1＝l0+Δl1，
Similarly, equation 17 is obtained:
equation 17 ln+1＝ln+Δln+1，
Wherein n is the number of iterations;
and e, carrying out iterative calculation on the steps a, b, c and d.
6. The apparatus according to claim 5, wherein the termination condition is that the solution is terminated when the correction amount Δ l is smaller than a preset threshold, and the formula of the scaled parameter estimation is formula 18:
equation 18 l ═ l11 l22 l31 l32 l33 l41 l42 l44)。
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