CN116520257B - Polarization calibration method for L-band full-polarization system - Google Patents

Abstract

The invention provides a polarization calibration method of an L-band full polarization system, which is used for obtaining full polarization data containing ground object real scattering information and comprises the following steps: estimating a system distortion parameter containing blur based on the scaler observation vector; and compensating errors of the general scene polarized data channels based on the estimated system distortion parameters to obtain error compensation data. Due to the space-time variation characteristic of the Faraday effect, the Faraday rotation angle is estimated and compensated based on the polarization observation vector of the general scene of the system distortion correction, so that the accurate correction of the full polarization data is realized, and the data product meeting the full polarization application requirement is obtained. The invention can accurately estimate and compensate the polarization SAR polarization distortion.

Description

Polarization calibration method for L-band full-polarization system

Technical Field

The invention belongs to the field of SAR calibration, and particularly relates to a polarization calibration method of an L-band full-polarization system.

Background

The polarized SAR data provides important basis and support for image interpretation and target parameter inversion. The full polarization SAR can acquire complete polarization information and is widely focused by researchers in the remote sensing field. Currently, on-orbit SAR satellites with full polarization mode mainly comprise Radarsat-2 system in Canada, tanDEM-X system in Germany, ALOS-2 system in Japan, high-resolution NO. three system in China and land exploration NO. one (LT-1) system. The LT-1 system consists of two advanced L-band full polarization multichannel SAR satellites. After the LT-1 system is transmitted and operated, the method fills up a plurality of gaps in the fields of satellite-borne differential interference, multi-mode polarization, single navigation over-polarization interference SAR, double-base broad width and the like in China, and improves the sensing and comprehensive environment monitoring capability of the multi-dimensional information of the country to the ground.

The full polarization SAR data acquired by the LT-1 system provides complete scattering information for feature target feature extraction. However, low-band polarized SAR data quality, including the L-band, is affected by Faraday Effect (FE). The electromagnetic field around the earth rotates the polarization direction of the electromagnetic wave by an angle called Faraday Rotation Angle (FRA). The size of the FRA is related to the total ionospheric electron concentration (TEC), the distribution of the earth's magnetic field, the angle between the direction of propagation of electromagnetic waves and the direction of the magnetic field, and the carrier wave band in the propagation path. When FRA is not zero, electromagnetic waves irradiated to the ground feature rotate in the polarization direction of the electromagnetic waves transmitted by the SAR transmitter, electromagnetic waves scattered by the ground feature rotate in the polarization direction of the electromagnetic waves received by the SAR receiver, and the directions of the two rotations are the same. The FE enables the polarization observed quantity acquired by the SAR system to be not observed quantity under a radar coordinate system, and uncalibrated FE can have serious influence on polarization information interpretation. For this purpose, channel distortion and FRA of the low-band full-polarization SAR system need to be estimated and compensated. Currently, polarization scaling methods include point-target-based scaling methods and distributed-target-based scaling methods. The point target scaling approach requires expensive scalers and scaler deployment costs. The scaling scheme of the distributed target requires priori FRA knowledge, and small errors between the priori FRA and the real FRA can influence the accuracy of SAR antenna crosstalk estimation; the idealized modeling of the distributed target real scattering matrix and noise leads to errors in estimated parameters and reduces polarization calibration accuracy.

The polarization scaling method of the low-band (L-band) SAR system has the following difficulties: the ionosphere causes the maximum FRA of electromagnetic wave generation to reach 40 degrees, so that the polarization observed quantity distortion caused by the maximum FRA cannot be ignored, and a corresponding evaluation method is lacked; the FRA is coupled with the distortion parameters of the polarization system, and the prior scheme lacks analysis of the blurring degree and the final scaling precision of the estimated parameters.

Disclosure of Invention

In order to solve the technical problems to obtain a polarized image containing ground object real scattering information, the invention provides a polarization calibration method of an L-band full polarization system, which comprises the following steps: an iterative estimation method for system distortion parameters is related; designing an FRA estimation method; the performance of the invention is verified by using simulation and on-orbit SAR measured data. Through simulation and actual measurement verification, the invention can accurately estimate and compensate the distortion error of the polarized SAR system.

In order to achieve the above purpose, the invention adopts the following technical scheme:

a polarization calibration method of an L-band full polarization system comprises the following steps:

step 1, designing a step iteration estimation algorithm of system distortion, and estimating a system distortion parameter containing blur based on a scaler observation vector;

step 2, the faraday rotation angle needs to be estimated again for a general scene due to the space-time variation characteristic of the faraday effect. And (3) compensating the channel error of the polarized data of the general scene based on the system distortion parameters estimated in the step (1) to obtain a polarized observation vector corrected by the channel error, and estimating and compensating the Faraday rotation angle based on the corrected polarized observation vector to realize the accurate correction of the full-polarization data and obtain a data product meeting the application requirement of the full-polarization.

Further, the step 1 includes:

the active scaler observance model of the distortion is constructed as follows:

（1），

（2），

wherein ,representing the actual observed quantity of the ground object>Is a straight line vector of->Representing Cronecker product, superscript +.>Representing the transpose of the matrix>Representing the absolute amplitude and phase coefficient of the scaler, +.>Representing the homopolar and cross-polar channel imbalance introduced by the artificial gain controller compensation error,/->Representing the imbalance value of the receive channel, +.> and />Representing crosstalk of the receiving channel->Representing the imbalance value of the transmit channel, +.> and />Representing crosstalk at the transmitting end->Representing Faraday rotation angle, & lt & gt>Representing the ground object scattering matrix, < >>Representing the reception->Polarized wave reflection->Complex scattering coefficient of polarized wave,/->Line straightening vectors of random error matrix representing system noise, interference signals, clutter and the like contributing to scaler observation vectors, +.>Representing an equivalent polarization distortion matrix;

minimizing a cost function through an optimization algorithm to obtain a group of distortion parameters conforming to reality; the cost function characterizes the difference F between the estimated observables and the actual observables, defined as follows:

（3），

wherein , and />Respectively represent +.>Time observations and estimated observations of the individual scalers, +.>Representing the 2 norms of the vector, ">Representing the real part of the complex number, ">An imaginary part representing a complex number;

there is a ambiguity between the Faraday rotation angle, the system distortion matrix and the absolute amplitude-phase coefficient, and the ambiguity problem of the Faraday rotation angle is described by the following two formulas:

（4），

（5），

for the receive matrix, the following relationship exists:

（6），

（7），

（8），

in combination of formulas (5) to (6), there is a ambiguity between the Faraday rotation matrix and the system distortion matrix, and the degree of ambiguity of the Faraday rotation angle isWhen (I)>Representing the blurring of the parameters caused to the absolute amplitude and phase coefficients, is-> and />Respectively corresponding to the ambiguous transmit and receive channel imbalance values,/-, respectively>，/>，/>，/>Is the corresponding ambiguous crosstalk value;

system distortion parameter presenceIs a phase ambiguity of:

（9），

a least squares solution of the distortion parameters of the system is calculated using the levenberg-marquardt.

Further, the step-and-step iterative estimation algorithm in the step 1 solves the system distortion parameter and the estimated faraday rotation angle in the step 2 includes:

the calculation is carried out by adopting a step-by-step estimation mode, and the equivalent model is as follows:

（10），

wherein ,

（11），

（12），

（13），

wherein ,representing an equivalent transmit distortion matrix, ">Representing an equivalent reception distortion matrix, ">Representing residual absolute amplitude and phase coefficients extracted by the equivalent distortion matrix with HH polarization channel as reference, < ->Represents the scaler equivalent absolute amplitude and phase coefficient under the model, subscript +.>Indicate->Data corresponding to the scalers; in the following description of iterative algorithms, < +.>Indicating true value(s)>Representing the estimated value; /> and />Representing crosstalk of equivalent receiving channels, +.>Representing the imbalance value of the equivalent receive channel, +.> and />Representing the crosstalk of the equivalent transmitting terminal +.>Representing an imbalance value of the transmit channel;

firstly, carrying out iterative solution on an equivalent model formed by the formula (10), adopting a strategy of iterative and compensating at the same time, and setting the initial value of the absolute amplitude-phase coefficient of a scaler to be 1 and the rest parameters after each iterationRepeating iteration by taking the iterative result as a new initial value; to avoid estimationDeviating from the actual situation, the amplitude range pairs based on the antenna pattern in the iterative processAdding constraint conditions>Representing estimated +.>The method comprises the steps of carrying out a first treatment on the surface of the After iteration convergence, judge->Whether the absolute value of the phase of (a) is smaller than +.>If not, correct->Is->Then compensate +.>Distortion of the observed quantity caused; the amplitude range increase inequality constraint based on the antenna pattern is shown as follows:

，

wherein ,representing the value of the variable when the objective function is minimized,/->Representing the scaler amplitude difference threshold, +.>Expressed in decibels @, @>The representation takes absolute value; for simplicity of expression, define:

（14），

wherein ,representing the absolute amplitude and phase coefficient of the scaler, +.>After the first iteration and compensation is completed, the observed quantity satisfies the following formula:

（15），

under the new model, after each iteration, except for the initial value of the system crosstalk which is kept to be 0, the rest parameters are iterated with the iterated result as a new initial value:

，

wherein, define:

（16），

further, the step 2 includes:

when the system has no distortion and noise is ignored, the polarization observation vector of the ground objectSatisfies the following formula:

（17），

the influence of Faraday rotation angle on the target covariance matrix is obtained through deduction, and the influence has the following relation:

（18），

defining characteristic complex values of estimated Faraday rotation anglesThe formula is as follows:

（19），

（20），

wherein , wherein Represents the m-th row and n-th column elements of the covariance matrix, and:

（21），

wherein ,representing conjugate operation;

equation (21) shows that the faraday rotation angle estimated from the observation vector of the feature satisfying reciprocity is expressed as follows:

（22），

wherein ,representing the argument of plural ++>In imaginary units.

The beneficial effects are that:

1. the invention provides a scheme for decoupling system distortion parameters and Faraday rotation angles, wherein under the conditions of low crosstalk and high signal-to-noise ratio, the estimated deviation of the Faraday rotation angles is smaller thanAnd verifies and explains that the fuzzy system distortion parameters do not affect the final correction accuracy.

2. The invention is suitable for any scaler group, and avoids the trouble of needing a specific scaler group.

3. The modeling is more complete, the processing process does not comprise an approximation process, and the precision is higher.

Drawings

FIG. 1 is a hardware block diagram of a fully polarized system T/R assembly;

fig. 2 is a statistical diagram of an estimation error index mno;

FIG. 3 is a chart of FRA estimation bias statistics based on an iterative algorithm;

FIG. 4 is a graph of variance of FRA estimate bias under various conditions;

FIG. 5 is a graph showing the residual error statistics of the equivalent system, wherein graph (a) is a graph showing the magnitude statistics of the residual MGC compensation error, graph (b) is a graph showing the phase statistics of the residual MGC compensation error, graph (c) is a graph showing the magnitude statistics of the residual channel imbalance, and graph (d) is a graph showing the phase statistics of the residual channel imbalance;

fig. 6 is a graph of FRA estimation results based on correction data, where (a) is a FRA estimation result for 2 months 15 days data, (b) is a FRA estimation result for 2 months 23 days data, and (c) is a FRA estimation result for 3 months 3 days data;

fig. 7 shows a polarization-resolved pseudocolor map of LT-1 full polarization data, a polarization-resolved pseudocolor map of 2 month 15 day data, a polarization-resolved pseudocolor map of 2 month 23 day data, and a polarization-resolved pseudocolor map of 3 month 3 day data.

Detailed Description

The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.

The invention provides a polarization calibration method of an L-band full polarization system, which is used for obtaining full polarization data containing ground object real scattering information and comprises the following steps: estimating a system distortion parameter containing blur based on the scaler observation vector; and compensating errors of the general scene polarized data channels based on the estimated system distortion parameters to obtain error compensation data. Due to the space-time variation characteristic of the Faraday effect, the Faraday rotation angle is estimated and compensated based on the polarization observation vector of the general scene of the system distortion correction, so that the accurate correction of the full polarization data is realized, and the data product meeting the full polarization application requirement is obtained. The invention can accurately estimate and compensate the polarization SAR polarization distortion.

Specifically, the polarization calibration method of the L-band full polarization system comprises the following steps:

step 1, designing an iterative estimation method of system distortion parameters:

a transmit/receive (T/R) component framework for a fully polarized system is shown in fig. 1, which shows FE for vertical (V) polarized waves and horizontal (H) polarized waves for Crosstalk (CT) emitted by the system. Systematic errors that exist in fully polarized systems include amplitude and phase deviations of the H and V polarized channels, crosstalk between the H and V polarized channels, and compensation errors of the Manual Gain Controller (MGC). In order to obtain high-precision full polarization data, the systematic errors are estimated and compensated based on the observation vector of the scaler. In fig. 1, amp denotes a power amplifier, PS denotes a phase shifter, DIV denotes a power divider, and S denotes a scattering matrix of the target.

The channel imbalance of the polarized SAR system means that the gains and phases of the two channels are inconsistent with preset values in actual operation due to the nonideal of H and V polarized channels, so that the observed quantity of the two channels has deviation of amplitude and phase. Inter-channel crosstalk means that the H and V channels cannot be completely isolated, and when an H (or V) polarized wave is transmitted or received, electromagnetic coupling causes noise signals to be generated in the V (or H) channel. Homopolar echoes (HH/VV) of the ground object are 6-10dB greater than cross-polar echoes (HV/VH). Therefore, it is necessary to equip the fully polarized system with MGCs to adjust the co-polarized and cross-polarized echo gains so that the echo energy of all polarization types is within the effective range of the receiver. Deviations of the actual gain value controlled by the MGC from the preset value also need to be corrected. For this purpose, an active scaler observance model of distortion is constructed as follows:

（1），

（2），

wherein ,representing the actual observed quantity of the ground object>Is a straight line vector of->Representing Cronecker product, superscript +.>Representing the transpose of the matrix>Representing the absolute amplitude and phase coefficient of the scaler, +.>Representing homopolarity introduced by MGC compensation errorsCross-polarized channel imbalance value, < >>Represents the imbalance value of the reception channel (H/V,)> and />Representing crosstalk of the receiving channel->Representing the imbalance value of the transmit channel, +.> and />Representing crosstalk at the transmitting end->Representing Faraday rotation angle, & lt & gt>Representing the ground object scattering matrix, < >>Representing the reception->Polarized wave reflection->Complex scattering coefficient of polarized wave,/->Line straightening vectors of random error matrix representing system noise, interference signals, clutter and the like contributing to scaler observation vectors, +.>Representing an equivalent polarization distortion matrix.

According to the invention, the cost function is minimized through an optimization algorithm, and a group of distortion parameters conforming to reality are obtained. The cost function characterizes the difference between the estimated observables and the actual observables, defined as follows,

（3），

wherein , and />Respectively represent +.>Time observations and estimated observations of the individual scalers, +.>Representing the 2 norms of the vector, ">Representing the real part of the complex number, ">Representing the imaginary part of the complex number. In order to estimate the required 7 complex system distortion parameters and FRA, at least three scalers are required to provide the observed data, i.e. a total of 10 complex parameters and 1 real parameter need to be estimated. The scaler can provide 12 complex observables, and then an overdetermined equation set can be established to realize parameter estimation. The existence of the system of equations is multi-solved due to the ambiguity between the FRA, the system distortion matrix and the absolute amplitude and phase coefficients. The ambiguity that exists between the parameters is analyzed in detail below.

The FRA blur problem can be described by two formulas,

（4），

（5），

taking the receiving matrix as an example, the following relationship exists:

（6），

（7），

（8），

as can be seen from the combination of the formulas (5) and (6), the fuzzy degree of the FRA is thatWhen (I)>Representing the blurring of the parameters caused to the absolute amplitude and phase coefficients, is-> and />Respectively corresponding to the ambiguous transmit and receive channel imbalance values,/-, respectively>，/>，/>，/>Then the corresponding ambiguous crosstalk value. It was found that small FRA estimation bias severely deviates the estimated crosstalk values from true values, but has less impact on the channel imbalance factor. As shown in formula (11), the system distortion parameter itself is also present +.>Is also contemplated in the present invention.

（9），

In order to achieve both efficiency and accuracy, an iterative solution of distortion parameters is achieved by using a Levenberg-Marquardt (LM) optimization algorithm. The following two problems are considered in the iterative process: if the scheme of estimating while compensating is not constrained, under the condition that the absolute amplitude-phase coefficient of the scaler is over-estimated, the observed quantity is approximately set to zero, the rank of the characteristic matrix of the equation set is reduced, the original problem is converted into an underdetermined problem, and the iterative algorithm is invalid. Secondly, there is blurring in the phase of the system distortion parameters, interfering with the evaluation of the system performance. The invention adopts a step-by-step estimation mode, reduces the complexity of equation solving and increases the robustness of the algorithm.

（10），

wherein ,

（11），

（12），

（13），

wherein ,representing an equivalent transmit distortion matrix, ">Representing an equivalent reception distortion matrix, ">Representing residual absolute amplitude and phase coefficients extracted by the equivalent distortion matrix with HH polarization channel as reference, < ->Represents the scaler equivalent absolute amplitude and phase coefficient under the model, subscript +.>Indicate->And data corresponding to the scalers. In the following expression for iterative calculations, < + >>Indicating true value(s)>Representing the estimated value. /> and />Representing crosstalk of equivalent receiving channels, +.>Representing the imbalance value of the transmit channel, and />Representing the crosstalk of the equivalent transmitting terminal +.>Representing the imbalance value of the equivalent receive channel.

Firstly, carrying out iteration solution on the equivalent model of the above formula, adopting a strategy of iterative and compensating at the same time, and after each iteration, setting the initial value of the absolute amplitude-phase coefficient of the scaler as 1, and repeating iteration by taking the result after iteration as a new initial value by the other parameters. Furthermore, to avoid estimationDeviating from the actual situation, the amplitude range pairs based on the antenna pattern in the iterative processThe constraint is increased. After iteration convergence, judge->Whether the absolute value of the phase of (a) is smaller than +.>If not, correctIs->Then compensate +.>The resulting observations are distorted in an appropriate amount. The amplitude range increase inequality constraint based on the antenna pattern is shown as follows,

，

wherein ,representing the value of the variable when the objective function is minimized,/->Representing the scaler amplitude difference threshold, +.>Expressed in decibels @, @>The representation takes absolute value. For simplicity of expression, define:

（14），

wherein ,and (3) representing absolute amplitude-phase coefficients of the scaler, wherein after the first step of iteration and compensation are completed, the observed quantity meets the following formula:

（15），

under the new model, after each iteration, the other parameters are iterated with the iterated result as a new initial value except that the initial value of the system crosstalk is kept to be 0.

，

Wherein, define:

（16），

the system distortion parameter estimation process comprises the following steps:

the first step: scaler amplitude difference threshold based on priori knowledgeExtracting the observed quantity of the scaler group-> ；

And a second step of: setting up super parameter and maximum iteration number of LM algorithm, initializingSuperscript->Iterating the initial value;

and a third step of: setting upAbsolute amplitude and phase coefficient of ∈>Sign->Representing the assignment of the calculated value on the right to the variable on the left. Will->As an initial value +.>Superscript->Representing the iteration number;

fourth step: compensating for observed vectorsUpdating estimated absolute amplitude and phase coefficients；

Fifth step: and performing the third step to the sixth step in a circulating way until the distortion parameters are converged. The convergence condition isAnd (2) and/>；

sixth step: correction and compensation，/>；

Seventh step: setting upCross-talk->. Will->As an initial value +.>Superscript->Representing the iteration number;

eighth step: and executing the seventh step circularly until the distortion parameters are converged. The convergence conditions were:；

step 2, designing a Faraday rotation angle FRA estimation method:

when the system has no distortion and noise is ignored, the polarization observation vector of the ground objectSatisfies the following formula:

（17），

the effect of the FRA on the target covariance matrix can be deduced as follows,

（18），

defining characteristic complex values of an estimated FRAAs described below,

（19），/>

（20），

wherein , wherein Represents the m-th row and n-th column elements of the covariance matrix, and:

（21），

wherein ,representing a conjugate operation. The equation shows that the estimated FRA can be obtained by observing vectors of features satisfying reciprocity as follows:

（22），

wherein ,representing the argument of plural ++>In imaginary units. The stability of the method depends on the sum of target co-polarization second order statisticsMost of the features have relatively strong co-polarized backscattering coefficients and high signal-to-noise ratio. When the channel noise is uncorrelated and the power of each channel noise is similar, +.>The subtraction of co-polarized power from cross-polarized power may further attenuate the interference of additive noise.

Example 1

1. Simulation experiment analysis

And verifying the accuracy of the iterative algorithm by adopting a mode of randomly generating system distortion parameters to perform Monte Carlo experiments in the simulation parameter range shown in the table I. Table I is used for parameter spans for system distortion parameter estimation simulations. In order to evaluate the overall accuracy of polarization correction, maximum Normalized Error (MNE) is used for characterization, and MNE represents the maximum value of the Euclidean norms of observed quantity and estimated observed quantity differences corresponding to the scattering matrix of any feature.

TABLE I

，

In order to accurately evaluate the estimation error, the error estimation index maximum normalization error (mno) is given below.

（23），

wherein ,representing the maximum eigenvalue of the attached matrix, +.>Represents the conjugate transpose->Is +.>Matrix of->

（24），

Notably, because of the small magnitude of crosstalk, the estimated error of crosstalk has little effect on the MNE, so the MNE mainly exhibits estimated channel imbalance andthe degree of distortion caused to the observed vector by the deviation of (c).

100000 Monte Carlo experiments are carried out so as to test the robustness and accuracy of the algorithm under different system performances and external conditions, corner reflectors are added in the simulation process to verify the correction precision, and the three-sided corner reflectors (TCR) after statistical correction meet the estimation results of polarization correction indexes shown in a table II.

Table II

，

When the signal-to-noise ratio is 45dB, the statistical histogram of the MNE is shown in figure 2, and the high-precision performance index of MNE < -30dB can be met under most conditions. It should be noted that the accuracy of the FRA cannot be expressed from the accuracy of the TCR correction, because the equivalent system distortion parameters obtained by coupling the FAR and the system distortion parameters when the TCR is corrected can only be explained by the MNE index and the index of the TCR correction result. FRA estimated bias as shown in fig. 3, the estimated bias of FRA approximately satisfies the normal distribution, variance 1.2149 ° of bias.

In order to evaluate the influence of crosstalk magnitude and signal-to-noise ratio on FRA estimation deviation, monte Carlo experiments are performed by setting different signal-to-noise ratios and maximum crosstalk magnitude, and the variance of the obtained estimated FRA deviation is shown in FIG. 4. It has been found that when the system is well designed, i.e. the crosstalk magnitude is less than-35 dB, the Radar Cross Section (RCS) of the scaler is large enough, i.e. the signal-to-noise ratio (SNR) is greater than40dB, it can be realized that the estimated deviation of FRA is smaller than。

Since the observation data of the TCR is also affected by noise and non-idealities of the TCR's own scattering matrix, the performance index obtained from the corrected TCR is not necessarily accurate, so the residual polarization distortion of the system under the above conditions is evaluated by simulation. An accuracy expression of the residual distortion is given below.

（25），

wherein ,representing residual reception distortion matrix,/>Representing residual transmit distortion matrix,/>Representing residual component->

，

，

Then the residual channel amplitude and phase is unbalancedResidual Crosstalk->Residual MGC compensation error->It is possible to define the following,

（26），

（27），

（28），

（29），

wherein ,a module representing plural numbers, ">Representing the argument of the complex number. Equations (21) - (23) can evaluate the correction accuracy that the active scaler can provide under noise interference. The statistical graph of the residual error is shown in fig. 5, where fig. 5 (a) is a graph of the magnitude of the residual MGC compensation error, fig. 5 (b) is a graph of the phase of the residual MGC compensation error, fig. 5 (c) is a graph of the magnitude of the residual channel imbalance, and fig. 5 (d) is a graph of the phase of the residual channel imbalance.

Combining the analysis and simulation results, the following conclusion can be obtained that the constraint point target calibration and calibration precision factors are: the signal-to-noise ratio (SNR) of the observed quantity of the point target, the difference between the scattering matrix of the scaler and the ideal scattering matrix and the selection of the reciprocity target are satisfied in FRA estimation. The above constraints can be improved by enhancing the performance of the device and algorithm, the most significant influencing factor being the stability of the system during the calibration period. Observing the law of the change of the distortion parameters of the system along with time, and determining a proper calibration period to enable the corrected full-polarization data to meet high-precision indexes.

2. Verification of measured data

Based on the full polarization data acquired by the LT-1 system, the accuracy of the calibration and correction results is evaluated from various aspects. Three-scene LT-1A star is selected to review data collected in Xinjiang Hami calibration places, imaging time is 2023, 2, 23 and 3 days, and distortion parameter calibration results are shown in Table III.

The result of the FRA estimation based on the formula (29) and the statistical chart are shown in fig. 6, where fig. 6 (a) is 2 months 15 days data, fig. 6 (b) is 2 months 23 days data, and fig. 6 (c) is 3 months 3 days data. It can be found that the FRA estimated by the active scaler differs from the FRA estimated based on the reciprocity assumption by less thanIt is explained that the FRA estimation method adopted is effective. To further verify the quality of the correction data, fig. 7 gives the result of polarization decomposition, fig. 7 (a) is data of 15 days for 2 months, fig. 7 (b) is data of 23 days for 2 months, and fig. 7 (c) is a polarization decomposition pseudo-color chart of data of 3 days for 3 months. In view of the existence of building areas in the calibration field scene, the four-component decomposition scheme proposed by An is adopted to reduce the volume scattering estimation of urban areas, and more visual results are displayed. From the results, it can be seen that the decomposition results are consistent with expectations except that urban areas with large orientation angles still have volume scattering overestimation. />

Table III

，

One of the drawbacks of the point target scaling scheme is that only the equivalent distortion parameters at a certain moment can be accurately scaled, when the system distortion parameters fluctuate, the absolute amplitude-phase coefficients are ignored, and the observed quantity actually used for estimating the FRA should satisfy the following formula:

（30），

wherein ,

（31），

wherein the subscriptRepresenting parameters for correction ∈ ->And->Representing the system residual polarization distortion matrix. When the system distortion parameter is similar to the compensation parameter, the result of FRA estimation is close to +.>After FRA compensation, the influence caused by the fuzzy parameter estimation is removed, high-precision polarization observance is still obtained, and residual distortion is mainly influenced by whether the target estimated by the FRA meets the scattering reciprocity assumption. As can be seen from equation (42), when the FRA estimation error satisfies less than + ->When the equivalent crosstalk is smaller than-35 dB, the index can be satisfied. The residual polarization distortion satisfies the following formula->

（32），

（33），

wherein ,。

since the true value of FRA can not be known, the stability of the crosstalk of the system is difficult to directly evaluate, the distortion parameter of the first scene is adopted as the correction parameter of the rest scenes, and the calibration flow is carried out, if the system parameter is stable, a good calibration result can be obtained. Two schemes for the comparative test, scheme 1, are given below: estimating all distortion parameters and compensating the three-view data by using the observed quantity of the corresponding active scaler; scheme 2: and compensating the system distortion parameters containing the blurring, which are estimated by the scene of 2 months and 15 days, and estimating and compensating FRA according to the flow. And finally, taking the correction result of the TCR as an evaluation index, and the correction result of the TCR which is independently calibrated and the correction result of the TCR which is not independently calibrated are shown in a table IV and a table V, wherein the full polarization data of 2 months 23 days and 2 months 23 days are well corrected, and the final result is consistent with the expectation.

TABLE IV

，

Table V

，

It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (1)

1. The polarization scaling method of the L-band full-polarization system is characterized by being applicable to any scaler group of three different scalers, and comprises the following steps:

step 1, designing a step iteration estimation algorithm of system distortion, estimating a system distortion parameter containing blur based on a scaler observation vector, wherein the step comprises the following steps:

the active scaler observance model of the distortion is constructed as follows:

（1），

（2），

wherein ,representing the actual observed quantity of the ground object>Is a straight line vector of->Representing Cronecker product, superscript +.>Representing the transpose of the matrix>Representing the absolute amplitude and phase coefficient of the scaler, +.>Representing the homopolar and cross-polar channel imbalance introduced by the artificial gain controller compensation error,/->Representing the imbalance value of the receive channel, +.> and />Representing the cross-talk of the receive channels,representing the imbalance value of the transmit channel, +.> and />Representing crosstalk at the transmitting end->Representing Faraday rotation angle, & lt & gt>Representing the ground object scattering matrix, < >>Representing the reception->Polarized wave reflection->Complex scattering coefficient of polarized wave,/->Line straightening vectors of a random error matrix representing the contribution of system noise, interference signals and clutter to the scaler observation vector, +.>Representing an equivalent polarization distortion matrix;

minimizing a cost function through an optimization algorithm to obtain a group of distortion parameters conforming to reality; the cost function characterizes the difference F between the estimated observables and the actual observables, defined as follows:

（3），

wherein , and />Respectively represent +.>Time observations and estimated observations of the individual scalers, +.>Representing the 2 norms of the vector, ">Representing the real part of the complex number, ">An imaginary part representing a complex number;

there is a ambiguity between the Faraday rotation angle, the system distortion matrix and the absolute amplitude-phase coefficient, and the ambiguity problem of the Faraday rotation angle is described by the following two formulas:

（4），

（5），

for the receive matrix, the following relationship exists:

（6），

（7），

（8），

in combination of formulas (5) to (6), there is a ambiguity between the Faraday rotation matrix and the system distortion matrix, and the degree of ambiguity of the Faraday rotation angle isWhen (I)>Representing the blurring of the parameters caused to the absolute amplitude and phase coefficients, is-> and />Respectively corresponding to the ambiguous transmit and receive channel imbalance values,/-, respectively>，/>，/>，/>Is the corresponding ambiguous crosstalk value;

system distortion parameter presenceIs a phase ambiguity of:

（9），

calculating a least square solution of a system distortion parameter by adopting a Levenberg-Marquardt;

the calculation is carried out by adopting a step-by-step estimation mode, and the equivalent model is as follows:

（10），

wherein , （11），

（12），

（13），

wherein ,representing an equivalent transmit distortion matrix, ">Representing an equivalent reception distortion matrix, ">Representing residual absolute amplitude and phase coefficients extracted by the equivalent distortion matrix with HH polarization channel as reference, < ->Represents the scaler equivalent absolute amplitude and phase coefficient under the model, subscript +.>Indicate->Data corresponding to the scalers; in the following description of iterative algorithms, < +.>Indicating true value(s)>Representing the estimated value; /> and />Representing crosstalk of equivalent receiving channels, +.>Representing the imbalance value of the equivalent receive channel, +.> and />Representing the crosstalk of the equivalent transmitting terminal +.>Representing an imbalance value of the transmit channel;

firstly, carrying out iterative solution on an equivalent model formed by the formula (10), adopting a strategy of iterative compensation at the same time, and after each iteration, setting the initial value of the absolute amplitude-phase coefficient of the scaler to be 1, and repeatedly iterating the rest parameters by taking the iterated result as a new initial value; to avoid estimationDeviating from the actual situation, the amplitude range pairs based on the antenna pattern in the iterative processAdding constraint conditions>Representing estimated +.>The method comprises the steps of carrying out a first treatment on the surface of the After iteration convergence, judge->Whether the absolute value of the phase of (a) is smaller than +.>If not, correct->Is->Then compensate +.>Distortion of the observed quantity caused; the amplitude range increase inequality constraint based on the antenna pattern is shown as follows:

，

wherein ,representing the value of the variable when the objective function is minimized,/->Representing the scaler amplitude difference threshold, +.>Expressed in decibels @, @>The representation takes absolute value; for simplicity of expression, define:

（14），

wherein ,representation ofAbsolute amplitude and phase coefficient of scaler, +.>After the first iteration and compensation is completed, the observed quantity satisfies the following formula:

（15），

under the new model, after each iteration, except for the initial value of the system crosstalk which is kept to be 0, the rest parameters are iterated with the iterated result as a new initial value:

，

wherein, define:

（16）

step 2, because of the space-time variation characteristic of Faraday effect, re-estimating Faraday rotation angle for a general scene, compensating the channel error of polarization data of the general scene based on the system distortion parameter estimated in step 1 to obtain a polarization observation vector corrected by the channel error, and then realizing accurate correction of full polarization data based on the polarization observation vector corrected by the channel error and the compensation Faraday rotation angle to obtain a data product meeting the application requirement of full polarization, wherein the method comprises the following steps:

when the system has no distortion and noise is ignored, the polarization observation vector of the ground objectSatisfies the following conditions:

（17），

the influence of Faraday rotation angle on the target covariance matrix is obtained through deduction, and the influence has the following relation:

（18），

defining characteristic complex values of estimated Faraday rotation anglesThe formula is as follows:

（19），

（20），

wherein , wherein Represents the m-th row and n-th column elements of the covariance matrix, and:

（21），

wherein ,representing conjugate operation;

equation (21) shows that the faraday rotation angle estimated from the observation vector of the feature satisfying reciprocity is expressed as follows:

（22），

wherein ,representing the argument of plural ++>In imaginary units.