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CN113567942A - Measurement accuracy analysis method for multi-baseline interferometric synthetic aperture radar system - Google Patents

Measurement accuracy analysis method for multi-baseline interferometric synthetic aperture radar system Download PDF

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CN113567942A
CN113567942A CN202110927363.XA CN202110927363A CN113567942A CN 113567942 A CN113567942 A CN 113567942A CN 202110927363 A CN202110927363 A CN 202110927363A CN 113567942 A CN113567942 A CN 113567942A
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CN113567942B (en
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陶利
曲圣杰
曹菡
张程
许涛
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CETC 38 Research Institute
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Abstract

The invention provides a method for analyzing the measurement accuracy of a multi-baseline interferometric synthetic aperture radar system, which comprises the steps of obtaining the parameters of a multi-baseline InSAR system; establishing a system interference coherence model; calculating the relative interference measurement precision; establishing a system interference measurement error equation; and calculating the absolute interferometric measurement accuracy. The invention has the advantages that: the method comprises the steps of determining an expression of interference phase errors through computing system coherence, analyzing relative measurement accuracy of a computing system based on a multi-baseline interference SAR system and combined phase, obtaining an absolute interference elevation error equation through analysis of sensitivity of influence factors of elevation measurement, calculating total measurement errors based on the absolute interference elevation error equation and parameter measurement errors, analyzing the measurement accuracy of the multi-baseline InSAR system, providing theoretical support for obtaining a DEM (dynamic effect model) of a high-accuracy complex terrain area, filling the blank that the influence of decoherence factors and system measurement parameter errors is not fully considered in the existing analysis, and providing an effective way for parameter design and performance analysis of a subsequent multi-baseline interference measurement system.

Description

Measurement accuracy analysis method for multi-baseline interferometric synthetic aperture radar system
Technical Field
The invention relates to the technical field of microwave remote sensing signal processing, in particular to a method for analyzing the measurement accuracy of a multi-baseline interference synthetic aperture radar system.
Background
Synthetic Aperture Radar (SAR) belongs to an active microwave imaging technology and can realize all-time and all-weather earth observation. Synthetic aperture radar Interferometry (InSAR) is a technique for extracting phase information from two or more SAR complex data to obtain three-dimensional information of the earth's surface or its variation information, and is one of the most effective methods for generating a Digital Elevation Model (DEM) for global mapping.
Conventional single baseline InSAR techniques face a number of challenges to obtaining high precision DEMs. On one hand, various decoherence factors such as an InSAR system and data processing restrict the phase measurement and elevation mapping precision of the system; on the other hand, phase information aliasing is caused by undersampling of areas of complex terrain such as steep mountainous areas, urban high-rise buildings and the like, and the reconstruction capability of the complex terrain is limited. The multi-baseline InSAR measurement has interference phases obtained by observing a plurality of baselines, so that the advantages can be complemented, the phase error of a system can be reduced, and the elevation estimation precision can be improved; meanwhile, the short base line can assist the line interference phase to be subjected to phase unwrapping in multi-base-line InSAR observation, the limitation that a single-base-line InSAR is unfolded to the phase of the complex terrain is overcome, and then the interference measurement precision of the system is improved, so that the high-precision DEM of the complex terrain is obtained.
The method considers the elevation mapping precision analysis, and is not only one of key indexes for measuring the performance of the InSAR system, but also an important guide for the performance design and the overall analysis of the InSAR system. Therefore, for the design of the multi-baseline interference SAR system, the analysis of the elevation measurement accuracy of the system is of great significance. The invention patent application with publication number CN102401892A discloses a performance evaluation method for a polarization interferometric synthetic aperture radar system, wherein an analysis object is a planned interferometric synthetic aperture radar system, and in addition, the evaluation method determines radar data of the synthetic aperture radar system with specific parameters in a specific scene according to simulation, and re-evaluates parameters of a target scene based on the radar data, so as to obtain a difference between a target value and an actual value.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for evaluating the measurement accuracy of a multi-baseline interferometric synthetic aperture radar system.
The invention solves the technical problems through the following technical scheme: a method for analyzing the measurement accuracy of multi-baseline interferometric synthetic aperture radar system includes
Acquiring parameters of a multi-baseline InSAR system;
establishing a system interference coherent model, respectively establishing a single baseline InSAR system coherent model and a multi-baseline InSAR system coherent model based on system coherence and an interference phase probability density function, establishing an interference phase error expression, and obtaining a system total coherence coefficient;
calculating relative interference measurement precision, and respectively calculating relative elevation measurement errors of the single-polarity InSAR and the multi-baseline InSAR according to the InSAR imaging geometric relation and the interference phase error;
establishing a system interference measurement error equation, respectively solving partial derivatives of interference height measurement parameters based on an interference SAR height measurement formula, and respectively establishing elevation measurement error equations under a multi-baseline interference configuration;
calculating absolute interferometric measurement accuracy, and calculating multi-baseline InSAR measurement accuracy by combining interferometric SAR system parameter measurement accuracy based on a multi-baseline interferometric configuration elevation measurement error equation.
The invention determines an expression of interference phase errors through the coherence of a computing system, then analyzes the relative measurement precision of the computing system based on the joint phase of a multi-baseline interference SAR system, obtains an absolute interference elevation error equation through the analysis of influence factors of elevation measurement, and calculates the total measurement error based on the absolute interference elevation error equation and parameter measurement errors, thereby respectively obtaining the relative elevation error and the absolute elevation error of the multi-baseline InSAR system, realizing the analysis of the measurement precision of the multi-baseline InSAR system, providing theoretical support for obtaining DEM (digital elevation model) of a high-precision complex terrain area, filling the blank that the influence of decoherence factors and system measurement parameter errors is not fully considered in the existing analysis, and providing an effective path for the parameter design and performance analysis of a subsequent multi-baseline interference measurement system.
Preferably, the parameters for acquiring the multi-baseline InSAR system include an interferometric measurement geometry of the multi-baseline InSAR system, SAR load parameter information, interferometric baseline parameter information, system measurement parameter precision, and data error items introduced by SAR imaging and interferometric processing.
Preferably, the method for constructing the coherency model of the single baseline InSAR system comprises the following steps:
under the condition of single-baseline interference, the phase of interference
Figure BDA0003205063690000021
Has a probability density function of
Figure BDA0003205063690000022
Figure BDA0003205063690000023
Wherein h(s) represents the elevation of the pixel point s, gamma is the complex interference coherence coefficient of the point, and alpha represents phase elevation conversion factors introduced by different baselines;
limiting the phase within the range of true values + -pi, the interference phase expectation and the interference phase error are expressed as follows:
Figure BDA0003205063690000024
Figure BDA0003205063690000031
wherein ,Φ0True phase, Li ═ arg (γ)2(. cndot.) is a function of the logarithm of the degree,
Figure BDA0003205063690000032
the construction method of the multi-baseline InSAR system coherence model comprises the following steps:
under the condition of multi-baseline interference, for a multi-baseline interference system with K independent interference phase measurements, considering the independence between interferograms, the interference phase joint probability density function F (phi(s); h (s)) of observation data of the multi-baseline InSAR system is expressed as follows:
Figure BDA0003205063690000033
wherein ,
Figure BDA0003205063690000034
for corresponding K interference phases [ ·]TRepresenting the transpose of the matrix.
Preferably, the influencing factors of the complex interference coherence coefficient γ include:
temporal decoherence gammatempCaused by changes in the surface scattering properties and atmospheric variations during image acquisition;
geometric or baseline decoherence gammageoCaused by the difference in viewing angle;
doppler centroid decoherence gammadcDue to the difference between the Doppler centroids of the two images;
volume scattering decoherence gammavolWhile electromagnetic waves are propagated inside a scatterer with a certain volume, decoherence influence caused by multiple scattering is caused;
thermal noise decoherence gammathermThe effects caused by system characteristics, including gain and antenna characteristics;
data processing decoherence gammaprocResults from the algorithms employed in the data processing process;
the overall system coherence is as follows:
|γ|＝γtemp×γgeo×γdc×γvol×γtherm×γproc (5)
wherein ,
Figure BDA0003205063690000035
Figure BDA0003205063690000036
Figure BDA0003205063690000041
Figure BDA0003205063690000042
Figure BDA0003205063690000043
Figure BDA0003205063690000044
wherein, Q represents the working mode of the interference SAR system, Q is 1 represents the primary and secondary SAR antennas to transmit and receive, Q is 2 represents the primary and secondary SAR antennas to transmit and receive; sigmay and σzRespectively representing the motion variances of the scatterers along the cross direction and the vertical direction; theta is the angle of view of the radar,
Figure BDA0003205063690000045
is a critical vertical base line, B⊥Bcos (θ - β) is the vertical baseline, R is the antenna slant distance, representing the distance of the antenna from the target; beta is the angle between the base line and the horizontal direction, i.e. the base line dip angle, tauyFor the terrain slope angle, rhoyFor pitch resolution,. DELTA.fDCIs the difference of the Doppler centroid of the main and auxiliary images, BAIs the azimuth Doppler bandwidth, hvIs the thickness of vegetation, betaσFor attenuation factor, SNR, of radar wavesjSignal to noise ratio, mu, of the jth antenna systemr and μaRegistration errors in the distance and orientation directions, respectively.
Preferably, the method for calculating the relative interferometric accuracy of the system comprises:
the formula of the relative elevation error caused by the phase error of the single baseline InSAR is as follows:
Figure BDA0003205063690000046
wherein ,
Figure BDA0003205063690000047
for a multi-baseline InSAR system, the combined phase error causes the relative elevation measurement error of the system, if the maximum likelihood function estimation is adopted to carry out the combined phase elevation estimation, the relative elevation measurement error is,
Figure BDA0003205063690000048
wherein ,
Figure BDA0003205063690000051
then
Figure BDA0003205063690000052
To obtain
Figure BDA0003205063690000053
wherein
Figure BDA0003205063690000054
Figure BDA0003205063690000055
Figure BDA0003205063690000056
wherein ,γkThe complex coherence coefficient corresponding to the kth baseline,
Figure BDA0003205063690000057
preferably, the method for establishing the interferometric error equation comprises:
deriving a relation between an elevation measurement result H and interference height measurement influence parameters based on an InSAR height measurement formula, wherein the interference height measurement influence parameters comprise antenna height H, antenna slant distance R, baseline parameters (B, beta) and absolute interference phase psi, and respectively calculating partial derivatives of the interference height measurement parameters to obtain parameter error influence factors:
Figure BDA0003205063690000058
for a multi-baseline InSAR system, the elevation inversion of any interferometric observation system to a certain measurement point on the ground has the following formula:
h＝H-Rcos(θa+β) (20)
Figure BDA0003205063690000059
wherein ,θaIs the echo direction of arrival angle;
assuming that the measurement variables (H, R, B, beta, psi) of each system are independent of each other, the error equation of the single-baseline interference elevation measurement obtained according to the error propagation formula is as follows:
Figure BDA00032050636900000510
wherein ,(σH，σR，σB，σβ，σψ) Measuring errors of height measurement influence parameters corresponding to the five systems; the calculation formula of the error influence factors of the parameters is as follows:
Figure BDA0003205063690000061
wherein ,θ0＝θa+ β, first four terms (σ)H，σR，σB，σβ) For systematic errors, interference phase errors σψDetermining the relative measurement precision of the DEM for random errors;
for a multi-baseline interference configuration, an elevation measurement error equation is as follows:
Figure BDA0003205063690000062
wherein ,(Bk，βk) For the kth baseline parameter, k may be selected as the longest baseline configuration.
Preferably, the method for calculating the accuracy of absolute interferometry is to use the error component (σ) of each parameterH，σR，σB，σβ，σψ) And substituting the formula (24) to obtain an elevation measurement error reflecting the interference measurement precision.
The method for analyzing the measurement accuracy of the multi-baseline interference synthetic aperture radar system has the advantages that: the method comprises the steps of determining an expression of interference phase errors through a calculation system coherence coefficient, analyzing relative measurement precision of the calculation system based on multi-baseline joint phase, simultaneously obtaining an absolute interference elevation error equation through analysis of influence factors of elevation measurement, calculating to obtain total measurement errors based on the absolute interference elevation error equation and parameter measurement errors, obtaining relative elevation errors and absolute elevation errors of a multi-baseline InSAR system respectively, realizing analysis of the measurement precision of the multi-baseline InSAR system, providing theoretical support for obtaining a high-precision complex terrain area DEM, filling the blank that influence of decoherence factors and system measurement parameter errors is not considered comprehensively in the existing analysis, and providing an effective way for parameter design and performance analysis of a subsequent multi-baseline interference measurement system. The multi-baseline interference phase quality is jointly estimated by a plurality of baseline measurement phases and greatly improved, and the long baseline determines higher altimetry sensitivity and lower parameter measurement error influence; the design of the InSAR system can be carried out according to the precision requirement, the measurement precision is calculated according to the design parameters, the system parameters are adjusted based on the compromise of the system baseline configuration and the radar system performance under the condition that the measurement precision does not meet the design requirement, the calculation is carried out again until the designed InSAR system meets the design requirement, and therefore the experiment cost is reduced. And a referable analysis method and a theoretical basis are provided for the performance design of the multi-baseline InSAR system.
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FIG. 1 is a schematic diagram of a multi-baseline interferometric synthetic aperture radar system provided by an embodiment of the present invention;
fig. 2 is a flowchart of a method for analyzing measurement accuracy of a multi-baseline interferometric synthetic aperture radar system according to an embodiment of the present invention.
Detailed Description
To make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention are described below in detail and completely with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. 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.
The embodiment provides a method for analyzing measurement accuracy of a multi-baseline interference synthetic aperture radar (InASR) system, wherein an InSAR system is generally divided into an intersection-orbit interference mode and a forward-orbit interference mode, the intersection-orbit interference SAR refers to a mode that a baseline (a connecting line of two pairs of antennas) formed by two pairs of SAR antennas is perpendicular to the flight direction of a platform, and the forward-orbit interference SAR refers to a mode that the baseline is parallel to the flight direction of the platform. FIG. 1 shows a multi-baseline InSAR systemThe SAR load flight direction is taken as the x direction, the sky direction is taken as the z direction, and the y direction is the side-looking ground distance direction vertical to the flight direction; the phase center position of the main antenna is A0The phase center positions of the auxiliary antennas are respectively A1、A２、、AKIn turn forming an interferometric system of different base length with the main antenna, where base | A0A1|＝B1、|A0A２|＝B2、...、|A0AK|＝BKAnd base line A0A1、A0A2、、A0AKRespectively having a base inclination angle beta with respect to the horizontal direction y1，β2，...，βKFor convenience of description, it is assumed here that β1＜β2＜...＜βKHowever, for a multi-baseline InSAR system that does not satisfy this condition, the precision analysis method provided by this embodiment is also applicable.
For a multi-baseline InSAR system, the main system measurement parameters are as follows: main antenna A0Height H of antenna, length B of base line of system interference measurement parameterkBase line inclination angle betakPhase of interference
Figure BDA0003205063690000071
Antenna slant distance RkWherein the antenna is at a slant distance RkIs an antenna AkDistance from target observation point P; also for ease of subsequent description of the accuracy analysis method, it is assumed here that the baseline B iskLocated in the yoz plane and interfering the phase for single-baseline InSAR elevation measurement
Figure BDA0003205063690000072
The slant distance R from the main and auxiliary antennas to the target point P0、RkAnd obtaining and then resolving the height h of the P point.
For a single baseline InSAR system, the phase is interfered
Figure BDA0003205063690000073
The formula is as follows:
Figure BDA0003205063690000074
wherein, Q represents the working mode of the interference SAR system, Q is 1 represents the primary and secondary SAR antennas to transmit and receive, Q is 2 represents the primary and secondary SAR antennas to transmit and receive; Δ rk＝Rk-R0And for the main and auxiliary antenna slant distance difference after registration, the interference phase is a winding phase which is a result of taking a mode of the actual terrain phase to 2 pi, phase unwrapping is needed to be carried out, constant phase deviation is compensated, and finally the ground height is inverted by the interference measurement parameters and the absolute interference phase calibrated by the system.
For a multi-baseline InSAR system with K pairs of measurement baselines, the SAR interferometric phase is represented as:
Figure BDA0003205063690000081
wherein h(s) represents the elevation of the pixel s, NxM is the image size, i.e. the total number of pixels, k represents the kth interferogram, ωkIs indicative of the incoherent noise that is,<·>2πdenotes 2 pi modulo winding, alphakIs represented as follows:
Figure BDA0003205063690000082
wherein ,λkFor the k-th interferogram wavelength, it is assumed here that all measurement systems have the same wavelength, i.e. λk＝λ，B⊥kIs the vertical baseline component of the kth interferogram, theta is the angle of incidence, R0Is the main antenna to scene slant.
From the above formula, it can be determined that the difference between the interference basis lines depends mainly on αkThe multi-baseline DEM reconstruction problem is that K winding phases obtained from measurement
Figure BDA0003205063690000083
In the method, a terrain true height value h(s) is estimated, namely the measurement accuracy problem of the multi-baseline InSAR system is actually the error estimation of the pixel point height h(s)Problem, and the error of elevation h(s) follows the interference phase
Figure BDA0003205063690000084
There is a direct association.
Referring to fig. 2, based on the above analysis, the method for analyzing the measurement accuracy of the multi-baseline interferometric synthetic aperture radar system provided in this embodiment includes,
acquiring parameters of a multi-baseline InSAR system;
establishing a system interference coherence model, respectively establishing a single baseline InSAR system coherence model and a multi-baseline InSAR system coherence model based on system coherence and an interference phase probability density function, establishing an interference phase error expression, and obtaining a system total coherence coefficient;
calculating the relative interference measurement precision of the system, and respectively calculating the relative elevation measurement errors of the single baseline InSAR and the multi-baseline InSAR according to the InSAR imaging geometric relation and the interference phase error;
establishing an interferometric measurement error equation, respectively solving partial derivatives of interferometric height measurement influence parameters based on an interferometric SAR height measurement formula, and then establishing single-baseline and multi-baseline interferometric measurement elevation error equations under the system configuration;
calculating absolute interferometric measurement accuracy, and calculating the absolute height measurement accuracy of the multi-baseline InSAR system by combining the height measurement influence parameter acquisition accuracy of the interferometric SAR system based on a multi-baseline interferometric configuration elevation measurement error equation.
In the embodiment, an expression of interference phase errors is determined by calculating the coherence of a system, then the relative measurement precision of the system is analyzed and calculated based on multi-baseline joint phase, meanwhile, an absolute interference elevation error equation is obtained by analyzing influence factors of elevation measurement, and a total measurement error is calculated based on the absolute interference elevation error equation and parameter measurement errors, so that the relative elevation errors and the absolute elevation errors of a multi-baseline InSAR system are respectively obtained, the analysis of the measurement precision of the multi-baseline InSAR system is realized, theoretical support is provided for obtaining a high-precision complex terrain area DEM, the blank that the influence of a decoherence factor and system measurement parameter errors is not fully considered in the existing analysis is filled, and an effective way is provided for parameter design and performance analysis of a subsequent multi-baseline interference measurement system.
Specifically, the method for analyzing the measurement accuracy of the multi-baseline INSAR system provided in this embodiment includes the following steps:
acquiring parameters of a multi-baseline InSAR system; the parameters of the InSAR system comprise a multi-baseline InSAR system interference measurement geometric configuration, SAR load parameter information, interference baseline parameter information, system measurement parameter precision, and data error items introduced by SAR imaging and interference processing.
Establishing an interference coherence model, respectively establishing a single baseline InSAR system coherence model and a multi-baseline InSAR system coherence model based on system coherence and an interference phase probability density function, establishing an interference phase error expression, and obtaining a total system coherence coefficient;
under the condition of single-baseline interference, the phase of interference
Figure BDA0003205063690000091
Has a probability density function of
Figure BDA0003205063690000092
Figure BDA0003205063690000093
Wherein h(s) represents the elevation of the pixel point s, gamma is the complex interference coherence coefficient of the point, and alpha represents phase elevation conversion factors introduced by different baselines;
limiting the phase within the range of true value + -pi, the interference phase expectation and the interference phase error
Figure BDA0003205063690000099
The expression is as follows:
Figure BDA0003205063690000094
Figure BDA0003205063690000095
wherein ,Φ0True phase, Li ═ arg (γ)2(. cndot.) is a function of the logarithm of the degree,
Figure BDA0003205063690000096
the construction method of the multi-baseline InSAR system coherence model comprises the following steps:
under the condition of multi-baseline interference, for a multi-baseline interference system with K independent interference phases, considering the independence between interferograms, the interference phase joint probability density function F (phi(s); h (s)) of observation data of the multi-baseline InSAR system is expressed as follows:
Figure BDA0003205063690000097
wherein ,
Figure BDA0003205063690000098
for corresponding K interference phases [ ·]TRepresenting the transpose of the matrix.
The influence factors of the complex interference coherence coefficient gamma include:
temporal decoherence gammatempCaused by changes in the surface scattering properties and atmospheric variations during image acquisition;
geometric or baseline decoherence gammageoCaused by the difference in viewing angle;
doppler centroid decoherence gammadcDue to the difference between the Doppler centroids of the two images;
volume scattering decoherence gammavolWhile electromagnetic waves are propagated inside a scatterer with a certain volume, decoherence influence caused by multiple scattering is caused;
thermal noise decoherence gammathermThe effects caused by system characteristics, including gain and antenna characteristics;
data processing decoherence gammaprocResults from the algorithms employed in the data processing process;
the overall system coherence is as follows:
|γ|＝γtemp×γgeo×γdc×γvol×γtherm×γproc (5)
wherein ,
Figure BDA0003205063690000101
Figure BDA0003205063690000102
Figure BDA0003205063690000103
Figure BDA0003205063690000104
Figure BDA0003205063690000105
Figure BDA0003205063690000106
wherein, Q represents the system working mode, Q ═ 1 represents one-sending and double-receiving, Q ═ 2 represents the self-sending and self-receiving; sigmay and σzRespectively representing the motion variances of the scatterers along the cross direction and the vertical direction; theta is the angle of view of the radar,
Figure BDA0003205063690000107
is a critical vertical base line, B⊥Bcos (θ - β) is the vertical baseline, R is the antenna slant distance, representing the distance of the antenna from the target; beta is the angle between the base line and the horizontal direction, i.e. the base line dip angle, tauyFor the terrain slope angle, rhoyFor pitch resolution,. DELTA.fDCIs the difference of the Doppler centroid of the main and auxiliary images, BAIs the azimuth Doppler bandwidth, hvIs the thickness of vegetation, betaσFor attenuation factor, SNR, of radar wavesjSignal to noise ratio, mu, of the jth antenna systemr and μaRegistration errors in the distance and orientation directions, respectively.
Calculating the relative interference measurement precision of the system, and respectively calculating the relative elevation measurement errors of the single baseline InSAR and the multi-baseline InSAR according to the InSAR imaging geometric relation and the interference phase error;
the formula of the relative elevation error caused by the phase error of the single baseline InSAR is as follows:
Figure BDA0003205063690000111
wherein ,
Figure BDA0003205063690000112
for relative elevation measurement errors caused by multi-baseline InSAR combined phase errors, the maximum likelihood function estimation is adopted to carry out the combined phase elevation estimation, the relative elevation measurement errors are,
Figure BDA0003205063690000113
wherein E [ ] represents the averaging, the subscript mb is the multi-baseline (multi-baseline) InSAR system,
Figure BDA0003205063690000114
then
Figure BDA0003205063690000115
To obtain
Figure BDA0003205063690000116
wherein
Figure BDA0003205063690000117
Figure BDA0003205063690000118
Figure BDA0003205063690000119
wherein ,γkThe complex coherence coefficient corresponding to the kth baseline,
Figure BDA00032050636900001110
establishing a system interference measurement error equation, respectively solving partial derivatives of interference height measurement parameters based on an interference SAR height measurement formula, and respectively establishing elevation measurement error equations under a multi-baseline interference configuration;
deriving a relation between an elevation measurement result H and an interference height measurement parameter based on an InSAR height measurement formula, wherein the interference height measurement parameter comprises an antenna height H, an antenna slant distance R, a baseline parameter (B, beta) and an interference phase psi, and respectively calculating a partial derivative of the interference height measurement parameter to obtain each error influence factor:
Figure BDA0003205063690000121
for a multi-baseline InSAR system, the elevation inversion of any interferometric observation system to a certain measurement point on the ground has the following formula:
h＝H-Rcos(θa+β) (20)
Figure BDA0003205063690000122
wherein ,θaIs the echo direction of arrival angle;
assuming that the variables (H, R, B, beta, psi) are independent of each other, the error equation of the single-baseline interferometric elevation measurement is obtained according to the error propagation formula as follows:
Figure BDA0003205063690000123
wherein ,(σH，σR，σB，σβ，σψ) Measuring errors corresponding to the 5 interference height measurement parameters respectively; the calculation formula of each error influence factor is as follows:
Figure BDA0003205063690000124
wherein ,θ0＝θa+ β, first four terms (σ)H，σR，σB，σβ) For system error, the accuracy of system measurement parameters can be further improved by ground calibration, and the latter term interferes with phase error sigmaψFor random errors caused by the coherence removal of the system, the performance can be improved by comprehensively optimizing the system design, and the relative height measurement precision of the DEM is determined;
for a multi-baseline interference configuration, the phase part in an error equation is subjected to precision improvement through multi-baseline phase joint estimation, and a high-quality interference phase observed value is obtained; meanwhile, the longest base line configuration in multi-base line observation is considered, so that the system measurement sensitivity is further improved, the influence of base line measurement errors and the like is reduced, and the absolute measurement accuracy of the system is improved; carrying out absolute height measurement precision analysis on the multi-baseline interference SAR system based on the longest baseline configuration and the multi-baseline joint estimation phase; the absolute elevation measurement error equation is as follows:
Figure BDA0003205063690000131
wherein ,(Bk，βk) Is the kth baseline parameter, k being the longest baseline configuration, in this example, k isThe kth baseline.
Calculating absolute interferometric measurement accuracy, based on multi-baseline interferometric configuration elevation measurement error equation, and combining with actual parameter measurement accuracy (sigma) of interferometric SAR systemH，σR，σB，σβ，σψ) And calculating the measurement accuracy of the multiple baseline InSAR.
Here, each measurement parameter error component (σ) is divided intoH，σR，σB，σβ，σψ) And substituting the formula (24) into the formula to obtain the elevation measurement error reflecting the interference measurement precision.
Based on the method for analyzing the measurement accuracy of the InSAR system provided by the embodiment, the design of the InSAR system can be performed according to the accuracy requirement, the measurement accuracy is calculated according to the design parameters, and under the condition that the measurement accuracy does not meet the design requirement, the parameters of the multi-baseline interference system are adjusted in a compromise mode based on the performance of the radar system, and the calculation is performed again until the designed InSAR system meets the design requirement, so that the experiment cost is reduced.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (7)

1. A method for analyzing the measurement accuracy of a multi-baseline interferometric synthetic aperture radar system is characterized by comprising the following steps: comprises that
Acquiring parameters of a multi-baseline InSAR system;
establishing a system interference coherence model, respectively establishing a single baseline InSAR system coherence model and a multi-baseline InSAR system coherence model based on system coherence and an interference phase probability density function, establishing an interference phase error expression, and obtaining a system total coherence coefficient;
calculating relative interference measurement precision, and respectively calculating relative elevation measurement errors of the single-polarity InSAR and the multi-baseline InSAR according to the InSAR imaging geometric relation and the interference phase error;
establishing a system interference measurement error equation, respectively solving partial derivatives of interference height measurement parameters based on an interference SAR height measurement formula, and respectively establishing elevation measurement error equations under a multi-baseline interference configuration;
calculating absolute interferometric measurement accuracy, and calculating multi-baseline InSAR measurement accuracy by combining interferometric SAR system parameter measurement accuracy based on a multi-baseline interferometric configuration elevation measurement error equation.
2. The method for analyzing the measurement accuracy of the multi-baseline interferometric synthetic aperture radar system according to claim 1, wherein: the parameters of the InSAR system comprise a multi-baseline InSAR system interference measurement geometric configuration, SAR load parameter information, interference baseline parameter information, system measurement parameter precision, and data error items introduced by SAR imaging and interference processing.
3. The method for analyzing the measurement accuracy of the multi-baseline interferometric synthetic aperture radar system according to claim 1, wherein: the method for constructing the coherence model of the single baseline InSAR system comprises the following steps:
under the condition of single-baseline interference, the phase of interference
Figure FDA0003205063680000011
Has a probability density function of
Figure FDA0003205063680000012
Figure FDA0003205063680000013
Wherein h(s) represents the elevation of the pixel point s, gamma is the complex interference coherence coefficient of the point, and alpha represents phase elevation conversion factors introduced by different baselines;
limiting the phase within the range of true values + -pi, the interference phase expectation and the interference phase error are expressed as follows:
Figure FDA0003205063680000014
Figure FDA0003205063680000015
wherein ,Φ0True phase, Li ═ arg (γ)2(. cndot.) is a function of the logarithm of the degree,
Figure FDA0003205063680000016
the construction method of the multi-baseline InSAR system coherence model comprises the following steps:
under the condition of multi-baseline interference, for a multi-baseline interference system with K independent interference phase measurements, considering the independence between interferograms, the interference phase joint probability density function F (phi(s); h (s)) of observation data of the multi-baseline InSAR system is expressed as follows:
Figure FDA0003205063680000021
wherein ,
Figure FDA0003205063680000022
for corresponding K interference phases [ ·]TRepresenting the transpose of the matrix.
4. The method for analyzing the measurement accuracy of the multi-baseline interferometric synthetic aperture radar system according to claim 3, wherein: the influence factors of the complex interference coherence coefficient gamma include:
temporal decoherence gammatempCaused by changes in the surface scattering properties and atmospheric variations during image acquisition;
geometric or baseline decoherence gammageoFromThe difference in viewing angle;
doppler centroid decoherence gammadcDue to the difference between the Doppler centroids of the two images;
volume scattering decoherence gammavolWhile electromagnetic waves are propagated inside a scatterer with a certain volume, decoherence influence caused by multiple scattering is caused;
thermal noise decoherence gammathermThe effects caused by system characteristics, including gain and antenna characteristics;
data processing decoherence gammaprocResults from the algorithms employed in the data processing process;
the overall system coherence is as follows:
|γ|＝γtemp×γgeo×γdc×γvol×γtherm×γproc (5)
wherein ,
Figure FDA0003205063680000023
Figure FDA0003205063680000024
Figure FDA0003205063680000025
Figure FDA0003205063680000026
Figure FDA0003205063680000027
Figure FDA0003205063680000031
wherein, Q represents the working mode of the interference SAR system, Q is 1 represents the primary and secondary SAR antennas to transmit and receive, Q is 2 represents the primary and secondary SAR antennas to transmit and receive; sigmay and σzRespectively representing the motion variances of the scatterers along the cross direction and the vertical direction; theta is the angle of view of the radar,
Figure FDA0003205063680000032
is a critical vertical base line, B⊥Bcos (θ - β) is the vertical baseline, R is the antenna slant distance, representing the distance of the antenna from the target; beta is the angle between the base line and the horizontal direction, i.e. the base line dip angle, tauyFor the terrain slope angle, rhoyFor slope to ground resolution, Δ fDCIs the difference of the Doppler centroid of the main and auxiliary images, BAIs the azimuth Doppler bandwidth, hvIs the thickness of vegetation, betaσFor attenuation factor, SNR, of radar wavesjSignal to noise ratio, mu, of the jth antenna systemr and μaRegistration errors in the distance and orientation directions, respectively.
5. The method for analyzing the measurement accuracy of the multi-baseline interferometric synthetic aperture radar system according to claim 4, wherein: the method for calculating the relative interference measurement precision comprises the following steps:
the formula of the relative elevation error caused by the phase error of the single baseline InSAR is as follows:
Figure FDA0003205063680000033
wherein ,
Figure FDA0003205063680000034
for relative elevation measurement errors caused by multi-baseline InSAR combined phase errors, the maximum likelihood function estimation is adopted to carry out the combined phase elevation estimation, the combined relative elevation measurement errors are,
Figure FDA0003205063680000035
wherein ,
Figure FDA0003205063680000036
then
Figure FDA0003205063680000037
To obtain
Figure FDA0003205063680000038
wherein
Figure FDA0003205063680000041
Figure FDA0003205063680000042
Figure FDA0003205063680000043
wherein ,γkThe complex coherence coefficient corresponding to the kth baseline,
Figure FDA0003205063680000044
6. the method for analyzing the measurement accuracy of the multi-baseline interferometric synthetic aperture radar system according to claim 5, wherein: the method for establishing the interferometric error equation comprises the following steps:
deriving a relation between an elevation measurement result H and interference height measurement influence parameters based on an InSAR height measurement formula, wherein the interference height measurement parameters comprise antenna height H, antenna slant distance R, baseline parameters (B, beta) and interference phase psi, and respectively calculating partial derivatives of the interference height measurement parameters to obtain parameter error influence factors:
Figure FDA0003205063680000045
for a multi-baseline InSAR system, the elevation inversion of any interferometric observation system to a certain measurement point on the ground has the following formula:
h＝H-Rcos(θa+β) (20)
Figure FDA0003205063680000046
wherein ,θaIs the echo direction of arrival angle;
assuming that the variables (H, R, B, beta, psi) are independent of each other, the error equation of the single-baseline interferometric elevation measurement is obtained according to the error propagation formula as follows:
Figure FDA0003205063680000047
wherein ,(σH,σR,σB,σβ,σψ) Measuring errors corresponding to the 5 interference height measurement influence parameters respectively; the calculation formula of each error influence factor is as follows:
Figure FDA0003205063680000051
wherein ,θ0＝θa+ β, first four terms (σ)H,σR,σB,σβ) For systematic errors, interference phase errors σψDetermining the relative measurement precision of the DEM for the system random error;
for a multi-baseline interference configuration, an elevation measurement error equation is as follows:
Figure FDA0003205063680000052
wherein ,(Bk，βk) K is the longest baseline configuration for the kth baseline parameter.
7. The method for analyzing the measurement accuracy of the multi-baseline interferometric synthetic aperture radar system according to claim 6, wherein: the method for calculating the absolute interferometric measurement precision comprises the step of obtaining each height measurement influence parameter error (sigma) through system setting and multi-baseline joint estimationH,σR,σB,σβ,σψ) And substituting the absolute elevation measurement error into a formula (24) to obtain the absolute elevation measurement error reflecting the interferometric measurement precision.
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