CN116559905A - Undistorted three-dimensional image reconstruction method for moving target of bistatic SAR sea surface ship - Google Patents
Undistorted three-dimensional image reconstruction method for moving target of bistatic SAR sea surface ship Download PDFInfo
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Abstract
The invention discloses a undistorted three-dimensional image reconstruction method of a double-base SAR sea-surface ship moving target, which comprises the steps of firstly establishing a double-base SAR space geometric configuration and a sea-surface ship moving target echo model, completing parameter initialization, obtaining double-base distance histories from the double-base SAR to any scattering point in the sea-surface ship moving target and pulse pressure echoes of the sea-surface ship moving target of the double-base SAR, preprocessing the echoes, removing Doppler blurring in the double-base SAR echoes and correcting range migration of the echoes, obtaining projection of a distance-centroid-frequency modulation domain, realizing three-dimensional image reconstruction of the ship moving target, and finally carrying out remapping based on a local Cartesian coordinate system, correcting three-dimensional distortion of the target, and realizing undistorted three-dimensional image reconstruction of the sea-surface ship moving target. The method of the invention eliminates the image distortion caused by unknown IPP, realizes undistorted three-dimensional image reconstruction in LCC, and increases the information dimension of the target and improves the information reliability of the target compared with the existing two-dimensional imaging and distorted and uncalibrated results.
Description
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a distortion-free three-dimensional image reconstruction method for a moving target of a bistatic SAR sea surface ship.
Background
Synthetic aperture radar (Synthetic Aperture Radar, SAR) is an all-day, all-weather modern high-resolution microwave remote sensing imaging radar that utilizes the relative motion between the radar antenna and the target area to obtain spatial high resolution. Synthetic aperture radars play an increasingly important role in the fields of topographic mapping, vegetation analysis, marine and hydrographic observation, environmental and disaster monitoring, resource exploration, crust micro-change detection, and the like. Synthetic aperture radars can be divided into two modes according to the configuration of the transceiver station: a single base mode, where the transmitter and receiver are mounted on the same platform; one is the dual base mode, where the transmitter and receiver are mounted on different platforms. In recent years, bistatic synthetic aperture radar (Bistatic SAR) has received increasing attention for its prospective imaging capabilities and geometric flexibility. Moving object imaging has been a long-term topic of interest for SAR communities, and moving object information is critical to wide area surveillance systems with limited revisit time in order to meet the increasing demands on surveillance systems.
In harsh environments, bistatic SAR is critical for extensive monitoring, imaging and identification of marine vessel targets. Current reports and literature on BiSAR focus mainly on stationary scene imaging algorithms such as range-doppler (RD) algorithm, w-k algorithm, non-chirped scaling (NLCS) algorithm. For stationary targets, the RCM and azimuthal doppler parameters are entirely dependent on the motion of the BiSAR platform. However, for moving targets, the motion information of the BiSAR platform cannot determine the RCM and doppler parameters due to the unknown nature of the motion. Moreover, as the ship target is unknown and largely rotates in three dimensions under the disturbance of sea waves, the Imaging Projection Plane (IPP) of the target is unknown and cannot be determined, so that the imaging result is randomly distorted in high dimension, and the target is difficult to effectively identify through the distorted two-dimensional image. Thus, none of the above methods can be achieved by imaging sea surface vessel moving targets in bistatic SAR.
Disclosure of Invention
In order to solve the technical problems, the invention provides a distortion-free three-dimensional image reconstruction method for a moving target of a double-base SAR sea ship, which aims at the defects of the prior art and solves the problem of high-dimensional random distortion of an imaging result caused by unknown movement of the target, thereby realizing distortion-free three-dimensional image reconstruction processing of the moving target of the double-base SAR sea ship.
The technical scheme of the invention is as follows: a undistorted three-dimensional image reconstruction method for a double-base SAR sea surface ship moving target comprises the following specific steps:
step one, establishing a double-base SAR space geometrical configuration and a sea surface ship moving target echo model, and completing parameter initialization;
in rectangular coordinate system O-XYZ, the position vectors of transmitting station and receiving station at azimuth zero time are respectively and />The speed vectors of the transmitting station and the receiving station are +.> and /> A transpose operation representing a vector; the position coordinate vector of the rotation center of the sea surface ship moving object in O-XYZ is +.>
Establishing a ship-to-solid coordinate system o-xyz by taking the ship head direction as an x axis and the port direction as a y axis; in the ship fixed coordinate system, the coordinate vector of any scattering point in the sea surface ship moving target is set asSea surface ship moving object is +.about rotation axis under the action of sea wave>Rotating anticlockwise at a rotation speed omega, wherein the rotation angle is theta (eta), and eta represents azimuth slow time; the three-dimensional rotation matrix of the sea surface ship moving target is:
M(η)＝I+sinθ(η)K+(1-cosθ(η))K 2
wherein I represents a 3×3 identity matrix, K represents a cross product matrix of the rotation axis b, and the expression is as follows:
any scattering point r in sea surface ship moving target p Coordinates after three-dimensional rotation under the action of ocean wavesExpressed as:
scattering point r in rectangular coordinate system O-XYZ p Three-dimensional coordinates of (a)Expressed as:
wherein ,MT The conversion matrix from the ship fixed coordinate system to the rectangular coordinate system O-XYZ is expressed as follows:
wherein ,θT Representing the rotation angle required for the conversion of the ship's fixed to rectangular coordinates O-XYZ.
Step two, obtaining a double-base distance course from the double-base SAR to any scattering point in the sea surface ship moving target;
arbitrary scattering point r from bistatic SAR to sea surface ship moving target p Is R (eta; R) p ) Expressed as:
wherein ,rT ＝r T0 +v Tη and rR ＝r R0 +v R η represents the position vectors of the transmitting station and the receiving station at the time η of the azimuth respectively.
The double-base distance course R (eta; R) p ) Performing Taylor expansion to obtain:
wherein ,R0 An initial double-base distance history representing the azimuth 0 moment; k (k) iT ，k iR The i-th order term coefficients representing the distance history of the transmitting station and the receiving station, respectively.
Step three, acquiring pulse pressure echoes of a sea surface ship moving target of the bistatic SAR;
the expression of the echo reflected by the moving target of the sea surface ship after down-conversion and distance compression is as follows:
wherein ,σp Radar cross section RCS, B representing a moving object r Represents the bandwidth of the transmitted signal, τ represents the distance-to-fast time, T a Represents the synthetic aperture time of the moving object, c represents the electromagnetic wave velocity, λ represents the wavelength of the emitted signal, and λ=c/f c ，f c Representing the carrier frequency of the transmitted signal.
Then the echo signal is subjected to distance fast fourier transform to obtain:
wherein ,fτ Represents the distance frequency variable, phi (f) τ η) represents a two-dimensional phase of the moving object echo in a distance frequency domain and an azimuth time domain, and the specific expression is as follows:
wherein ,fdc 、f dr 、f d3 The Doppler mass center, the Doppler modulation frequency and the third-order Doppler frequency respectively represent the moving targets of the sea surface ship, and are specifically expressed as follows:
preprocessing the echo, removing Doppler blurring in the bistatic SAR echo, and correcting range migration of the echo;
construction of deblurring filter H using motion information of bistatic SAR platform de The expression is as follows:
wherein ,and->And respectively representing the Doppler mass center and the Doppler frequency modulation caused by the double-base SAR platform at the azimuth 0 moment.
Then pass through the filter H de The filtered signal phase is:
removing f τ And removing the distance walk of the hollow change of echo distance migration through KT transformation, wherein the KT transformation is expressed as:
where ζ represents the new azimuth time variable.
After KT transformation, the phase of the echo signal becomes:
wherein R (ζ; R) p ) Arbitrary scattering point r from bistatic SAR corresponding to azimuth time variable xi to sea surface ship moving target p Is a dual base range history of (2).
And finally, realizing consistent compensation on residual distance bending and third-order distance migration through an envelope alignment algorithm.
Fifthly, projecting the distance-centroid-frequency modulation frequency domain to realize three-dimensional image reconstruction of the ship moving target;
the azimuth signal within the nth distance is modeled as a multicomponent QFM signal s n (ξ)：
Wherein K represents the firstnumber of QFM signals over n distances. Sigma (sigma) i 、α i 、β i 、γ i The amplitude, doppler centroid, doppler tone frequency, and third-order Doppler frequency of the signal representing the ith scattering point, respectively.
QFM signal for single componentThe fourth order function is expressed as:
wherein ,representing a delay time variable s * (ζ) represents the complex conjugate of s (ζ), and σ, α, β, γ represent the amplitude, the Doppler centroid, the Doppler shift frequency, and the third-order Doppler frequency of the single-component QFM signal, respectively.
For a pair ofAnd performing variable-scale Fourier transform to obtain:
wherein ,fξ Representing the frequency variable to which the azimuth time variable ζ corresponds, δ () represents the impulse function.
By means of a rimThe variable-scale fourier transform of the axes enables accumulation of the signal, namely:
wherein ,representing the delay time variable +.>Corresponding frequency variation.
The doppler tone frequency and the third order doppler frequency passAt->The position of the peak in the domain is obtained, namely:
wherein , and />Representing the estimated values of γ and β, respectively.
Then construct a signal s using the Doppler centroid and Doppler shift frequency estimates c (ζ) is as follows:
then compensate the signal s c (ζ), and after adopting the de-frequency modulation technology and the fast fourier transform, the QFM signal doppler centroid and the amplitude estimation value are respectively:
through the obtained Doppler centroid, frequency modulation, third-order Doppler frequency and signal amplitude estimation value of one scattering point, the Doppler centroid and frequency modulation estimation of all scattering points in the range gate is realized by means of the CLEAN technology, and the projection of the range gate signal to the DC-DFR domain is completed. The three-dimensional projection of the sea surface ship target in the range-centroid-frequency modulation domain (R-DC-DFR domain) is realized by carrying out the same projection processing on all the range gate signals.
Then a projection result set Q of echo data of the double-base SAR in the R-DC-DFR domain can be obtained R After the same processing is carried out on the single-base SAR data, a projection result set Q of the single-base SAR data in the R-DC-DFR domain can be obtained T ，Q T And Q is equal to R Expressed as:
wherein N and M each represent Q T And Q is equal to R The number of elements in the matrix;representing the three-dimensional coordinates of the jth scattering point in the R-DC-DFR domain in the transmitting station data, for>Representing three-dimensional coordinates of a kth scattering point in the R-DC-DFR domain in the data of the receiving station, wherein the three-dimensional coordinates are as follows:
step six, remapping a local Cartesian coordinate system to correct three-dimensional distortion of the target;
and establishing a mapping relation of the sea surface ship moving target in the R-DC-DFR domain and the LCC domain through the three-dimensional rotation parameters of the target, and realizing remapping from the R-DC-DFR domain to the LCC domain.
The re-projection results of the sea surface ship moving target transmitting station and the receiving station in the LCC domain are respectively expressed as follows:
wherein F represents the mapping relation between the R-DC-DFR domain and the local Cartesian coordinates, and ω represents the rotation speed vector of the sea surface ship moving object, namely and />Representing scattering points in the R-DC-DFR domain> and />Remapping to three-dimensional coordinates of a local cartesian coordinate system, namely:
estimating three-dimensional rotation parameters of a target, and adopting similarity S (omega) to estimate a re-projection result set G of a transmitting station and a receiving station in LCC T And G R Is the degree of similarity of (1), namely:
and optimizing three-dimensional rotation parameters of a target by taking the maximum similarity S (omega) as an objective function to obtain a distortion-free remapping result in an LCC domain, thereby obtaining the following constraint optimization problems:
wherein ,ωmax Indicating the maximum rotational speed.
And solving the constraint optimization problem by using a particle swarm optimization algorithm PSO to obtain the three-dimensional rotation parameters of the target, and realizing the undistorted three-dimensional image reconstruction of the sea surface ship moving target.
Further, the three-dimensional image reconstruction method further comprises a step seven of providing three-dimensional image reconstruction indexes and evaluating three-dimensional image reconstruction capability of targets under different configurations and rotating speeds, wherein the three-dimensional image reconstruction capability is specifically as follows:
according to gradient resolution theory, the distance resolution vector ρ r Doppler frequency resolution vector ρ a Doppler frequency modulation resolution vector ρ h Expressed as:
wherein , and />Respectively represent a distance gradient, a Doppler centroid gradient and a Doppler frequency modulation rateThe gradient is expressed as follows:
wherein ,uT and uR Line-of-sight direction unit vectors, M, respectively representing the radars of the transmitting station and the receiving station 2 Representing the second derivative of M (eta) with respect to the azimuth time eta variable at azimuth 0 moment, i.e
Evaluating whether the target has imaging capability under a certain three-dimensional rotation, and defining a resolution matrix lambda consisting of the three resolution unit vectors as follows:
Λ＝[Θ r ,Ξ a ,Γ h ]
wherein ,Γh Representing Doppler frequency resolution vector, Θ r Representing a distance resolution vector, xi a The Doppler frequency resolution vector is represented as follows:
then the Doppler frequency resolution vector Γ h At the distance resolution vector Θ r And Doppler frequency resolution vector Xi a Projection length ρ on formed two-dimensional planar normal 3D As a performance index, expressed as:
the invention has the beneficial effects that: the method comprises the steps of firstly establishing a double-base SAR space geometric configuration and a sea surface ship moving target echo model, completing parameter initialization, obtaining double-base distance process from the double-base SAR to any scattering point in the sea surface ship moving target and pulse pressure echo of the sea surface ship moving target of the double-base SAR, preprocessing the echo, removing Doppler blurring in the double-base SAR echo, correcting the distance migration of the echo, obtaining projection of a distance-centroid-frequency modulation rate domain, realizing three-dimensional image reconstruction of the ship moving target, and finally, carrying out remapping on the basis of a local Cartesian coordinate system, correcting three-dimensional distortion of the target, and realizing undistorted three-dimensional image reconstruction of the sea surface ship moving target. The method of the invention eliminates the image distortion caused by unknown IPP, realizes undistorted three-dimensional image reconstruction in LCC, and increases the information dimension of the target and improves the information reliability of the target compared with the existing two-dimensional imaging and distorted and uncalibrated results.
Drawings
Fig. 1 is a flow chart of a undistorted three-dimensional image reconstruction method of a moving target of a bistatic SAR sea surface ship.
Fig. 2 is a diagram of a bistatic SAR geometry and a model of a sea surface vessel motion target employed in an embodiment of the present invention.
Fig. 3 is a shape diagram of a moving object of a marine vessel in an embodiment of the present invention.
Fig. 4 is an echo diagram of a moving target of a sea surface ship obtained after the third step in the embodiment of the present invention.
Fig. 5 is an echo diagram of a sea surface ship moving target after range migration correction obtained in the fourth step in the embodiment of the present invention.
Fig. 6 is a three-dimensional image reconstruction result diagram of a single-base SAR sea surface ship moving target in a distance-centroid-tone frequency domain, which is obtained after the fifth step in the embodiment of the present invention.
Fig. 7 is a three-dimensional image reconstruction result diagram of a bistatic SAR sea surface ship moving target in a distance-centroid-tone frequency domain, which is obtained after the fifth step in the embodiment of the present invention.
Fig. 8 is a diagram of a distortion-free three-dimensional image reconstruction result of a sea surface ship moving target obtained after the step six in the embodiment of the invention in a local cartesian coordinate system.
Detailed Description
The invention is mainly verified by adopting a simulation experiment mode, and the simulation verification platform is Matlab2021a. The invention is described in further detail below with reference to the drawings and examples.
As shown in FIG. 1, the undistorted three-dimensional image reconstruction method for the moving target of the bistatic SAR sea surface ship comprises the following specific steps:
step one, establishing a double-base SAR space geometrical configuration and a sea surface ship moving target echo model, and completing parameter initialization;
as shown in fig. 2, the system parameters and the moving target parameters used in the dual-base SAR geometric configuration diagram and the moving target model diagram of the sea surface ship are shown in table 1. In rectangular coordinate system O-XYZ, the position vectors of transmitting station and receiving station at azimuth zero time are respectively and />The speed vectors of the transmitting station and the receiving station are +.> and /> A transpose operation representing a vector; the position coordinate vector of the rotation center of the sea surface ship moving object in O-XYZ is +.>
TABLE 1
Establishing a ship-to-solid coordinate system o-xyz by taking the ship head direction as an x axis and the port direction as a y axis; in the ship fixed coordinate system, the coordinate vector of any scattering point in the sea surface ship moving target is set asThe shape of the sea surface ship moving object is shown in fig. 3. Sea surface ship moving object is +.about rotation axis under the action of sea wave>Rotating anticlockwise at a rotation speed omega, wherein the rotation angle is theta (eta), and eta represents azimuth slow time; the three-dimensional rotation matrix of the sea surface ship moving target is:
M(η)＝I+sinθ(η)K+(1-cosθ(η))K 2
wherein I represents a 3×3 identity matrix, K represents a cross product matrix of the rotation axis b, and the expression is as follows:
any scattering point r in sea surface ship moving target p Coordinates after three-dimensional rotation under the action of ocean wavesExpressed as:
scattering point r in rectangular coordinate system O-XYZ p Three-dimensional coordinates of (a)Expressed as:
wherein ,MT The conversion matrix from the ship fixed coordinate system to the rectangular coordinate system O-XYZ is expressed as follows:
wherein ,θT Representing the rotation angle required for the conversion of the ship's fixed to rectangular coordinates O-XYZ.
Step two, obtaining a double-base distance course from the double-base SAR to any scattering point in the sea surface ship moving target;
arbitrary scattering point r from bistatic SAR to sea surface ship moving target p Is R (eta; R) p ) Expressed as:
wherein ,rT ＝r T0 +v Tη and rR ＝r R0 +v R η represents the position vectors of the transmitting station and the receiving station at the time η of the azimuth respectively.
The double-base distance course R (eta; R) p ) Performing Taylor expansion to obtain:
wherein ,R0 An initial double-base distance history representing the azimuth 0 moment; k (k) iT ，k iR The i-th order term coefficients representing the distance history of the transmitting station and the receiving station, respectively.
Step three, acquiring pulse pressure echoes of a sea surface ship moving target of the bistatic SAR;
the expression of the echo reflected by the moving target of the sea surface ship after down-conversion and distance compression is as follows:
wherein ,σp Radar cross section RCS, B representing a moving object r Represents the bandwidth of the transmitted signal, τ represents the distance-to-fast time, T a The synthetic aperture time of the moving object is represented, and the electromagnetic wave speed c is 3×10 8 m/s. λ represents the wavelength of the transmitted signal, and λ=c/f c ，f c Representing the carrier frequency of the transmitted signal.
Then the echo signal is subjected to distance fast fourier transform to obtain:
wherein ,fτ Represents the distance frequency variable, phi (f) τ η) represents a two-dimensional phase of the moving object echo in a distance frequency domain and an azimuth time domain, and the specific expression is as follows:
wherein ,fdc 、f dr 、f d3 The Doppler mass center, the Doppler modulation frequency and the third-order Doppler frequency respectively represent the moving targets of the sea surface ship, and are specifically expressed as follows:
fig. 4 is an echo diagram of a moving target of a sea surface ship obtained after the third step.
Preprocessing the echo, removing Doppler blurring in the bistatic SAR echo, and correcting range migration of the echo;
due to the motion of the double-base SAR platform, the echo of the double-base SAR sea surface ship target can have the problems of Doppler ambiguity, broadening and the like. Doppler ambiguity refers to the signal Doppler of an echoThe frequency is greater than the pulse repetition frequency of the system, while doppler spread exacerbates the potential for ambiguity. Moreover, doppler ambiguity can lead to failure of KT (Keystone) algorithm, and thus correction of space-variant distance migration cannot be achieved. Therefore, before KT processing, the doppler ambiguity needs to be removed to locate the doppler of the echo signal within a PRF. Therefore, the deblurring filter H is constructed by utilizing the information such as the motion of the bistatic SAR platform de The method comprises the following steps:
wherein ,and->And respectively representing the Doppler mass center and the Doppler frequency modulation caused by the double-base SAR platform at the azimuth 0 moment.
Then pass through the filter H de The filtered signal phase is:
at this time, the coefficients of the first-order term and the second-order term in the dual-base distance history of the moving target of the sea surface ship are greatly reduced after the coefficients pass through the deblurring filter, and the purposes of Doppler deblurring and widening removal are achieved. And, as can be seen from this, f τ With eta and eta 2 、η 3 There are coupling terms between them. Thus, in order to remove f τ Coupling terms with eta, at this time, echo range migration hollow variable range walk can be removed through KT transformation, and KT transformation is expressed as:
where ζ represents the new azimuth time variable.
After KT transformation, the phase of the echo signal becomes:
wherein R (ζ; R) p ) Arbitrary scattering point r from bistatic SAR corresponding to azimuth time variable xi to sea surface ship moving target p Is a dual base range history of (2).
Thus, after KT transformation, f τ The coupling term with the new azimuth time variable ζ has been removed, so that the variable range walk in the echo range migration has been removed. However, as can be seen from the above formula, f still exists τ With xi 2 、ξ 3 Is a coupling term of (a). Due to f τ With xi 2 、ξ 3 The range migration caused by the coupling term of (c) is small and therefore considered to be space-invariant. Therefore, the residual distance curvature and third-order distance migration can realize consistent compensation through an envelope alignment algorithm.
Fig. 5 is an echo diagram of a sea surface ship moving target after the range migration correction obtained in the fourth step.
Fifthly, projecting the distance-centroid-frequency modulation frequency domain to realize three-dimensional image reconstruction of the ship moving target;
due to the three-dimensional rotation of the sea surface ship moving target, the third-order Doppler frequency of the scattering point in the echo is still not negligible. The azimuth signal within the nth distance is modeled as a multicomponent QFM signal s n (ξ)：
/>
Where K represents the number of QFM signals within the nth distance. Sigma (sigma) i 、α i 、β i 、γ i The amplitude, doppler centroid, doppler tone frequency, and third-order Doppler frequency of the signal representing the ith scattering point, respectively.
QFM signal for single componentThe fourth order function is expressed as:
wherein ,representing a delay time variable s * (ζ) represents the complex conjugate of s (ζ), and σ, α, β, γ represent the amplitude, the Doppler centroid, the Doppler shift frequency, and the third-order Doppler frequency of the single-component QFM signal, respectively.
For a pair ofAnd performing variable-scale Fourier transform to obtain:
wherein ,fξ Representing the frequency variable corresponding to the azimuth time variable ζ, and δ (·) represents the impulse function.
In this case, the index phase contains onlyItems can thus pass along->The variable-scale fourier transform of the axes enables accumulation of the signal, namely:
wherein ,representing time delayInter-variable->Corresponding frequency variation.
The doppler tone frequency and the third order doppler frequency can be passed throughAt->The position of the peak in the domain is obtained, namely:
wherein , and />Representing the estimated values of γ and β, respectively.
Then construct a signal s using the Doppler centroid and Doppler shift frequency estimates c (ζ) is as follows:
then compensate the signal s c (ζ), and after adopting the de-frequency modulation technology and the fast fourier transform, the QFM signal doppler centroid and the amplitude estimation value are respectively:
the Doppler mass center, the frequency modulation frequency, the third-order Doppler frequency and the estimated value of the signal amplitude of one scattering point are obtained, and the Doppler mass center and the frequency modulation frequency estimation of all scattering points in the range gate can be realized by means of the CLEAN technology, so that the projection of the range gate signal to the DC-DFR domain is completed. By carrying out the same projection processing on all the range gate signals, the three-dimensional projection of the sea surface ship target in the range-centroid-frequency modulation domain (R-DC-DFR domain) is realized.
So far, the projection result set Q of the echo data (the signal transmitted by the transmitting station and received by the receiving station radar) of the double-base SAR in the R-DC-DFR domain can be obtained R . Because the transmitting station has the functions of signal transmission and signal reception, the transmitting station can acquire the self-received single-base SAR data at the same time of acquiring the double-base SAR data. After the same processing is carried out on the single-base SAR data, a projection result set Q of the single-base SAR data in the R-DC-DFR domain can be obtained T 。Q T And Q is equal to R Can be expressed as:
wherein N and M each represent Q T And Q is equal to R The number of elements in the matrix;representing the three-dimensional coordinates of the jth scattering point in the R-DC-DFR domain in the transmitting station data, for>Representing three-dimensional coordinates of a kth scattering point in the R-DC-DFR domain in the data of the receiving station, wherein the three-dimensional coordinates are as follows:
however, as the three-dimensional rotation parameters of the sea surface ship target are unknown, the three-dimensional calibration processing of the projection result in the R-DC-DFR domain cannot be completed, so that the sea surface ship target has unknown three-dimensional distortion, and the feasibility in terms of size and shape is lost, so that the sea surface ship target is difficult to realize the target feature extraction and target identification processing. Therefore, in order to obtain a distortion-free three-dimensional result, further distortion removal processing is necessary.
Fig. 6 is a three-dimensional image reconstruction result of the single-base SAR sea surface ship moving target in the distance-centroid-tone frequency domain, which is obtained after the fifth step; fig. 7 is a three-dimensional image reconstruction result of the bistatic SAR sea surface ship moving object in the distance-centroid-tone frequency domain, which is obtained after the fifth step.
Step six, remapping a local Cartesian coordinate system to correct three-dimensional distortion of the target;
and establishing a mapping relation of the sea surface ship moving target in the R-DC-DFR domain and the LCC domain through the three-dimensional rotation parameters of the target, and realizing remapping from the R-DC-DFR domain to the LCC domain. The re-projection results of the sea surface ship moving target transmitting station and the receiving station in the LCC domain are respectively expressed as follows:
wherein F represents the mapping relation between the R-DC-DFR domain and the local Cartesian coordinates, and ω represents the rotation speed vector of the sea surface ship moving object, namely and />Representing scattering points in the R-DC-DFR domain> and />Remapping to three-dimensional coordinates of a local cartesian coordinate system, namely:
to estimate the three-dimensional rotation parameters of the target, the similarity S (omega) is used to evaluate the re-projection result set G of the transmitting station and the receiving station in the LCC T And G R Is the degree of similarity of (1), namely:
therefore, in order to obtain a distortion-free remapping result in the LCC domain, the three-dimensional rotation parameters of the target are optimized with the similarity S (ω) maximum as the objective function, so that the following constraint optimization problem can be obtained:
wherein ,ωmax Indicating the maximum rotational speed.
And solving the constraint optimization problem by using a particle swarm optimization algorithm (Particle Swarm Optimization, PSO) to obtain the three-dimensional rotation parameters of the target, thereby realizing undistorted three-dimensional image reconstruction of the sea surface ship moving target.
Fig. 8 is a distortion-free three-dimensional image reconstruction result of the sea surface ship moving target obtained after the step six in a local cartesian coordinate system.
In this embodiment, the three-dimensional image reconstruction method further includes a step seven of providing three-dimensional image reconstruction indexes, and evaluating three-dimensional image reconstruction capabilities of the target under different configurations and rotation speeds, specifically including the following steps:
according to gradient resolution theory, the distance resolution vector ρ r Doppler frequency resolution vector ρ a Doppler frequency modulation resolution vector ρ h Expressed as:
wherein , and />Respectively representing a distance gradient, a Doppler centroid gradient and a Doppler frequency gradient, wherein the specific expression is as follows:
wherein ,uT and uR Line-of-sight direction unit vectors, M, respectively representing the radars of the transmitting station and the receiving station 2 Representing the second derivative of M (eta) with respect to the azimuth time eta variable at azimuth 0 moment, i.e
In order to evaluate whether the object has imaging capability under a certain three-dimensional rotation, a resolution matrix Λ consisting of the three resolution unit vectors is defined as follows:
Λ＝[Θ r ,Ξ a ,Γ h ]
wherein ,Γh Representing Doppler frequency resolution vector, Θ r Representing a distance resolution vector, xi a The Doppler frequency resolution vector is represented as follows:
therefore, the Doppler frequency resolution vector Γ h At the distance resolution vector Θ r And Doppler frequency resolution vector Xi a Projection length ρ on formed two-dimensional planar normal 3D As a performance index, expressed as:
in summary, the method of the present invention projects a two-dimensional echo of a marine vessel target into the R-DC-DFR domain by constructing a three-dimensional R-DC-DFR domain to obtain a three-dimensional result of the target in the R-DC-DFR domain to separate scatterers. And then establishing an LCC domain, combining data of a transmitting station and a receiving station, establishing a mapping relation between the LCC domain and an R-DC-DFR domain, realizing the remapping of the LCC domain, obtaining target three-dimensional undistorted reconstruction, providing three-dimensional image reconstruction indexes, analyzing target three-dimensional image reconstruction performances under different rotating shaft directions, different rotating speeds and different double-base configurations, and providing guidance significance for target three-dimensional image reconstruction in practical application. Compared with the existing two-dimensional imaging result and distorted and unsealed result, the method increases the information dimension of the target and improves the information reliability of the target.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Various modifications and variations of the present invention will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (2)
1. A undistorted three-dimensional image reconstruction method for a double-base SAR sea surface ship moving target comprises the following specific steps:
step one, establishing a double-base SAR space geometrical configuration and a sea surface ship moving target echo model, and completing parameter initialization;
in rectangular coordinate system O-XYZ, the position vectors of transmitting station and receiving station at azimuth zero time are respectively and />The speed vectors of the transmitting station and the receiving station are +.> and /> A transpose operation representing a vector; the position coordinate vector of the rotation center of the sea surface ship moving target in O-XYZ is
Establishing a ship-to-solid coordinate system o-xyz by taking the ship head direction as an x axis and the port direction as a y axis; then sit on the boatIn the standard system, the coordinate vector of any scattering point in the sea surface ship moving target is set asSea surface ship moving object is +.about rotation axis under the action of sea wave>Rotating anticlockwise at a rotation speed omega, wherein the rotation angle is theta (eta), and eta represents azimuth slow time; the three-dimensional rotation matrix of the sea surface ship moving target is:
M(η)＝I+sinθ(η)K+(1-cosθ(η))K 2
wherein I represents a 3×3 identity matrix, K represents a cross product matrix of the rotation axis b, and the expression is as follows:
any scattering point r in sea surface ship moving target p Coordinates after three-dimensional rotation under the action of ocean wavesExpressed as:
scattering point r in rectangular coordinate system O-XYZ p Three-dimensional coordinates of (a)Expressed as:
wherein ,MT Representing the ship's fixed coordinate system to rectangular coordinate systemThe transformation matrix of O-XYZ has the expression:
wherein ,θT Representing the rotation angle required by O-XYZ conversion from a ship fixed coordinate system to a rectangular coordinate system;
step two, obtaining a double-base distance course from the double-base SAR to any scattering point in the sea surface ship moving target;
arbitrary scattering point r from bistatic SAR to sea surface ship moving target p Is R (eta; R) p ) Expressed as:
wherein ,rT ＝r T0 +v Tη and rR ＝r R0 +v R η represents the position vectors of the transmitting station and the receiving station at the azimuth η moment respectively;
the double-base distance course R (eta; R) p ) Performing Taylor expansion to obtain:
wherein ,R0 An initial double-base distance history representing the azimuth 0 moment; k (k) iT ，k iR The i-th order term coefficients respectively representing the distance histories of the transmitting station and the receiving station;
step three, acquiring pulse pressure echoes of a sea surface ship moving target of the bistatic SAR;
the expression of the echo reflected by the moving target of the sea surface ship after down-conversion and distance compression is as follows:
wherein ,σp Radar cross section RCS, B representing a moving object r Represents the bandwidth of the transmitted signal, τ represents the distance-to-fast time, T a Represents the synthetic aperture time of the moving object, c represents the electromagnetic wave velocity, λ represents the wavelength of the emitted signal, and λ=c/f c ，f c Representing the carrier frequency of the transmitted signal;
then the echo signal is subjected to distance fast fourier transform to obtain:
wherein ,fτ Represents the distance frequency variable, phi (f) τ η) represents a two-dimensional phase of the moving object echo in a distance frequency domain and an azimuth time domain, and the specific expression is as follows:
wherein ,fdc 、f dr 、f d3 The Doppler mass center, the Doppler modulation frequency and the third-order Doppler frequency respectively represent the moving targets of the sea surface ship, and are specifically expressed as follows:
preprocessing the echo, removing Doppler blurring in the bistatic SAR echo, and correcting range migration of the echo;
construction of deblurring filter H using motion information of bistatic SAR platform de The expression is as follows:
wherein ,and->Respectively representing Doppler mass center and Doppler frequency modulation caused by the azimuth 0 moment double-base SAR platform;
then pass through the filter H de The filtered signal phase is:
removing f τ And removing the distance walk of the hollow change of echo distance migration through KT transformation, wherein the KT transformation is expressed as:
where ζ represents a new azimuth time variable;
after KT transformation, the phase of the echo signal becomes:
wherein R (ζ; R) p ) Arbitrary scattering point r from bistatic SAR corresponding to azimuth time variable xi to sea surface ship moving target p Is a dual base distance history of (2);
finally, realizing consistent compensation on residual distance bending and third-order distance migration through an envelope alignment algorithm;
fifthly, projecting the distance-centroid-frequency modulation frequency domain to realize three-dimensional image reconstruction of the ship moving target;
the azimuth signal within the nth distance is modeled as a multicomponent QFM signal s n (ξ)：
Wherein K represents the number of QFM signals in the nth distance; sigma (sigma) i 、α i 、β i 、γ i The amplitude, doppler mass center, doppler tone frequency and third-order Doppler frequency of the signal of the ith scattering point are respectively represented;
QFM signal for single componentThe fourth order function is expressed as:
wherein ,representing a delay time variable s * (ζ) represents complex conjugate of s (ζ), and σ, α, β, γ represent amplitude, doppler centroid, doppler tone frequency, and third-order Doppler frequency of the single-component QFM signal, respectively;
for a pair ofAnd performing variable-scale Fourier transform to obtain:
wherein ,fξ Representing a frequency variable corresponding to an azimuth time variable xi, and delta () represents an impulse function;
by means of a rimThe variable-scale fourier transform of the axes enables accumulation of the signal, namely:
wherein ,representing the delay time variable +.>A corresponding frequency variable;
the doppler tone frequency and the third order doppler frequency passAt->The position of the peak in the domain is obtained, namely:
wherein , and />Respectively representing estimated values of gamma and beta;
then construct a signal s using the Doppler centroid and Doppler shift frequency estimates c (ζ) is as follows:
then compensate the signal s c (xi) and using the de-FM technique and the fast Fourier transform to obtain the Doppler quality of the QFM signalThe heart and amplitude estimates are:
through the obtained Doppler centroid, frequency modulation, third-order Doppler frequency and signal amplitude estimation value of one scattering point, the Doppler centroid and frequency modulation frequency estimation of all scattering points in the range gate is realized by means of the CLEAN technology, and the projection of the range gate signal to the DC-DFR domain is completed; the three-dimensional projection of the sea surface ship target in a distance-centroid-frequency modulation domain (R-DC-DFR domain) is realized by carrying out the same projection processing on all the distance gate signals;
then a projection result set Q of echo data of the double-base SAR in the R-DC-DFR domain can be obtained R After the same processing is carried out on the single-base SAR data, a projection result set Q of the single-base SAR data in the R-DC-DFR domain can be obtained T ，Q T And Q is equal to R Expressed as:
wherein N and M each represent Q T And Q is equal to R The number of elements in the matrix;representing the three-dimensional coordinates of the jth scattering point in the R-DC-DFR domain in the transmitting station data, for>Representing three-dimensional coordinates of a kth scattering point in the R-DC-DFR domain in the data of the receiving station, wherein the three-dimensional coordinates are as follows:
step six, remapping a local Cartesian coordinate system to correct three-dimensional distortion of the target;
establishing a mapping relation of a sea surface ship moving target in an R-DC-DFR domain and an LCC domain through three-dimensional rotation parameters of the target, and realizing remapping from the R-DC-DFR domain to the LCC domain;
the re-projection results of the sea surface ship moving target transmitting station and the receiving station in the LCC domain are respectively expressed as follows:
wherein F represents the mapping relation between the R-DC-DFR domain and the local Cartesian coordinates, and ω represents the rotation speed vector of the sea surface ship moving object, namely and />Representing scattering points in the R-DC-DFR domain> and />Remapping to three-dimensional coordinates of a local cartesian coordinate system, namely:
estimating three-dimensional rotation parameters of a target, and adopting similarity S (omega) to estimate a re-projection result set G of a transmitting station and a receiving station in LCC T And G R Is the degree of similarity of (1), namely:
and optimizing three-dimensional rotation parameters of a target by taking the maximum similarity S (omega) as an objective function to obtain a distortion-free remapping result in an LCC domain, thereby obtaining the following constraint optimization problems:
s.t.||ω||∈(0,ω max ]
wherein ,ωmax Indicating the maximum rotational speed;
and solving the constraint optimization problem by using a particle swarm optimization algorithm PSO to obtain the three-dimensional rotation parameters of the target, and realizing the undistorted three-dimensional image reconstruction of the sea surface ship moving target.
2. The undistorted three-dimensional image reconstruction method of the moving target of the bistatic SAR sea surface ship according to claim 1, wherein the three-dimensional image reconstruction method further comprises the step seven of providing three-dimensional image reconstruction indexes for evaluating the three-dimensional image reconstruction capability of the target under different configurations and rotating speeds, and the method is specifically as follows:
according to gradient resolution theory, the distance resolution vector ρ r Doppler frequency resolution vector ρ a Doppler frequency modulation resolution vector ρ h Expressed as:
wherein ,▽R0 、▽f dc and ▽fdr Respectively representing a distance gradient, a Doppler centroid gradient and a Doppler frequency gradient, wherein the specific expression is as follows:
▽R 0 ＝u T +u R
wherein ,uT and uR Line-of-sight direction unit vectors, M, respectively representing the radars of the transmitting station and the receiving station 2 Representing the second derivative of M (eta) with respect to the azimuth time eta variable at azimuth 0 moment, i.e
Evaluating whether the target has imaging capability under a certain three-dimensional rotation, and defining a resolution matrix lambda consisting of the three resolution unit vectors as follows:
Λ＝[Θ r ,Ξ a ,Γ h ]
wherein ,Γh Representing Doppler frequency resolution vector, Θ r Representation ofDistance resolution vector, xi a The Doppler frequency resolution vector is represented as follows:
then the Doppler frequency resolution vector Γ h At the distance resolution vector Θ r And Doppler frequency resolution vector Xi a Projection length ρ on formed two-dimensional planar normal 3D As a performance index, expressed as:
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