A method for reconstructing distortion-free 3D images of moving ships on the sea surface using bistatic SAR

Abstract

The present invention discloses a method for reconstructing a distortion-free three-dimensional image of a moving ship target on a sea surface using bistatic SAR. First, a bistatic SAR spatial geometric configuration and a model of the moving ship target echo are established, parameter initialization is completed, and the bistatic range history from the bistatic SAR to any scattering point in the moving ship target and the pulse pressure echo of the moving ship target of the bistatic SAR are obtained. The echo is preprocessed to remove Doppler blur in the bistatic SAR echo and correct the range migration of the echo. A projection in the range-center-of-mass-frequency domain is obtained to achieve three-dimensional image reconstruction of the moving ship target. Finally, remapping is performed based on a local Cartesian coordinate system to correct the three-dimensional distortion of the target and achieve distortion-free three-dimensional image reconstruction of the moving ship target on the sea surface. The method of the present invention eliminates image distortion caused by unknown IPP and achieves distortion-free three-dimensional image reconstruction in LCC. Compared with the existing two-dimensional imaging and distorted and uncalibrated results, the information dimension of the target is increased and the information reliability of the target is improved.

Description

Technical Field

[0001] The present invention belongs to the field of radar imaging technology, and in particular relates to a method for reconstructing a distortion-free three-dimensional image of a moving target of a sea surface ship using a bistatic SAR. Background Art

[0002] Synthetic Aperture Radar (SAR) is a modern, all-weather, high-resolution microwave remote sensing imaging radar. It exploits the relative motion between the radar antenna and the target area to achieve high spatial resolution. SAR is playing an increasingly important role in terrain mapping, vegetation analysis, oceanographic and hydrological observation, environmental and disaster monitoring, resource exploration, and crustal micro-deformation detection. SAR can be divided into two modes depending on the configuration of the transceiver station: monostatic mode, in which the transmitter and receiver are installed on the same platform; and bistatic mode, in which the transmitter and receiver are installed on different platforms. In recent years, bistatic SAR has attracted increasing attention for its forward-looking imaging capabilities and geometric flexibility. Imaging moving targets has been a long-standing topic in the SAR community. To meet the growing demand for surveillance systems, information about moving targets is crucial for wide-area surveillance systems with limited revisit times.

[0003] Bistatic SAR is crucial for extensive surveillance, imaging, and identification of maritime ship targets in harsh environments. Current reports and literature on BiSAR primarily focus on stationary scene imaging algorithms, such as the range-Doppler (RD) algorithm, the wk algorithm, and the nonlinear frequency-modulated scaling (NLCS) algorithm. For stationary targets, the RCM and azimuth Doppler parameters are completely dependent on the motion of the BiSAR platform. However, for moving targets, due to the inherent unknown nature of motion, the BiSAR platform's motion information cannot determine the RCM and Doppler parameters. Furthermore, due to the unknown and large-scale three-dimensional rotation of ship targets under wave disturbances, the target's imaging projection plane (IPP) is unknown and cannot be determined, resulting in high-dimensional random distortion in the imaging results, making it difficult to effectively identify targets using the distorted two-dimensional images. Therefore, all of the aforementioned methods cannot be implemented for imaging moving surface ship targets using bistatic SAR. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes a method for reconstructing distortion-free three-dimensional images of moving targets of sea surface ships using bistatic SAR. This method addresses the defects of the existing technology and solves the problem of high-dimensional random distortion of imaging results caused by unknown target motion, thereby realizing distortion-free three-dimensional image reconstruction processing of moving targets of sea surface ships using bistatic SAR.

[0005] The technical solution of the present invention is: a method for reconstructing a distortion-free three-dimensional image of a moving target of a sea surface ship using bistatic SAR, the specific steps of which are as follows:

[0006] Step 1: Establish the bistatic SAR spatial geometric configuration and the sea surface ship moving target echo model, and complete parameter initialization;

[0007] In the rectangular coordinate system O-XYZ, the position vectors of the transmitting station and the receiving station at the azimuth zero time are and The velocity vectors of the transmitting station and the receiving station are and Represents the transposition operation of the vector; the position coordinate vector of the rotation center of the moving target of the sea ship in O-XYZ is

[0008] With the bow direction as the x-axis and the port direction as the y-axis, a ship-fixed coordinate system o-xyz is established; then in the ship-fixed coordinate system, the coordinate vector of any scattering point in the moving target of the sea ship is The moving target of the ship on the sea rotates around the axis under the action of the waves. The rotation speed is ω and the rotation angle is θ(η), where η represents the azimuth slow time. The three-dimensional rotation matrix of the moving target of the sea surface ship is:

[0009] M(η)=I+sinθ(η)K+(1-cosθ(η))K 2

[0010] Where I represents the 3×3 identity matrix and K represents the cross product matrix of the rotation axis b. The expression is as follows:

[0011]

[0012] Then any scattering point r in the moving target of the sea ship p Coordinates after three-dimensional rotation under the action of waves Expressed as:

[0013]

[0014] Scattering point r in the rectangular coordinate system O-XYZ p The three-dimensional coordinates of Expressed as:

[0015]

[0016] Among them, M T The transformation matrix from the ship-fixed coordinate system to the rectangular coordinate system O-XYZ is expressed as follows:

[0017]

[0018] Among them, θ T Indicates the rotation angle required to transform the ship-fixed coordinate system to the rectangular coordinate system O-XYZ.

[0019] Step 2: Obtain the bistatic range history from the bistatic SAR to any scattering point of the moving target of the sea ship;

[0020] Bistatic SAR to any scattering point r in the moving target of the sea ship p The double base distance history R(η;r p ) is expressed as:

[0021]

[0022] Among them, r T =r T0 +v T η and r R =r R0 +v R η represents the position vector of the transmitting station and the receiving station at the time of azimuth η respectively.

[0023] The double base distance history R(η; r p ) and perform Taylor expansion to obtain:

[0024]

[0025] Where R0 represents the initial bi-base distance history at time 0; k iT , k iR They represent the i-th order coefficients of the distance history between the transmitting station and the receiving station.

[0026] Step 3: Obtain the pulse pressure echo of the moving target of the sea ship by bistatic SAR;

[0027] The echo reflected by the moving target of the sea ship after down-conversion and range compression is expressed as:

[0028]

[0029] Among them, σ p Indicates the radar cross section RCS of the moving target, B r represents the bandwidth of the transmitted signal, τ represents the distance to the fast time, T a represents the synthetic aperture time of the moving target, c represents the speed of the electromagnetic wave, λ represents the wavelength of the transmitted signal, and λ=c / f c , f c Indicates the carrier frequency of the transmitted signal.

[0030] Then perform range-direction fast Fourier transform on the echo signal and obtain:

[0031]

[0032] Among them, f τ represents the distance frequency variable, Φ(f τ ,η) represents the two-dimensional phase of the moving target echo in the range frequency domain and azimuth time domain. The specific expression is as follows:

[0033]

[0034] Among them, f dc 、f dr 、f d3 They represent the Doppler centroid, Doppler modulation frequency, and third-order Doppler frequency of the moving target of the sea surface ship, respectively. They are specifically expressed as:

[0035]

[0036] Step 4: Preprocess the echo to remove Doppler ambiguity in the bistatic SAR echo and correct the range migration of the echo;

[0037] Using the motion information of the bistatic SAR platform, a deblurring filter H is constructed. de The expression is as follows:

[0038]

[0039] in, and They represent the Doppler centroid and Doppler modulation frequency caused by the bistatic SAR platform at azimuth 0, respectively.

[0040] Then through the filter H de The phase of the filtered signal is:

[0041]

[0042] Remove f τ The coupling term with η is used to remove the range migration of the echo range by KT transform. The KT transform is expressed as:

[0043]

[0044] Where ξ represents the new azimuth time variable.

[0045] After the KT transformation, the phase of the echo signal becomes:

[0046]

[0047] Among them, R(ξ;r p) represents the azimuth time variable ξ corresponding to the bistatic SAR to any scattering point r in the moving target of the sea ship p The double base distance process.

[0048] Finally, the envelope alignment algorithm is used to achieve consistent compensation for the residual range curvature and third-order range migration.

[0049] Step 5: Projection in the range-center-frequency modulation domain to achieve 3D image reconstruction of the moving ship target;

[0050] The azimuth signal within the nth distance is modeled as a multi-component QFM signal s n (ξ):

[0051]

[0052] Where K represents the number of QFM signals within the nth distance. i , α i , β i , γ i They represent the amplitude, Doppler centroid, Doppler modulation rate, and third-order Doppler frequency of the signal at the i-th scattering point, respectively.

[0053] For a single-component QFM signal Its fourth-order function is expressed as:

[0054]

[0055] in, Represents the delay time variable, s * (ξ) represents the complex conjugate of s(ξ), σ, α, β, and γ represent the amplitude, Doppler centroid, Doppler modulation frequency, and third-order Doppler frequency of the single-component QFM signal, respectively.

[0056] right Performing variable scale Fourier transform, we can get:

[0057]

[0058] Among them, f ξ represents the frequency variable corresponding to the azimuth time variable ξ, and δ() represents the impulse function.

[0059] By along The variable-scale Fourier transform of the axis realizes the accumulation of the signal, that is:

[0060]

[0061] in, Delay time variable The corresponding frequency variable.

[0062] Then the Doppler modulation frequency and the third-order Doppler frequency are exist The peak position in the domain is obtained, that is:

[0063]

[0064] in, and are the estimated values ​​of γ and β, respectively.

[0065] Then, the estimated values ​​of Doppler centroid and Doppler modulation frequency are used to construct the signal s c (ξ) is as follows:

[0066]

[0067] Then the compensation signal s c (ξ), and after using the de-frequency modulation technology and fast Fourier transform, the Doppler centroid and amplitude estimation values ​​of this QFM signal can be obtained respectively:

[0068]

[0069]

[0070] By obtaining the estimated Doppler centroid, frequency modulation rate, third-order Doppler frequency, and signal amplitude for a scattering point, the CLEAN technique is used to estimate the Doppler centroid and frequency modulation rate for all scattering points within the range gate, completing the projection of the range gate signal into the DC-DFR domain. By performing the same projection processing on all range gate signals, a three-dimensional projection of surface ship targets in the range-centroid-frequency modulation rate domain (R-DC-DFR domain) is achieved.

[0071] Then the projection result set Q of the bistatic SAR echo data in the R-DC-DFR domain can be obtained R After the same processing is performed on the monostatic SAR data, its projection result set Q in the R-DC-DFR domain can be obtained. T , Q T With Q R Respectively expressed as:

[0072]

[0073]

[0074] Among them, N and M represent Q T With Q R The number of elements in ; represents the three-dimensional coordinates of the j-th scattering point in the R-DC-DFR domain in the transmitting station data, It represents the three-dimensional coordinates of the kth scattering point in the R-DC-DFR domain in the receiving station data, as follows:

[0075]

[0076]

[0077] Step 6: Remapping the local Cartesian coordinate system to correct the target 3D distortion;

[0078] Through the three-dimensional rotation parameters of the target, the mapping relationship between the moving target of the sea surface ship in the R-DC-DFR domain and the LCC domain is established, and the remapping from the R-DC-DFR domain to the LCC domain is realized.

[0079] The reprojection results of the transmitting station and receiving station of the moving target of the sea surface ship in the LCC domain are expressed as follows:

[0080]

[0081]

[0082] Among them, F represents the mapping relationship between the R-DC-DFR domain and the local Cartesian coordinates, and ω represents the rotation velocity vector of the moving target of the sea surface ship, that is, and Represents the scattering points in the R-DC-DFR domain and The 3D coordinates remapped to the local Cartesian coordinate system are:

[0083]

[0084]

[0085] Estimate the three-dimensional rotation parameters of the target and use the similarity S(ω) to evaluate the reprojection result set G of the transmitting station and the receiving station in the LCC T With G R The degree of similarity, that is:

[0086]

[0087] Taking the maximum similarity S(ω) as the objective function, we optimize the three-dimensional rotation parameters of the target to obtain a distortion-free remapping result in the LCC domain, and obtain the following constrained optimization problem:

[0088]

[0089] Among them, ω max Indicates the maximum rotation speed.

[0090] The particle swarm optimization algorithm (PSO) is used to solve the above constrained optimization problem, obtain the three-dimensional rotation parameters of the target, and realize the distortion-free three-dimensional image reconstruction of the moving target of the sea surface ship.

[0091] Furthermore, the three-dimensional image reconstruction method further includes step seven, proposing a three-dimensional image reconstruction index to evaluate the three-dimensional image reconstruction capability of the target under different configurations and rotation speeds, as follows:

[0092] According to the gradient resolution theory, the distance resolution vector ρ r , Doppler frequency resolution vector ρ a , Doppler frequency modulation resolution vector ρ h Respectively expressed as:

[0093]

[0094] in, and They represent the range gradient, Doppler centroid gradient, and Doppler frequency gradient respectively. The specific expressions are as follows:

[0095]

[0096]

[0097]

[0098] Among them, u T and u R Represent the line-of-sight direction unit vectors of the transmitting station and receiving station radars respectively, and M2 represents the second-order derivative of M(η) with respect to the azimuth time η variable at azimuth 0, that is,

[0099] To evaluate whether the target has imaging capability under a certain three-dimensional rotation, the resolution matrix Λ composed of the three resolution unit vectors mentioned above is defined as:

[0100] Λ=[Θ r ,Ξ a ,Γ h ]

[0101] Among them, Γ h represents the Doppler frequency resolution vector, Θ r represents the distance resolution vector, Ξ a represents the Doppler frequency resolution vector, as follows:

[0102]

[0103] Then the Doppler frequency resolution vector Γ h The distance resolution vector Θ rand the Doppler frequency resolution vector Ξ a The projected length ρ on the normal line of the two-dimensional plane formed 3D As a performance indicator, it is expressed as:

[0104]

[0105] Beneficial effects of the present invention: The method of the present invention first establishes a bistatic SAR spatial geometric configuration and an echo model of a moving sea ship target, completes parameter initialization, obtains the bistatic range history from the bistatic SAR to any scattering point in the moving sea ship target and the pulse pressure echo of the moving sea ship target of the bistatic SAR, pre-processes the echo, removes Doppler blur in the bistatic SAR echo and corrects the range migration of the echo, obtains a projection in the range-center-of-mass-frequency domain, realizes three-dimensional image reconstruction of the moving ship target, and finally remaps based on the local Cartesian coordinate system to correct the three-dimensional distortion of the target and realize distortion-free three-dimensional image reconstruction of the moving sea ship target. The method of the present invention eliminates image distortion caused by unknown IPP and realizes distortion-free three-dimensional image reconstruction in LCC. Compared with the existing two-dimensional imaging and distorted and uncalibrated results, it increases the information dimension of the target and improves the information reliability of the target. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 The present invention provides a flow chart of a method for reconstructing a distortion-free three-dimensional image of a moving target of a sea ship using bistatic SAR.

[0107] Figure 2 This is a diagram of the bistatic SAR geometric configuration and a diagram of the sea surface ship moving target model used in the embodiment of the present invention.

[0108] Figure 3 This is a shape diagram of a moving target of a ship on the sea surface in an embodiment of the present invention.

[0109] Figure 4 This is the echo map of the moving target of the sea ship obtained after step three in the embodiment of the present invention.

[0110] Figure 5 This is the echo map of the moving target of the sea ship after range migration correction obtained after step 4 in the embodiment of the present invention.

[0111] Figure 6 This is a three-dimensional image reconstruction result diagram of a monostatic SAR sea surface ship moving target in the range-center of mass-frequency domain obtained after step five in an embodiment of the present invention.

[0112] Figure 7 This is a diagram showing the three-dimensional image reconstruction result of the bistatic SAR sea surface ship moving target in the range-center of mass-frequency domain obtained after step five in the embodiment of the present invention.

[0113] Figure 8 This is a distortion-free three-dimensional image reconstruction result diagram of the moving target of the sea ship in the local Cartesian coordinate system obtained after step six in an embodiment of the present invention. DETAILED DESCRIPTION

[0114] The present invention is mainly verified by simulation experiments, and the simulation verification platform is Matlab 2021a. The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0115] like Figure 1 As shown in FIG, a flow chart of a method for reconstructing a distortion-free three-dimensional image of a moving target of a sea ship using bistatic SAR of the present invention is shown, and the specific steps are as follows:

[0116] Step 1: Establish the bistatic SAR spatial geometric configuration and the sea surface ship moving target echo model, and complete parameter initialization;

[0117] like Figure 2 As shown in the figure, the bistatic SAR geometric configuration diagram and the sea surface ship moving target model diagram used in this embodiment, the system parameters and moving target parameters used are shown in Table 1. In the rectangular coordinate system O-XYZ, the position vectors of the transmitting station and the receiving station at the azimuth zero time are respectively and The velocity vectors of the transmitting station and the receiving station are and Represents the transposition operation of the vector; the position coordinate vector of the rotation center of the moving target of the sea ship in O-XYZ is

[0118] Table 1

[0119]

[0120] With the bow direction as the x-axis and the port direction as the y-axis, a ship-fixed coordinate system o-xyz is established; then in the ship-fixed coordinate system, the coordinate vector of any scattering point in the moving target of the sea ship is The shape of the moving target of the ship on the sea surface is as follows Figure 3 As shown. The moving target of the ship on the sea surface rotates around the axis under the action of the waves. The rotation speed is ω and the rotation angle is θ(η), where η represents the azimuth slow time. The three-dimensional rotation matrix of the moving target of the sea surface ship is:

[0121] M(η)=I+sinθ(η)K+(1-cosθ(η))K 2

[0122] Where I represents the 3×3 identity matrix and K represents the cross product matrix of the rotation axis b. The expression is as follows:

[0123]

[0124] Then any scattering point r in the moving target of the sea ship p Coordinates after three-dimensional rotation under the action of waves Expressed as:

[0125]

[0126] Scattering point r in the rectangular coordinate system O-XYZ p The three-dimensional coordinates of Expressed as:

[0127]

[0128] Among them, M T The transformation matrix from the ship-fixed coordinate system to the rectangular coordinate system O-XYZ is expressed as follows:

[0129]

[0130] Among them, θ T Indicates the rotation angle required to transform the ship-fixed coordinate system to the rectangular coordinate system O-XYZ.

[0131] Step 2: Obtain the bistatic range history from the bistatic SAR to any scattering point of the moving target of the sea ship;

[0132] Bistatic SAR to any scattering point r in the moving target of the sea ship p The double base distance history R(η;r p ) is expressed as:

[0133]

[0134] Among them, r T =r T0 +v T η and r R =r R0 +v R η represents the position vector of the transmitting station and the receiving station at the time of azimuth η respectively.

[0135] The double base distance history R(η; r p ) and perform Taylor expansion to obtain:

[0136]

[0137] Where R0 represents the initial bi-base distance history at time 0; k iT , k iR They represent the i-th order coefficients of the distance history between the transmitting station and the receiving station.

[0138] Step 3: Obtain the pulse pressure echo of the moving target of the sea ship by bistatic SAR;

[0139] The echo reflected by the moving target of the sea ship after down-conversion and range compression is expressed as:

[0140]

[0141] Among them, σ p Indicates the radar cross section RCS of the moving target, B r represents the bandwidth of the transmitted signal, τ represents the distance to the fast time, T a represents the synthetic aperture time of the moving target, and the electromagnetic wave speed c is 3×10 8 m / s. ,λ represents the wavelength of the transmitted signal, andλ=c / f c , f c Indicates the carrier frequency of the transmitted signal.

[0142] Then perform range-direction fast Fourier transform on the echo signal and obtain:

[0143]

[0144] Among them, f τ represents the distance frequency variable, Φ(f τ ,η) represents the two-dimensional phase of the moving target echo in the range frequency domain and azimuth time domain. The specific expression is as follows:

[0145]

[0146] Among them, f dc 、f dr 、f d3 They represent the Doppler centroid, Doppler modulation frequency, and third-order Doppler frequency of the moving target of the sea surface ship, respectively. They are specifically expressed as:

[0147]

[0148] Figure 4 After step three, the echo map of the moving target of the sea ship is obtained.

[0149] Step 4: Preprocess the echo to remove Doppler ambiguity in the bistatic SAR echo and correct the range migration of the echo;

[0150] Due to the motion of the bistatic SAR platform, the echo of the bistatic SAR sea surface ship target will have problems such as Doppler ambiguity and broadening. Doppler ambiguity refers to the signal Doppler frequency of the echo being greater than the pulse repetition frequency of the system, and Doppler broadening will increase the possibility of ambiguity. Moreover, Doppler ambiguity will cause the KT (Keystone) algorithm to fail, making it impossible to correct the space-varying range migration. Therefore, before KT processing, it is necessary to remove the Doppler ambiguity and broadening so that the Doppler of the echo signal is within a PRF. Therefore, using the information such as the motion of the bistatic SAR platform, a deblurring filter H is constructed. de for:

[0151]

[0152] in, and They represent the Doppler centroid and Doppler modulation frequency caused by the bistatic SAR platform at azimuth 0, respectively.

[0153] Then through the filter H de The phase of the filtered signal is:

[0154]

[0155] At this point, the first-order and second-order coefficients in the dual-base distance history of the surface ship moving target have been greatly reduced after passing through the deblurring filter, achieving the purpose of Doppler deblurring and removing the broadening. Moreover, it can be seen that f τ and η, η 2 ,η 3 There are coupling terms between them. Therefore, in order to remove f τ The coupling term with η can be used to remove the range movement of the echo range migration by KT transformation. The KT transformation is expressed as:

[0156]

[0157] Where ξ represents the new azimuth time variable.

[0158] After the KT transformation, the phase of the echo signal becomes:

[0159]

[0160] Among them, R(ξ;r p ) represents the azimuth time variable ξ corresponding to the bistatic SAR to any scattering point r in the moving target of the sea ship p The double base distance process.

[0161] Therefore, after KT transformation, f τThe coupling term with the new azimuth time variable ξ has been removed, so the range migration of the echo range has been removed. However, it can be seen from the above formula that f still exists. τ With ξ 2 ,ξ 3 The coupling term. Since f τ With ξ 2 ,ξ 3 The range migration caused by the coupling term is small and is therefore considered to be space-invariant. Therefore, the residual range curvature and third-order range migration can be consistently compensated by the envelope alignment algorithm.

[0162] Figure 5 This is the echo map of the moving target of the sea ship after range migration correction obtained in step 4.

[0163] Step 5: Projection in the range-center-frequency modulation domain to achieve 3D image reconstruction of the moving ship target;

[0164] Due to the three-dimensional rotation of the moving target of the sea surface ship, the third-order Doppler frequency of the scattering point in the echo cannot be ignored. The azimuth signal within the nth distance is modeled as a multi-component QFM signal s n (ξ):

[0165]

[0166] Where K represents the number of QFM signals within the nth distance. i , α i , β i , γ i They represent the amplitude, Doppler centroid, Doppler modulation rate, and third-order Doppler frequency of the signal at the i-th scattering point, respectively.

[0167] For a single-component QFM signal Its fourth-order function is expressed as:

[0168]

[0169] in, Represents the delay time variable, s * (ξ) represents the complex conjugate of s(ξ), σ, α, β, and γ represent the amplitude, Doppler centroid, Doppler modulation frequency, and third-order Doppler frequency of the single-component QFM signal, respectively.

[0170] right Performing variable scale Fourier transform, we can get:

[0171]

[0172] Among them, f ξrepresents the frequency variable corresponding to the azimuth time variable ξ, and δ(·) represents the impulse function.

[0173] At this time, the exponential phase only contains Item, so it can be The variable-scale Fourier transform of the axis realizes the accumulation of the signal, that is:

[0174]

[0175] in, Delay time variable The corresponding frequency variable.

[0176] Then the Doppler modulation frequency and the third-order Doppler frequency can be obtained by exist The peak position in the domain is obtained, that is:

[0177]

[0178] in, and denote the estimated values ​​of γ and β, respectively.

[0179] Then, the estimated values ​​of Doppler centroid and Doppler modulation frequency are used to construct the signal s c (ξ) is as follows:

[0180]

[0181] Then the compensation signal s c (ξ), and after using the de-frequency modulation technology and fast Fourier transform, the Doppler centroid and amplitude estimation values ​​of this QFM signal can be obtained respectively:

[0182]

[0183]

[0184] At this point, the Doppler centroid, frequency modulation, third-order Doppler frequency, and signal amplitude estimates for a scattering point are obtained. Using CLEAN technology, the Doppler centroid and frequency modulation estimates for all scattering points within this range gate are achieved, thereby projecting the range gate signal into the DC-DFR domain. By performing the same projection processing on all range gate signals, a three-dimensional projection of surface ship targets in the range-centroid-frequency modulation domain (R-DC-DFR domain) is achieved.

[0185] At this point, the projection result set Q of the bistatic SAR echo data (the signal transmitted by the transmitting station received by the receiving station radar) in the R-DC-DFR domain can be obtained. RSince the transmitting station has the function of transmitting and receiving signals at the same time, the monostatic SAR data can be obtained while the bistatic SAR data is obtained. After the monostatic SAR data is processed in the same way, the projection result set Q in the R-DC-DFR domain can be obtained. T .Q T With Q R They can be expressed as:

[0186]

[0187]

[0188] Among them, N and M represent Q T With Q R The number of elements in ; represents the three-dimensional coordinates of the j-th scattering point in the R-DC-DFR domain in the transmitting station data, It represents the three-dimensional coordinates of the kth scattering point in the R-DC-DFR domain in the receiving station data, as follows:

[0189]

[0190]

[0191] However, due to the unknown 3D rotation parameters of surface ship targets, it is impossible to complete 3D calibration of the projection results in the R-DC-DFR domain. This results in unknown 3D distortion and loss of feasibility in terms of size and shape, making it difficult to achieve target feature extraction and target recognition. Therefore, in order to obtain distortion-free 3D results, further distortion removal processing is essential.

[0192] Figure 6 The 3D image reconstruction result of the monostatic SAR sea surface ship moving target in the range-center-frequency modulation domain obtained after step 5; Figure 7 This is the three-dimensional image reconstruction result of the bistatic SAR sea surface ship moving target in the range-center of mass-frequency domain obtained after step five.

[0193] Step 6: Remapping the local Cartesian coordinate system to correct the target 3D distortion;

[0194] Through the three-dimensional rotation parameters of the target, the mapping relationship between the surface ship moving target in the R-DC-DFR domain and the LCC domain is established, and the remapping from the R-DC-DFR domain to the LCC domain is realized. The reprojection results of the surface ship moving target transmitting station and receiving station in the LCC domain are expressed as follows:

[0195]

[0196]

[0197] Among them, F represents the mapping relationship between the R-DC-DFR domain and the local Cartesian coordinates, and ω represents the rotation velocity vector of the moving target of the sea surface ship, that is, and Represents the scattering points in the R-DC-DFR domain and The 3D coordinates remapped to the local Cartesian coordinate system are:

[0198]

[0199]

[0200] In order to estimate the three-dimensional rotation parameters of the target, the similarity S(ω) is used to evaluate the reprojection result set G of the transmitting station and the receiving station in the LCC. T With G R The degree of similarity, that is:

[0201]

[0202] Therefore, in order to obtain a distortion-free remapping result in the LCC domain, the 3D rotation parameters of the target are optimized with the maximum similarity S(ω) as the objective function, which leads to the following constrained optimization problem:

[0203]

[0204] Among them, ω max Indicates the maximum rotation speed.

[0205] The particle swarm optimization algorithm (PSO) is used to solve the above constrained optimization problem and obtain the three-dimensional rotation parameters of the target, thereby realizing the distortion-free three-dimensional image reconstruction of the moving target of the sea surface ship.

[0206] Figure 8 This is the distortion-free three-dimensional image reconstruction result of the moving target of the sea surface ship in the local Cartesian coordinate system obtained after step six.

[0207] In this embodiment, the 3D image reconstruction method further includes step seven, proposing a 3D image reconstruction index to evaluate the 3D image reconstruction capability of the target under different configurations and rotation speeds, as follows:

[0208] According to the gradient resolution theory, the distance resolution vector ρ r , Doppler frequency resolution vector ρ a , Doppler frequency modulation resolution vector ρ h Respectively expressed as:

[0209]

[0210] in, and They represent the range gradient, Doppler centroid gradient, and Doppler frequency gradient respectively. The specific expressions are as follows:

[0211]

[0212]

[0213]

[0214] Among them, u T and u R Represent the line-of-sight direction unit vectors of the transmitting station and the receiving station radar respectively, and M2 represents the second-order derivative of M(η) with respect to the azimuth time η variable at azimuth 0, that is,

[0215] In order to evaluate whether the target has imaging capability under a certain three-dimensional rotation, the resolution matrix Λ composed of the above three resolution unit vectors is defined as:

[0216] Λ=[Θ r ,Ξ a ,Γ h ]

[0217] Among them, Γ h represents the Doppler frequency resolution vector, Θ r represents the distance resolution vector, Ξ a represents the Doppler frequency resolution vector, as follows:

[0218]

[0219] Therefore, the Doppler frequency resolution vector Γ h The distance resolution vector Θ r and the Doppler frequency resolution vector Ξ a The projected length ρ on the normal line of the two-dimensional plane formed 3D As a performance indicator, it is expressed as:

[0220]

[0221] In summary, the method of the present invention constructs a three-dimensional R-DC-DFR domain, projects the two-dimensional echo of the marine ship target into the R-DC-DFR domain, and obtains the three-dimensional result of the target in the R-DC-DFR domain to separate the scatterer. Then, an LCC domain is established, and the data of the transmitting station and the receiving station are combined to establish a mapping relationship between the LCC domain and the R-DC-DFR domain, realize the remapping of the LCC domain, obtain the three-dimensional distortion-free reconstruction of the target, and propose a three-dimensional image reconstruction index. The target three-dimensional image reconstruction performance under different shaft directions, different speeds, and different dual-base configurations is analyzed, providing guidance for the three-dimensional image reconstruction of the target in practical applications. Compared with the existing two-dimensional imaging results and distorted and uncalibrated results, the method of the present invention increases the information dimension of the target and improves the information reliability of the target.

[0222] Those skilled in the art will appreciate that the embodiments described herein are intended to aid the reader in understanding the principles of the present invention, and it should be understood that the scope of the present invention is not limited to such specific descriptions and embodiments. Various modifications and variations are readily apparent to those skilled in the art. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are intended to be included within the scope of the claims.

Claims

1. A method for reconstructing a distortion-free 3D image of a moving target ship on a sea surface using bistatic SAR, the specific steps of which are as follows: Step 1: Establish the bistatic SAR spatial geometric configuration and the sea surface ship moving target echo model, and complete parameter initialization; In the rectangular coordinate system O-XYZ, the position vectors of the transmitting station and the receiving station at the azimuth zero time are and The velocity vectors of the transmitting station and the receiving station are and Represents the transposition operation of the vector; the position coordinate vector of the rotation center of the moving target of the sea ship in O-XYZ is With the bow direction as the x-axis and the port direction as the y-axis, a ship-fixed coordinate system o-xyz is established; then in the ship-fixed coordinate system, the coordinate vector of any scattering point in the moving target of the sea ship is The moving target of the ship on the sea rotates around the axis under the action of the waves. The rotation speed is ω and the rotation angle is θ(η), where η represents the azimuth slow time. The three-dimensional rotation matrix of the moving target of the sea surface ship is: M(η)=I+sinθ(η)K+(1-cosθ(η))K 2 in, I represents the 3×3 identity matrix, K represents the cross product matrix of the rotation axis b, and the expression is as follows: Then any scattering point r in the moving target of the sea ship p Coordinates after three-dimensional rotation under the action of waves Expressed as: Scattering point r in the rectangular coordinate system O-XYZ p The three-dimensional coordinates of Expressed as: Among them, M T The transformation matrix from the ship-fixed coordinate system to the rectangular coordinate system O-XYZ is expressed as follows: Among them, θ T Indicates the rotation angle required to transform the ship-fixed coordinate system to the rectangular coordinate system O-XYZ; Step 2: Obtain the bistatic range history from the bistatic SAR to any scattering point of the moving target of the sea ship; Bistatic SAR to any scattering point r in the moving target of the sea ship p The double base distance history R(η;r p ) is expressed as: Among them, r T =r T0 +v T η and r R =r R0 +v R η represents the position vectors of the transmitting station and the receiving station at the time of azimuth η respectively; The double base distance history R(η; r p ) and perform Taylor expansion to obtain: Where R0 represents the initial bi-base distance history at time 0; k iT , k iR They represent the coefficient of the i-th order term of the distance history between the transmitting station and the receiving station respectively; Step 3: Obtain the pulse pressure echo of the moving target of the sea ship by bistatic SAR; The echo reflected by the moving target of the sea ship after down-conversion and range compression is expressed as: Among them, σ p Indicates the radar cross section RCS of the moving target, B r represents the bandwidth of the transmitted signal, τ represents the distance to the fast time, T a represents the synthetic aperture time of the moving target, c represents the speed of the electromagnetic wave, λ represents the wavelength of the transmitted signal, and λ=c / f c , f c Indicates the carrier frequency of the transmitted signal; Then perform range-direction fast Fourier transform on the echo signal and obtain: Among them, f τ represents the distance frequency variable, Φ(f τ ,η) represents the two-dimensional phase of the moving target echo in the range frequency domain and azimuth time domain. The specific expression is as follows: Among them, f dc 、f dr 、f d3 They represent the Doppler centroid, Doppler modulation frequency, and third-order Doppler frequency of the moving target of the sea surface ship, respectively. They are specifically expressed as: Step 4: Preprocess the echo to remove Doppler ambiguity in the bistatic SAR echo and correct the range migration of the echo; Using the motion information of the bistatic SAR platform, a deblurring filter H is constructed. de The expression is as follows: in, and They represent the Doppler centroid and Doppler modulation rate caused by the bistatic SAR platform at azimuth 0, respectively; Then through the filter H de The phase of the filtered signal is: Remove f τ The coupling term with η is used to remove the range migration of the echo range by KT transform. The KT transform is expressed as: Among them, ξ represents the new azimuth time variable; After the KT transformation, the phase of the echo signal becomes: Among them, R(ξ;r p ) represents the azimuth time variable ξ corresponding to the bistatic SAR to any scattering point r in the moving target of the sea ship p The double base distance history; Finally, the envelope alignment algorithm is used to achieve consistent compensation for the residual range curvature and third-order range migration. Step 5: Projection in the range-center-frequency modulation domain to achieve 3D image reconstruction of the moving ship target; The azimuth signal within the nth distance is modeled as a multi-component QFM signal s n (ξ): Where K represents the number of QFM signals within the nth distance; σ i , α i , β i , γ i Represent the amplitude, Doppler centroid, Doppler modulation rate, and third-order Doppler frequency of the signal at the i-th scattering point respectively; For a single-component QFM signal Its fourth-order function is expressed as: in, Represents the delay time variable, s * (ξ) represents the complex conjugate of s(ξ), σ, α, β, and γ represent the amplitude, Doppler centroid, Doppler modulation rate, and third-order Doppler frequency of the single-component QFM signal, respectively; right Performing variable scale Fourier transform, we can get: Among them, f ξ represents the frequency variable corresponding to the azimuth time variable ξ, and δ() represents the impulse function; By along The variable-scale Fourier transform of the axis realizes the accumulation of the signal, that is: in, Delay time variable the corresponding frequency variable; Then the Doppler modulation frequency and the third-order Doppler frequency are exist The peak position in the domain is obtained, that is: in, and denote the estimated values ​​of γ and β, respectively; Then, the estimated values ​​of Doppler centroid and Doppler modulation frequency are used to construct the signal s c (ξ) is as follows: Then the compensation signal s c (ξ), and after using the de-frequency modulation technology and fast Fourier transform, the Doppler centroid and amplitude estimation values ​​of this QFM signal can be obtained respectively: By obtaining the estimated values ​​of the Doppler centroid, frequency modulation, third-order Doppler frequency, and signal amplitude of a scattering point, the CLEAN technology is used to estimate the Doppler centroid and frequency modulation of all scattering points within this range gate, completing the projection of the range gate signal into the DC-DFR domain. By performing the same projection processing on all range gate signals, the three-dimensional projection of the surface ship target in the range-centroid-frequency modulation domain (R-DC-DFR domain) is achieved. Then the projection result set Q of the bistatic SAR echo data in the R-DC-DFR domain can be obtained R After the same processing is performed on the monostatic SAR data, its projection result set Q in the R-DC-DFR domain can be obtained. T , Q T With Q R Respectively expressed as: Among them, N and M represent Q T With Q R The number of elements in ; represents the three-dimensional coordinates of the j-th scattering point in the R-DC-DFR domain in the transmitting station data, It represents the three-dimensional coordinates of the kth scattering point in the R-DC-DFR domain in the receiving station data, as follows: Step 6: Remapping the local Cartesian coordinate system to correct the target 3D distortion; Through the three-dimensional rotation parameters of the target, the mapping relationship between the moving target of the sea surface ship in the R-DC-DFR domain and the LCC domain is established, and the remapping from the R-DC-DFR domain to the LCC domain is realized; The reprojection results of the transmitting station and receiving station of the moving target of the sea surface ship in the LCC domain are expressed as follows: Among them, F represents the mapping relationship between the R-DC-DFR domain and the local Cartesian coordinates, and ω represents the rotation velocity vector of the moving target of the sea surface ship, that is, and Represents the scattering points in the R-DC-DFR domain and The 3D coordinates remapped to the local Cartesian coordinate system are: Estimate the three-dimensional rotation parameters of the target and use the similarity S(ω) to evaluate the reprojection result set G of the transmitting station and the receiving station in the LCC T With G R The degree of similarity, that is: Taking the maximum similarity S(ω) as the objective function, we optimize the three-dimensional rotation parameters of the target to obtain a distortion-free remapping result in the LCC domain, and obtain the following constrained optimization problem: st||ω||∈(0,ω max ] Among them, ω max Indicates the maximum rotation speed; The particle swarm optimization algorithm (PSO) is used to solve the above constrained optimization problem, obtain the three-dimensional rotation parameters of the target, and realize the distortion-free three-dimensional image reconstruction of the moving target of the sea surface ship.

2. The method for reconstructing a distortion-free three-dimensional image of a moving target of a sea ship using bistatic SAR according to claim 1, characterized in that: The three-dimensional image reconstruction method further includes step seven, proposing a three-dimensional image reconstruction index to evaluate the three-dimensional image reconstruction capability of the target under different configurations and rotation speeds, as follows: According to the gradient resolution theory, the distance resolution vector ρ r , Doppler frequency resolution vector ρ a , Doppler frequency modulation resolution vector ρ h Respectively expressed as: Among them, ▽R0, ▽f dc and ▽f dr They represent the range gradient, Doppler centroid gradient, and Doppler frequency gradient respectively. The specific expressions are as follows: ▽R0=u T +in R Among them, u T and u R Represent the line-of-sight direction unit vectors of the transmitting station and the receiving station radar respectively, and M2 represents the second-order derivative of M(η) with respect to the azimuth time η variable at azimuth 0, that is, To evaluate whether the target has imaging capability under a certain three-dimensional rotation, the resolution matrix Λ composed of the above three resolution unit vectors is defined as: L=[Θ r ,X a ,C h ] Among them, Γ h represents the Doppler frequency resolution vector, Θ r represents the distance resolution vector, Ξ a represents the Doppler frequency resolution vector, as follows: Then the Doppler frequency resolution vector Γ h The distance resolution vector Θ r and the Doppler frequency resolution vector Ξ a The projected length ρ on the normal line of the two-dimensional plane formed 3D As a performance indicator, it is expressed as:

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