MIMO GB-SAR amplitude-phase error estimation method

Abstract

According to the MIMO ground-based SAR, multiple-input multiple-output antennas are arranged in a certain array, and uniformly distributed virtual array apertures are formed to image a target area. Inconsistency exists between different transmitting channels and receiving channels under the influence of various factors, specifically, radar echoes received by virtual array elements have gain errors and phase errors, and the amplitude-phase errors need to be corrected. The invention provides an M IMO GB-SAR amplitude-phase error estimation method, starting from the improvement of an imaging algorithm, errors introduced by imaging are reduced at the beginning, then an amplitude-phase error model is established to carry out constraint solution on amplitude errors and phase errors, amplitude-phase error initial values are estimated according to a standard reflector, and the amplitude-phase error initial values are calculated. And a rapid and reliable initial value estimation method can be provided for subsequent fine correction.

Description

Technical Field

[0001] The invention relates to a MIMO GB-SAR amplitude and phase error estimation method, and belongs to the field of ground-based SAR radar signal processing. Background Art

[0002] Synthetic Aperture Radar (SAR) uses a small aperture antenna that moves relative to the object to coherently process the echoes received at different positions, thereby obtaining a high-resolution radar image. The measurement principle of Ground-Based Synthetic Aperture Radar (GB-SAR) is the same as that of general payload SAR. It is a new deformation monitoring technology that has emerged in recent years. It has the advantages of high accuracy and full coverage. It can well meet the needs of geological disaster monitoring and has been widely used in the monitoring field.

[0003] According to the implementation method of synthetic aperture, ground-based SAR can be divided into linear scanning ground-based SAR, arc scanning ground-based SAR and MIMO ground-based SAR. Linear scanning ground-based SAR obtains the synthetic aperture of azimuth dimension through linear track, while arc scanning ground-based SAR obtains the synthetic aperture of azimuth dimension through circular motion of transceiver antenna in horizontal plane. Different from the first two radar systems, MIMO ground-based SAR uses multiple transmitting and receiving antennas to arrange in a certain array to form a uniformly distributed virtual array aperture. During the operation of MIMO ground-based SAR, each transmitting antenna transmits in time, and the receiving antenna receives at the same time, and it only takes tens of milliseconds to a few seconds to complete the complete scan. Therefore, the radar can quickly capture the deformation information in the monitoring area, realize more accurate and rapid deformation measurement, and thus meet the requirements of rapidity and emergency response of geological disaster monitoring. In addition, MIMO ground-based SAR does not require physical tracks and has the characteristics of lighter weight and portability.

[0004] In the actual working environment, MIMO radar will be affected by a variety of non-ideal factors such as process, temperature and humidity, hardware aging, and coupling between antenna units, resulting in inconsistent amplitude and phase characteristics of each transceiver channel. This inconsistency is manifested as the radar echo received by the virtual array element having gain error and phase error. Unlike the phase error caused by the movement of airborne SAR, which usually has a slowly varying characteristic, the amplitude and phase errors between adjacent virtual array elements of MIMO ground-based SAR vary more dramatically and show periodic characteristics. This not only causes envelope broadening and sidelobe increase during the imaging process, but also produces several pairs of false objects, further affecting the deformation measurement accuracy, so the system error must be corrected.

[0005] Considering the characteristics of wide beam and sub-aperture of ground-based SAR, common imaging algorithms include BP algorithm, FPFA algorithm, KSD algorithm and omega-k algorithm. Although BP algorithm has high accuracy as a time domain imaging algorithm, its calculation speed is slow, and each iteration process requires multiple complete imaging, which greatly increases the complexity of the algorithm. FPFA algorithm only uses two-dimensional Fourier transform, resulting in more phase error and migration error residual, thus affecting the amplitude and phase error estimation. Although KSD algorithm and omega-k algorithm have sufficiently accurate imaging results, they introduce new errors due to the use of interpolation factors. Summary of the invention

[0006] The technical problem solved by the present invention is: starting from the imaging characteristics, the imaging algorithm is improved, and a MIMO GB-SAR amplitude and phase error estimation method is provided by using a standard reflector test, thereby reducing the error introduced by imaging from the beginning and providing a fast and reliable rough estimation initial value for the fine correction of the amplitude and phase errors.

[0007] The technical solution of the present invention is: a MIMO GB-SAR amplitude and phase error estimation method, comprising:

[0008] Use MIMO radar to image a single standard reflector and ensure that there are no other objects in the entire azimuth dimension except the standard reflector;

[0009] The amplitude and phase errors of the imaging results of a single standard reflector are estimated based on the standard reflector to obtain the amplitude and phase error estimation values ​​of the transmitting and receiving channels.

[0010] The method of using MIMO radar to image a single standard reflector comprises:

[0011] 1.1) According to the MIMO radar array arrangement, establish the channel amplitude and phase error model of the MIMO ground-based SAR system, and obtain the amplitude and phase error function corresponding to each transmitting channel and receiving channel;

[0012] 1.2) Perform range pulse compression on the original echo signal received by the MIMO radar to obtain the range migration amount; if the correction condition is met, it indicates that the original echo signal needs to be corrected for RCMC range migration; if the correction condition is not met, proceed to step 1.4);

[0013] 1.3) According to the obtained amplitude and phase error functions, based on the sub-aperture division method, RCMC range motion correction is performed on the echo signal that needs RCMC range motion correction to obtain a motion-corrected image;

[0014] 1.4) Perform azimuth focusing on the original echo signal after range pulse compression to complete imaging.

[0015] In the step 1.1), according to the MIMO radar array arrangement, a MIMO ground-based SAR system channel amplitude and phase error model is established, and the amplitude and phase error functions corresponding to each transmitting channel and receiving channel are obtained, including:

[0016] The channel amplitude and phase error model of the MIMO ground-based SAR system is established. For the mth transmission channel, the amplitude and phase error function expression is:

[0017]

[0018] where g tm and Represent the amplitude and phase errors of the mth channel respectively, and M represents the number of transmitting channels;

[0019] For the nth receiving channel, the amplitude and phase error function expression is:

[0020]

[0021] where g rn and Represent the amplitude and phase errors of the nth channel, respectively, and N represents the number of receiving channels;

[0022] According to the phase center equivalence principle, the MIMO ground-based SAR with M transmitters and N receivers is equivalent to the existence of M*N independent virtual transceiver channels; when the mth transmitting channel and the nth receiving channel form the jth virtual transceiver channel, its amplitude and phase error function is:

[0023]

[0024] Wherein j(m, n) represents a virtual transceiver channel formed by the mth transmitting channel and the nth receiving channel.

[0025] The above 1.2) performs range pulse compression on the original echo signal received by the MIMO radar to obtain the range migration amount; if the correction condition is met, it indicates that the original echo signal needs to be corrected for RCMC range migration, including:

[0026] For a point object P in the monitoring area of ​​MIMO ground-based SAR, the distance from the point object P to the center O of the MIMO radar synthetic aperture is ρ0, and the angle is θ0; the radar echo signal reflected from point P after distance compression is expressed as:

[0027]

[0028] Where f represents the distance dimension frequency, x is the location of the radar virtual array element, A0 represents the reflection intensity of the object at point P, T prepresents the signal pulse width, L represents the synthetic aperture length, λ is the signal wavelength, c represents the speed of light, and B r represents the signal bandwidth, R(x; ρ0, α0) represents the slant range history;

[0029] Through Taylor expansion, R(x; ρ0, θ0) is expressed as:

[0030]

[0031] Among them, r3 (x) is a high-order term about x, which can be ignored in imaging because ρ0>>L;

[0032] In the case of maximum distance migration, if the maximum migration amount Lsinθ max Resolution in the range dimension compared to MIMO ground-based SAR At the same order of magnitude, RCMC distance migration correction is required; where θ max Indicates the maximum angle from the point object P to the center O of the MIMO radar synthetic aperture.

[0033] In the step 1.3), according to the obtained amplitude and phase error function, based on the sub-aperture division method, RCMC range motion correction is performed on the echo signal that needs to be corrected for RCMC range motion to obtain a motion-corrected image, including:

[0034] The virtual array of the azimuth dimension of the MIMO radar is divided into blocks, and a complete aperture is divided into K sub-apertures, and the distance from each sub-aperture to the center of the complete aperture is different;

[0035] Perform azimuth dimension FFT and range dimension inverse Fourier transform on all sub-aperture signals. The transformed sub-aperture signal model contains the phase term that causes range migration. The corresponding sub-aperture compensation factor is designed according to the distance between the divided sub-aperture center and the complete aperture center to correct the range migration.

[0036] All sub-aperture signals after range motion correction are added together and then range-dimensional Fourier transform is performed to obtain a motion-corrected image.

[0037] The step of obtaining the image after the motion correction according to the obtained amplitude-phase error function specifically includes:

[0038] The virtual array of the azimuth dimension of the MIMO radar is divided into blocks, and a complete aperture is divided into K sub-apertures. The center C of the kth sub-aperture is k The distance to the center O of the complete aperture is |l k |;

[0039] The original echo signal S of the kth sub-aperture Sk (f,xk ) is expressed as:

[0040]

[0041] Perform azimuth FFT and range inverse Fourier transform on all sub-aperture signals, ignore the quadratic terms and above in R(x; ρ0, θ0), and obtain the signal of the kth sub-aperture:

[0042]

[0043] where p x ( ) is the envelope in azimuth, γ is the modulation frequency in range dimension; is the term that causes distance migration. The compensation factor is designed by the distance between the center of the divided sub-aperture and point O:

[0044]

[0045] Add all sub-aperture signals after motion correction, and then perform range-dimensional Fourier transform to finally obtain the motion-corrected image.

[0046]

[0047] In the step 1.4), the azimuth dimension of the original echo signal after the range pulse compression is focused to complete the imaging, including: according to the established MIMO ground-based SAR system channel amplitude and phase error model, the error influence of the channel amplitude gain and phase is added to the original echo signal after the range pulse compression, and the azimuth dimension focusing factor of the original echo signal after the range pulse compression is phase compensated. When the residual phase meets the preset conditions, it is considered that the image azimuth dimension is well focused and the imaging is completed.

[0048] The azimuth focusing of the original echo signal after the range pulse compression is specifically performed as follows:

[0049] The propagation path error can be written as follows through Taylor expansion:

[0050]

[0051] Where x(m,n) represents the location of the j(m,n)th virtual transceiver channel; Tm ,x Rn They represent the x-axis positions of the mth transmitting channel and the nth receiving channel, respectively, and their relationship is

[0052] After RCMC range migration correction, the approximate error is substituted into the original echo signal model to obtain a signal model with amplitude and phase errors:

[0053]

[0054] In the formula, The term is a quadratic term that causes the envelope to broaden in the azimuth direction. As the azimuth focusing factor and S s rc_er (f,x ) Multiply; the remaining quadratic term is

[0055] The image azimuth dimension is considered to be well focused when the residual phase is required to meet the following conditions:

[0056]

[0057] From the above formula, we get ρ0. When the closest observation distance of MIMO-SAR is greater than this value ρ0, it is considered that the azimuth dimension is well focused after correction by the correction factor H2.

[0058] Ignoring the residual azimuthal quadratic term, the imaged signal is written as:

[0059]

[0060] The step of performing amplitude and phase error estimation based on the standard reflector on the imaging result of the single standard reflector to obtain an estimated value of the amplitude and phase error of the transceiver channel includes: calculating an estimated value of the phase error of the transceiver channel and an estimated value of the amplitude error of the transceiver channel, wherein:

[0061] Calculating an estimated value of a phase error of a transmitting and receiving channel includes: imaging a single standard reflector by a MIMO ground-based SAR to obtain imaging data, estimating a channel phase error, and setting all data amplitudes of the azimuth dimension where the standard reflector is located to 1 during the estimation; removing the linear phase term therein according to the circular shift method in the PGA algorithm and extracting the phase data in the azimuth time domain, then windowing the azimuth where the object is located, and extracting the azimuth time domain phase data; subtracting the two extracted phases to obtain a phase error; the phase error is composed of a transmitting channel phase error, a receiving channel phase error, other phase errors, and noise; solving the constraints of the obtained phase error by the least squares method to reduce the influence of other phase errors on the phase error between channels, and obtaining an estimated value of the phase error of the transmitting and receiving channel;

[0062] Calculating an estimated value of the amplitude error of the transmitting and receiving channels includes: extracting amplitude information of a standard reflector to obtain an amplitude error; the amplitude error includes a gain error between the transmitting and receiving channels as well as noise and amplitude modulation, and gradually converging the transmitting gain and the receiving gain in an iterative manner. The specific iterative process is: applying least squares to the transmitting gain and the receiving gain to obtain the amplitude gain, correcting the obtained transmitting and receiving gain according to an iterative formula, and then continuing to iterate. After multiple iterations, the gains obtained in each iteration are multiplied to obtain an estimated value of the amplitude error of the transmitting and receiving channels.

[0063] The specific process of calculating the estimated value of the phase error of the transmitting and receiving channels is as follows:

[0064] Calculate the estimated value of the phase error of the transmit and receive channels, including:

[0065] The data amplitude of the azimuth dimension where the standard reflector is located is set to 1 through the following formula to obtain the azimuth dimension data;

[0066] Ss phase (m, n) = Ss rc_er (R0,m,n) / |Ss rc_er (R0, m, n)|

[0067] Where R0 represents the distance between the standard reflector and the center of the synthetic aperture;

[0068] The circular shift method in the PGA algorithm is used to remove the linear phase term in the azimuth dimension data and extract the phase data φ in the azimuth time domain. point_error , then add a window to the azimuth of the single standard reflector and extract the azimuth time domain phase data φ point ; Subtract the two extracted phases to get the phase error φ error =φ point_error -φ point ;at the same time, in It represents the phase error value of the j(m, n)th virtual array element, which has the following relationship with the phase error between channels in are other phase errors and noises of the jth channel;

[0069] The phase error φ is obtained by using the least squares method. error Solve constraints

[0070] φ error =H φ_array φ TR +φ w

[0071] Among them, H φ_arrayThe matrix represents the relationship between the phase error of the transceiver channel and the phase error of the virtual transceiver channel. The columns of the matrix represent the virtual array elements arranged in sequence, and the rows of the matrix represent the transceiver channels arranged in sequence. The matrix is ​​composed of 0 and 1, where the transceiver channel element corresponding to each virtual array element is 1, and the rest are 0; φ w represents other phase errors,

[0072] Then the estimated phase error of the transmit and receive channels is for:

[0073]

[0074] The calculating an estimated value of the amplitude error of the transmitting and receiving channels includes:

[0075] Extract the amplitude information of a single standard reflector;

[0076] Ss am (m, n) = |Ss rc_er (R0, m, n)|

[0077] Among them, Ss am (m, n) is the amplitude error g that needs to be extracted error =[g error_1 g error_2 … g error_j …g error_MN ] T ;

[0078] Amplitude error g error It is not only caused by inter-channel gain error, but also includes noise and amplitude modulation;

[0079] g error_j =g Tm g Rn +g Reflect (j)

[0080] where g error_j represents the amplitude error value of the j(m, n)th virtual array element, g Reflect Represents the amplitude modulation and noise brought by the standard reflector;

[0081] Create two matrices and Represent the relationship between the transmit channel and the receive channel and the virtual array respectively. The columns of the matrix represent the virtual array elements arranged in sequence, and the rows of the matrix represent the transmit and receive channels arranged in sequence. The matrix is ​​composed of 0 and 1, where the transmit and receive channel element corresponding to each virtual array element is 1, and the rest are 0;

[0082] The transmission gain and receiving gain are gradually converged through iteration, including:

[0083] The transmit gain is obtained by least squares:

[0084]

[0085] The receiving gain is obtained by least squares:

[0086]

[0087] Correct the received and transmitted gains once, and then continue to iterate:

[0088]

[0089] After NUM iterations, multiply the gains obtained in each iteration to get the receive channel amplitude error value. And the transmit channel amplitude error value in

[0090] The advantages of the present invention compared with the prior art are:

[0091] 1) Taking into account the influence of MIMO ground-based SAR array arrangement and amplitude and phase errors on imaging, the present invention proposes an algorithm that uses sub-aperture division to perform range motion correction and azimuth focusing. By improving the imaging algorithm, the error introduced by imaging is minimized from the beginning. Compared with traditional algorithms, the speed and accuracy of range motion correction can be improved to a certain extent.

[0092] 2) Through the near-field standard reflector test, the amplitude and phase error data is extracted according to the array arrangement characteristics, and the amplitude and phase error is initially estimated, which can also reduce the number of iterations required for the subsequent fine correction stage. Compared with the existing amplitude and phase error estimation methods, a simple and fast amplitude and phase error estimation method with a standard reflector is proposed, which can preliminarily estimate relatively accurate amplitude and phase error information. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 Schematic diagram of the MIMO ground-based SAR array arrangement structure.

[0094] Figure 2 Schematic diagram of the MIMO ground-based SAR imaging model.

[0095] Figure 3 is the sub-aperture partition diagram.

[0096] Figure 4 Schematic diagram of the receiving and transmitting channels and virtual array element process model.

[0097] Figure 5 This is the imaging flow chart before amplitude and phase correction.

[0098] FIG6(a) shows an image of a standard reflector, and FIG6(b) shows an azimuthal cross-sectional view of the standard reflector.

[0099] Figure 7(a) is the image of the reflector after the pre-correction data corrects itself, Figure 7(b) shows the azimuth-dimensional cross-sectional view of the reflector after the pre-correction data corrects itself, Figure 7(c) shows the image of the reflector after the pre-correction data corrects the 21m standard reflector, and Figure 7(d) shows the azimuth-dimensional cross-sectional view of the reflector after the pre-correction data corrects the 21m standard reflector. DETAILED DESCRIPTION

[0100] The method of the invention comprises: MIMO ground-based SAR system analysis, MIMO ground-based SAR system RCMC method analysis, correction of range migration based on sub-aperture division, MIMO ground-based SAR system channel error analysis and azimuth dimension focusing processing, and amplitude and phase error estimation based on standard reflectors.

[0101] 1. Analysis of MIMO Ground-Based SAR System

[0102] MIMO ground-based SAR has multiple transmitting antennas and receiving antennas, and a large number of equally spaced virtual transceiver array elements are simulated through a special array arrangement to form a synthetic aperture. The MIMO ground-based SAR system involved in the present invention is composed of 16 transmitting antennas and 8 receiving antennas, which can equivalently synthesize 128 virtual transceiver array elements.

[0103] Table 1 shows the main parameters of MIMO ground-based SAR. Figure 1 It is the array arrangement structure of MIMO ground-based SAR.

[0104] Table 1 Main parameters of MIMO ground-based SAR

[0105]

[0106] 2. Establish channel amplitude and phase error model of MIMO ground-based SAR system

[0107] First, the amplitude and phase error model of MIMO-SAR is established. For the mth transmission channel, the amplitude and phase error function expression can be expressed as

[0108]

[0109] Among them, gt m and Represent the amplitude and phase errors respectively, and M represents the number of transmitting channels.

[0110] For the nth receiving channel, let its amplitude and phase error function expression be

[0111]

[0112] where g rn and Represent the amplitude and phase errors respectively, and N represents the number of receiving channels.

[0113] According to the phase center equivalence principle, the MIMO ground-based SAR with M transmitters and N receivers is equivalent to having M*N independent virtual transceiver channels. When the mth transmitting channel and the nth receiving channel form a virtual transceiver channel, the amplitude and phase error function can be written as:

[0114]

[0115] Where j(m, n) represents the virtual transceiver channel composed of the mth transmission channel and the nth reception channel, but it does not mean that j(m, n) is the m*nth virtual transceiver channel. There is a special correspondence between them. According to the MIMO ground-based SAR designed by our team, this correspondence can be expressed as:

[0116]

[0117] Where M=16, N=8.

[0118] The above correspondence is applicable to the MIMO-SAR involved in the present invention. If the array arrangement is different, the correspondence will also be different.

[0119] 3. RCMC Processing Analysis of MIMO Ground-Based SAR System

[0120] like Figure 2 As shown in the figure, a point object P is placed in the monitoring area of ​​the MIMO ground-based SAR. The distance from the point object P to the center O of the synthetic aperture is ρ0, and the angle is θ0. The radar echo signal model reflected from point P after distance compression can be expressed as:

[0121]

[0122] Where f represents the distance dimension frequency, x is the location of the radar virtual array element, A0 represents the reflection intensity of the object at point P, T p represents the signal pulse width, L represents the synthetic aperture length, λ is the signal wavelength, c represents the speed of light, and B r represents the signal bandwidth, and R(x; ρ0, θ0) represents the slant range. Through Taylor expansion, R(x; ρ0, θ0) can be expressed as:

[0123]

[0124] Among them, r3 (x) is a high-order term related to x, and since ρ0>>L, it can be ignored during imaging.

[0125] For the distance migration of the distance dimension, the sinθ0x term is the main component, and the quadratic term has little effect on the distance migration. When the distance migration is the largest, the maximum migration amount is:

[0126] Lsinθ max =0.287m

[0127] The resolution of the range dimension of MIMO ground-based SAR is Therefore, the impact of range migration on the image range resolution cannot be ignored.

[0128] If the keystone interpolation method is used to correct the motion of MIMO ground-based SAR, the estimation of the amplitude and phase errors between channels will be affected due to the use of azimuth interpolation. Based on this, the present invention proposes an algorithm for correcting range motion based on dividing sub-apertures.

[0129] 4. For the echo signal that needs RCMC, use the sub-aperture division method to perform RCMC to obtain the image after migration correction

[0130] First, the virtual array of the MIMO radar azimuth dimension is divided into blocks, such as Figure 3 As shown, a complete aperture is divided into K sub-apertures, and the center C of the kth sub-aperture k The distance to the center O of the complete aperture is |l k |.

[0131] Therefore, the signal model of the kth sub-aperture can be expressed as:

[0132]

[0133] Then perform azimuth FFT and range inverse Fourier transform on all sub-aperture signals, ignore the quadratic terms and above in R(x; ρ0, θ0), and obtain the signal model of the kth sub-aperture:

[0134]

[0135] where p x (·) is the envelope in azimuth and γ is the modulation frequency in range dimension. is the term that causes distance migration. The compensation factor is designed based on the distance between the center of the divided sub-aperture and point O:

[0136]

[0137] After the migration correction, the residual distance migration is (x k -l k )sinθ. Due to the division of sub-apertures, the virtual array element position xk The value range is

[0138] Therefore, the maximum residual distance migration after migration correction is When divided into 8 sub-apertures, the residual migration is only 0.035m, which can be ignored.

[0139] Finally, all sub-aperture signals after motion correction are added together and then the range-dimensional Fourier transform is performed to obtain the motion-corrected image.

[0140]

[0141] 5. For the echo signal that needs RCMC, use the sub-aperture division method to perform RCMC to obtain the image after migration correction

[0142] like Figure 4 As shown in the figure, the dual-station mode of one transmission and one reception is equivalent to the midpoint self-transmission and self-reception. There is a propagation path error. The Taylor expansion expression ΔR array It can be written as:

[0143]

[0144] Where x(m,n) represents the location of the j(m,n)th virtual transceiver channel. Tm ,x Rn They represent the x-axis positions of the mth transmitting channel and the nth receiving channel, respectively, and their relationship is:

[0145] Since ρ0>>L, the residual range migration error caused by this approximate processing can be ignored. However, there is still a certain impact on the phase in the azimuth direction. Under the condition of far-field imaging, this impact can be completely ignored, but for near-field imaging, this kind of impact needs to be taken into account.

[0146] After RCMC, the approximate error in the above formula is substituted into the original echo signal model to obtain the signal model with amplitude and phase errors:

[0147]

[0148] In this formula, The term is a quadratic term that causes the envelope to broaden in the azimuthal direction. As a directional focusing factor and Ss rc_er (f,x) is multiplied. The remaining quadratic term is

[0149] The image azimuth dimension can be considered to be well focused only when the residual phase satisfies the following conditions:

[0150]

[0151] From this formula, we can get ρ0>16.5663m. For example, if the closest observation distance of MIMO-SAR is 20m, it can be considered that the azimuth dimension is well focused after correction by this correction factor.

[0152] Ignoring the residual azimuth quadratic term, the signal model can be written as:

[0153]

[0154] Finally, the algorithm flow chart for the MIMO-SAR imaging part can be obtained as follows Figure 5 shown.

[0155] 6. Estimation of the amplitude and phase errors of the imaged data based on the standard reflector to obtain the channel amplitude and phase error estimation value

[0156] Both phase error and amplitude error will lead to false objects in the entire azimuth dimension. In order to have a quick and rough estimate of the amplitude and phase errors of the system, it is necessary to let the MIMO ground-based SAR image a single standard reflector and try to ensure that there are no other objects in the entire azimuth dimension except the standard reflector.

[0157] First, the channel phase error should be estimated. In order to eliminate the influence of amplitude error, the pre-estimation of phase error requires that the data amplitude of the azimuth dimension where the standard reflector is located is set to 1.

[0158] Ss phase (m, n) = Ss rc_er (R0,m,n) / |Ss rc_er (R0, m, n)|

[0159] Where R0 represents the distance between the standard reflector and the center of the synthetic aperture.

[0160] According to the circular shift method in the PGA algorithm, the linear phase term is removed and the phase data φ in the azimuth time domain is extracted. point_error , then add a window to the object's position (the window can be appropriately larger), and extract the position time domain phase data φ point Subtract the two extracted phases φ error =φ point_error -φ point , and the phase error is obtained. The extracted phase error is mainly the phase error caused by the false object.

[0161]

[0162] in It represents the phase error value of the j(m, n)th virtual array element, which has the following relationship with the phase error between channels in are other phase errors and noise.

[0163] The phase error obtained at this time does not conform to the characteristics of the phase error between MIMO-SAR channels. It is necessary to solve the constraints of the obtained phase error to reduce the impact of other phase errors on the phase error between channels by solving the constraints. error Solve constraints.

[0164] φ error =H φ_array φ TR +φ w

[0165] Among them, H φ_array Represents the relationship matrix between the phase error of the transceiver channel and the phase error of the virtual channel. The columns of the matrix represent the virtual array elements arranged in sequence, and the rows of the matrix represent the transceiver channels arranged in sequence. The matrix is ​​composed of 0 and 1, where the transceiver channel element corresponding to each virtual array element is 1, and the rest are O. φ w represents other phase errors,

[0166] Then we can get:

[0167]

[0168] Obtained It is the phase error value of the transmitting and receiving channels.

[0169] After obtaining the phase error value, the amplitude error value needs to be solved.

[0170] First, the amplitude information of the standard reflector is extracted.

[0171] Ss am (m, n) = |Ss rc_er (R0, m, n)|

[0172] SS am (m, n) is the amplitude error g that needs to be extracted error =[g error_1 g error_2 … g error_j …g error_MN ] T .

[0173] Similar to the phase error, the amplitude error also has problems such as standard reflector modulation, so g errorIt is not just the inter-channel gain error that causes this, but also noise and amplitude modulation.

[0174] g error_j =g Tm g Rn +g Reflect (j)

[0175] where g Reflect Represents the amplitude modulation and noise caused by the standard reflector.

[0176] In order to eliminate g Reflect The impact brought about by this requires the creation of two matrices and The matrix composition is the same as above. It represents the relationship between the transmit channel and the receive channel and the virtual array, and is used to estimate the transmit channel gain g T =[g T1 …g TM ]T and receiving channel gain g R =[g R1 …g RN ] T .

[0177] Since the transmission gain and the receiving gain are multiplicative, it is not possible to directly constrain them using the least squares method. Instead, the transmission gain and the receiving gain need to be gradually converged through iteration. The algorithm flow is as follows:

[0178] First, the transmit gain is least squared to obtain:

[0179]

[0180] Then the least square method of the receiving gain is obtained:

[0181]

[0182] Correct the received transmit and receive gain once, and then continue iterating:

[0183]

[0184] After NUM iterations, the gains obtained in each iteration are multiplied to obtain the estimated amplitude error value of the transmitting and receiving channels.

[0185]

[0186]

[0187] in Num is the number of iterations. Generally, NUM takes 5 times to get the result.

[0188] The pre-correction data obtained by the above method can achieve good correction effects for the correction of the standard reflector itself and other standard reflectors. It also has certain reference significance for correcting other ground object echoes. The initial values ​​of amplitude and phase errors can be obtained to facilitate further fine correction.

[0189] Algorithm Application Examples

[0190] MIMO ground-based SAR was used to collect standard reflector data, and the selectable standard reflector positions were set to 21m, 27m, and 32.5m.

[0191] The data of the 27m standard reflector were collected and imaged using the method of the present invention to obtain the result shown in FIG6 .

[0192] As can be seen from Figure 6(a), in the case of azimuth plus Hamming window, due to the influence of periodic amplitude and phase errors, the false objects are mainly located at ±22.5 degrees and ±45 degrees, almost covering the entire azimuth beam width. From the profile diagram, it can be seen that the maximum peak value of the false object is about -15.9B, which can easily cause misjudgment or cover up some other objects.

[0193] According to the method of the present invention, the phase and amplitude errors of the standard reflector data are extracted to pre-correct the data. From the correction results of Figure 7 (ad), it can be seen that these pre-corrected data can achieve good results when used to correct the standard reflector itself or other standard reflector data.

[0194] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention by using the technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A MIMO GB-SAR amplitude and phase error estimation method, characterized in that: include: Use MIMO radar to image a single standard reflector, and ensure that there are no other objects in the entire azimuth dimension except the standard reflector during imaging; The amplitude and phase errors of the imaging results of a single standard reflector are estimated based on the standard reflector to obtain the amplitude and phase error estimation values ​​of the transmitting and receiving channels.

2. A MIMO GB-SAR amplitude and phase error estimation method according to claim 1, characterized in that: The method of using MIMO radar to image a single standard reflector comprises: 1.1) According to the MIMO radar array arrangement, establish the channel amplitude and phase error model of the MIMO ground-based SAR system, and obtain the amplitude and phase error function corresponding to each transmitting channel and receiving channel; 1.2) Perform range pulse compression on the original echo signal received by the MIMO radar to obtain the range migration amount; if the correction condition is met, it indicates that the original echo signal needs to be corrected for RCMC range migration; if the correction condition is not met, directly enter step 1.4); 1.3) According to the obtained amplitude and phase error functions, based on the sub-aperture division method, RCMC range motion correction is performed on the echo signal that needs RCMC range motion correction to obtain a motion-corrected image; 1.4) Perform azimuth focusing on the original echo signal after range pulse compression to complete imaging.

3. A MIMO GB-SAR amplitude and phase error estimation method according to claim 1, characterized in that: In the step 1.1), according to the MIMO radar array arrangement, a MIMO ground-based SAR system channel amplitude and phase error model is established, and the amplitude and phase error functions corresponding to each transmitting channel and receiving channel are obtained, including: The channel amplitude and phase error model of the MIMO ground-based SAR system is established. For the mth transmission channel, the amplitude and phase error function expression is: where g tm and Represent the amplitude and phase errors of the mth channel respectively, and M represents the number of transmitting channels; For the nth receiving channel, the amplitude and phase error function expression is: where g rn and Represent the amplitude and phase errors of the nth channel, respectively, and N represents the number of receiving channels; According to the phase center equivalence principle, the MIMO ground-based SAR with M transmitters and N receivers is equivalent to having M*N independent virtual transceiver channels. When the mth transmitting channel and the nth receiving channel form the jth virtual transceiver channel, the amplitude and phase error function is: Wherein j(m,n) represents a virtual transceiver channel formed by the mth transmitting channel and the nth receiving channel.

4. A MIMO GB-SAR amplitude and phase error estimation method according to claim 3, characterized in that: The step 1.2) performs range pulse compression on the original echo signal received by the MIMO radar to obtain the range migration amount; If the correction conditions are met, it means that the original echo signal needs to be corrected by RCMC range migration, including: For a point object P in the monitoring area of ​​MIMO ground-based SAR, the distance from the point object P to the center O of the MIMO radar synthetic aperture is ρ0, and the angle is θ0; the radar echo signal reflected from point P after distance compression is expressed as: Where f represents the distance dimension frequency, x is the location of the radar virtual array element, A0 represents the reflection intensity of the object at point P, T p represents the signal pulse width, L represents the synthetic aperture length, λ is the signal wavelength, c represents the speed of light, and B r represents the signal bandwidth, R(x;ρ0,θ0) represents the slant range history; Through Taylor expansion, R(x; ρ0, θ0) is expressed as: Among them, r3 (x) is a high-order term about x, which can be ignored in imaging because ρ0>>L; In the case of maximum distance migration, if the maximum migration amount Lsinθ max Resolution in the range dimension compared to MIMO ground-based SAR At the same order of magnitude, RCMC distance migration correction is required; where θ max Indicates the maximum angle from the point object P to the center O of the MIMO radar synthetic aperture.

5. A MIMO GB-SAR amplitude and phase error estimation method according to claim 4, characterized in that: In the step 1.3), according to the obtained amplitude and phase error function, based on the sub-aperture division method, RCMC range motion correction is performed on the echo signal that needs to be corrected for RCMC range motion to obtain a motion-corrected image, including: The virtual array of the azimuth dimension of the MIMO radar is divided into blocks, and a complete aperture is divided into K sub-apertures, and the distance from each sub-aperture to the center of the complete aperture is different; Perform azimuth dimension FFT and range dimension inverse Fourier transform on all sub-aperture signals. The transformed sub-aperture signal model contains the phase term that causes range migration. The corresponding sub-aperture compensation factor is designed according to the distance between the divided sub-aperture center and the complete aperture center to correct the range migration. All sub-aperture signals after range motion correction are added together and then range-dimensional Fourier transform is performed to obtain a motion-corrected image.

6. A MIMO GB-SAR amplitude and phase error estimation method according to claim 5, characterized in that: The step of obtaining the image after the motion correction according to the obtained amplitude-phase error function specifically includes: The virtual array of the azimuth dimension of the MIMO radar is divided into blocks, and a complete aperture is divided into K sub-apertures. The center C of the kth sub-aperture is k The distance to the center O of the complete aperture is |l k |; The original echo signal S of the kth sub-aperture Sk (f,x k ) is expressed as: Perform azimuth FFT and range inverse Fourier transform on all sub-aperture signals, ignore the quadratic terms and above in R(x; ρ0, θ0), and obtain the signal of the kth sub-aperture: where p x (·) is the envelope in azimuth, γ is the modulation frequency in range dimension; is the term that causes distance migration. The compensation factor is designed by the distance between the center of the divided sub-aperture and point O: Add all sub-aperture signals after motion correction, and then perform range-dimensional Fourier transform to finally obtain the motion-corrected image.

7. A MIMO GB-SAR amplitude and phase error estimation method according to claim 2, characterized in that: In the step 1.4), the azimuth dimension of the original echo signal after the range pulse compression is focused to complete the imaging, including: according to the established MIMO ground-based SAR system channel amplitude and phase error model, the error influence of the channel amplitude gain and phase is added to the original echo signal after the range pulse compression, and the azimuth dimension focusing factor of the original echo signal after the range pulse compression is phase compensated. When the residual phase meets the preset conditions, it is considered that the image azimuth dimension is well focused and the imaging is completed.

8. A MIMO GB-SAR amplitude and phase error estimation method according to claim 7, characterized in that: The azimuth focusing of the original echo signal after the range pulse compression is specifically performed as follows: The propagation path error is expressed by Taylor expansion ΔR array It is expressed as: Where x(m,n) represents the location of the j(m,n)th virtual transceiver channel; Tm ,x Rn They represent the x-axis positions of the mth transmitting channel and the nth receiving channel, respectively, and their relationship is After RCMC range migration correction, the approximate error is substituted into the original echo signal model to obtain a signal model with amplitude and phase errors: In the formula, The term is a quadratic term that causes the envelope to broaden in the azimuth direction. As a directional focusing factor and Ss rcer (f,x) are multiplied; the remaining quadratic term is The image azimuth dimension is considered to be well focused when the residual phase is required to meet the following conditions: From the above formula, we get ρ0. When the closest observation distance of MIMO-SAR is greater than this value ρ0, it is considered that the azimuth dimension is well focused after correction by the correction factor H2. Ignoring the residual azimuthal quadratic term, the imaged signal is written as:

9. A MIMO GB-SAR amplitude and phase error estimation method according to claim 8, characterized in that: The step of performing amplitude and phase error estimation based on the standard reflector on the imaging result of the single standard reflector to obtain an estimated value of the amplitude and phase error of the transceiver channel includes: calculating an estimated value of the phase error of the transceiver channel and an estimated value of the amplitude error of the transceiver channel, wherein: Calculating an estimated value of a phase error of a transmitting and receiving channel includes: imaging a single standard reflector by a MIMO ground-based SAR to obtain imaging data, estimating a channel phase error, and setting all data amplitudes of the azimuth dimension where the standard reflector is located to 1 during the estimation; removing the linear phase term therein according to the circular shift method in the PGA algorithm and extracting the phase data in the azimuth time domain, then windowing the azimuth where the object is located, and extracting the azimuth time domain phase data; subtracting the two extracted phases to obtain a phase error; the phase error is composed of a transmitting channel phase error, a receiving channel phase error, other phase errors, and noise; solving the constraints of the obtained phase error by the least squares method to reduce the influence of other phase errors on the phase error between channels, and obtaining an estimated value of the phase error of the transmitting and receiving channel; Calculating an estimated value of the amplitude error of the transmitting and receiving channels includes: extracting amplitude information of a standard reflector to obtain an amplitude error; the amplitude error includes a gain error between the transmitting and receiving channels as well as noise and amplitude modulation, and gradually converging the transmitting gain and the receiving gain in an iterative manner. The specific iterative process is: applying least squares to the transmitting gain and the receiving gain to obtain the amplitude gain, correcting the obtained transmitting and receiving gain according to an iterative formula, and then continuing to iterate. After multiple iterations, the gains obtained in each iteration are multiplied to obtain an estimated value of the amplitude error of the transmitting and receiving channels.

10. A MIMO GB-SAR amplitude and phase error estimation method according to claim 9, characterized in that: The specific process of calculating the estimated value of the phase error of the transmitting and receiving channels is as follows: Calculate the estimated value of the phase error of the transmit and receive channels, including: The data amplitude of the azimuth dimension where the standard reflector is located is set to 1 through the following formula to obtain the azimuth dimension data; Ss phase (m,n)=Ss rc_er (R0,m,n) / |Ss rc_er (R0,m,n)| Where R0 represents the distance between the standard reflector and the center of the synthetic aperture; The circular shift method in the PGA algorithm is used to remove the linear phase term in the azimuth dimension data and extract the phase data φ in the azimuth time domain. point_error , then add a window to the azimuth of the single standard reflector and extract the azimuth time domain phase data φ point ; Subtract the two extracted phases to get the phase error φ error =φ point_error -φ point ;at the same time, in It represents the phase error value of the j(m,n)th virtual array element, which has the following relationship with the phase error between channels in are other phase errors and noises of the jth channel; The phase error φ is obtained by using the least squares method. error Solve constraints f error =H φ_array f TR +φ w Among them, H φ_array The matrix represents the relationship between the phase error of the transceiver channel and the phase error of the virtual transceiver channel. The columns of the matrix represent the virtual array elements arranged in sequence, and the rows of the matrix represent the transceiver channels arranged in sequence. The matrix is ​​composed of 0 and 1, where the transceiver channel element corresponding to each virtual array element is 1, and the rest are 0; φ w represents other phase errors, Then the estimated phase error of the transmit and receive channels is for:

11. A MIMO GB-SAR amplitude and phase error estimation method according to claim 9, characterized in that: The specific process of calculating the estimated value of the amplitude error of the transmitting and receiving channels is as follows: Extract the amplitude information of a single standard reflector; Ss am (m,n)=|Ss rc_er (R0,m,n)| Among them, Ss am (m,n) is the amplitude error g that needs to be extracted error =[g error_1 g error_2 …g error_j …g error_MN ] T ; Amplitude error g error It is not only caused by inter-channel gain error, but also includes noise and amplitude modulation; g error_j =g Tm g Rn +g Reflect (j) where g error_j represents the amplitude error value of the j(m,n)th virtual array element, g Reflect Represents the amplitude modulation and noise brought by the standard reflector; Create two matrices and Represent the relationship between the transmit channel and the receive channel and the virtual array respectively. The columns of the matrix represent the virtual array elements arranged in sequence, and the rows of the matrix represent the transmit and receive channels arranged in sequence. The matrix is ​​composed of 0 and 1, where the transmit and receive channel element corresponding to each virtual array element is 1, and the rest are 0; The transmission gain and receiving gain are gradually converged through iteration, including: The transmit gain is obtained by least squares: The receiving gain is obtained by least squares: Correct the received and transmitted gains once, and then continue to iterate: After NUM iterations, multiply the gains obtained in each iteration to get the receive channel amplitude error value. And the transmit channel amplitude error value in

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