A MIMO ground-based SAR amplitude and phase error correction method and device

Abstract

The application provides a MIMO ground-based SAR amplitude-phase error correction method, which comprises the following steps: imaging, generating an amplitude-phase correction factor, pre-correction, initialization, phase error estimation correction, amplitude error estimation correction, local optimal determination and solution, global optimal determination and the like. The method provided by the application can accurately estimate the channel amplitude-phase error existing in the MIMO ground-based SAR, and improve the SAR imaging quality and accuracy through the correction of the error. The application further provides a MIMO ground-based SAR amplitude-phase error correction device.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and specifically to a method and apparatus for correcting amplitude and phase errors in MIMO ground-based SAR. Background Technology

[0002] Synthetic Aperture Radar (SAR) utilizes a small-aperture antenna that moves relative to the target to coherently process echoes received at different locations, thereby obtaining high-resolution radar images. Ground-based Synthetic Aperture Radar (GB-SAR) operates on the same measurement principle as conventional spaceborne SAR. It is a novel deformation monitoring technology that has emerged in recent years, offering advantages such as high accuracy and comprehensive coverage. It effectively meets the needs of geological disaster monitoring and has been widely applied in the monitoring field.

[0003] Based on the method of synthetic aperture (SAR) realization, 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 azimuth dimension synthetic aperture through a linear orbit, while arc scanning ground-based SAR obtains the azimuth dimension synthetic aperture through the circular motion of transmitting and receiving antennas in the horizontal plane. Unlike the previous two radar systems, MIMO ground-based SAR uses multiple transmitting and receiving antennas arranged in a specific array to form a uniformly distributed virtual array aperture. During the operation of MIMO ground-based SAR, each transmitting antenna transmits at different times, and the receiving antenna receives simultaneously, completing a full scan in only tens of milliseconds to a few seconds. Therefore, this radar can quickly capture deformation information within the monitoring area, achieving more accurate and rapid deformation measurement, thus meeting the requirements of speed and emergency response in geological disaster monitoring. Furthermore, MIMO ground-based SAR does not require a physical orbit, making it more lightweight and portable.

[0004] The appearance of a certain type of MIMO ground-based SAR is as follows Figure 1 As shown, its array arrangement structure is as follows: Figure 2 As shown, it consists of 16 transmitting antennas and 8 receiving antennas, which can be equivalently synthesized into 128 virtual transceiver array elements. Its main technical parameters are shown in Table 1.

[0005] Table 1. Main parameters of MIMO ground-based SAR

[0006] MIMO radar is affected by various non-ideal factors in its actual operating environment, such as manufacturing processes, temperature and humidity, hardware aging, and coupling between antenna elements, leading to amplitude and phase inconsistencies in the transmit and receive channels. This inconsistency manifests as gain and phase errors in the radar echo received by the virtual array elements. MIMO ground-based SAR is a type of coherent MIMO radar, with close spacing between its virtual array elements and slow phase changes. Without amplitude and phase error correction, the imaging results of MIMO ground-based SAR will be severely affected. Besides causing envelope broadening and increased sidelobes, it can also lead to false targets or even target position changes throughout the azimuth dimension. For example, simulation analysis shows... Figures 4-7 As shown, where Figure 4 This represents the simulation results for a point target without amplitude and phase errors. Figure 5 This represents the simulation results under the influence of inter-channel amplitude errors. Figure 6 This represents the simulation results under the influence of inter-channel phase error. Figure 7 This represents the comparison between the point target and the original signal under the influence of amplitude and phase errors. The simulation results show that both amplitude and phase errors result in false targets generated by a single point target distributed throughout the entire azimuth dimension, thus requiring amplitude and phase correction.

[0007] For the amplitude and phase errors of MIMO ground-based SAR, existing correction methods are mainly divided into two categories. One category is the error estimation method based on spectrum estimation, which is based on traditional array signal processing and aims at DOA estimation of a few signal sources. The other category is the high-precision amplitude and phase error estimation method based on radar imaging processing, which is based on the entire scene target.

[0008] Error estimation methods based on spectral estimation can be categorized into active correction techniques and passive correction (self-correction) techniques. Active correction techniques require placing one or more external radiation correction sources in a designated space and utilizing the prior information of these sources to estimate the echo data. Xu Qing, in his paper titled "A Method for Estimating Amplitude and Phase Errors of MIMO Radar" published in the *Acta Aeronautica et Astronautica Sinica*, Mar. 25, 2012, Vol. 33, No. 3530-536, presented an array model of a monostatic correlated MIMO radar and proposed a method for estimating the amplitude and phase errors of MIMO radar. This method uses matched filtering of the transmitted orthogonal signals to separate the received array signals, obtaining a "virtual array" similar to a traditional array. Using time-division multiplexing source data, the phase and amplitude errors caused by the direction of arrival (DOA) of the source in the real steering vector of this array are separated. By constructing a cost function, the DOA estimate is obtained, and thus, the amplitude and phase errors of the transmitting and receiving arrays are estimated separately. This type of method relies on the correction sources, and the accuracy of their prior information affects the accuracy of the array error estimation. Furthermore, the correction process places high demands on the experimental site. In contrast, self-calibration technology does not require an external radiation source and can simultaneously estimate the target azimuth and array amplitude and phase errors, offering greater flexibility. However, it generally requires only a few targets in the scenario, making it difficult to adapt to ground-based SAR observation scenarios with a large number of targets.

[0009] Research on high-precision amplitude and phase error estimation methods for the entire scene target is relatively limited. The main algorithms proposed include methods for correcting amplitude and phase errors and echo nonlinear errors in frequency-modulated continuous wave array SAR systems, algorithms for correcting amplitude and phase errors in 3D SAR applications, and algorithms for estimating and correcting inter-channel amplitude and phase errors based on raw data. In his paper "Fast Entropy Minimization Based Autofocusing Technique for ISAR Imaging," published in IEEE TRANSACTIONS SIGNALPROCESSING, VOL.63, NO.13, JULY 1, 2015, Shuanghui Zhang addressed the phase correction problem in airborne ISAR imaging. Recognizing the high computational cost of traditional Minimize Image Entropy (MEA) algorithms for phase estimation, he derived the MEA phase error search process using Newton's method, ignoring some less important but computationally intensive parts of the iterative formula. This resulted in a Newton-based MEA (N-MEA), significantly improving the computational efficiency of MEA. Furthermore, the simplified Newton's method (SN) and the improved Newton's method (MN) are introduced into MEA to further improve its computational efficiency. However, this method only corrects phase errors and fails to correct amplitude errors.

[0010] In summary, existing technologies for amplitude and phase error correction in MIMO ground-based SAR have the following problems: (1) The active correction technique based on spectrum estimation depends on the correction source. The accuracy of its prior information will affect the accuracy of array error estimation. The correction process also has high requirements for the experimental site.

[0011] (2) Self-correction techniques based on spectrum estimation require only a few targets in the scene, which is difficult to adapt to ground-based SAR observation scenarios with a large number of targets.

[0012] (3) Error correction based on the minimum image entropy algorithm mainly targets the phase error estimation problem. If the minimum image entropy algorithm is directly used to estimate the amplitude error, since the phase between the transmitting and receiving channels is additive and the amplitude is multiplicative during the entire iterative correction process, the amplitude gain between the transmitting and receiving channels is easily coupled, and multiple iterations are prone to getting trapped in local optima. Summary of the Invention

[0013] The technical problem to be solved by the present invention is to provide a method and apparatus for MIMO ground-based SAR amplitude and phase error correction that can adapt to a large number of targets in MIMO ground-based SAR observation scenarios, avoid getting trapped in local optima, and converge quickly.

[0014] To address the aforementioned technical problems, this invention provides a method for correcting amplitude and phase errors in MIMO ground-based SAR, comprising the following steps: S1, Image the demodulated MIMO ground-based SAR two-dimensional echo data to obtain an imaging signal. The imaging signal consists of the product of the amplitude and phase error system function of the corresponding transmit channel and the amplitude and phase error system function of the corresponding receive channel, the pulse-compressed range dimension envelope, and the original phase. S2, using the angle reflection imaging data to extract amplitude and phase error information, an initial estimate of the amplitude and phase error is obtained, and an amplitude and phase correction factor is generated from the initial estimate of the amplitude and phase error. The amplitude and phase correction factor is composed of the relationship matrix between the amplitude gain of the transmit channel and the amplitude gain of the virtual channel, the relationship matrix between the amplitude gain of the receive channel and the amplitude gain of the virtual channel, and the relationship matrix between the phase error of the transmit and receive channels and the phase error of the virtual channel, together with the estimated values ​​of the transmit channel gain, the receive channel gain, and the phase error of the transmit and receive channels. S3, perform amplitude and phase correction on the imaging signal using a correction formula, which is obtained by multiplying the amplitude and phase correction factor by the imaging signal and adding the phases; S4, Initialization, let the number of iterations be... Both the phase error search direction vector and the amplitude error search direction vector are 0, and the amplitude and phase error vector is the initial estimate of the amplitude and phase error obtained in step S2. S5, the phase error is estimated and corrected using the minimum image entropy algorithm; S6, The minimum image entropy algorithm is used to estimate and correct the amplitude error; S7, determine if the system is trapped in a local optimum. If so, update the amplitude error estimate using the product of the impulse and the current amplitude error estimate, and proceed to step S8; otherwise, let... Proceed to step S5; the impulse is composed of a combination of the amplitude error search direction and random white noise with a variance of 1; S8, determine if the global optimum has been reached. If so, output the amplitude and phase error estimate of the last iteration; otherwise, let... Proceed to step S6.

[0015] Furthermore, the amplitude and phase error system function of the corresponding transmission channel in step S1 is composed of the signal amplitude of the transmission channel multiplied by the signal phase of the transmission channel expressed as a natural logarithm, and the amplitude and phase error system function of the corresponding receiving channel is composed of the signal amplitude of the receiving channel multiplied by the signal phase of the receiving channel expressed as a natural logarithm.

[0016] Furthermore, the relationship matrix between the transmit channel amplitude gain and the virtual channel amplitude gain mentioned in step S2 is generated according to the following method: The relation matrix consists of 0s and 1s. The rows of the relation matrix represent virtual array elements arranged in order, and the columns of the relation matrix represent transmission channels arranged in order. The transmission channel element corresponding to each virtual array element is 1, and the rest are 0. The relationship matrix between the received channel amplitude gain and the virtual channel amplitude gain mentioned in step S2 is generated according to the following method: The relation matrix consists of 0s and 1s. The rows of the relation matrix represent the virtual array elements arranged in order, and the columns of the relation matrix represent the receiving channels arranged in order. The receiving channel element corresponding to each virtual array element is 1, and the rest are 0. The relationship matrix between the transmit / receive channel phase error and the virtual channel phase error in step S2 is generated according to the following method: The relation matrix consists of 0s and 1s. The rows of the relation matrix represent virtual array elements arranged in order, and the columns of the relation matrix represent transceiver channels arranged in order. The transceiver channel element corresponding to each virtual array element is 1, and the rest are 0.

[0017] Furthermore, the step S5, which involves estimating and correcting the phase error using the minimum image entropy algorithm, is as follows: S51, use the imaging signal to calculate the first derivative with respect to the previous phase error; S52, calculate the phase error relationship scalar, where the phase error relationship scalar is the ratio of the 2-norm of the first derivative of the phase error in the current iteration to the 2-norm of the phase error search direction in the previous iteration. When the phase error relationship is directly calculated, the scalar value is set to 0. S53, add the first derivative of the phase error in this iteration to the product of the current phase error relation scalar and the previous phase error search direction, in order to update the phase error search direction; S54, let the initial value of the phase search step size be 1, and use the phase search step size update iterative formula to iterate 4 or 5 times to update the phase search step size. The phase search step size update iterative formula is the current iteration search step size minus a gradient term. The gradient term is the first derivative of the image entropy with respect to the original step size divided by the second derivative of the image entropy with respect to the original step size. S55, add the product of the phase search step size and the phase error search direction obtained this time to the previous phase error estimate to obtain the updated phase error estimate; S56, Substitute the updated phase error estimate into the correction formula described in step S3 to perform phase correction on the imaging signal.

[0018] Furthermore, the step S6, which involves estimating and correcting the amplitude error using the minimum image entropy algorithm, is as follows: S61, use the imaging signal to calculate the first derivative with respect to the previous amplitude error; S62, calculate the amplitude error relationship scalar, where the amplitude error relationship scalar is the ratio of the 2-norm of the first derivative of the amplitude error in the current iteration to the 2-norm of the amplitude error search direction in the previous iteration. When calculating the scalar value based on the amplitude error relationship, directly set the value to 0. S63, add the first derivative of the amplitude error in this iteration to the product of the current amplitude error relation scalar and the previous amplitude error search direction, in order to update the amplitude error search direction; S64, let the initial value of the amplitude search step size be 1, and update the amplitude search step size using the amplitude search step size update iterative formula 4 or 5 times. The amplitude search step size update iterative formula is the current iteration search step size minus a gradient term. The gradient term is the first derivative of the image entropy with respect to the original step size divided by the second derivative of the image entropy with respect to the original step size. S65, add the product of the amplitude search step size and the amplitude error search direction obtained this time to the previous amplitude error estimate to obtain the updated amplitude error estimate; S66, divide the amplitude error estimate by the 1 norm of the amplitude error estimate to obtain the normalized amplitude error estimate; S67, Substitute the normalized amplitude error estimate into the correction formula described in step S3 to perform amplitude correction on the imaging signal.

[0019] Going further, The method for determining whether a region is trapped in a local optimum in step S7 is as follows: If the absolute value of the difference between the image entropy obtained after the current iteration and the image entropy obtained after the previous iteration is less than the threshold for determining local optima, then it is determined that the image has fallen into a local optimum. The method for determining whether the global optimum has been reached in step S8 is as follows: If the absolute value of the difference between the image entropy before and after updating the amplitude error using impulse is less than the global optimum determination threshold, then the global optimum has been determined.

[0020] Furthermore, the impulse mentioned in step S7 is a linear combination term: The first term of the linear combination term is 1, the second term is the product of the first step length and the amplitude error search direction, and the third term is the product of the second step length, white noise, and the amplitude error search direction.

[0021] Furthermore, the threshold for determining the local optimum is: The global optimal decision threshold is .

[0022] Furthermore, the first step has a length of 0.6, and the second step has a length of 0.1.

[0023] The present invention also provides an apparatus for MIMO ground-based SAR amplitude and phase error correction, comprising a non-volatile memory and one or more processors, wherein the non-volatile memory stores executable code, characterized in that, when the processor executes the executable code, it is used to implement the aforementioned method for MIMO ground-based SAR amplitude and phase error correction.

[0024] Compared with the prior art, the present invention has the following advantages: This invention discloses an amplitude and phase error estimation method based on minimizing image entropy. Unlike traditional spectral estimation algorithms that start from DOA estimation, the amplitude and phase error estimation proposed in this invention is a parameter estimation achieved by optimizing image quality using the minimum image entropy criterion. This allows for faster convergence of estimation and completion of amplitude and phase correction. Unlike previous entropy minimization algorithms that primarily address phase error estimation in amplitude and phase correction, the method disclosed in this invention not only estimates the phase but also the more complex amplitude gain. Furthermore, by adding an impulse during the iteration process and incorporating random white noise into the impulse design, the impulse is continuously changed and its magnitude can be adjusted according to the gradient. Adding white noise to construct the impulse is equivalent to adjusting the position of the estimated amplitude error, thus avoiding local optima and helping the algorithm find the global optimum. In summary, this method can accurately estimate the channel amplitude and phase errors in MIMO SAR and improve imaging quality and accuracy through error correction.

[0025] Moreover, the method disclosed in this invention can be used not only to correct single radar images, but also to stitch together multiple radar images, thereby improving the accuracy and versatility of the estimated amplitude and phase errors. For example, near-field angular reflection targets have strong angular reflection modulation, affecting the estimation of amplitude and phase errors. If the angular reflection image and any monitoring image are stitched together and amplitude and phase correction is performed on both simultaneously, a more accurate amplitude and phase error can be obtained. Attached Figure Description

[0026] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0027] Figure 1 This is an external view of a certain type of MIMO ground-based SAR system.

[0028] Figure 2 This is a schematic diagram of the layout structure of a certain type of MIMO ground-based SAR array.

[0029] Figure 3 This is a schematic diagram of the MIMO ground-based SAR transceiver channel and virtual array element process. In the diagram, triangles represent receiving antennas, squares represent transmitting antennas, and trapezoids represent virtual array element antennas.

[0030] Figure 4 This is a simulation result of the point target echo signal when there is no amplitude or phase error in the MIMO ground-based SAR simulation.

[0031] Figure 5 This is a simulation result of the point target echo signal when there is amplitude error between channels in the MIMO ground-based SAR simulation.

[0032] Figure 6 This is a simulation result of the point target echo signal when there is phase error between channels in the MIMO ground-based SAR simulation.

[0033] Figure 7 This is a simulation result comparing the echo signals of point targets under the conditions of no amplitude and phase error and amplitude and phase error between channels in MIMO ground-based SAR.

[0034] Figure 8 This is a flowchart of the MIMO ground-based SAR amplitude and phase error correction method provided in a specific embodiment of the present invention.

[0035] Figure 9This is a structural diagram of the MIMO ground-based SAR amplitude and phase error correction device provided in a specific embodiment of the present invention.

[0036] Figure 10 This is an uncorrected SAR image of a mine scene acquired by a certain type of MIMO ground-based SAR system during an imaging experiment provided in a specific embodiment of the present invention.

[0037] Figure 11 This is a scene of data acquisition by a certain type of MIMO ground-based SAR system during an imaging experiment provided in a specific embodiment of the present invention.

[0038] Figure 12 The image is a stitched image obtained by correcting the amplitude and phase error of a certain type of MIMO ground-based SAR system in an imaging experiment provided in a specific embodiment of the present invention using the MIMO ground-based SAR amplitude and phase error correction method disclosed in the specific embodiment.

[0039] Figure 13 This is a result image obtained from an imaging experiment of a certain type of MIMO ground-based SAR system provided in a specific embodiment of the present invention, in which the amplitude and phase error correction factor is used to correct other images; wherein... Figure 13 (a) is an uncorrected SAR image. Figure 13 (b) is a pre-corrected SAR image. Figure 13 (c) is the SAR image after correction using the obtained amplitude and phase correction factor. Figure 13 (d) The SAR image is obtained by correcting the image using the MIMO ground-based SAR amplitude and phase error correction method proposed in a specific embodiment of the present invention.

[0040] Figure 14 This is a graph showing the relationship between image entropy and the number of iterations in an imaging experiment of a certain type of MIMO ground-based SAR system provided in a specific embodiment of the present invention, when the MIMO ground-based SAR amplitude and phase error correction method disclosed in the specific embodiment is used for correction.

[0041] Figure 15 This is a graph showing the relationship between image entropy and iteration number in an imaging experiment of a certain type of MIMO ground-based SAR system provided in a specific embodiment of the present invention, when the MIMO ground-based SAR amplitude and phase error correction method disclosed in the specific embodiment is used for correction, under two conditions: without impulse processing of local optima and with impulse processing of local optima. The light-colored line represents the relationship between image entropy and iteration number under the condition of not using impulse processing of local optima, and the dark-colored line represents the relationship between image entropy and iteration number under the condition of using impulse processing of local optima. Detailed Implementation

[0042] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0044] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0045] The present invention will be further explained below with reference to specific embodiments. Specific Implementation Example 1 like Figure 8 As shown, a method for correcting amplitude and phase errors of MIMO ground-based SAR includes the following steps: Step S801: Considering the characteristics of wide beamwidth and sub-aperture of ground-based SAR, the BP algorithm, FPFA algorithm, KSD algorithm, or omega-k algorithm are used to image the demodulated two-dimensional echo data. The expression after imaging is: (1) in , Indicates distance resolution. This indicates the distance from the pulse pressure envelope. Indicates the cell index of the distance dimension. This represents the maximum value in the distance dimension, and is related to the number of pixels in the distance dimension used during imaging. Represents the synthetic aperture length. This represents the wavelength of the emitted electromagnetic wave. The cell index representing the orientation dimension. This indicates the distance between adjacent virtual array elements. Indicates the first The amplitude and phase error functions of each transmission channel are expressed as follows: For the m-th transmission channel, the amplitude and phase error function expression is:

[0047] in and These represent amplitude and phase errors, respectively, and M represents the number of transmission channels.

[0048] Indicates the first The amplitude and phase error functions of each receiving channel are expressed as follows: For the nth receiving channel, the amplitude and phase error function expression is:

[0049] in and These represent amplitude and phase errors, respectively. N Indicates the number of receive channels.

[0050] The distance from point target P to the center of the synthetic aperture is , angle is (like Figure 3 (As shown).

[0051] Step S802: Using the angular reflection imaging data, amplitude and phase error information is extracted to obtain initial estimates of the amplitude and phase errors. , and These represent the estimated transmit channel gain, receive channel gain, and the correction factor for the phase error of both, respectively.

[0052] Step 803: Use the initial estimate of the amplitude and phase error to pre-correct the imaging signal according to the following formula: (2) Where the matrix The matrix represents the relationship between the phase error of the transmit / receive channel and the phase error of the virtual channel. and These represent the relationship matrices between the transmit channel and the receive channel and the virtual array, respectively. In the last three terms of the above formula, the first term represents the correction for the channel phase error, the second term represents the correction for the transmit channel amplitude error, and the third term represents the correction for the receive channel amplitude error.

[0053] matrix The rows of the matrix represent the virtual array elements arranged in sequence, and the columns represent the transmit and receive channels arranged in sequence. The matrix consists of 0s and 1s, where each virtual array element corresponds to a transmit / receive channel element with a 1, and the rest are 0s. and Composition and The composition is consistent.

[0054] Step S804, Initialization, let the number of iterations be... , , , and These are the values ​​obtained from the pre-correction. Wherein, , These represent the search directions for phase error and amplitude error, respectively. and These represent the amplitude error of the receiving channel and the amplitude error of the transmitting channel, respectively. , Indicates the first The amplitude and phase error after the next iteration update; , They represent the first Gain error of the receiving and transmitting channels in the next iteration.

[0055] Step S805: Estimate and correct the phase error.

[0056] 1) Use formula (2) to calculate the phase error of the previous step. Taking the derivative, we get , Indicates the first The first derivative of the phase error obtained in the second iteration.

[0057] 2) Calculate scalars based on relationships ,when Direct order ,in This represents the 2-norm.

[0058] 3) Update the phase error search direction .

[0059] 4) Calculate the update phase search step size : The expression for obtaining the phase search step size using Newton's method is:

[0060] in Representing image entropy pairs The first derivative, Representing image entropy pairs The second derivative, let Iterate the above equation 4 or 5 times to obtain the updated phase search step size. .

[0061] 5) Update phase error

[0062] 6) Use the updated phase error Substitute into formula (2) for correction.

[0063] Step S806: Estimate and correct the amplitude error.

[0064] 1) Use formula (2) to calculate the amplitude error of the previous time. Taking the derivative, we get , Indicates the first The first derivative of the amplitude error obtained in the second iteration.

[0065] 2) Calculate scalars based on relationships ,when Direct order ,in This represents the 2-norm.

[0066] 3) Update the search direction for amplitude error .

[0067] 4) Calculate the update magnitude search step size : The expression for obtaining the amplitude search step size using Newton's method is:

[0068] in Representing image entropy pairs The first derivative, Representing image entropy pairs The second derivative, let Iterate the above formula 4 or 5 times to obtain the search step size for the update magnitude. .

[0069] 5) Update amplitude error

[0070] 6) Normalize the amplitude error ,in Represents the 1-norm 7) Use the updated amplitude error Substitute into formula (2) for correction.

[0071] Step S807: Determine if the system is trapped in a local optimum. If so, proceed to step S808; otherwise, let... Proceed to step S805. The specific method for determining whether a local optimum has been reached is as follows: Since the phases of the transmitting and receiving channels are additive and the amplitudes are multiplicative during the entire iterative correction process, the amplitude gain between the transmitting and receiving channels is easily coupled, which can easily lead to local optima when iteratively solving for the amplitude error.

[0072] If the decrease in image entropy in a single iteration is less than If the condition is such that the system is trapped in a local optimum, then the system is considered to be trapped in a local optimum. This represents the threshold for determining local optima, generally speaking. .

[0073] Step S808: Update the amplitude error estimate by multiplying the impulse by the current amplitude error estimate.

[0074] Step S809: Determine if the global optimum has been reached. If yes, proceed to step S810; otherwise, let... Proceed to step S806.

[0075] Step S810, output amplitude and phase error. The output... Multiply by the estimated initial value The amplitude error of the transmit and receive channels is obtained. ,Will sum and estimated initial values By adding them together, we can obtain the phase error of the transmit and receive channels. . Specific Implementation Example 2 Specific embodiment 2, based on specific embodiment 1, calculates the amplitude gain gradient. random white noise with variance of 1 Combined to form the impulse, two additional fixed step sizes are designed. and This serves as the step size for both. Step size The size is related to the size. The larger the step size The smaller it is. Generally speaking, when , We take values ​​of 0.6 and 0.1. The amplitude error estimate is updated using the product of the impulse and the current amplitude error estimate, expressed as: . Specific Implementation Example 3 Since the phases of the transmitting and receiving channels are additive and the amplitudes are multiplicative during the entire iterative correction process, the amplitude gain between the transmitting and receiving channels is easily coupled, which can easily lead to local optima when iteratively solving for the amplitude error.

[0078] Based on Specific Embodiment 1, Specific Embodiment 3 further designs a specific method for determining whether the algorithm iteration has fallen into a local optimum, as follows: If the decrease in image entropy in a single iteration is less than If so, it is determined that the system is trapped in a local optimum, where This represents the threshold for determining local optima, generally speaking. .

[0079] The image entropy calculation method is as follows: , in This represents the energy of the entire image, which can be represented by the image's grayscale values. This represents the estimated amplitude error of the transmit / receive channel. This indicates the result of imaging processing on the amplitude-phase corrected signal. . Specific Implementation Example 4 Based on Specific Embodiment 2, Specific Embodiment 4 further designs a specific method for determining whether the algorithm iteration has reached the global optimum, as follows: Because random white noise is used as the impulse, it's possible that after adding the impulse, the image entropy might be higher in the second instance of falling into a local optimum than in the first. Therefore, it's necessary to record the data that minimizes the image entropy (the image entropy calculation method here is the same as in specific embodiment 3). And to achieve the minimum phase error and amplitude error If, for the second time, it gets stuck in a local optimum, then... At this point, the phase error and amplitude gain need to be updated respectively. , Conversely, update the phase and amplitude gain using the updated values. and If the impulse is used to update the amplitude error, the image entropy... There wasn't much change due to the update in sales volume, i.e. If the global optimum is reached, then it is determined that the global optimum is achieved. The value of is generally taken as .

[0081] To evaluate the effectiveness of the specific embodiments of the present invention, measured data were used to measure and analyze the correction effect of the proposed MIMO ground-based SAR amplitude and phase error correction method on the amplitude and phase errors of MIMO ground-based SAR. The measured data was provided by a certain type of MIMO ground-based SAR, and data was collected from three opposing targets at angles of 21m, 27m, and 32.5m, respectively, as correction benchmarks. Figure 11The method involves collecting data on mountains in a real-world scenario as the calibration target to verify the calibration results. To accelerate convergence, a pre-calibration is performed before using the minimum entropy algorithm for amplitude and phase calibration.

[0082] To eliminate the influence of inverse modulation, the image iteratively corrected using the MIMO ground-based SAR amplitude and phase error correction method provided in the specific embodiment of this invention needs to have a sufficient number of targets. Therefore, it is possible to consider stitching the large scene image and the inverse image together. Before stitching, the amplitude value of each stitched scene is adjusted so that the amplitude value of the strongest target in each scene is equal, such as... Figure 10 As shown. Figure 10 The left and right sides of the stitched image show angular reflection images at 21m, 27m, and 32.5m, respectively, while the right side is an uncorrected image of a mine scene acquired using a certain type of MIMO ground-based SAR. The stitched image shows that amplitude and phase errors significantly impact scene imaging, especially in scenes with strong reflective points. False targets generated by these strong reflective points almost completely obscure all other targets in their azimuth dimension, greatly affecting the visibility and monitoring accuracy of the MIMO ground-based SAR image. The image entropy of the scene before correction is 6.9304.

[0083] Using a specific embodiment of the present invention, a MIMO ground-based SAR amplitude and phase error correction method is proposed to correct the amplitude and phase of an image, and the results are as follows: Figure 12 As shown. From Figure 12 As can be seen, false targets generated by strong point targets have been almost eliminated. After correction using the MIMO ground-based SAR amplitude and phase error correction method proposed in the specific embodiment of this invention, the image entropy is 6.3299.

[0084] At this point, the obtained amplitude and phase error correction factor is used to correct other images, and the result is as follows. Figure 13 As shown. Figure 13 In the image, (a) is an uncorrected SAR image with an entropy of 6.7161, (b) is a precorrected SAR image with an entropy of 6.5192, (c) is a SAR image corrected using the obtained amplitude and phase correction factor with an entropy of 6.2494, and (d) is a SAR image obtained after correcting the image using the MIMO ground-based SAR amplitude and phase error correction method proposed in the specific embodiment of this invention with an entropy of 6.2073.

[0085] Due to the influence of factors such as temperature, humidity, system restart, and hardware technology, the amplitude and phase errors of MIMO ground-based SAR will undergo slight changes when placed in different environments. Figure 13As can be seen, the amplitude and phase correction factor estimated by the MIMO ground-based SAR amplitude and phase error correction method proposed in the specific embodiment of this invention has strong versatility, and direct use of it for correction can yield good results. If even better correction results are required, the MIMO ground-based SAR amplitude and phase error correction method proposed in the specific embodiment of this invention can be used again to correct the image. Furthermore, because a better pre-correction factor is used, this method can reach the convergence condition more quickly, such as... Figure 14 As shown, the algorithm begins to converge after 15 iterations, completing the entire amplitude and phase correction in just a few seconds. Therefore, with a good pre-correction factor, this method also possesses strong real-time performance.

[0086] In addition, such as Figure 15 As shown, when using this method for iterative computation, it converges after a certain number of iterations, but it does not converge to the global optimum. Figure 15 As shown by the light-colored lines, without using impulse to address local optima, the algorithm will stop converging after reaching a certain point. After reaching a local optimum, the two optimization curves begin to diverge, as shown... Figure 15 As shown by the dark lines, the optimized curve using impulse processing will continue to converge downwards after rising a little, until it reaches the global optimum. Specific Implementation Example 5 like Figure 9 As shown in the figure, a MIMO ground-based SAR amplitude and phase error correction device provided in specific embodiment 5 of the present invention includes a non-volatile memory and one or more processors. The non-volatile memory stores executable code. When the processor executes the executable code, it is used to implement the MIMO ground-based SAR amplitude and phase error correction method in the above embodiment.

[0088] The embodiments of the MIMO ground-based SAR amplitude and phase error correction device of the present invention can be applied to any device with data processing capabilities, such as a computer. The device embodiments can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 9 The diagram shown is a hardware structure diagram of any data processing-capable device, including the MIMO ground-based SAR amplitude and phase error correction device of this invention. (Except for...) Figure 9In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0089] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0090] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for correcting amplitude and phase errors of MIMO ground-based SAR, characterized in that, Includes the following steps: S1, Image the demodulated MIMO ground-based SAR two-dimensional echo data to obtain an imaging signal. The imaging signal consists of the product of the amplitude and phase error system function of the corresponding transmit channel and the amplitude and phase error system function of the corresponding receive channel, the pulse-compressed range dimension envelope, and the original phase. S2, using the angle reflection imaging data to extract amplitude and phase error information, an initial estimate of the amplitude and phase error is obtained, and an amplitude and phase correction factor is generated from the initial estimate of the amplitude and phase error. The amplitude and phase correction factor is composed of the relationship matrix between the amplitude gain of the transmit channel and the amplitude gain of the virtual channel, the relationship matrix between the amplitude gain of the receive channel and the amplitude gain of the virtual channel, and the relationship matrix between the phase error of the transmit and receive channels and the phase error of the virtual channel, together with the estimated values ​​of the transmit channel gain, the receive channel gain, and the phase error of the transmit and receive channels. S3, perform amplitude and phase correction on the imaging signal using a correction formula, which is obtained by multiplying the amplitude and phase correction factor by the imaging signal and adding the phases; S4, Initialization, let the number of iterations be... Both the phase error search direction vector and the amplitude error search direction vector are 0, and the amplitude and phase error vector is the initial estimate of the amplitude and phase error obtained in step S2. S5, the phase error is estimated and corrected using the minimum image entropy algorithm; S6, The minimum image entropy algorithm is used to estimate and correct the amplitude error; S7, determine if the system is trapped in a local optimum. If so, update the amplitude error estimate using the product of the impulse and the current amplitude error estimate, and proceed to step S8; otherwise, let... Proceed to step S5; the impulse is a linear combination term: The first term of the linear combination term is 1, the second term is the product of the first step length and the amplitude error search direction, and the third term is the product of the second step length, white noise, and amplitude error search direction. S8, determine if the global optimum has been reached. If so, output the amplitude and phase error estimate of the last iteration; otherwise, let... Proceed to step S6.

2. The method according to claim 1, characterized in that, The amplitude and phase error system function of the corresponding transmission channel in step S1 is composed of the signal amplitude of the transmission channel multiplied by the signal phase of the transmission channel expressed as a natural logarithm, and the amplitude and phase error system function of the corresponding reception channel is composed of the signal amplitude of the reception channel multiplied by the signal phase of the reception channel expressed as a natural logarithm.

3. The method according to claim 1, characterized in that, The relationship matrix between the transmit channel amplitude gain and the virtual channel amplitude gain mentioned in step S2 is generated according to the following method: The relation matrix consists of 0s and 1s. The rows of the relation matrix represent virtual array elements arranged in order, and the columns of the relation matrix represent transmission channels arranged in order. The transmission channel element corresponding to each virtual array element is 1, and the rest are 0. The relationship matrix between the received channel amplitude gain and the virtual channel amplitude gain mentioned in step S2 is generated according to the following method: The relation matrix consists of 0s and 1s. The rows of the relation matrix represent the virtual array elements arranged in order, and the columns of the relation matrix represent the receiving channels arranged in order. The receiving channel element corresponding to each virtual array element is 1, and the rest are 0. The relationship matrix between the transmit / receive channel phase error and the virtual channel phase error in step S2 is generated according to the following method: The relation matrix consists of 0s and 1s. The rows of the relation matrix represent virtual array elements arranged in order, and the columns of the relation matrix represent transceiver channels arranged in order. The transceiver channel element corresponding to each virtual array element is 1, and the rest are 0.

4. The method according to claim 1, characterized in that, The step S5, which involves estimating and correcting the phase error using the minimum image entropy algorithm, is as follows: S51, use the imaging signal to calculate the first derivative with respect to the previous phase error; S52, calculate the phase error relationship scalar, where the phase error relationship scalar is the ratio of the 2-norm of the first derivative of the phase error in the current iteration to the 2-norm of the phase error search direction in the previous iteration. When the phase error relationship is directly calculated, the scalar value is set to 0. S53, add the first derivative of the phase error in this iteration to the product of the current phase error relation scalar and the previous phase error search direction, in order to update the phase error search direction; S54, let the initial value of the phase search step size be 1, and use the phase search step size update iterative formula to iterate 4 or 5 times to update the phase search step size. The phase search step size update iterative formula is the current iteration search step size minus a gradient term. The gradient term is the first derivative of the image entropy with respect to the original step size divided by the second derivative of the image entropy with respect to the original step size. S55, add the product of the phase search step size and the phase error search direction obtained this time to the previous phase error estimate to obtain the updated phase error estimate; S56, Substitute the updated phase error estimate into the correction formula described in step S3 to perform phase correction on the imaging signal.

5. The method according to claim 1, characterized in that, The step S6, which involves estimating and correcting the amplitude error using the minimum image entropy algorithm, is as follows: S61, use the imaging signal to calculate the first derivative with respect to the previous amplitude error; S62, calculate the amplitude error relationship scalar, where the amplitude error relationship scalar is the ratio of the 2-norm of the first derivative of the amplitude error in the current iteration to the 2-norm of the amplitude error search direction in the previous iteration. When calculating the scalar value based on the amplitude error relationship, directly set the value to 0. S63, add the first derivative of the amplitude error in this iteration to the product of the current amplitude error relation scalar and the previous amplitude error search direction, in order to update the amplitude error search direction; S64, let the initial value of the amplitude search step size be 1, and update the amplitude search step size using the amplitude search step size update iterative formula 4 or 5 times. The amplitude search step size update iterative formula is the current iteration search step size minus a gradient term. The gradient term is the first derivative of the image entropy with respect to the original step size divided by the second derivative of the image entropy with respect to the original step size. S65, add the product of the amplitude search step size and the amplitude error search direction obtained this time to the previous amplitude error estimate to obtain the updated amplitude error estimate; S66, divide the amplitude error estimate by the 1 norm of the amplitude error estimate to obtain the normalized amplitude error estimate; S67, Substitute the normalized amplitude error estimate into the correction formula described in step S3 to perform amplitude correction on the imaging signal.

6. The method according to claim 1, characterized in that, The method for determining whether a region is trapped in a local optimum in step S7 is as follows: If the absolute value of the difference between the image entropy obtained after the current iteration and the image entropy obtained after the previous iteration is less than the threshold for determining local optima, then it is determined that the image has fallen into a local optimum. The method for determining whether the global optimum has been reached in step S8 is as follows: If, after updating the amplitude error using impulse, the absolute value of the difference between the image entropy before and after the update is less than the global optimal decision threshold, then the global optimal decision has been reached.

7. The method according to claim 6, characterized in that, The threshold for determining local optima is: The global optimal decision threshold is .

8. The MIMO ground-based SAR amplitude and phase error correction method according to claim 7, characterized in that, The first step has a length of 0.6, and the second step has a length of 0.

1.

9. A MIMO ground-based SAR amplitude and phase error correction device, comprising a non-volatile memory and one or more processors, wherein the non-volatile memory stores executable code, and when the processor executes the executable code, it is used to implement a MIMO ground-based SAR amplitude and phase error correction method as described in any one of claims 1-8.

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