UAV cluster motion error compensation method, system, equipment, medium, terminal

Abstract

The present invention belongs to the field of radar imaging technology, and discloses a method, system, device, medium, and terminal for compensating the motion error of a drone cluster. A signal model is established, and a scene complex image in a Cartesian coordinate system is projected to a polar coordinate system to obtain a SAR complex image; the established signal model and wave number vector decomposition are used to derive the spectrum analytical expression of the SAR complex image in the polar coordinate system; the relationship between the motion errors in the echo signal is obtained, and the relevant compensation formula is obtained to preliminarily compensate the echo signal; after the compensated signal becomes a sparse signal with sparse characteristics under the transformation of a sparse basis, sparse observation is performed to obtain sparse observation values; the observation values ​​observed by the measurement matrix are processed by a reconstruction algorithm to realize reconstruction from low-dimensional data to high-dimensional signals, and the original sparse signal is restored to finally obtain a high-resolution image. The present invention can realize multi-directional detection of targets under the condition of saving a lot of manpower and material resources.

Description

Technical Field

[0001] The present invention belongs to the field of radar imaging technology, and in particular relates to a method, system, equipment, medium and terminal for compensating motion errors of unmanned aerial vehicle clusters. Background Art

[0002] At present, Synthetic Aperture Radar (SAR) is an all-day, all-weather microwave remote sensing technology with important advantages such as long range, high resolution, and strong penetration. In recent years, it has been widely used in advanced technologies. Small unmanned aerial vehicles (UAVs) have the advantages of low cost, flexible take-off and landing, and suitable for long-term operations under harsh conditions. Application research based on UAV platforms has been a hot topic in recent years. With the rapid development of antenna technology, chip technology, and digital processing technology, the high integration of SAR sensors has made it possible for them to be carried on small UAV platforms, which has greatly improved the active remote sensing capabilities of UAVs all day and all weather. At present, research on SAR imaging technology based on UAV mode has gradually emerged, and related application research is also being carried out extensively.

[0003] Faced with increasingly complex application environments and actual needs, the shortcomings of a single UAV in performing tasks are obvious. For example, a single UAV is more likely to be attacked or fail due to its own faults, often unable to form sustained and powerful reconnaissance and strikes, and has problems such as blind spots in observation angles. Existing UAV-SAR equipment based on a single platform usually has a relatively simple working mode and limited active detection capabilities. For example, due to the limitations of flight trajectory and illumination range, a single drone platform SAR sensor is difficult to perform all-round and multi-angle high-resolution observations, and there are problems such as blind spots in forward, downward and rearward imaging and obstacles. UAV swarm (UAVS) based on intelligent interactive technology is a new application model proposed in recent years. Compared with the existing single-platform UAV-SAR technology, UAVS-SAR has the following important advantages: 1. By forming multiple UAV platforms and designing effective transmit-receive configurations (for example: one transmit and multiple receive, multiple transmit and multiple receive, external radiation source mode) and flight tracks, UAVS-SAR can achieve all-round and multi-angle high-resolution observations; 2. By flexibly configuring the array configuration of multiple UAV platforms, it has detection functions such as forward vision, downward vision, rear vision, three-dimensional imaging, and tomographic imaging; 3. Since SAR sensors are distributed on multiple UAV platforms, in a battlefield environment, even if some UAVs are damaged, it will not have a fatal impact on the overall detection performance of UAVS-SAR. Therefore, UAVS-SAR has high fault tolerance and battlefield survivability; 4. Different UAV platforms can perform parallel perception, calculation and execution, thereby further improving the active detection performance of UAVS-SAR.

[0004] Although the radar platform configuration design of UAVS-SAR is more flexible, the motion error processing problem is also more complicated, especially for many small UAV platforms, which are limited by factors such as cost, load and working environment. Various unknown errors are more severe than conventional aircraft platforms, and small UAV platforms are usually difficult to be equipped with high-precision inertial navigation measurement equipment. Therefore, it is necessary to adopt an error estimation method based on SAR signals to eliminate the influence of unknown errors on imaging to ensure the focusing quality of the image. At present, the classic self-focusing error compensation method (such as MDA, PGA, MEA, etc.) and its improved form combined with the frequency domain imaging algorithm have been widely used in SAR imaging. However, due to certain differences in signal representation and imaging principles between the time domain fast imaging algorithm and the frequency domain imaging algorithm, the classic self-focusing method is difficult to combine with the time domain fast imaging in the multi-platform application mode to achieve effective error compensation, which greatly limits the engineering application of the time domain fast imaging algorithm in UAVS-SAR. Therefore, in view of the application needs of UAVS-SAR, it is necessary to study the motion error compensation method that is effectively combined with the time domain fast imaging algorithm.

[0005] Through the above analysis, the problems and defects of the prior art are as follows:

[0006] (1) Existing single UAVs are more vulnerable to attack or mission failure due to their own faults, are often unable to form sustained and effective reconnaissance and strikes, and have problems such as blind spots in observation vision.

[0007] (2) Existing UAV-SAR equipment based on a single platform usually has a relatively simple working mode and limited active detection capabilities. For example, due to the limitations of flight trajectory and illumination range, it is difficult for a single UAV platform to perform high-resolution observations from all directions and angles. There are also problems such as blind spots in forward, downward and rearward imaging and obstruction by obstacles.

[0008] (3) The motion error processing problem of the existing UAVS-SAR radar platform is more complicated. The classic self-focusing method is difficult to achieve effective error compensation in combination with time-domain rapid imaging in the multi-platform application mode, which greatly limits the engineering application of the time-domain rapid imaging algorithm in UAVS-SAR.

[0009] The difficulty in solving the above problems and defects lies in: how to select an efficient, accurate and widely applicable SAR imaging processing algorithm method, how to compensate for the motion errors of the UAV cluster and improve the imaging clarity.

[0010] The significance of solving the above problems and defects is:

[0011] (1) In view of the shortcomings of the current detection mode, the present invention proposes a one-transmit-multiple-receive detection mode, which overcomes the shortcomings of the previous single-base detection: it is impossible to achieve high-resolution observation in all directions and angles, and there are visual blind spots. The UAV cluster mode can effectively solve these shortcomings. The radar platform configuration design under the cluster mode is more flexible, and it has detection functions such as forward vision, downward vision, three-dimensional imaging, and tomographic imaging.

[0012] (2) Compared with traditional single-platform SAR imaging, UAVS-SAR has more complex problems such as unknown error processing of radar platforms. Although classic self-focus error compensation methods (such as MDA, PGA, MEA, etc.) and their improved forms combined with frequency domain imaging algorithms have been widely used in SAR imaging. However, due to the geometric configuration of the UAV cluster mode, its spectrum is discontinuous, resulting in defocused imaging. Compressed sensing can make up for the missing spectrum, thereby improving image quality and obtaining high-resolution images.

[0013] (3) The present invention adopts a motion error compensation algorithm based on FFBP, which is easy to implement pipeline processing and real-time processing in engineering to obtain high-resolution images. Summary of the invention

[0014] In view of the problems existing in the prior art, the present invention provides a method, system, device, medium and terminal for compensating motion errors of a drone cluster, and in particular, relates to a motion error compensation method and system for a novel drone cluster based on the FFBP algorithm.

[0015] The present invention is implemented as follows: a method for compensating for motion errors of a drone cluster, the method comprising:

[0016] A signal model is established, and the scene complex image in the Cartesian coordinate system is projected into the polar coordinate system to obtain the SAR complex image in the polar coordinate system; the SAR complex image in the polar coordinate system is subjected to a two-dimensional FFT and transformed into a two-dimensional frequency domain, and at the same time, the established signal model and wave number vector decomposition are used to derive the spectrum analytical expression of the SAR complex image in the polar coordinate system; the relationship between the motion errors in the echo signal is obtained based on the analytical analysis of the spectrum, and the relevant compensation formula is obtained to preliminarily compensate the echo signal; after the compensated signal becomes a sparse signal with sparse characteristics under the transformation of a sparse basis, sparse observation is performed to obtain sparse observation values; a reconstruction algorithm, i.e., a convex optimization algorithm, is used to process the observation values ​​observed by the measurement matrix, so as to realize the reconstruction from low-dimensional data to high-dimensional signals, and then restore the original sparse signal.

[0017] Furthermore, the UAV cluster motion error compensation method comprises the following steps:

[0018] Step 1: simulate and obtain an echo signal containing errors, obtain an expression of the echo signal in a Cartesian coordinate system by analysis, obtain an image in the Cartesian coordinate system, and project the image into an elliptical orthogonal polar coordinate system to obtain a SAR image in a polar coordinate system;

[0019] Step 2: Perform two-dimensional FFT on the SAR image in the polar coordinate system and transform it into the two-dimensional frequency domain; use the established signal model and wave number vector decomposition to derive the spectrum analytical expression of the SAR image in the polar coordinate system; obtain the relevant expression of the phase error based on the analysis of the spectrum, and obtain the compensation expression by analysis, and use the expression to compensate for the motion error;

[0020] Step three, under the sparse basis transformation, transform the signal into a sparse signal with sparse features; perform sparse observation on the sparse signal to obtain sparse observation values; multiply the measurement matrix and the sparse basis to obtain the recovery matrix, combine it with the low-dimensional observation values, use CVX to obtain the sparse mapping, and obtain the original sparse signal.

[0021] Further, in step 1, the simulation obtains an echo signal containing an error, obtains an expression of the echo signal in a Cartesian coordinate system by analysis, obtains an image in the Cartesian coordinate system, and projects the image into an elliptical orthogonal polar coordinate system to obtain a SAR image in a polar coordinate system, including:

[0022] (1) The radar is installed on a moving flight platform. The receiver and n transmitters fly along an arbitrary curve. At any time t, the position of the transmitter antenna phase center APC is represented by x T and T The position of the transmitter’s antenna phase center APC is represented by x Rm and Rm Indicates that x T ,y T 、x Rm and Rm is a function of t; P 0 is the scattering point at the center of the radar illumination scene, and P is any scattering point in the radar illumination scene. In the Cartesian coordinate system, P 0 Position P 0 (x 0 ,y 0 ) means that in the polar coordinate system, P 0 Position P 0 (a 0 ,θ 0 ) In the Cartesian coordinate system, the SAR complex image containing this point is expressed as:

[0023]

[0024] In the formula, Represents the Cartesian coordinate system origin to P 0 The distance vector of represents the distance vector from the origin of the Cartesian coordinate system to P, Represents the scattering point P 0 The distance vector to the scattering point P, and are the error vectors of the transmitter and receiver respectively, represents the wave number vector corresponding to the transmitted signal, represents the wave number vector corresponding to the m received signals, represents the wave number vector corresponding to the transmitted signal; is the sum of the beam vectors of the m received and transmitted signals.

[0025] (2) Project the SAR complex image represented by into the polar coordinate system to obtain the SAR complex image i(a,θ ⊥ ).

[0026] Further, in step 2, the SAR image in the polar coordinate system is subjected to a two-dimensional FFT and transformed into a two-dimensional frequency domain; the spectrum analytical expression of the SAR image in the polar coordinate system is derived by using the established signal model and wave number vector decomposition; the relevant expression of the phase error is obtained according to the analysis of the spectrum, and the compensation expression is obtained by analysis, and the motion error is compensated by using the expression, including:

[0027] (1) Introduce a set of orthogonal wave number vectors and Get i(a,θ ⊥ ) spectrum analytical expression, all distance vectors and wave number vectors along and The direction is decomposed, and the stationary phase point principle POSP is used to obtain i(a,θ ⊥ ) is the approximate expression:

[0028]

[0029] Among them, K a =K r / cosβ 0 , β 0 =∠F ET P 0 F ER , F ET 、F ER are the two foci of the elliptical coordinate system, and the variables η, ηθ, η c , η k is the proportional coefficient between a single receiver and the final equivalent receiver. Here we have m receivers, corresponding to m β 0 ,γ=Πcosβ 0m , r 0 For vector The modulus length, ΔR r⊥ for and Along The sum of ΔR r for and Along The sum of

[0030] The spectrum expression of SAR complex image in polar coordinates is:

[0031]

[0032] (2) The corresponding relationship between the echo signal, SAR image and spectrum of the drone cluster is obtained, and the phase error contained in the echo signal is analyzed as follows:

[0033]

[0034] The corresponding compensation expression is:

[0035]

[0036] Further, in step 3, the signal is transformed into a sparse signal with sparse features under a sparse basis transformation; the sparse signal is sparsely observed to obtain a sparse observation value; the measurement matrix and the sparse basis are multiplied to obtain a recovery matrix, and a sparse mapping is obtained by using CVX in combination with the low-dimensional observation value to obtain the original sparse signal and the sparse basis, including:

[0037] (1) The compensated signal is represented as a finite length signal x, which is a one-dimensional discrete signal to be processed x∈R N×1 , the compensated echo signal is added to the sparse basis ψ∈R N×N Under the transformation, it becomes a sparse signal with sparse characteristics, then the signal to be processed x is expressed as:

[0038] x=ψ·α,(α=[α 1 ,α 2 ,...,α N ] T ).

[0039] (2) After determining the sparsity of the signal to be processed, the sparse signal is sparsely observed to obtain sparse observation values; using the measurement matrix φ∈R N×N Treat the observed signal x as a linear observation, and make the measurement matrix satisfy the finite isometry constraint RIP property during the compressed sampling process. This property states that the recovery matrix Θ formed by the measurement matrix φ and the sparse basis ψ is constant δ k ∈(0,1) and any K sparse signals satisfy the following formula:

[0040]

[0041] (3) The reconstruction algorithm is used to process the observed values ​​​​observed by the measurement matrix to achieve reconstruction from low-dimensional data to high-dimensional signals, and then restore the original sparse signal.

[0042] Further, in step (1), the sparse basis is a linear combination of orthogonal basis functions;

[0043] The sparsity of the signal depends on the number of non-zero elements of the sparse basis. The smaller the number, the greater the sparsity, and the fewer the observed values ​​observed from the signal to be processed.

[0044] Another object of the present invention is to provide a drone cluster motion error compensation system using the drone cluster motion error compensation method, the drone cluster motion error compensation system comprising:

[0045] A SAR image acquisition module is used to simulate and obtain an echo signal containing an error, obtain an expression of the echo signal in a Cartesian coordinate system by analysis, obtain an image in the Cartesian coordinate system, and project the image into an elliptical orthogonal polar coordinate system to obtain a SAR image in a polar coordinate system;

[0046] The spectrum analysis module is used to perform two-dimensional FFT on the SAR image in the polar coordinate system and transform it into the two-dimensional frequency domain; the spectrum analysis expression of the SAR image in the polar coordinate system is derived by using the established signal model and wave number vector decomposition;

[0047] The motion error compensation module is used to obtain the relevant expression of the phase error according to the analysis of the spectrum, obtain the compensation expression by analysis, and use the expression to compensate the motion error;

[0048] The sparse observation module is used to transform the signal into a sparse signal with sparse features under a sparse basis transformation; perform sparse observation on the sparse signal to obtain sparse observation values; multiply the measurement matrix and the sparse basis to obtain a recovery matrix, combine it with the low-dimensional observation values, use CVX to obtain a sparse mapping, and finally obtain the original sparse signal.

[0049] Another object of the present invention is to provide a computer device, the computer device comprising a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor performs the following steps:

[0050] A signal model is established, and the scene complex image in the Cartesian coordinate system is projected into the polar coordinate system to obtain the SAR complex image in the polar coordinate system; the SAR complex image in the polar coordinate system is subjected to a two-dimensional FFT and transformed into a two-dimensional frequency domain, and at the same time, the established signal model and wave number vector decomposition are used to derive the spectrum analytical expression of the SAR complex image in the polar coordinate system; the relationship between the motion errors in the echo signal is obtained based on the analytical analysis of the spectrum, and the relevant compensation formula is obtained to preliminarily compensate the echo signal; after the compensated signal becomes a sparse signal with sparse characteristics under the transformation of a sparse basis, sparse observation is performed to obtain sparse observation values; a reconstruction algorithm, i.e., a convex optimization algorithm, is used to process the observation values ​​observed by the measurement matrix, so as to realize the reconstruction from low-dimensional data to high-dimensional signals, and then restore the original sparse signal.

[0051] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the following steps:

[0052] A signal model is established, and the scene complex image in the Cartesian coordinate system is projected into the polar coordinate system to obtain the SAR complex image in the polar coordinate system; the SAR complex image in the polar coordinate system is subjected to a two-dimensional FFT and transformed into a two-dimensional frequency domain, and at the same time, the established signal model and wave number vector decomposition are used to derive the spectrum analytical expression of the SAR complex image in the polar coordinate system; the relationship between the motion errors in the echo signal is obtained based on the analytical analysis of the spectrum, and the relevant compensation formula is obtained to preliminarily compensate the echo signal; after the compensated signal becomes a sparse signal with sparse characteristics under the transformation of a sparse basis, sparse observation is performed to obtain sparse observation values; a reconstruction algorithm, i.e., a convex optimization algorithm, is used to process the observation values ​​observed by the measurement matrix, so as to realize the reconstruction from low-dimensional data to high-dimensional signals, and then restore the original sparse signal.

[0053] Another object of the present invention is to provide an information data processing terminal, which is used to implement the drone cluster motion error compensation system.

[0054] In combination with all the above technical solutions, the advantages and positive effects of the present invention are as follows: the UAV cluster motion error compensation method provided by the present invention particularly relates to a motion error compensation algorithm of an Unmanned Aerial Vehicle swarm synthetic aperture radar (UAVS-SAR) based on fast factorized back projection (FFBP). The present invention can realize multi-directional detection of targets in the UAVS-SAR mode, and can compensate for the motion errors contained therein through an algorithm to obtain a clear image.

[0055] In order to solve the motion error caused by force majeure factors in the process of UAVS-SAR detecting signals, the present invention introduces a compressed sensing algorithm, because the SAR imaging algorithm directly or indirectly depends on the mathematical model corresponding to the observation process. In the theory of compressed sensing, the focus is on designing and improving the performance index of the reconstruction model so that the original signal can be accurately and efficiently restored using a certain number of low-dimensional observations. The error of the mathematical model is generally manifested as a phase error in the SAR echo data. In order to obtain a high-resolution imaging scene, it is necessary to eliminate the phase error caused by various reasons (platform jitter, atmospheric disturbance during propagation, etc.) in the echo signal from all scattering points. Compressed sensing strictly depends on the mathematical model, which comes from the linear observation of the target by the SAR system. If there is a certain error in the observation system, there will also be an error in the observation matrix in the corresponding mathematical model. This error will often eventually be reflected in the phase of the echo data, and a direct consequence is the defocusing of the image. Therefore, in order to obtain a high-resolution imaging scene, it is necessary to consider the possible errors in the mathematical model, adopt a data-based self-focusing technology to compensate for these phase errors, and compensate for this error by certain means, so as to achieve accurate imaging. Finally, the convex optimization algorithm is used to optimize the imaging results.

[0056] Compared with the prior art, single-platform UAV-SAR equipment usually has a relatively simple working mode, limited active detection capabilities, and the motion error compensation algorithm is difficult to solve the errors caused by the drone cluster detection signal to the imaging, and improve the imaging clarity. The method provided by the present invention can well overcome the above two shortcomings: The single working mode of UAV-SAR cannot achieve all-round and multi-angle detection. The UAVS-SAR mode adopted by the present invention can realize detection functions such as forward-looking, downward-looking, three-dimensional imaging and tomographic imaging. Since the radar detection signal meets the sparsity, the present invention proposes a motion error compensation algorithm based on FFBP combined with compressed sensing. Since the FFBP imaging algorithm has high precision, fast computing speed, and is applicable to UAVS-SAR imaging applications on almost any trajectory and any platform, the method of the present invention also has high precision, fast computing speed, and is applicable to UAVS-SAR imaging echo simulation applications on almost any trajectory and any platform, and the compressed sensing algorithm only needs to collect useful components in the signal, so the signal can be collected at a sampling rate far lower than the sampling rate specified by the Nyquist sampling theorem, which not only reduces the amount of data, but also the imaging resolution can break the limitations of the Nyquist sampling theorem; the present invention adopts the FFBP imaging algorithm, and the echo signal is sparse, so combined with the compressed sensing algorithm, it is easy to realize pipeline processing and real-time processing in engineering, and further speed up the computing speed.

[0057] The present invention discloses a motion error compensation algorithm for unmanned aerial vehicle clusters based on FFBP. The method uses the spectrum characteristics of SAR images in polar coordinates to analyze the mutual relationship between phase errors contained in the echo signal, uses the self-focusing error compensation algorithm to compensate, and then uses the convex optimization algorithm to optimize the imaging result. Specifically: (1) The scene complex image in the Cartesian coordinate system is projected to the polar coordinate system to obtain the SAR complex image in the polar coordinate system; (2) The SAR image in the polar coordinate system is subjected to two-dimensional FFT and transformed to the two-dimensional frequency domain. At the same time, the spectrum analytical expression of the SAR image in the polar coordinate system is derived by using the established signal model and wave number vector decomposition; According to the analysis of the spectrum, the relevant expression of the motion error is obtained, and the compensation expression is obtained by analysis, and the motion error is compensated by using the expression; (3) Under the sparse basis transformation, the signal is transformed into a sparse signal with sparse characteristics. Then, the sparse signal is sparsely observed to obtain a sparse observation. The measurement matrix and the sparse basis are multiplied to obtain a recovery matrix, and then combined with the low-dimensional observation value, CVX is used to obtain a sparse mapping, and finally the original sparse signal and the sparse basis are obtained. The present invention solves the error compensation problem of drone clusters and has good engineering practicability. In the simulation test process, the feasibility and effectiveness of the method proposed in the present invention are verified. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0059] Figure 1 It is a flow chart of a method for compensating UAV cluster motion errors provided by an embodiment of the present invention.

[0060] Figure 2 It is a schematic diagram of a method for compensating for motion errors of a drone cluster provided in an embodiment of the present invention.

[0061] Figure 3 It is a structural block diagram of a UAV cluster motion error compensation system provided by an embodiment of the present invention;

[0062] In the figure: 1. SAR image acquisition module; 2. Spectrum analysis module; 3. Motion error compensation module; 4. Compressed sensing optimization module.

[0063] Figure 4 It is a signal model diagram provided by an embodiment of the present invention.

[0064] Figure 5(a)-Figure 5(c) It is a point target simulation result diagram provided by an embodiment of the present invention.

[0065] Figure 6(a)-Figure 6(c) This is a diagram of surface target simulation results provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical scheme and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the embodiments. The present invention has carried out simulation experiments on nine point targets and surface targets to verify the algorithm proposed by the present invention. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0067] In view of the problems existing in the prior art, the present invention provides a method, system, device, medium and terminal for compensating motion errors of a drone cluster. The present invention is described in detail below with reference to the accompanying drawings.

[0068] like Figure 1 As shown, the UAV cluster motion error compensation method provided by the embodiment of the present invention includes the following steps:

[0069] S101, establishing a signal model, projecting a scene complex image in a Cartesian coordinate system to a polar coordinate system, and obtaining a SAR complex image in a polar coordinate system;

[0070] S102, performing a two-dimensional FFT transformation on the SAR complex image in the polar coordinate system to a two-dimensional frequency domain, and using the established signal model and wave number vector decomposition to derive a spectrum analytical expression of the SAR complex image in the polar coordinate system;

[0071] S103, obtaining the relationship of motion errors in the echo signal according to the analytical analysis of the frequency spectrum, and obtaining a related compensation formula to preliminarily compensate the echo signal;

[0072] S104, transforming the compensated signal into a sparse signal with sparse characteristics under a sparse basis, and then performing sparse observation to obtain a sparse observation value;

[0073] S105, using a reconstruction algorithm, namely a convex optimization algorithm, to process the observed values ​​observed by the measurement matrix, to achieve reconstruction from low-dimensional data to high-dimensional signals, and then to restore the original sparse signal.

[0074] The principle diagram of the UAV cluster motion error compensation method provided by the embodiment of the present invention is as follows: Figure 2 shown.

[0075] like Figure 3 As shown, the UAV cluster motion error compensation system provided by the embodiment of the present invention includes:

[0076] SAR image acquisition module 1, used for simulating and obtaining an echo signal containing an error, obtaining an expression of the echo signal in a Cartesian coordinate system by analysis, obtaining an image in a Cartesian coordinate system, and projecting the image into an elliptical orthogonal polar coordinate system to obtain a SAR image in a polar coordinate system;

[0077] The spectrum analysis module 2 is used to perform two-dimensional FFT on the SAR image in the polar coordinate system and transform it into a two-dimensional frequency domain; the spectrum analysis expression of the SAR image in the polar coordinate system is derived by using the established signal model and wave number vector decomposition;

[0078] The motion error compensation module 3 is used to obtain a relevant expression of the phase error according to the analysis of the frequency spectrum, obtain a compensation expression by analysis, and use the expression to compensate the motion error;

[0079] The compressed sensing optimization module 4 is used to transform the signal into a sparse signal with sparse features under a sparse basis transformation; perform sparse observation on the sparse signal to obtain a sparse observation value; multiply the measurement matrix and the sparse basis to obtain a recovery matrix, combine the low-dimensional observation value, use CVX to obtain a sparse mapping, and finally obtain the original sparse signal.

[0080] The technical solution of the present invention is further described below in conjunction with specific embodiments.

[0081] like Figure 4 As shown in the figure, the SAR geometric configuration, the radar is installed on a moving flight platform, the receiver and n transmitters fly along an arbitrary curve, and at any time t, the position of the antenna phase center APC of the transmitter is represented by x T and T The position of the transmitter’s antenna phase center APC is represented by x Rm and Rm Indicates that x T , y T 、x Rm and Rm is a function of t; P 0 is the scattering point at the center of the radar illumination scene, and P is any scattering point in the radar illumination scene. In the Cartesian coordinate system, P 0 Position P 0 (x 0 ,y 0 ) means that in the polar coordinate system, P 0 Position P 0 (a 0 ,θ 0 ); Imaging adopts BP algorithm. In Cartesian coordinate system, the SAR complex image containing this point is expressed as:

[0082]

[0083] In the formula, Represents the Cartesian coordinate system origin to P 0 The distance vector of represents the distance vector from the origin of the Cartesian coordinate system to P, Represents the scattering point P 0 The distance vector to the scattering point P, and are the error vectors of the transmitter and receiver respectively, represents the wave number vector corresponding to the transmitted signal, represents the wave number vector corresponding to the m received signals, represents the wave number vector corresponding to the transmitted signal; is the sum of the beam vectors of the m received and transmitted signals.

[0084] Project the SAR complex image represented by into the polar coordinate system to obtain the SAR complex image i(a, θ ⊥ ).

[0085] In order to obtain i(a,θ ⊥ ) spectrum analytical expression, introducing a set of orthogonal wave number vectors and Get i(a,θ ⊥ ) is a spectrum analytical expression, where all distance vectors and wave number vectors are and The direction is decomposed, and the stationary phase point principle POSP is used to obtain i(a,θ ⊥ ) is the approximate expression:

[0086]

[0087] Among them, K a =K r / cosβ 0 , β 0 =∠F ET P 0 F ER , F ET 、F ER are the two foci of the elliptical coordinate system, and the variables η, ηθ, η c , η k is the proportional coefficient between a single receiver and the final equivalent receiver. Here we have m receivers, corresponding to m β 0 ,γ=Πcosβ 0m , r 0 For vector The modulus length, ΔR r⊥ for and Along The sum of ΔR r for and Along The sum of

[0088] The spectrum expression of SAR complex image in polar coordinates is:

[0089]

[0090] The corresponding relationship between the echo signal, SAR image and spectrum of the drone cluster is obtained, and the phase error contained in the echo signal is analyzed:

[0091]

[0092] The corresponding compensation expression is:

[0093]

[0094] The compensated signal is represented as a finite length signal x, which is a one-dimensional discrete signal to be processed x∈R N×1 , in a sparse basis ψ∈R N×N (linear combination of orthogonal basis functions) transformation becomes a sparse signal with sparse characteristics. Therefore, the signal to be processed x can be expressed as:

[0095] x=ψ·α,(α=[α 1 ,α 2 ,...,α N ] T );

[0096] Next, we need to perform sparse observations on the sparse signal to obtain sparse observations. N×N Treat the observed signal x as a linear observation, and conger obtains a low-dimensional observation value y∈R M ×1 In order to make the observation value y contain all the useful information of the original sparse signal and accurately restore the original high-dimensional signal in the subsequent reconstruction process, the measurement matrix needs to meet certain conditions during the compressed sampling process. This condition is the restricted isometry constraint (RIP) property, which states that the recovery matrix Θ composed of the measurement matrix φ and the sparse basis ψ is constant δ k ∈(0,1) and any K sparse signals satisfy the following formula:

[0097]

[0098] Once the recovery matrix Θ satisfies the above formula under inherent conditions, that is, satisfies the RIP property, the same observed signal will not correspond to multiple K sparse signals during the measurement matrix observation process, but will ensure that they are uniquely corresponding, and also ensure that the reconstruction algorithm can accurately reconstruct the original sparse signal later. The convex optimization algorithm is used to process the observed values ​​observed by the measurement matrix to achieve reconstruction from low-dimensional data to high-dimensional signals, and then restore the original sparse signal.

[0099] The technical effects of the present invention are described in detail below in conjunction with simulation experiments.

[0100] 1. Simulation experiment

[0101] Some parameters used in the simulation of the present invention are shown in Table 1. The SAR imaging geometry is shown in Figure 4 shown.

[0102] Table 1 Simulation parameter settings

[0103]

[0104] The simulation experiment of the present invention takes one transmitter and four receivers as an example to detect nine point targets and surface targets respectively. The band is Ku, the bandwidth is 180MHz, the pulse repetition frequency is 1000Hz, and the radar platform is based on Figure 2 The curve shown is flying.

[0105] The receiver is located at (-5000, 0), and the transmitter is located at (200, 0), (300, 0), (400, 0), (500, 0). In the simulation experiment of nine point targets, the R ET About 8944m, R ER About 4007m, the transmitter's velocity is (0, 20)m / s, and the acceleration along the X direction is 1.8m / s 2 , the acceleration along the Y direction is -2.25m / s 2 , the receiver's velocity is (-2, 10) m / s, and the acceleration along the X direction is -2.25 m / s 2 , the acceleration along the Y direction is 1.8m / s 2 The position of the center point target is (300, 4000), the point interval is (50, 50), and in the simulation experiment of the surface target, the RET of the drone cluster is about 8944m, the RER is about 4825m, the speed of the transmitter is (0, 100)m / s, and the acceleration along the X direction is 0.2m / s 2 , the acceleration along the Y direction is -0.3m / s 2 , the receiver's velocity is (-20, 80) m / s, and the acceleration along the X direction is -0.3 m / s 2, the acceleration along the Y direction is 0.2m / s 2 The pixel matrix is ​​set to 256×256 (X direction×Y direction). According to the radar parameters shown in Table 1, the echo signal simulation is performed using the method of the present invention. The simulation conditions are a 64-bit Windows 10 system matlab environment, a PC hardware platform of i59400f CPU, and 16GB memory. The method of the present invention is used to process point targets and surface targets, and high-quality imaging results can be obtained.

[0106] 2. By comparison, it can be seen that the method of the present invention has higher efficiency than the traditional motion error compensation method. The peak sidelobe ratio (PSLR) and the integrated sidelobe ratio (ISLR) of the point target compensated by the method of the present invention are significantly reduced. The results are shown in Table 2. The overall imaging results are shown in Figure 5. The simulation of the entire point target took about two hours. For the surface target, the imaging results are shown in the figure. The image entropy value of the same area is analyzed. The image entropy value of area A is 9.0448; the image entropy value of area B is 9.0143, and the image entropy value of area C is 8.4579. The simulation of the entire point target took about three hours and fifty minutes. By comparing Figure 6 (a), Figure 6 (b) and Figure 6 (c), it can be seen that the surface target has obvious improvement. Therefore, it can be considered that the method of the present invention can improve the imaging results and compensate for motion errors.

[0107] Table 2 Analysis of point target imaging results

[0108]

[0109] The invention discloses a motion error compensation algorithm for unmanned aerial vehicle clusters based on FFBP. The method uses the spectrum characteristics of SAR images under polar coordinates to analyze the mutual relationship between phase errors contained in the echo signal, uses the self-focusing error compensation algorithm to compensate, and then uses the convex optimization algorithm to optimize the imaging result. Specifically: 1. The scene complex image under the Cartesian coordinate system is projected to the polar coordinate system to obtain the SAR complex image under the polar coordinate system; 2. The SAR image under the polar coordinate system is subjected to two-dimensional FFT and transformed to the two-dimensional frequency domain. At the same time, the spectrum analytical expression of the SAR image under the polar coordinate system is derived by using the established signal model and wave number vector decomposition; according to the analysis of the spectrum, the relevant expressions of NsRCM and APE are obtained, and the compensation expression is obtained by analysis, and the motion error is compensated by the expression; 3. Under the sparse basis transformation, the signal is transformed into a sparse signal with sparse characteristics. Then, the sparse signal is sparsely observed to obtain a sparse observation. The measurement matrix and the sparse basis are multiplied to obtain a recovery matrix, and then combined with the low-dimensional observation value, CVX is used to obtain a sparse mapping, and finally the original sparse signal and the sparse basis are obtained. The present invention solves the error compensation problem of drone clusters and has good engineering practicability. In the simulation test process, the feasibility and effectiveness of the method proposed in the present invention are verified.

[0110] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When the use is implemented in whole or in part in the form of a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL) or wireless (e.g., infrared, wireless, microwave, etc.) mode) to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state hard disk SolidState Disk (SSD)), etc.

[0111] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for compensating motion errors of drone clusters, characterized in that: The UAV cluster motion error compensation method comprises: establishing a signal model, projecting a scene complex image in a Cartesian coordinate system to a polar coordinate system, and obtaining a SAR complex image in the polar coordinate system; performing two-dimensional FFT on the SAR complex image in the polar coordinate system, transforming it to a two-dimensional frequency domain, and simultaneously using the established signal model and wave number vector decomposition to derive a spectrum analytical expression of the SAR complex image in the polar coordinate system; obtaining a relationship between motion errors in an echo signal according to an analytical analysis of the spectrum analytical expression, and obtaining a related compensation expression, and preliminarily compensating the echo signal; after the compensated signal becomes a sparse signal with sparse characteristics under a sparse basis transformation, sparse observation is performed to obtain sparse observation values; using a reconstruction algorithm to process the observation values ​​observed by the measurement matrix, reconstruction from low-dimensional data to high-dimensional signals is achieved, and the original sparse signal is restored; The UAV cluster motion error compensation method comprises the following steps: Step 1: simulate and obtain an echo signal containing errors, obtain an expression of the echo signal in a Cartesian coordinate system by analysis, obtain an image in the Cartesian coordinate system, and project the image into an elliptical orthogonal polar coordinate system to obtain a SAR image in a polar coordinate system; Step 2: Perform two-dimensional FFT on the SAR image in the polar coordinate system and transform it into the two-dimensional frequency domain; use the established signal model and wave number vector decomposition to derive the spectrum analytical expression of the SAR image in the polar coordinate system; according to the analysis of the spectrum analytical expression, obtain the relevant expression of the phase error, obtain the compensation expression by analysis, and use the expression to compensate for the motion error; Step 3: Under the sparse basis transformation, the signal is transformed into a sparse signal with sparse features; the sparse signal is sparsely observed to obtain sparse observation values; the measurement matrix and the sparse basis are multiplied to obtain a recovery matrix, and the sparse mapping is obtained by using CVX in combination with the low-dimensional observation values ​​to obtain the original sparse signal; In step 3, the signal is transformed into a sparse signal with sparse features under a sparse basis transformation; the sparse signal is sparsely observed to obtain a sparse observation value; the measurement matrix and the sparse basis are multiplied to obtain a recovery matrix, and the sparse mapping is obtained by using CVX in combination with the low-dimensional observation value to obtain the original sparse signal and the sparse basis, including: (1) The compensated signal is represented as a finite length signal x, which is a one-dimensional discrete signal to be processed x∈R N×1 , the compensated echo signal is added to the sparse basis ψ∈R N×N Under the transformation, it becomes a sparse signal with sparse characteristics, then the signal to be processed x is expressed as: x=ψ·α,(α=[α1,α2,...,α N ] T ); (2) After determining the sparsity of the signal to be processed, the sparse signal is sparsely observed to obtain sparse observation values; using the measurement matrix φ∈R N×N Treat the observed signal x as a linear observation, and make the measurement matrix satisfy the finite isometry constraint RIP property during the compressed sampling process. This property states that the recovery matrix Θ formed by the measurement matrix φ and the sparse basis ψ is constant δ k ∈(0,1) and any K sparse signals satisfy the following formula: (3) The reconstruction algorithm is used to process the observed values ​​​​observed by the measurement matrix to achieve reconstruction from low-dimensional data to high-dimensional signals, and then restore the original sparse signal.

2. The UAV cluster motion error compensation method according to claim 1, characterized in that: In step 1, the simulation obtains an echo signal containing an error, obtains an expression of the echo signal in a Cartesian coordinate system by analysis, obtains an image in the Cartesian coordinate system, and projects the image into an elliptical orthogonal polar coordinate system to obtain a SAR image in a polar coordinate system, including: (1) The radar is installed on a moving flight platform. The receiver and n transmitters fly along an arbitrary curve. At any time t, the position of the transmitter antenna phase center APC is represented by x T and T The position of the transmitter’s antenna phase center APC is represented by x Rm and Rm Indicates that x T ,y T 、x Rm and Rm is a function of t; P0 is the scattering point at the center of the radar illumination scene, and P is any scattering point in the radar illumination scene. In the Cartesian coordinate system, the position of P0 is represented by P0(x0,y0), and in the polar coordinate system, the position of P0 is represented by P0(a0,θ0); in the Cartesian coordinate system, the SAR complex image containing the position of P0 is represented as: In the formula, represents the distance vector from the origin of the Cartesian coordinate system to P0, represents the distance vector from the origin of the Cartesian coordinate system to P, represents the distance vector from scattering point P0 to scattering point P, and are the error vectors of the transmitter and receiver respectively, represents the wave number vector corresponding to the transmitted signal, represents the wave number vector corresponding to the m received signals, represents the wave number vector corresponding to the transmitted signal; is the sum of the beam vectors of m receiving and transmitting signals; (2) Project the SAR complex image represented by ⊥ ), where a is the major axis length of the defined elliptical polar coordinate system, θ ⊥ is the central angle of the ellipse, and in the Cartesian coordinate system there exists x=acosθ ⊥ and y = bsinθ ⊥ The conversion relationship is finally obtained, and the SAR complex image i(a,θ ⊥ ).

3. The UAV cluster motion error compensation method according to claim 1, characterized in that: In step 2, the SAR image in the polar coordinate system is subjected to a two-dimensional FFT and transformed into a two-dimensional frequency domain; the spectrum analytical expression of the SAR image in the polar coordinate system is derived by using the established signal model and wave number vector decomposition; According to the analysis of the spectrum, the relevant expression of the phase error is obtained, and the compensation expression is obtained by analysis. The expression is used to compensate the motion error, including: (1) Introduce a set of orthogonal wave number vectors and Get i(a,θ ⊥ ) is the spectrum analytical expression, O ⊥ is the origin of the elliptical orthogonal coordinate system, Along the vector Direction, Along the tangent direction of P0, all distance vectors and wave number vectors are and The direction is decomposed, and the stationary phase point principle POSP is used to obtain i(a,θ ⊥ ) is the approximate expression: Among them, K a =K r / cosβ0,β0=∠F ET P0F ER , F ET 、F ER are the two foci of the elliptical coordinate system, and the variables η, η θ , η c , η k is the proportional coefficient between a single receiver and the final equivalent receiver. Here we have m receivers, corresponding to m β0, γ=Πcosβ 0m , r0 is a vector The modulus length, ΔR r⊥ for and Along The sum of ΔR r for and Along The sum of The spectrum expression of SAR complex image in polar coordinates is: (2) The corresponding relationship between the echo signal, SAR image and spectrum of the drone cluster is obtained, and the phase error contained in the echo signal is analyzed as follows: in, represents the wave number vector corresponding to variable a, K a is the length of the vector, K a0 K a The central value of is perpendicular to The wave number vector, the corresponding compensation expression is:

4. The UAV cluster motion error compensation method according to claim 1, characterized in that: In step (1), the sparse basis is a linear combination of orthogonal basis functions; The sparsity of the signal depends on the number of non-zero elements of the sparse basis. The smaller the number, the greater the sparsity, and the fewer the observed values ​​observed from the signal to be processed.

5. A drone cluster motion error compensation system implementing the drone cluster motion error compensation method according to any one of claims 1 to 4, characterized in that: The UAV cluster motion error compensation system comprises: A SAR image acquisition module is used to simulate and obtain an echo signal containing an error, obtain an expression of the echo signal in a Cartesian coordinate system by analysis, obtain an image in the Cartesian coordinate system, and project the image into an elliptical orthogonal polar coordinate system to obtain a SAR image in a polar coordinate system; The spectrum analysis module is used to perform two-dimensional FFT on the SAR image in the polar coordinate system and transform it into the two-dimensional frequency domain; the spectrum analysis expression of the SAR image in the polar coordinate system is derived by using the established signal model and wave number vector decomposition; The motion error compensation module is used to obtain the relevant expression of the phase error according to the analysis of the spectrum, obtain the compensation expression by analysis, and use the expression to compensate the motion error; The sparse observation module is used to transform the signal into a sparse signal with sparse features under a sparse basis transformation; perform sparse observation on the sparse signal to obtain sparse observation values; multiply the measurement matrix and the sparse basis to obtain a recovery matrix, combine it with the low-dimensional observation values, use CVX to obtain a sparse mapping, and finally obtain the original sparse signal.

6. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the drone cluster motion error compensation method as described in any one of claims 1 to 4.

7. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the drone cluster motion error compensation method as described in any one of claims 1 to 4.

8. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the drone cluster motion error compensation system as described in claim 5.

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