A high-speed motion platform forward-looking three-dimensional super-resolution imaging method

Abstract

The application discloses a kind of high-speed motion platform front view three-dimensional super-resolution imaging methods, first derivation moving target and the distance history of platform, accurately describe the front view Doppler phase change caused by high-speed relative motion, then adopt random sparse azimuth-elevation two-dimensional scanning strategy, reduce target coherent processing time, ensure the secondary approximation accuracy of distance history under high-speed motion, then based on sparse scanning matrix and Doppler phase matrix, construct sparse Doppler convolution model to obtain echo accurate representation under high-speed platform, finally through iterative noise variance estimation, utilize weighted least square criterion derivation adaptive iterative estimation method, obtain front view super-resolution imaging result.The method of the application solves the problem of front view azimuth-elevation super-resolution performance decline caused by high-speed motion, compared with prior art, can realize front view three-dimensional super-resolution imaging under high-speed condition, while effectively reducing echo dimension, improve front view three-dimensional super-resolution imaging algorithm efficiency.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar imaging, and particularly relates to a high-speed moving platform forward-looking three-dimensional super-resolution imaging method. BACKGROUND

[0002] The scanning radar has been widely concerned in the field of forward-looking imaging due to its all-weather, all-day, full-viewing direction and fast revisit capability. The existing high-resolution remote sensing technology, such as synthetic aperture radar (SAR) or inverse synthetic aperture radar (ISAR), forms a large synthetic aperture through the motion of the platform or target, thereby obtaining high azimuth resolution. However, for SAR and ISAR imaging, the azimuth resolution is greatly reduced in the super-resolution forward-looking imaging radar due to the small difference in Doppler frequency, which is difficult to meet the needs of practical applications.

[0003] In recent years, some new methods have been proposed for super-resolution imaging of scanning radar. The document “Z. Meng, Y. Li, C. Li, M. Xing, and Z. Bao, ‘A raw data simulator for bistatic forward-looking high-speed maneuvering-platform sar,’ Signal Processing, vol. 117, pp. 151-164, 2015” improves the azimuth resolution by placing the transmitting and receiving antennas apart to provide additional Doppler phase information, but its performance will be severely degraded due to angle glint when it encounters two or more targets within a single beam. The document “Y. Zhang, X. Tuo, Y. Huang, and J. Yang, ‘A TV forward-looking super-resolution imaging method based on TVD strategy for scanning radar,’ IEEE Transactions on Geoscience and Remote Sensing, vol. 58, no. 7, pp. 4517-4528, 2020” uses truncated singular value decomposition and total variation methods to avoid the ill-conditioned problem caused by the low-pass characteristics of the antenna pattern in the inversion process and improves the azimuth resolution, but this method does not consider the two-dimensional convolution relationship between the antenna pattern in the elevation dimension and the target scattering, and cannot be used for forward-looking three-dimensional imaging. The document “J. Karlsson, W. Rowe, L. Xu, G.-O. Glentis, and J. Li, ‘Fast missing-data IAA with application to notched spectrum sar,’ IEEE Transactions on Aerospace and Electronic Systems, vol. 50, no. 2, pp. 959-971, 2014” proposes a scanning radar azimuth-elevation two-dimensional angle super-resolution method based on the iterative adaptive method (IAA), which further improves the two-dimensional angle resolution and adaptive ability, and realizes three-dimensional imaging of airborne targets. However, the above methods are only suitable for fixed or low-speed platforms, and for high-speed relative motion platforms and targets, the existing super-resolution imaging methods based on two-dimensional deconvolution will cause poor imaging performance due to model mismatch. SUMMARY

[0004] To solve the above technical problems, the application provides a high-speed motion platform forward-looking three-dimensional super-resolution imaging method to solve the imaging blur problem of the existing azimuth-elevation super-resolution method when the platform moves at high speed.

[0005] The technical scheme adopted by the application is as follows: a high-speed motion platform forward-looking three-dimensional super-resolution imaging method, and the specific steps are as follows:

[0006] Step 1, geometric modeling of the high-speed motion platform and the moving target;

[0007] In the Oxyz coordinate system, the radar platform is located at point A at the initial moment, the velocity is v, the height is h, and the platform moves at a constant speed along the z-axis direction. The platform moves to point G at the moment t. The projection of the target point P on the xy plane is point P'. The distance between the radar platform and the target at the initial moment is represented by r0, the elevation angle of the target relative to the radar platform is represented by θ, and the azimuth angle of the target relative to the z-axis direction is represented by φ. The instantaneous slant range expression is as follows: (1)

[0008] Suppose that a target with approximate radial motion is located at point P' at the initial moment, and the velocity is v'.

[0009] (2)

[0010] Suppose that a target with approximate radial motion is located at point P' at the initial moment, and the velocity is v'.

[0011] Among them, vx, vy and vz respectively represent the x-axis, y-axis and z-axis velocities of the target. Suppose that a two-dimensional planar array radar performs random sparse scanning on the forward-looking area in a short time. The distance history expression is as follows:

[0012] (3)

[0013] Among them, τ represents the slow time under the sparse scanning mode.

[0014] The geometric relationship is as follows:

[0015] (4)

[0016] Therefore, the following can be obtained:​​​​​​​​​​​​​​

[0017] (4)

[0018] Step two, second order approximation of the range history;

[0019] Taylor expansion of is as follows:

[0020] (5)

[0021] where represents the higher order terms of .

[0022] The second order and higher order terms of the range history can be directly neglected, and equation (4) is approximated as the following expression:

[0023] (6)

[0024] Step three, establishment of the continuous Doppler phase convolution echo signal model;

[0025] Let the transmitted linear frequency modulation signal be , and the expression is as follows:

[0026] (7)

[0027] where represents the radar fast time, represents the pulse width, represents the rectangular window function, represents the carrier frequency, represents the linear frequency modulation slope.

[0028] Considering the linear frequency modulation pulse signal , after pulse compression and range migration correction, the expression of the echo signal is as follows:

[0029] (8)

[0030] where represents the azimuth angle, represents the elevation angle, represents the initial distance between the radar and the target, represents the scanning region, represents an arbitrary point in , represents the scattering coefficient of the point; represents a constant containing various gains and losses, represents the antenna pattern function, and the function is , denotes signal bandwidth, denotes electromagnetic wave propagation speed, denotes wavelength; denotes Doppler phase term, denotes instantaneous slant range; denotes a mapping function constructed according to the random sparse scanning wave position timing.

[0031] It can be seen from equation (6) that the echo signal of a single range slice is a two-dimensional vector convolution of the reflection coefficient and the mapped antenna pattern, and equation (8) can be simplified as follows:

[0032] (9)

[0033] wherein, denotes convolution operation. Considering additive noise, equation (8) can be rewritten as follows:

[0034] (10)

[0035] wherein, denotes Hadamard product, denotes impulse function, denotes noise component in the received signal.

[0036] Step four, construct a sparse scanning Doppler phase matrix;

[0037] Let denote the mth range unit of the sparse scanning received signal vector, and denote, denote the transpose of the matrix, denote the number of sparse sampling points of the sparse scanning in the azimuth-elevation two-dimensional space. Equation (10) can be rewritten in matrix-vector form as follows:

[0038] (11)

[0039] wherein, denotes target scattering coefficient, denotes vector form of noise; denotes sparse scanning antenna pattern mapping matrix, composed of 0 and 1, the row sequence of which represents the beam scanning timing, consistent with , the kth row of which is composed of zero and one, wherein one represents scanning at the wave position at time k, denotes complex set, denotes the number of discrete azimuth angles, denotes the number of discrete elevation angles; denotes azimuth-elevation joint steering matrix; denotes a sparse-scan Doppler phase matrix, expressed as

[0040] (12)

[0041] where, ; , denotes the number of sampling points in two different dimensions; denotes the pulse repetition interval, and , denotes the pulse repetition frequency.

[0042] Rewriting equation (11), we have

[0043] (13)

[0044] where, denotes the azimuth-elevation sparse-scan Doppler steering matrix, denotes the kth column vector of .

[0045] Step five, target scattering estimation;

[0046] The optimized IAA method is a spectral estimation method based on weighted least squares, whose iterative expression is as follows:

[0047] (14)

[0048] where, , denotes the conjugate transpose of a matrix, denotes the data covariance matrix, expressed as

[0049] (15)

[0050] where, denotes the scattering coefficient of the kth target.

[0051] Step six, noise variance adaptive iterative estimation;

[0052] Diagonal loading equation (14), we have

[0053] (16)

[0054] where, the diagonal elements of are obtained by iteratively estimating the noise power, whose process is expressed as

[0055] (17)

[0056] wherein, denotes the nth column of the identity matrix The noise power of each direction is initialized to 0 or a small constant.

[0057] Finally, the adaptive iterative estimation method is derived by using the weighted least square criterion through the iteration of the noise variance estimation, and the forward-looking super-resolution imaging result is obtained.

[0058] The method of the present application first derives the distance history of the moving target and the platform, accurately describes the forward-looking Doppler phase change caused by high-speed relative motion, then adopts a random sparse azimuth-elevation two-dimensional scanning strategy to reduce the target coherent processing time and ensure the accuracy of the quadratic approximation of the distance history under high-speed motion, and then constructs a sparse Doppler convolution model based on the sparse scanning matrix and the Doppler phase matrix to obtain the accurate representation of the echo under the high-speed platform, and finally derives the adaptive iterative estimation method by using the weighted least square criterion through the iteration of the noise variance estimation, and obtains the forward-looking super-resolution imaging result. The method of the present application solves the problem of decline of forward-looking azimuth-elevation super-resolution performance caused by high-speed motion, and compared with the existing method, can realize forward-looking three-dimensional super-resolution imaging under high-speed conditions, while effectively reducing the echo dimension and improving the efficiency of the forward-looking three-dimensional super-resolution imaging algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 is a flow chart of a forward-looking three-dimensional super-resolution imaging method of a high-speed moving platform of the present application.

[0060] Figure 2 is a forward-looking three-dimensional super-resolution imaging geometric model diagram in an embodiment of the present application.

[0061] Figure 3 is a two-dimensional original scene diagram of a point target in an embodiment of the present application.

[0062] Figure 4 is a three-dimensional original target diagram in an embodiment of the present application.

[0063] Figure 5 is a comparison diagram of the IAA two-dimensional imaging result of the existing convolution model and the IAA two-dimensional imaging result of the method of the present application in an embodiment of the present application.

[0064] Figure 6 is a comparison diagram of the IAA three-dimensional imaging result of the existing convolution model and the IAA three-dimensional imaging result of the method of the present application in an embodiment of the present application. DETAILED DESCRIPTION

[0065] This invention uses simulation experiments to demonstrate the effectiveness of the proposed fast radar imaging super-resolution method. All steps and conclusions of this invention have been verified as correct on the Matlab 2019b simulation platform. The method of this invention will be further described below with reference to the accompanying drawings and embodiments.

[0066] like Figure 1 The flowchart of a forward-looking three-dimensional super-resolution imaging method for a high-speed motion platform according to the present invention is shown below, and the specific steps are as follows:

[0067] Step 1: Geometric modeling of the high-speed motion platform and moving target;

[0068] Forward-looking 3D super-resolution imaging geometric model as follows Figure 2 As shown, in the Oxyz coordinate system, assume the radar platform is in... At point A, the speed is The height is h, along It moves at a constant speed along the axial direction. The platform moves to point G. The target point P is about... The projection of the plane is point. This indicates the initial distance between the radar platform and the target. This indicates the target's elevation angle relative to the radar platform. Indicates the target relative to Azimuth angle along the axis.

[0069] The instantaneous slant distance expression is as follows:

[0070] (1)

[0071] Set a target with approximate radial motion When located The speed is .

[0072] in, , , Representing the target Axial, Axial and Axial velocity.

[0073] Imagine a two-dimensional planar array radar performing a random, sparse scan of the forward-looking area over a short period of time. Then, the range history... The expression is as follows:

[0074] (2)

[0075] in, This represents the slow time in sparse scan mode. The geometric relationship is as follows:

[0076] (3)

[0077] Then we have:

[0078] (4)

[0079] Step two, the second order approximation of the range history;

[0080] Taylor expansion is performed on , and the expression is as follows:

[0081] (5)

[0082] where represents the high order terms of .

[0083] Because of the sparse scanning, CPI (coherent processing interval) is significantly reduced, and still satisfies . And because the look-ahead angle is always less than . The second order and higher order terms of the range history can be directly ignored, and the expression (4) is approximated as the following expression:

[0084] (6)

[0085] Step three, the establishment of the continuous Doppler phase convolution echo signal model;

[0086] The transmitted linear frequency modulation signal is set as , and the expression is as follows:

[0087] (7)

[0088] wherein represents the radar fast time, represents the pulse width, represents the rectangular window function, represents the carrier frequency, represents the linear frequency modulation slope.

[0089] Considering the linear frequency modulation pulse signal , after the pulse compression and range migration correction, the expression of the echo signal is as follows:

[0090] (8)

[0091] wherein represents the azimuth angle, represents the elevation angle, represents the initial distance between the radar and the target, represents the scanning region, represents any point inside, denotes the scattering coefficient of this point; denotes a constant containing various gains and losses, denotes the antenna pattern function, the function is , denotes the signal bandwidth, denotes the electromagnetic wave propagation speed, denotes the wavelength; denotes the Doppler phase term, denotes the instantaneous slant range; denotes a mapping function constructed according to the random sparse scanning wave position timing.

[0092] From equation (6), it can be seen that the echo signal of a single range slice is a two-dimensional vector convolution of the reflection coefficient and the mapped antenna pattern, and equation (8) can be simplified as follows:

[0093] (9)

[0094] wherein, denotes the convolution operation. Considering additive noise, equation (8) can be rewritten as:

[0095] (10)

[0096] wherein, denotes the Hadamard product, denotes the impulse function, denotes the noise component in the received signal.

[0097] Step four, construct a sparse scanning Doppler phase matrix;

[0098] Let denote the mth range unit of the sparse scanning received signal vector, and denote, denote the transpose of the matrix, denote the number of sparse sampling points in the azimuth-elevation two-dimensional space of the sparse scanning. Equation (10) can be rewritten in matrix-vector form as follows:

[0099] (11)

[0100] wherein, denotes the target scattering coefficient, denotes the vector form of the noise; denotes the sparse scanning antenna pattern mapping matrix, which is composed of 0 and 1, and the row sequence represents the beam scanning timing, which is consistent with , and the kth row is composed of one 0 and one 1, where 1 indicates that scanning is performed at the wave position at time k, denotes a complex set, denotes the number of azimuth angles after discretization, denotes the number of elevation angles after discretization; denotes the azimuth-elevation joint steering matrix; denotes the sparse-scan Doppler phase matrix, which is expressed as follows:

[0101] (12)

[0102] where, ; , denotes the number of sampling points in two different dimensions; denotes the pulse repetition interval, and , denotes the pulse repetition frequency.

[0103] Rewriting equation (11), the expression is as follows:

[0104] (13)

[0105] where, denotes the azimuth-elevation sparse-scan Doppler steering matrix, denotes the kth column vector of .

[0106] Step five, target scattering estimation;

[0107] As shown in model equation (12), forward-looking super-resolution reconstruction can be mathematically represented as a set of linear equations, which allows various super-resolution methods to be applied to reconstruct forward-looking aerial targets. The optimized IAA method is a spectral estimation method based on weighted least squares, and its iterative expression is as follows:

[0108] (14)

[0109] where, , denotes the conjugate transpose of the matrix, denotes the data covariance matrix, which is expressed as follows:

[0110] (15)

[0111] where, denotes the scattering coefficient of the kth target.

[0112] Step six, noise variance adaptive iterative estimation;

[0113] To avoid the ill-conditioned problem in the inverse process, the equation (14) is diagonally loaded, and the expression is as follows:

[0114] (16)

[0115] where, the diagonal elements of, is obtained by iteratively estimating the noise power, and the process expression is as follows:

[0116] (17)

[0117] where, denotes the nth column of the unit matrix . The noise power of each direction is initialized to 0 or a small constant.

[0118] Finally, by iteratively estimating the noise variance, the adaptive iterative estimation method is derived using the weighted least square criterion, and the forward-looking super-resolution imaging result is obtained.

[0119] In this embodiment, the original scene of the point target is as shown in Figure 3 . In the point target imaging simulation, the radar system parameters are set according to Table 1. The three-dimensional original target is as shown in Figure 4 . In the three-dimensional body target imaging simulation, the radar system parameters are set according to Table 2.

[0120] Table 1

[0121]

[0122] Table 2

[0123]

[0124] In this embodiment, the IAA two-dimensional imaging results of the existing convolution model and the IAA two-dimensional imaging results of the method of the application are as shown in Figure 5 . From the two-dimensional simulation results, it can be seen that, Figure 5 (a) is the imaging result of the optimized IAA method under the existing convolution model. At a signal-to-noise ratio SNR = 20 dB, the existing model cannot completely display the target result. Figure 5 (b) is the imaging result of the method of the application. It can be seen that at a signal-to-noise ratio SNR = 20 dB, the target can be reconstructed with the best effect without any user parameters.

[0125] In this embodiment, the IAA three-dimensional imaging results of the existing convolution model and the IAA three-dimensional imaging results of the method of the application are as shown in Figure 6 . From the three-dimensional simulation results, it can be seen that, Figure 6(a) is the three-dimensional imaging result of the IAA method optimized under the existing convolution model, and it can be seen that the three-dimensional resolution is poor. Figure 6 (b) is the three-dimensional imaging result of the method of the present application, and the details of the aircraft such as the wing and the tail are shown in the figure, which enhances the practicability of target recognition of the method of the present application.

[0126] The algorithm complexity is shown in Table 3, wherein represents the number of iterations of the imaging algorithm. It can be seen that the calculation complexity of the method of the present application is lower than that under the existing model.

[0127] Table 3

[0128]

[0129] In summary, for two-dimensional and three-dimensional scanning radars, the low-complexity high-speed motion platform azimuth-elevation forward-looking super-resolution imaging method based on sparse Doppler convolution model proposed by the method of the present application expands the applicability of the two-dimensional convolution model under high-speed conditions and reduces the echo dimension, greatly reduces the calculation complexity of the existing method, has strong robustness, and can adapt to the super-resolution imaging of two-dimensional and three-dimensional scanning radars under low signal-to-noise ratio conditions.

[0130] Those skilled in the art will realize that the embodiments described herein are for the purpose of helping the reader understand the principles of the present application and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspiration disclosed by the present application without departing from the essence of the present application, and these modifications and combinations are still within the scope of protection of the present application.

Claims

1. A high-speed motion platform forward-looking three-dimensional super-resolution imaging method, the specific steps are as follows: Step one, high-speed motion platform and motion target geometric modeling; In the Oxyz coordinate system, assume the radar platform is in... At point A, the speed is The height is h, along Uniform motion along the axial direction; The platform moves to point G; the target point P is about... The projection of the plane is point; This indicates the initial distance between the radar platform and the target. This indicates the target's elevation angle relative to the radar platform. Indicates the target relative to Azimuth angle along the axis; Then the instantaneous slant range expression is as follows: （1）； Setting a target for approximate radial motion when located at a speed of ; wherein , , respectively denote the target's axial, axial and axial velocity; A two-dimensional planar array radar is set to randomly and sparsely scan a forward-looking area in a short time; then the distance history The expression is as follows: （2）； wherein, denotes the slow time in the sparse scan mode; the geometric relation is as follows: （3）； Then we can get: （4）； Step two, second-order approximation of distance history; For Carrying out a Taylor expansion, the expression is as follows: （5）； wherein represents higher order terms of The quadratic term and higher order terms of the distance history can be directly ignored, and equation (4) is approximated as the following expression: （6）； Step three, establish a continuous Doppler phase convolution echo signal model; Setting a transmit chirp signal The expression is as follows: （7）； wherein, denotes the radar fast time, denotes the pulse width, denotes the rectangular window function, denotes the carrier frequency, denotes the chirp slope; Consider a linear frequency modulated pulse signal After pulse compression and range migration correction, the echo signal is expressed as follows: （8）； wherein denotes the azimuth angle, denotes the elevation angle, denotes the initial distance of the radar to the target, denotes the scanning region, denotes any point within the region, denotes the scattering coefficient of this point; denotes a constant containing various gains and losses, denotes the antenna pattern function, the function is , denotes the signal bandwidth, denotes the electromagnetic wave propagation speed, denotes the wavelength; denotes the Doppler phase term, denotes the instantaneous slant range; denotes a mapping function constructed according to the timing of the random sparse scanning wave positions; From equation (6), the echo signal of a single range slice is a two-dimensional vector convolution of the reflection coefficient and the mapped antenna pattern, and the simplified expression of equation (8) is as follows: （9）； where denotes a convolution operation; taking into account additive noise, equation (8) is then rewritten as follows: （10）； wherein denotes a Hadamard product, denotes an impulse function, denotes a noise component in the received signal; Step four, construct a sparse scanning Doppler phase matrix; Set represents the mth range cell of the received signal vector of sparse scanning, where represents, represents the transpose of a matrix, represents the number of sparse sampling points in the azimuth-elevation two-dimensional space of sparse scanning; then formula (10) is rewritten in matrix-vector form, and the expression is as follows: （11）； wherein, denotes the target scattering coefficient, denotes the vector form of noise; denotes the sparse scanning antenna pattern mapping matrix, composed of 0, 1, the row sequence indicates the beam scanning time sequence, and consistent with it, the kth row is composed of 0 and a 1, wherein the 1 indicates that scanning is performed at the wave position at the kth moment, denotes a complex set, denotes the number of discrete azimuth angles, denotes the number of discrete elevation angles; denotes the azimuth-elevation joint steering matrix; denotes the sparse scanning Doppler phase matrix, and the expression is as follows: （12）； wherein ; , denotes the number of sampling points in two different dimensions; denotes the pulse repetition interval, and , denotes the pulse repetition frequency; Rewrite equation (11) as follows: （13）； wherein, represents an azimuth-elevation sparse-scan Doppler steering matrix, represents the kth column vector of Step five, target scattering estimation; The optimized IAA method is a spectral estimation method based on weighted least squares, and its iterative expression is as follows: （14）； wherein , denotes the conjugate transpose of a matrix, denotes the data covariance matrix, expressed as follows: （15）； wherein, denotes the scattering coefficient of the kth object; Step six, adaptive iterative estimation of noise variance; Diagonal loading of equation (14) is as follows: （16）； wherein the diagonal elements of the matrix is obtained by iteratively estimating the noise power, the procedure of which is expressed as follows: （17）； wherein represents the nth column of the identity matrix ; the noise power in each direction is initialized to 0 or a small constant; Finally, through iterative noise variance estimation, an adaptive iterative estimation method is derived using the weighted least squares criterion to obtain the forward-looking super-resolution imaging result.

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