Cone target sparse aperture three-dimensional ISAR imaging method based on compressed sensing
By optimizing the precession parameters using a sparse dictionary and the OMP algorithm, the problem of adapting micro-motion features of conical targets under sparse aperture conditions was solved, achieving high-precision three-dimensional imaging, which is suitable for high-speed micro-motion target identification with limited radar resources.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-24
- Publication Date
- 2026-03-31
AI Technical Summary
Existing compressed sensing-based ISAR imaging methods cannot effectively adapt to the micro-motion characteristics of cone targets under sparse aperture conditions, resulting in low dictionary atom matching degree and insufficient scattering point positioning accuracy, which cannot meet the three-dimensional imaging requirements of high-speed micro-motion targets.
By employing a sparse dictionary combined with the target spin-cone micro-motion characteristics, the precession parameters are optimized using the OMP algorithm, and combined with multi-base radar observations, three-dimensional imaging under sparse aperture is achieved.
While reducing pulse resource consumption, it improves imaging and positioning accuracy, and is suitable for cone target recognition under sparse aperture conditions.
Smart Images
Figure CN121763284A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of radar signal processing technology, specifically to a sparse aperture three-dimensional inverse synthetic aperture radar (ISAR) imaging method for conical targets based on compressed sensing. It is applicable to sparse observation and three-dimensional reconstruction of high-speed, micro-moving targets such as ballistic missiles and hypersonic vehicles, and is particularly suitable for single / multi-base radar imaging scenarios where radar resources are limited. Background Technology
[0002] Three-dimensional imaging and feature recognition of high-speed, micro-moving targets such as ballistic missiles are core components of missile defense systems. Traditional ISAR three-dimensional imaging relies on continuous observation across the entire aperture, requiring the transmission of a large number of linear frequency modulated pulse signals, resulting in high radar time and energy resource occupancy. Modern radars, however, must simultaneously perform multiple tasks such as search and tracking, and the pulse resources allocated to imaging tasks are often discontinuous, creating sparse aperture observation conditions. Furthermore, traditional imaging algorithms, due to incomplete data, are prone to problems such as blurred scattering points and large positioning errors, failing to meet target recognition requirements.
[0003] Compressed sensing (CS) theory overcomes the constraints of the Nyquist sampling theorem, enabling the reconstruction of high-dimensional signals from low-dimensional sparse data and providing a technical path for sparse aperture ISAR imaging. However, existing CS-based ISAR imaging methods have two drawbacks: first, the sparse dictionary does not adapt to the micro-motion characteristics of the "spin-cone-spin" coupling of conical targets, resulting in low matching degree between atoms and real echoes; second, the imaging process is not optimized by incorporating target precession parameters, leading to insufficient accuracy due to blind sparse reconstruction. Therefore, there is an urgent need to design a sparse aperture imaging method that combines "micro-motion adapted dictionary + precession parameter optimization + OMP precise positioning" to ensure imaging accuracy while reducing pulse resources. Summary of the Invention
[0004] The purpose of this invention is to overcome the defects in the existing technology and provide a three-dimensional ISAR imaging method for conical targets with sparse aperture based on compressed sensing, which solves the problems of difficulty in extracting micro-motion parameters of conical targets under sparse aperture, low dictionary atom matching degree, and insufficient scattering point positioning accuracy.
[0005] The specific process of a sparse aperture 3D ISAR imaging method for cone targets based on compressed sensing is as follows:
[0006] Step 1: The multi-base radar transmits a linear frequency modulated (LFM) signal; the conical target receives the LFM signal transmitted by the radar; the conical target reflects the echo back to the radar.
[0007] Step 2: After the radar receives the echo from the conical target, it compares the echo signal with the reference signal. Multiplying the conjugates of the signals yields the decoupling frequency-modulated signal.
[0008] A fast time-domain Fourier transform is performed on the demodulated frequency-modulated signal to obtain a pulse-compressed one-dimensional range image sequence of the target.
[0009] Pulses are randomly selected from the target one-dimensional range image sequence. The selected pulses are flattened into a one-dimensional vector in slow time order. The one-dimensional vector is used as the range image sequence of sparse observations.
[0010] Step 3: Construct a sparse dictionary based on Step 2 ;
[0011] Step 4: Based on Step 3, obtain the target spin angular velocity unit vector in the reference coordinate system. The unit vector of conical spin angular velocity in the reference coordinate system and the coordinates of the cone apex in the local coordinate system. ;
[0012] Step 5: Based on the target spin angular velocity unit vector in the reference coordinate system and the unit vector of conical spin angular velocity in the reference coordinate system Output the three-dimensional imaging results of the cone target.
[0013] The beneficial effects of this invention are as follows:
[0014] Low resource consumption: Pulse resources are significantly reduced, lowering radar energy and time consumption;
[0015] High imaging accuracy: The mean square error under sparse aperture is slightly larger than that under full aperture, and the imaging accuracy is close to that under full aperture, which meets the requirements of target recognition.
[0016] High adaptability: The sparse dictionary combined with the "spin-cone spin" micro-motion feature, the OMP algorithm further improves the positioning accuracy through precession parameter optimization, and is suitable for typical ballistic targets such as flat-bottomed cones. Attached Figure Description
[0017] Figure 1 This is a three-dimensional imaging scene diagram of the method of the present invention; multiple radars observe a spatial cone target that is undergoing slight movement, and the echoes are processed by translational compensation and pulse compression to obtain a one-dimensional range image sequence of the target.
[0018] Figure 2 This is a schematic diagram of a precession target model; while the target spins around its own axis of symmetry, it also conically rotates around a certain directional axis in space.
[0019] Figure 3 This is a schematic diagram of the model's scattering points; the cone-shaped target is 2.4m high and has a base radius of 1m.
[0020] Figure 4 This is a schematic diagram of the model's scattering points in the reference coordinate system;
[0021] Figure 5 This is a slow-time-range image sequence diagram observed by Radar 1; the horizontal axis represents slow time and the vertical axis represents range; the five curves in the figure are the range-slow-time functions (dictionary atoms) corresponding to the cone apex and the four tail fin scattering points, respectively. The cone apex curve is a pure sine, and the tail fin curve is a multi-frequency superposition, reflecting the differences in the target's micro-motion characteristics.
[0022] Figure 6 This is a slow-time-range image sequence diagram of radar 2 observations; the horizontal axis represents slow time and the vertical axis represents range; the five curves in the figure are the range-slow-time functions (dictionary atoms) corresponding to the cone apex and the four tail fin scattering points, respectively. The cone apex curve is a pure sine, and the tail fin curve is a multi-frequency superposition, reflecting the differences in the target's micro-motion characteristics.
[0023] Figure 7 The image shows a sparse slow time-range image sequence after the radar 1 echo is extracted. Randomly extract the obtained full aperture slow time-range image to obtain a slow time-range image under sparse aperture.
[0024] Figure 8 The image shows a sparse slow time-range image sequence after the radar echo 2 is extracted. Randomly extracting the obtained full aperture slow time-range image yields a slow time-range image under sparse aperture.
[0025] Figure 9 This is a schematic diagram of the 3D imaging results for sparse apertures; the range of the 3D coordinate system. , , The red dots represent the actual scattering points, and the blue dots represent the OMP imaging points. Detailed Implementation
[0026] Specific Implementation Method 1: The specific process of this implementation method for a sparse aperture three-dimensional ISAR imaging method for cone targets based on compressed sensing is as follows:
[0027] Radar echoes contain information such as target range, velocity, and micro-motions. The core of preprocessing is to improve range resolution by "de-interpolation frequency modulation + pulse compression" and then reduce the amount of observation data by sparse sampling, while preserving the target's micro-motion characteristics.
[0028] Step 1: The multi-base (multiple base station) radar transmits a linear frequency modulated (LFM) signal; the conical target receives the LFM signal transmitted by the radar; the conical target reflects the echo back to the radar.
[0029] Step 2: After the radar receives the echo from the conical target, it compares the echo signal with the reference signal. Multiplying the conjugates of the signals yields the decoupling frequency-modulated signal.
[0030] A fast time-domain Fourier transform is performed on the demodulated frequency-modulated signal to obtain a pulse-compressed one-dimensional range image sequence of the target.
[0031] Pulses are randomly selected from the target one-dimensional range image sequence (the number of sparse pulses is 30% to 40% of the total number of pulses in the full aperture). The selected pulses are flattened into a one-dimensional vector in slow time order. The one-dimensional vector is used as the range image sequence of sparse observation.
[0032] Step 3: Construct a sparse dictionary based on Step 2 ;
[0033] Step 4: Based on Step 3, obtain the target spin angular velocity unit vector in the reference coordinate system. The unit vector of conical spin angular velocity in the reference coordinate system and the coordinates of the cone apex in the local coordinate system. ;
[0034] Step 5: Based on the target spin angular velocity unit vector in the reference coordinate system and the unit vector of conical spin angular velocity in the reference coordinate system Output the three-dimensional imaging results of the cone target.
[0035] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that, in step one, the multi-base (multiple base station) radar transmits a linear frequency modulated signal; the conical target receives the linear frequency modulated signal transmitted by the radar; the conical target reflects the echo back to the radar; the specific process is as follows:
[0036] Step 11: The linear frequency modulated signal transmitted by the multi-base radar is a time-domain finite linear frequency modulated pulse, expressed as:
[0037] (1)
[0038] in, The signal is a linear frequency modulated signal transmitted by a multi-base radar; multi-base refers to two base stations.
[0039] For rectangular window functions; To save time; The pulse width; The imaginary unit, ;
[0040] For carrier frequency, To adjust the frequency, , For signal bandwidth;
[0041] Steps 1 and 2, the goal is... Composed of several strong scattering points, slow time Next The echoes from each scattering point are:
[0042] (2)
[0043] in, For the first Echoes from each scattering point; For slow time, The scattering intensity at the scattering point, for The distance from the scattering point to the radar at any given time. , For the first One pulse, The pulse repetition frequency; The speed of light;
[0044] slow time Down The echoes from each scattering point are: ;
[0045] in, for Echoes from each scattering point;
[0046] Step 13, Slow Time Down The total echo from each scattering point is Echoes from each scattering point Addition of additive white Gaussian noise .
[0047] The other steps and parameters are the same as in Specific Implementation Method 1.
[0048] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that, in step two, after the radar receives the echo from the conical target, it compares the echo signal with the reference signal. Multiplying the conjugates of the signals yields the decoupling frequency-modulated signal.
[0049] A fast time-domain Fourier transform is performed on the demodulated frequency-modulated signal to obtain a pulse-compressed one-dimensional range image sequence of the target.
[0050] Pulses are randomly selected from the target one-dimensional range image sequence (the number of sparse pulses is 30% to 40% of the total number of pulses in the full aperture). The selected pulses are flattened into a one-dimensional vector in slow time order. The one-dimensional vector is used as the range image sequence of sparse observation.
[0051] The specific process is as follows:
[0052] Step Two: Reference Signal The expression is:
[0053] (3)
[0054] in, The distance at which the radar reaches the target's center of mass;
[0055] For reference signal pulse width, To avoid signal envelope truncation after conjugate multiplication;
[0056] Step 22: Compare the echo signal with the reference signal By multiplying the conjugates of the signals, the linear frequency modulation slope is eliminated, and the de-linear frequency modulation signal is obtained. ; indicates as:
[0057] (4)
[0058] in, Reference signal The conjugate;
[0059] For slow time Down The total echo from each scattering point is Echoes from each scattering point The summation of additive white Gaussian noise;
[0060] Steps two and three: Deconstructing the frequency modulation signal The signal is expanded to obtain the de-figuration frequency modulation signal. ; indicates as:
[0061] (5)
[0062] in, , The distance from each slow-time target scattering point to the target's centroid. The distance from the target scattering point to the radar; The wavelength of the signal;
[0063] After expansion, it can be simplified into a single-frequency signal containing only distance difference modulation, which greatly reduces the sampling rate requirement for subsequent processing.
[0064] Step 24: Perform a fast time-domain Fourier transform on the expanded de-figuration frequency-modulated signal to obtain the pulse-compressed one-dimensional range image sequence of the target; represented as:
[0065] (6)
[0066] in, This is a one-dimensional range image sequence of the target after pulse compression;
[0067] The dimension is ;
[0068] for The distance dimension, A one-dimensional range image sequence of the target after pulse compression. Full aperture pulse count;
[0069] The target scattering coefficient;
[0070] ;
[0071] The frequency is the result of the fast time-domain Fourier transform.
[0072] Step 25: Randomly select pulses from the target one-dimensional range image sequence (the number of sparse pulses should be 30%–40% of the total number of pulses in the full aperture). Flatten the selected pulses into a one-dimensional vector in slow time order. This one-dimensional vector serves as the range image sequence for sparse observations. The specific process is as follows:
[0073] Sparse pulse filtering is achieved through random sampling, where the number of sampled pulses satisfies...
[0074] (7)
[0075] in, This represents the number of pulses sampled.
[0076] The total aperture pulse count in the one-dimensional range image sequence of the target. For sparsity ratio, ; To round up;
[0077] right Each pulse is flattened into a one-dimensional vector in slow time sequence. , , As a range image sequence of sparse observations;
[0078] in, It is a complex number.
[0079] Other steps and parameters are the same as in specific implementation method one or two.
[0080] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that, in step three, a sparse dictionary is constructed based on step two. The specific process is as follows:
[0081] The sparse dictionary is the core of compressed sensing reconstruction, and its atoms must be highly matched with the micro-motion features of the target. By establishing a coordinate system to describe the micro-motion of scattering points, deriving the distance-slow time function, and discretizing the imaging region into grid points, the micro-motion response of each grid point constitutes the dictionary atoms.
[0082] Step 31: Define the radar coordinate system The origin of the radar coordinate system is the radar position. The axis is in the horizontal direction. The axis is perpendicular to Horizontal direction The axis is vertically upward and the axis system is fixed. It is used to describe the absolute position of the radar and the target.
[0083] Define reference coordinate system The origin of the reference coordinate system is the centroid of the target. Axis and radar coordinate system The axes are parallel. Axis and radar coordinate system The axes are parallel. Axis and radar coordinate system The axes are parallel. It moves with the target's center of mass and is used to connect the radar coordinate system and the target's local coordinate system;
[0084] Define the target local coordinate system The origin of the target's local coordinate system is the target's centroid. The axis is a conical rotation axis, and the target is in the local coordinate system. The axis is the target's local coordinate system. Axis and Reference Coordinate System Cross product of axes, target local coordinate system The axis is the target's local coordinate system. Axis and target local coordinate system Cross product of axes;
[0085] Step 3.2: When the target is located in the radar far field, the cone scattering point (one scattering point at the cone apex) is in the pulse-compressed one-dimensional range image sequence of the target. The micro-motion curve on is:
[0086] (8)
[0087] in, The coordinates of the scattering point in the reference coordinate system;
[0088] The conic-rotation matrix in the reference coordinate system;
[0089] This is the unit vector in the radar line-of-sight direction;
[0090] , The distance from each slow-time target scattering point to the target's centroid. The distance from the target scattering point to the radar;
[0091] Step 3: The imaging area is a cube centered on the target's centroid, ensuring coverage of all scattering points;
[0092] The discretization range of the three-dimensional coordinates of the scattering points in the reference coordinate system within the imaging region is: , , , For the target maximum size times, ;
[0093] The discrete interval of the scattering points in the reference coordinate system within the imaging region is:
[0094] And satisfy , To maximize signal bandwidth, avoid atomic redundancy caused by grid point spacing exceeding resolution;
[0095] Reference coordinate system Off-axis discrete interval, Reference coordinate system Off-axis discrete interval, Reference coordinate system The discretization interval below the axis;
[0096] Reference coordinate system Number of discrete points under the axis; Reference coordinate system Number of discrete points under the axis; Reference coordinate system Number of discrete points under the axis;
[0097] For slow-time discretization, the number of discrete points is ;
[0098] Steps three and four: Constructing dimensions as dictionary , For dictionary The first dictionary atom, For dictionary The second dictionary atom in the middle, For dictionary The Middle A dictionary atom, For dictionary The Middle One dictionary atom;
[0099] Each dictionary atom (each dictionary atom is...) The column vector is represented as:
[0100] (9)
[0101] in, Dictionary The A dictionary atom, Indicates the imaging area Axis No. discrete points, Indicates the imaging area Axis No. discrete points, Indicates the imaging area Axis No. discrete points, , , , ;
[0102] Step 35: Based on the pulse index sampled in Step 2, retain the dictionary. The corresponding rows in the dictionary are used to obtain the sparse dictionary. ;
[0103] Sparse dictionary The dimension is .
[0104] The other steps and parameters are the same as those in one of the specific implementation methods one to three.
[0105] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that, in step four, the target spin angular velocity unit vector in the reference coordinate system is obtained based on step three. The unit vector of conical spin angular velocity in the reference coordinate system and the coordinates of the cone apex in the local coordinate system. ;
[0106] The specific process is as follows:
[0107] Step 4.1: From the pulse-compressed target one-dimensional range image sequence Extract the peak value of the range-direction sequence sine curve to obtain the range image sequence of the cone apex scattering point;
[0108] The inverse Radon transform (SIRT) of the range image sequence at the cone apex scattering point is expressed as follows:
[0109] (10)
[0110] in,
[0111] This is the result of the inverse Radon transform; The frequency of the sinusoidal curve at the cone apex scattering point;
[0112] A one-dimensional range image sequence of the target after pulse compression. The result after time-domain filtering;
[0113] These are the target one-dimensional range image sequences after pulse compression, representing the scattering point at the cone apex (one scattering point at the cone apex). The amplitude, phase, and offset of the micro-motion curve;
[0114] Solve This yields an estimate of the amplitude. Phase estimate The estimated value of the bias ;
[0115] Step 4.2, the basic unit vectors of the reference coordinate system are respectively , It is the identity matrix in the reference coordinate system, therefore a transformation matrix exists. Make
[0116] (11)
[0117] in, Reference coordinate system The fundamental unit vector of the axis, Reference coordinate system The fundamental unit vector of the axis, Reference coordinate system The fundamental unit vector of the axis; To derive;
[0118] For the target local coordinate system The fundamental unit vector of the axis, For the target local coordinate system The fundamental unit vector of the axis, For the target local coordinate system The fundamental unit vector of the axis;
[0119] Transformation matrix for
[0120] (12)
[0121] in, It is a conical axis (it spins while revolving around a certain directional axis in space). The cone rotation angular velocity, (where ω is the spin angular velocity) in the reference coordinate system;
[0122] It is a conical axis (it spins while revolving around a certain directional axis in space). The cone rotation angular velocity, (where ω is the spin angular velocity) in the reference coordinate system as the angle of elevation;
[0123] Step 4.3: Using the transformation matrix The coordinates of the cone apex in the reference coordinate system Transforming from the reference coordinate system to the local coordinate system is represented as:
[0124] (13)
[0125] in, Indicates the coordinates of the cone apex in the target's local coordinate system;
[0126] Represents the coordinates of the cone apex in the target's local coordinate system; the superscript T indicates transpose.
[0127] Indicates intermediate variables. ; Indicates intermediate variables. ;
[0128] Step 44: In the target local coordinate system Describe the cone-shaped rotational motion of the target;
[0129] Calculate the cone rotation matrix in the target's local coordinate system The expression is:
[0130] (14)
[0131] in, The frequency of the sinusoidal curve at the cone apex scattering point;
[0132] Steps four and five: Based on the coordinates of the cone apex in the target's local coordinate system Conical rotation matrix in the target local coordinate system and transformation matrix Obtain the one-dimensional range image sequence of the target after pulse compression by the cone scattering point. The micro-motion curve on is:
[0133] (15)
[0134] in, This represents the cone rotation matrix in the target's local coordinate system. Indicates the azimuth angle of the target under radar line of sight. Indicates the elevation angle of the target under radar line of sight;
[0135] , The distance from each slow-time target scattering point to the target's centroid. The distance from the target scattering point to the radar;
[0136] This is the unit vector in the radar line-of-sight direction;
[0137] unknown;
[0138] make
[0139] (16)
[0140] in, , , Indicates intermediate variables;
[0141] Step 46: Obtain three nonlinear equations by observing the target with a radar; expressed as:
[0142] (17)
[0143] in, This represents an estimated value of the magnitude. This represents an estimated value of the phase. This represents an estimate of the bias.
[0144] Because the parameters of the sine curve include With five unknowns, the underdetermined system of equations may have non-unique solutions. Therefore, multiple radars are deployed to observe the target from different perspectives to obtain a unique solution to the system of equations, while ensuring that the exact solutions to the overdetermined system are compatible.
[0145] Step 47
[0146] The three nonlinear equations above are solved using the quasi-Newton method to obtain the unknowns. ;
[0147] Step 48: Based on the results obtained in Step 47 Solve for the target spin angular velocity unit vector and the target conic spin angular velocity unit vector.
[0148] The other steps and parameters are the same as those in one of the specific implementation methods one to four.
[0149] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that, in step four and seven...
[0150] The three nonlinear equations above are solved using the quasi-Newton method to obtain the unknowns. The solution process is as follows:
[0151] Step 471: Let the number of iterations be... ;
[0152] Given the number of iterations initial value of time ;
[0153] Step 472: Based on the number of iterations time Calculate the number of iterations corresponding ; indicates as:
[0154] (18)
[0155] in, ; ;
[0156] Indicates the first The next iteration , Indicates the first The next iteration ;
[0157] Indicates the first The approximate Hessian matrix of the nth iteration. Indicates the first The approximate Hessian matrix for the next iteration;
[0158] Indicates the first The next iteration , Indicates the first The next iteration ;
[0159] Indicates intermediate variables. Indicates intermediate variables;
[0160] Indicates the number of iterations. ;
[0161] Step 473, Judgment Is the change less than ;
[0162] If so, obtain the unknown. ;
[0163] If not, let the number of iterations... Repeat step 472 until... The change is less than Obtain the unknown ;
[0164] express The norm of .
[0165] The other steps and parameters are the same as those in one of the specific implementation methods one to five.
[0166] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that step Four-Eight is based on the results obtained in step Four-Seven. Solve for the target spin angular velocity unit vector and the target conic spin angular velocity unit vector;
[0167] Represented as:
[0168] (19)
[0169] in, This represents the unit vector of the target's spin angular velocity in the reference coordinate system. Represents the norm, This represents the unit vector of conical spin angular velocity in the reference coordinate system. This represents the coordinates of the cone apex in the local coordinate system.
[0170] The other steps and parameters are the same as those in one of the specific implementation methods one to six.
[0171] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that, in step five, the target spin angular velocity unit vector in the reference coordinate system is used. and the unit vector of conical spin angular velocity in the reference coordinate system Output the three-dimensional imaging results of the cone-shaped target;
[0172] The specific process is as follows:
[0173] Step 51: Based on the target spin angular velocity unit vector in the reference coordinate system and the unit vector of conical spin angular velocity in the reference coordinate system The spin matrix in the reference coordinate system is obtained. With conical spiral matrix ; indicates as:
[0174] (20)
[0175] in,
[0176] This represents the spin matrix in the reference coordinate system. Represents the identity matrix. Represents a unit vector antisymmetric matrix, This indicates the magnitude of the spin angular velocity;
[0177] Represents the conic-rotation matrix in the reference coordinate system. Represents a unit vector antisymmetric matrix, Indicates the magnitude of the cone's angular velocity;
[0178] in,
[0179] (twenty one)
[0180] (twenty two)
[0181] in, This represents the azimuth angle of the spin axis in the reference coordinate system. This indicates the elevation angle of the spin axis in the reference coordinate system;
[0182] Step 5.2: Spin Matrix Based on Reference Coordinate System With conical spiral matrix For the sparse dictionary in step 3 Perform calculations to fill in the gaps and obtain a sparse dictionary. The value;
[0183] The specific process is as follows:
[0184] Spin matrix in reference coordinate system Conical-rotation matrix The coordinates of the scattering point P in the imaging region in the reference coordinate system Substituting into formula (23), we obtain the sparse dictionary. The value of the atom ;
[0185] (twenty three)
[0186] in, Let P be the coordinates of the scattering point P in the imaging region in the reference coordinate system;
[0187] For dictionary The Middle One dictionary atom;
[0188] The target scattering point is a part of the scattering points in the imaging area, and the number of scattering points in the imaging area is far greater than the number of target scattering points;
[0189] Step 53: Establish a sparse representation model:
[0190] (twenty four)
[0191] in, For sparse dictionaries, It is a sparse coefficient vector. For noise; This is a range image sequence of sparse observations;
[0192] Step 54: Solve the sparse optimization problem model using the Orthogonal Matching Pursuit (OMP) algorithm to obtain the optimal sparse coefficient vector. ;
[0193] The sparse optimization problem model is as follows:
[0194] (25)
[0195] in, For a norm, It is a norm 2. Noise threshold;
[0196] Step 55: Extract the optimal sparse coefficient vector The dictionary atom index corresponding to the non-zero element is used to obtain the three-dimensional coordinates of the corresponding scattering point from the pre-stored grid point coordinate matrix. Output the three-dimensional imaging results of the cone-shaped target;
[0197] The pre-stored grid point coordinate matrix is Dimension, each column corresponds to a discrete grid point Coordinates are used for the direct mapping between atomic indices and three-dimensional coordinates.
[0198] Image quality verification: Calculate the imaging results and the coordinates of the actual scattering points. mean square error ( (The number of scattering points) verifies the imaging accuracy.
[0199] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.
[0200] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that, in step five-four, the Orthogonal Matching Pursuit (OMP) algorithm is used to solve the sparse optimization problem model to obtain the optimal sparse coefficient vector. The specific process is as follows:
[0201] The sparse optimization problem model is as follows:
[0202] (26)
[0203] in, For a norm, It is a norm 2. Noise threshold;
[0204] The specific process is as follows:
[0205] (1) Initialization:
[0206] initial residual Matching atomic index sets Atomic matrix Maximum number of iterations (Take 1.2 to 1.5 times the number of target scattering points);
[0207] Represents the empty set;
[0208] Let the number of iterations ;
[0209] (2) Calculation Second iteration residual With sparse dictionaries Inner product of all atoms Select the dictionary atom corresponding to the maximum absolute value of the inner product. index ,renew , ;
[0210] in, For the first The next iteration matches the atomic index set. For the first The set of matching atomic indices for the next iteration. For the first The atomic matrix of the next iteration. For the first The atomic matrix of the next iteration. For index The corresponding atoms;
[0211] The dictionary atom corresponds to the maximum absolute value of the selected inner product. Set to zero to avoid repeated selections in subsequent iterations;
[0212] (3) Based on the first Atomic matrix of the next iteration Update # The optimal coefficients of the atoms in the next iteration ;
[0213] in, For the first The optimal coefficients of the atoms in the next iteration; the superscript T indicates the transpose;
[0214] (4) Based on the first Atomic matrix of the next iteration and the The optimal coefficients of the atoms in the next iteration Update # The residual of the next iteration ; indicates as: If satisfied or Terminate the iteration, corresponding to The optimal sparse coefficient vector If not satisfied or ,make Repeat steps (2)-(4);
[0215] in, For the first The residual of the next iteration This represents the maximum number of iterations. for The 2-norm, for The 2-norm.
[0216] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.
[0217] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the noise threshold is... ;
[0218] in, The standard deviation of noise. for The distance dimension.
[0219] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.
[0220] Example:
[0221] Using bistatic radar observation of a flat-bottomed conical target as a scenario, the implementation effect of this invention is verified, and the core results are as follows:
[0222] 1. Data basis: The radar transmits a linear frequency modulated signal with a carrier frequency of 10 GHz and a bandwidth of 3 GHz, with a full aperture pulse count of 512 and a sparse pulse count of 140; the target is a flat-bottomed cone (3m high, 1m base radius), containing 5 scattering points;
[0223] 2. Imaging results: After multiple OMP iterations, focused imaging of the target was achieved. At a signal-to-noise ratio of 10dB, the MSE was 0.1687, which is slightly higher than the imaging result of 0.1486 under full aperture, indicating good robustness.
[0224] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.
Claims
1. A three-dimensional ISAR imaging method for cone-shaped targets with sparse apertures based on compressed sensing, characterized in that: The method specifically comprises the following steps: Step one, a multi-base radar transmits a linear frequency modulation signal; a conical target receives the linear frequency modulation signal transmitted by the radar; and the conical target reflects a radar echo back to the radar; Step two, after the radar receives the echo of the cone target, the echo signal is multiplied by the conjugate of the reference signal to obtain the dechirp signal. of the reference signal to obtain the dechirp signal. Fast time domain Fourier transform is performed on the dechirped signal to obtain a target one-dimensional range image sequence after pulse compression; Pulses are randomly selected from the target one-dimensional range image sequence, and the selected pulses are flattened into one-dimensional vectors in a slow time sequence, and the one-dimensional vectors are taken as sparse observation range image sequences; Step three, constructing a sparse dictionary based on step two ; Step four, obtaining the unit vector of the target spin angular velocity in the reference coordinate system based on step three , the unit vector of the coning spin angular velocity in the reference coordinate system , and the coordinates of the coning top in the local coordinate system ; Step five, based on the reference coordinate system under the target spin angular velocity unit vector and the reference coordinate system under the conical spin angular velocity unit vector , output the conical target three-dimensional imaging result.
2. The method according to claim 1, wherein the method is characterized in that: The linear frequency modulation signal transmitted by the multi-base (multiple base stations) radar in step one is a time domain limited linear frequency modulation pulse, and the expression is as follows: Fast time domain Fourier transform is performed on the dechirped signal to obtain a target one-dimensional range image sequence after pulse compression; (1) wherein, is a linear frequency modulated signal transmitted by a multi-static radar; multi-static is 2 base stations; is a rectangular window function; is a fast time; is a pulse width; is an imaginary unit, ; for a carrier frequency, for a modulation frequency, , for a signal bandwidth; Step one two, the target is composed of slow time the echo of the next scattering point is: (2) wherein, is the echo of the th scattering point; is the slow time, is the scattering intensity of the scattering point, is the distance of the scattering point to the radar at the time instant, , is the th pulse, is the pulse repetition frequency; is the speed of light; slow time down The echo from a single scattering point is: ; wherein is echoes from a few scattering points; Step one three, slow time The total echo from The echo from and additive white Gaussian noise . 3. The method according to claim 2, wherein the method is characterized in that: After receiving the echo signal of the target in the radar receiving cone in step two, the echo signal is multiplied by the conjugate of the reference signal to obtain a dechirped signal. of the reference signal to obtain a dechirped signal. Pulses are randomly selected from the target one-dimensional range image sequence, and the selected pulses are flattened into one-dimensional vectors in a slow time sequence, and the one-dimensional vectors are taken as sparse observation range image sequences; The specific process is as follows: Step two four, fast time domain Fourier transform is performed on the unfolded dechirped signal to obtain a target one-dimensional range image sequence after pulse compression; and the expression is as follows: Step two one, reference signal The expression is: (3) wherein, is the distance to the target center of mass; for the reference signal pulse width, ; Step two, multiply the echo signal with the conjugate of the reference signal to obtain the dechirped signal ; which is represented as: (4) wherein is a conjugate of the reference signal ; slow time down the total return of the return of and additive white Gaussian noise Step two three, to the dechirped signal is unfolded, to get the unfolded dechirped signal ; expressed as: (5) wherein, , is the distance of each slow-time target scatterer point to the target centroid, is the distance of the target scatterer point to the radar; is the signal wavelength; Step two five, pulses are randomly selected from the target one-dimensional range image sequence, and the selected pulses are flattened into one-dimensional vectors in a slow time sequence, and the one-dimensional vectors are taken as sparse observation range image sequences; and the specific process is as follows: (6) wherein, is the target one-dimensional range profile sequence after pulse compression; the dimension of ; is the distance-to-dimension, is the distance-to-dimension, is the target one-dimensional range profile sequence after pulse compression is the total number of pulses in the aperture. Target scattering coefficient; ； f is the frequency after the fast time domain Fourier transform; The number of sampled pulses satisfies The specific process is as follows: (7) wherein, is the number of pulses sampled; Np is the number of full aperture pulses in the target one-dimensional range profile sequence, is the sparsity ratio, ; is the ceiling function; to one pulse flattened into a one-dimensional vector in slow time , , as a sequence of range images sparsely observed; wherein is a complex number.
4. The method of claim 3, wherein the method is a compressive sensing based 3D ISAR imaging method for a sparse-aperture conic target. The step three constructs the sparse dictionary based on the step two ; Step three three, the imaging region is a cube with the target mass center as the center; Step three one, define radar coordinate system , the origin of the radar coordinate system is the radar position, axis along the horizontal direction, axis along the vertical direction perpendicular to horizontal direction, axis vertically upward, the shaft system is fixed; Definition of reference coordinate system with origin at the target center of mass, parallel to the radar coordinate system's axis, parallel to the radar coordinate system's axis, parallel to the radar coordinate system's axis, with origin at the target center of mass, defining a target local coordinate system with a target local coordinate system origin at a target center of mass, a target local coordinate system with a target local coordinate system axis as a conical spin axis, a target local coordinate system with a target local coordinate system axis as a target local coordinate system axis, a cross product of the target local coordinate system axis and the reference coordinate system axis, a cross product of the target local coordinate system axis and the reference coordinate system axis, a cross product of the target local coordinate system axis and the target local coordinate system axis, a cross product of the target local coordinate system axis and the target local coordinate system axis Step three two, when the target is in the far field of the radar, the curve of the conical top scattering point on the one-dimensional range image sequence of the target after pulse compression is: (8) wherein, is the coordinate of the scattering point in the reference coordinate system; is the conical rotation matrix in the reference coordinate system; is the unit vector in the radar line-of-sight direction; , is the distance of each slow-time target scatterer to the target centroid, is the distance of the target scatterer to the radar; The discrete interval of the scattering point in the reference coordinate system in the imaging region is as follows: The discrete range of the three-dimensional coordinates of the scattering points in the reference coordinate system within the imaging area is , , , is times the maximum size of the target, ; Each dictionary atom is expressed as: , and satisfies , is the signal bandwidth; for the reference coordinate system discrete intervals below the axis, for the reference coordinate system discrete intervals below the axis, for the reference coordinate system discrete intervals below the axis; is a reference coordinate system is the number of discrete points under the axis; is a reference coordinate system is the number of discrete points under the axis; is a reference coordinate system is the number of discrete points under the axis; For slow time discretization, the number of discrete points is ; Step three four, construct a dictionary of dimension , The specific process is as follows: (9) wherein, represents the i-th dictionary atom of a dictionary, represents the i-th discrete point in the imaging region along the x-axis, represents the i-th discrete point in the imaging region along the x-axis, represents the i-th discrete point in the imaging region along the x-axis, , , , ; Step three five, according to step 2 sampled pulse index, keep dictionary Corresponding row in the middle, get sparse dictionary .
5. The method according to claim 4, wherein the method is characterized in that: The step four obtains the unit vector of the target spin angular velocity in the reference coordinate system based on the step three The unit vector of the coning spin angular velocity in the reference coordinate system And the coordinates of the coning top in the local coordinate system ; Inverse Radon transform is performed on the range image sequence of the conical top scattering point, and the expression is as follows Step four, extracting the peak value of the distance direction sequence sinusoidal curve from the pulse compressed target one-dimensional range image sequence to obtain the range image sequence of the cone top scattering point; Wherein, (10) Let for the inverse Radon transform result; for the frequency of the cone tip scatter point sinusoid; for the pulse-compressed target one-dimensional range profile sequence the time domain filtered result; amplitude, phase, bias of the curve of the conical top scattering point on the target one-dimensional range image sequence after pulse compression, respectively amplitude, phase, bias of the curve of the conical top scattering point on the target one-dimensional range image sequence after pulse compression, respectively solving , to obtain an estimate of the amplitude , to obtain an estimate of the phase , to obtain an estimate of the bias ; Step four two, the basic unit vectors of the reference coordinate system are respectively , In the reference coordinate system, it is a unit matrix, so there is a transformation matrix So that (11) wherein, is a reference coordinate system is a basic unit vector of the axis, is a reference coordinate system is a basic unit vector of the axis, is a reference coordinate system is a basic unit vector of the axis; is derived; target local coordinate system basic unit vector of the axis, target local coordinate system basic unit vector of the axis, target local coordinate system basic unit vector of the axis; Transform matrix To (12) wherein is the azimuth angle of the conical rotation axis in the reference coordinate system; is the elevation angle of the conical rotation axis in the reference coordinate system; Step four three, utilizing a transformation matrix Coordinates of the cone tip in the reference coordinate system Transforming from the reference coordinate system to the local coordinate system is represented as: (13) wherein, represents the coordinates of the apex of the cone in the target local coordinate system; represents the coordinates of the apex of the cone in the target local coordinate system, and the superscript T represents the transpose; represents an intermediate variable, ; represents an intermediate variable, ; Step four, calculate the coning matrix in the target local coordinate system The expression is: (14) wherein is the frequency of the conic-top scattering point sinusoidal curve; Step four five, the coordinates of the cone vertex based on the target local coordinate system , the cone rotation matrix of the target local coordinate system and the transformation matrix , the micro-motion curve of the cone vertex scattering point on the target one-dimensional range image sequence after pulse compression is: (15) wherein, denotes a conical rotation matrix in the target local coordinate system, denotes the azimuth angle of the target in the radar line of sight, denotes the elevation angle of the target in the radar line of sight; , is the distance of each slow-time target scatterer to the target centroid, is the distance of the target scatterer to the radar; is the unit vector in the radar line-of-sight direction; Step four six, three nonlinear equations are obtained by observing the target through a radar; and the expression is as follows: (16) wherein , , denotes an intermediate variable; Step four seven, (17) wherein represents an estimate of the amplitude, represents an estimate of the phase, represents an estimate of the bias; The expression is as follows: The above three nonlinear equations are solved by using the quasi-Newton method to obtain the unknowns ; Step four eight, based on the obtained in step four seven , solving the target spin angular velocity unit vector and the target coning angular velocity unit vector.
6. The method of claim 5, wherein the method is a compressive sensing based 3D ISAR imaging method for a sparse-aperture conic target. The step four seven solves the above 3 nonlinear equations by using Newton method to obtain the unknown number ; the solving process is: Step four seven one, let the iteration number ; Given the number of iterations Initial value at time ; Step four seven two, based on the number of iterations At the time of Calculating the number of iterations Corresponding ; is expressed as: (18) wherein ; ； represents the first iteration of , represents the first iteration of ; denotes the approximate Hessian matrix of the denotes the approximate Hessian matrix of the denotes the approximate Hessian matrix of the denotes the approximate Hessian matrix of the represents the first iteration of , represents the first iteration of ; represents an intermediate variable, represents an intermediate variable; represents the number of iterations, ; Step four seven three, judge whether the change amount of the ; If yes, obtain unknowns ; If not, let the iteration number , repeat the iteration step 4472 until the change of is less than , obtain the unknown ; denotes the norm of .
7. The method according to claim 6, wherein the method is a compressive sensing based 3D ISAR imaging method for a sparse-aperture conic target. The step four eight obtains the target spin angular velocity unit vector and the target coning angular velocity unit vector based on the step four seven , solving the target spin angular velocity unit vector and the target coning angular velocity unit vector; The specific process is as follows: (19) wherein, denotes the unit vector of the target spin angular velocity in the reference coordinate system, denotes the norm, denotes the unit vector of the coning spin angular velocity in the reference coordinate system, denotes the coordinates of the coning apex in the local coordinate system.
8. The method according to claim 7, wherein the method is characterized in that: The step five is based on the target spin angular velocity unit vector in the reference coordinate system And the conical spin angular velocity unit vector in the reference coordinate system Output the conical target three-dimensional imaging result; Wherein, Step five, based on the reference coordinate system under the target spin angular velocity unit vector and the reference coordinate system under the conical spin angular velocity unit vector , get the spin matrix under the reference coordinate system and the conical spin matrix ; expressed as: (20) Wherein, denotes a spin matrix in the reference coordinate system, denotes the identity matrix, denotes a unit vector denotes the skew-symmetric matrix of denotes the magnitude of the spin angular velocity; denotes a conical rotation matrix in the reference coordinate system, denotes a unit vector denotes the skew-symmetric matrix of denotes the magnitude of the conical angular velocity; The specific process is as follows: (21) (22) wherein denotes an azimuth angle of the spin axis in the reference coordinate system, denotes an elevation angle of the spin axis in the reference coordinate system; Step five two, spin matrix based on reference coordinate system with a conical spin matrix , sparse dictionary of step 3 performing a calculation fill to get a sparse dictionary values; Step five three, a sparse representation model is established: Spin matrix in reference coordinate system Conical-rotation matrix The coordinates of the scattering point P in the imaging region in the reference coordinate system Substituting into formula (23), we obtain the sparse dictionary. The value of the atom ; (23) wherein, P is the coordinate of the scattering point P in the reference coordinate system; is a dictionary in the dictionary first dictionary atom; The sparse optimization problem model is specifically as follows: (24) wherein, is a sparse dictionary, is a sparse coefficient vector, is noise; is a sequence of sparse observed range images; Step five, the orthogonal matching pursuit (OMP) algorithm is used to solve the sparse optimization problem model, and the optimal sparse coefficient vector is obtained ; The sparse optimization problem model is specifically as follows: (25) wherein is a norm, is a norm, is a noise threshold; Step five, extracting the optimal sparse coefficient vector The dictionary atom index corresponding to the non-zero element, the three-dimensional coordinates of the corresponding scattering point are obtained from the pre-stored grid point coordinate matrix , output the cone target three-dimensional imaging result; The pre-stored matrix of grid point coordinates is dimensions.
9. The method according to claim 8, wherein the method is characterized in that: The step five in the application adopts the orthogonal matching pursuit algorithm to solve the sparse optimization problem model, and obtains the optimal sparse coefficient vector The specific process is as follows: The specific process is as follows: (26) wherein, is a norm, is a norm, is a noise threshold; (1) initialization: initial residual , matching atom index set , atom matrix , maximum iteration number ; denotes the empty set; Let the number of iterations ; (2), compute sub-iteration residual with sparse dictionary inner product of all atoms , select the dictionary atom corresponding to the maximum absolute value of the inner product index of , update , ; wherein, is the set of matching atom indices for the set of matching atom indices for the set of matching atom indices for the atom matrix for the atom matrix for the atom matrix for the atom matrix for the index corresponding atom; selecting the inner product absolute value maximum value corresponding dictionary atom zeroing; (3) based on the first iteration of the atomic matrix the atomic matrix of the second iteration updating the optimal coefficients of the atoms of the second iteration the optimal coefficients of the atoms of the second iteration ; wherein is the first optimal coefficient of the atom of the Tth iteration; the upper index T denotes the transposition; (4) Based on the first Atomic matrix of the next iteration and the The optimal coefficients of the atoms in the next iteration Update # The residual of the next iteration ; indicates as: If satisfied or Terminate the iteration, corresponding to The optimal sparse coefficient vector If not satisfied or ,make Repeat steps (2)-(4); wherein, is the first iteration, is the residual of the nth iteration, is the maximum number of iterations; is the two-norm of is the two-norm of is the two-norm of is the two-norm of 10. The method of claim 9, wherein the method is a compressive sensing based sparse-aperture 3D ISAR imaging method for a conic target. the noise threshold ; wherein, is the noise standard deviation, is the distance vector dimension.