Kalman filter based three-dimensional imaging method for spatial spin group target

Abstract

The application relates to a three-dimensional imaging method for a spatial spin group target based on Kalman filtering, and relates to a three-dimensional imaging method for a spatial spin group target.The application aims to solve the problems of large search calculation amount, long operation time, and limited parameter estimation accuracy caused by search range and search parameter setting in the prior art three-dimensional imaging method for a spatial spin group target.The process is as follows: I. obtaining a one-dimensional range image based on a spatial spin group target; II. performing binaryzation processing on the one-dimensional range image, and performing skeleton extraction processing on the binaryzation image to obtain an image; III. extracting each sinusoidal curve in the image; IV. obtaining spin frequency estimation values of scattering points corresponding to each sinusoidal curve; V. estimating the z-axis direction coordinate values of the corresponding scattering points according to the values of the centers of each sinusoidal curve deviating from the center of the distance dimension; and VI. estimating the x-axis and y-axis direction coordinate values of the scattering points by using an I Radon transform.The application belongs to the technical field of radars.

Description

Technical Field

[0001] This invention belongs to the field of radar technology and relates to a three-dimensional imaging method for space spin swarm targets. Background Technology

[0002] Ballistic missiles, with their large size, long range, and powerful destructive force, have become formidable weapons for attacking enemy targets in warfare. To ensure directional motion, missiles themselves undergo significant spin rotation. Simultaneously, to achieve penetration, missiles employ specific penetration techniques and release fragments and decoys, which, along with the missile target, constitute a spinning swarm of targets, each with varying speeds, spin rates, and other motion states. Due to the greater maneuverability of spinning swarm targets, achieving high-resolution imaging of such targets is more challenging than that of single targets, and accurately identifying warheads within a swarm is crucial for missile interception. Currently, methods for solving the three-dimensional imaging of space spinning swarm targets mainly rely on matching search and particle swarm optimization algorithms. The former suffers from high computational cost and long processing time, while the latter's accuracy is affected by the search range and parameter settings, and it is prone to getting trapped in local optima. Therefore, reducing computational cost and improving parameter estimation accuracy are essential for the three-dimensional imaging of space spinning swarm targets. Summary of the Invention

[0003] The purpose of this invention is to solve the problems of large search computation, long operation time, and the limitation of parameter estimation accuracy by the search range and search parameter settings in existing three-dimensional imaging methods for space spin swarm targets. Therefore, this invention proposes a three-dimensional imaging method for space spin swarm targets based on Kalman filtering.

[0004] The specific process of the three-dimensional imaging method for space spin swarm targets based on Kalman filtering is as follows:

[0005] Step 1: Perform range compression and motion compensation processing sequentially on the echo signal of the space spin swarm target to obtain the compensated one-dimensional range profile S. r (r,t m );

[0006] Where r is the distance dimension, t m This refers to the pulse signal transmission time, i.e., the slow time.

[0007] Step 2: Set an appropriate threshold for the one-dimensional distance image S r (r,t m The image is binarized, and then a skeleton is extracted from the binarized image to obtain image S. r (m,n);

[0008] Where (m,n) represents the image S rThe position coordinates of (m,n); m = 1, 2, ..., M, n = 1, 2, ..., N, where M is the number of sampling points in a single pulse and N is the number of pulse accumulations;

[0009] Step 3: Based on image S r (m,n) determines that the number of sine curves is n1. The Kalman filter algorithm is then used to process the image S. r Extract each sine curve from (m,n);

[0010] Step 4: Use the EMD algorithm to perform frequency analysis on each extracted sine curve to obtain the estimated spin frequency of the scattering point corresponding to each sine curve, and divide the scattering points with the same spin frequency into the same sub-target.

[0011] Step 5: Estimate the z-axis coordinates of the corresponding scattering points based on the deviation of the center of each sine curve from the center of the dimensional axis.

[0012] Step 6: Based on Steps 4 and 5, use the IRadon transform to estimate the x-axis and y-axis coordinates of the scattering point.

[0013] The beneficial effects of this invention are as follows:

[0014] This invention proposes a three-dimensional imaging method for space spin swarm targets based on Kalman filtering. This method directly estimates the spin frequency and z-axis coordinate of the target by separating the sinusoidal curves in the one-dimensional range image. It transforms the four-dimensional parameter search of the traditional matching search method into a two-dimensional search, reducing the amount of computation and shortening the operation time. Compared with the parameter search based on particle swarm optimization algorithm, the accuracy of the search results of this method is not limited by the search range setting or trapped in local optima. In addition, the separation of the curves in the one-dimensional range image also facilitates the differentiation of targets, making it easier to analyze each target individually in the subsequent process. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention;

[0016] Figure 2 Flowchart for curve extraction using the Kalman filter algorithm;

[0017] Figure 3 Flowchart for EMD algorithm for estimating spin frequency;

[0018] Figure 4 This is a model diagram of the spin group target scattering point used in Example 1;

[0019] Figure 5a This is a one-dimensional range profile of the spin swarm target echo after range compression.

[0020] Figure 5bExtract the results from each sine curve;

[0021] Figure 5c Curve 1 is obtained by separation in a one-dimensional distance image;

[0022] Figure 5d Curve 2 is obtained by separation in a one-dimensional distance image;

[0023] Figure 5e Curve 3 is obtained by separation in a one-dimensional distance image;

[0024] Figure 5f Curve 4 is obtained by separation in a one-dimensional distance image;

[0025] Figure 5g Curve 5 is obtained by separation in a one-dimensional distance image;

[0026] Figure 5h Curve 6 is obtained by separation in a one-dimensional distance image;

[0027] Figure 6a Two-dimensional imaging results of the IRadon transform for a subtarget with a spin frequency estimate of 7.90 Hz;

[0028] Figure 6b Two-dimensional imaging results of the IRadon transform for a subtarget with a spin frequency estimate of 6.25 Hz;

[0029] Figure 6c Two-dimensional imaging results of the IRadon transform for a subtarget with a spin frequency estimate of 5.20 Hz;

[0030] Figure 7 This is a comparison image of the initial position of the spin swarm target and the three-dimensional imaging results. Detailed Implementation

[0031] Specific implementation method one: Combining Figure 1 , 2 3. This embodiment describes the specific process of the three-dimensional imaging method for space spin swarm targets based on Kalman filtering.

[0032] Step 1: Perform range compression and motion compensation processing sequentially on the echo signal of the space spin swarm target to obtain the compensated one-dimensional range profile S. r (r,t m );

[0033] Where r is the distance dimension, t m This refers to the pulse signal transmission time, i.e., the slow time.

[0034] Step 2: Set an appropriate threshold for the one-dimensional distance image S r (r,t mThe image is binarized, and then a skeleton is extracted from the binarized image to obtain image S. r (m,n);

[0035] Where (m,n) represents the image S r The position coordinates of (m,n); m = 1, 2, ..., M, n = 1, 2, ..., N, where M is the number of sampling points in a single pulse and N is the number of pulse accumulations;

[0036] Step 3: Based on image S r (m,n) determines that the number of sine curves is n1. The Kalman filter algorithm is then used to process the image S. r Extract each sine curve from (m,n);

[0037] Step 4: Use the EMD algorithm to perform frequency analysis on each extracted sine curve to obtain the estimated spin frequency of the scattering point corresponding to each sine curve, and divide the scattering points with the same spin frequency into the same sub-target.

[0038] Step 5: Estimate the z-axis coordinates of the corresponding scattering points based on the deviation of the center of each sine curve from the center of the dimensional axis.

[0039] Step 6: Based on Steps 4 and 5, use the IRadon transform to estimate the x-axis and y-axis coordinates of the scattering point.

[0040] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: the instantaneous slant range expression for each scattering point of the space spin swarm target in step one is ΔR. P (t m )=x' p sin(ωt m )+y' p cos(ωt m )+z' p The instantaneous slant range of each scattering point at each moment forms a sine curve (the instantaneous slant range of each scattering point is a point on the sine curve, and the instantaneous slant range at each moment forms a sine curve, which changes with time).

[0041] In the formula, x' p =xsin(φ),y' p =ysin(φ), z' p = zcos(φ), where φ represents the angle between the target's spin axis (the sub-targets in a group of targets spin around their respective spin axes) and the radar line of sight, and x, y, and z are the actual coordinates of the scattering point.

[0042] The other steps and parameters are the same as in Specific Implementation Method 1.

[0043] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that: the one-dimensional distance image S in step one... r (r,t m It contains a set of sine curves with different amplitudes, periods, and initial phases, S r (r,t m ) is an M×N two-dimensional matrix.

[0044] Other steps and parameters are the same as in specific implementation method one or two.

[0045] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that: in step two, a suitable threshold is set for the one-dimensional distance image S. r (r,t m The image is binarized, and then a skeleton is extracted from the binarized image to obtain image S. r (m,n); The specific process is as follows:

[0046] Skeleton extraction algorithms are image processing methods, and their operations can be represented as follows:

[0047]

[0048] In the formula, This indicates that structuring element B continuously erodes the binarized image A. Second-rate, It is the last iteration number before the binarized image A is eroded to the empty set;

[0049] Binarization can avoid the influence of noise by setting the position of points where the curve exists to 1 and the position of points where the curve does not exist to 0, which facilitates the subsequent extraction and separation of curves.

[0050] Skeleton extraction from one-dimensional distance images can effectively suppress the influence of high side lobes of the curve, making the curve "thinner".

[0051] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0052] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that: in step three, based on image S... r (m,n) Determine the number of sine curves as n1 (directly observed from the image), and use the Kalman filter algorithm on image S. r Extract the sine curves from (m,n); the specific process is as follows:

[0053] Step 3: Based on the principle that adjacent points of a sine curve have similar slopes, extract the first 30 points of each sine curve. These 30 points have been correctly correlated and serve as prior information for recorrelation using Kalman filtering. Based on this prior information, obtain the system state value and variance value of the j-th curve at time k. At this point, k = 31, j = 1; the specific process is as follows:

[0054] Image S r Each curve in (m,n) can be considered as being formed by the motion of a target point a1 along the echo number direction in a two-dimensional plane. Since the points on the sine curves are relatively smooth, the accelerations of target points on different curves at the same time differ significantly. Based on this motion characteristic, a two-dimensional continuous Wiener acceleration model is adopted. The system motion state of target point a1 at time k can be expressed as:

[0055]

[0056] Where, x′ k and y′ k This represents the current position of target point a1 in the coordinate system. This represents the velocity of target point a1 along the two coordinate axes. This represents the acceleration of the target point a1 along the two coordinate axes;

[0057] The expressions for the measurement matrix and the observation matrix are:

[0058]

[0059] y k =[y′ k x′ k ] T

[0060] Where H represents the measurement matrix of the two-dimensional continuous Wiener acceleration model, y k The observation matrix represents the two-dimensional continuous Wiener acceleration model, and T denotes the transpose;

[0061] The Kalman filter algorithm consists of two parts: prediction and update.

[0062] First, the system motion state at the current moment is predicted based on the system motion state at the previous moment, thus obtaining the predicted value of the system motion state at the current moment. The expression for the prediction stage is:

[0063]

[0064]

[0065] in, and A represents the predicted value and variance of the system's motion state at the current moment, respectively. k-1 Let Q represent the system state transition matrix at time k. k-1 This represents the variance of the state noise, before the current system measurements are used; x k-1 P represents the mean of the actual values ​​of the system's motion state at time k-1. k-1 This represents the actual variance of the system's motion state at time k-1;

[0066] Based on the predicted value of the system's motion state at the current moment and the measured value of the system's motion state at the current moment, y k Update the system state; the current measurement value of the system's motion state is y. k This is manifested in image S r The expression for updating the x-coordinate of the point with a value of 1 in the column (m,n) where n=k is the same as the x-coordinate of the point with a value of 1 is:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Among them, v k S represents the estimation deviation of the measured value. k It is the variance of the new information, K k It is the filter gain, x k and P k The updated mean and variance of the system state at time k can be used to predict the system state at time k+1; H k R represents the measurement matrix of the system. k The covariance matrix representing the noise;

[0073] Based on the above principle, each sine curve in the one-dimensional range image is extracted. The extracted results are stored in a matrix C(i,j) of size N×n1. C(i,j) represents the position of the j-th curve in the range dimension at the time of the i-th echo. It is assumed that there are n1 curves in the initial judgment.

[0074] Step 3.2: Utilize the system state value and variance value at time k-1. Make a prediction at time k to obtain the predicted value of the system state at time k. With the predicted variance

[0075] Step 33: Search image S r In the matrix (m,n), the x-coordinates of all points with a value of 1 in column n=k are stored in matrix row1. If there are n2 points with a value of 1, then row1 is a matrix of size 1×n2; if there are no points with a value of 1, then row1 = [C(k-1,j)-5,C(k-1,j)-4,...,C(k-1,j)+5].

[0076] In the formula, C(k-1,j) represents the coordinate matrix of the j-th curve at time k-1 in the distance dimension;

[0077] Steps 3 and 4: Using each point in row1 as an observation, predict the value at the current time. Perform an update to obtain the state value after updating the predicted value at the i-th position of the j-th curve at time k.

[0078] Based on state values Generate matrix X;

[0079]

[0080] If the minimum value is located at position n3 in the search matrix X, then (k, row1(n3)) is the point closest to the current curve state. This point is taken as the point of the j-th curve at time k. Let S... r (k,row1(n3))=0;

[0081] Step 35: If k > N, jump to step 36; otherwise, let k = k + 1 and repeat steps 32 to 35.

[0082] In the formula, N represents the image S. r The number of columns in (m,n), i.e., the number of pulse accumulations;

[0083] Step 36: If j > n1, stop the search and output the curve coordinate matrix C; otherwise, let j = j + 1 and repeat steps 32 to 36.

[0084] The other steps and parameters are the same as those in specific implementation methods one through four.

[0085] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that: in step four, the EMD algorithm is used to perform frequency analysis on each extracted sine curve to obtain the estimated spin frequency of the scattering point corresponding to each sine curve, and scattering points with the same spin frequency are divided into the same sub-target; the specific process is as follows:

[0086] The EMD algorithm can decompose the original signal into multiple eigenmode functions. The final decomposition result is as follows:

[0087]

[0088] In the formula, s(t) represents the original signal, and IMF l Let represent the l-th signal obtained from the decomposition. IMF1 is the highest frequency component in the signal. As the IMF order increases, the corresponding frequency components become lower. r(t) represents the residual quantity after decomposition. For a sine curve generated by spin motion that has undergone motion compensation, the highest frequency component after decomposition corresponds to the spin frequency. The specific process of spin frequency estimation is as follows:

[0089] Step 4: Let j = 1, s(t) = C(:,j);

[0090] In the formula, j represents the j-th curve, and C(:,j) represents the position vector of the j-th curve at each time step;

[0091] Step 4.2: Based on the upper envelope v1(t) and lower envelope v2(t) of the signal s(t), use the formula... Find the mean m of the upper envelope v1(t) and lower envelope v2(t) of the signal s(t);

[0092] Step 43: Let h = s(t) - m, and determine whether h satisfies the conditions of the intrinsic mode function (IMF). If it does, proceed to step 44; otherwise, let s(t) = h and repeat steps 42 to 43.

[0093] The condition for the intrinsic mode function (IMF) is:

[0094] The absolute value of the difference between the number of extreme points (the sum of maximum and minimum points) and the number of zero-crossing points is less than or equal to 1, and the envelope of the maximum and minimum points is symmetric about the time axis;

[0095] Step 4: Let the intrinsic mode function IMF1 = h, perform an FFT transform on the signal IMF1, and the frequency value corresponding to the peak point on the positive half axis of the spectrum is the spin frequency w of the scattering point corresponding to the curve. j ;

[0096] Steps 4 and 5: If j > n1, output the spin frequency of each curve; otherwise, let j = j + 1 and repeat steps 4 and 5.

[0097] The other steps and parameters are the same as those in specific implementation methods one through five.

[0098] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: in step five, the z-axis coordinate value of the corresponding scattering point is estimated based on the value of the deviation of the center of each sine curve from the center of the dimension; the specific process is as follows:

[0099] Since the position coordinates of each sine curve at each time are known, the center value of the sine curve can be obtained by averaging the position coordinates of the same sine curve at each time.

[0100] The distance from the center of the dimension is half the number of samples in a single pulse;

[0101] The z-axis coordinate of the scattering point corresponding to the sine curve is estimated based on the value of the deviation of the center of the sine curve from the center of the dimension.

[0102] The formula for estimating the z-axis coordinate value is as follows:

[0103]

[0104]

[0105] In the formula, r j Let z represent the mean of the envelope of the j-th curve. j Let C(i,j) represent the estimated z-axis coordinate of the scattering point corresponding to the j-th curve, and let C(i,j) represent the position vector of the j-th curve at time i. Indicates the distance from the center of the dimension. Let c represent the resolution of the distance dimension, c′ represent the speed of light, and B represent the signal bandwidth.

[0106] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0107] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that: in step six, based on steps four and five, the IRadon transform is used to estimate the x-axis and y-axis coordinates of the scattering point; the specific process is as follows:

[0108] The IRadon transform is equivalent to a two-dimensional search for values ​​along the x and y axes, and the search formula is:

[0109]

[0110] In the formula, S r (r,t m S is the compensated one-dimensional distance image. IRT (x,y) represents the IRadon transform values ​​of the sine curve to be searched within the search range (since M and N are given, the numerical range of the x and y axes is finite). j and y j The two-dimensional coordinates of the peak point after applying the IRadon transform to the curve are the estimated values ​​of the scattering point corresponding to the sine curve to be searched in the x and y directions; t m This refers to the pulse signal transmission time, i.e., the slow time.

[0111] The other steps and parameters are the same as those in specific implementation methods one through seven.

[0112] The beneficial effects of the present invention are verified using the following embodiments:

[0113] Example 1:

[0114] This invention utilizes simulation data to verify the effectiveness of the Kalman filter-based three-dimensional imaging method for spin swarm targets. The spin swarm target model used in the simulation experiment is as follows: Figure 4 As shown, to simplify the model, there are 3 sub-targets, each with 2 scattering points. Scattering points belonging to the same sub-target are connected by a straight line. The spin frequencies of each target are different, and the angle between the spin axis of each sub-target and the radar line of sight is 30°. The obstruction between scattering points is not considered. The parameters of each scattering point are shown in Table 1, and the system simulation parameters are shown in Table 2.

[0115] Table 1. Spin swarm target scattering point parameters

[0116]

[0117] Table 2 Radar Simulation Parameters

[0118]

[0119] Figure 5a The image shows a one-dimensional range profile of the spin swarm target echo after range compression. Six sinusoidal curves, corresponding to six scattering points, can be identified from the image. Kalman filtering is then used to... Figure 5a The sine curve in the image is separated and extracted. Figure 5b For the reconstructed one-dimensional distance image after separating the curves, compare... Figure 5a and Figure 5b It can be seen that the two are the same. Figure 5c , Figure 5d , Figure 5e , Figure 5f , Figure 5g , Figure 5h The separated curves, as shown in these six graphs, are all sinusoidal curves, indicating no correlation errors. The spin frequency can be estimated using the EMD algorithm, according to... Figure 5aThe estimated spin frequencies of the curves from top to bottom are 7.9056 Hz, 7.8987 Hz, 6.2508 Hz, 6.2508 Hz, 5.2002 Hz, and 5.1979 Hz, respectively. Since different sub-targets have different spin frequencies, the scattering points can be classified according to their spin frequencies. That is, the first and second curves belong to the same target with a spin frequency of approximately 7.90 Hz; the third and fourth curves belong to the same target with a spin frequency of approximately 6.25 Hz; and the fifth and sixth curves belong to the same target with a spin frequency of approximately 5.20 Hz.

[0120] Figure 6a , Figure 6b , Figure 6c The two-dimensional search results of the IRadon transform show peak points at the corresponding x, y positions. These peak points allow for the determination of the estimated x-axis and y-axis coordinates of the corresponding scattering point. Since ΔR... P (t m )=x' p sin(ωt m )+y' p cos(ωt m )+z' p The result obtained by estimating using the above method is (x') p ,y' p ,z' p ), where x' p =xsin(φ),y' p =ysin(φ), z' p = zcos(φ), where φ represents the angle between the target's spin axis and the radar line of sight, and x, y, z are the actual coordinates of the scattering point. Since solving for the angle φ is not the key point in this invention, it is assumed that φ is obtained through bistatic radar measurement. Therefore, the final coordinate estimate is... in The final estimation results of the scattering point parameters are shown in Table 3:

[0121] Table 3 Estimated values ​​of scattering point parameters

[0122]

[0123] Figure 7 The figure shows a comparison between the initial model and the reconstructed model, drawn according to Tables 1 and 3. It can be seen from the figure that the two are basically overlapping, indicating that the three-dimensional imaging method of space spin swarm targets based on Kalman filtering is valid.

[0124] 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 imaging method for space spin swarm targets based on Kalman filtering, characterized in that: The specific process of the method is as follows: Step 1: Perform range compression and motion compensation processing sequentially on the echo signal of the space spin swarm target to obtain the compensated one-dimensional range profile S. r (r,t m ); Where r is the distance dimension, t m This refers to the pulse signal transmission time, i.e., the slow time. Step 2: Set an appropriate threshold for the one-dimensional distance image S r (r,t m The image is binarized, and then a skeleton is extracted from the binarized image to obtain image S. r (m,n); Where (m,n) represents the image S r The position coordinates of (m,n); m = 1, 2, ..., M, n = 1, 2, ..., N, where M is the number of sampling points in a single pulse and N is the number of pulse accumulations; Step 3: Based on image S r (m,n) determines that the number of sine curves is n1. The Kalman filter algorithm is then used to process the image S. r Extract each sine curve from (m,n); Step 4: Use the EMD algorithm to perform frequency analysis on each extracted sine curve to obtain the estimated spin frequency of the scattering point corresponding to each sine curve, and divide the scattering points with the same spin frequency into the same sub-target. Step 5: Estimate the z-axis coordinates of the corresponding scattering points based on the deviation of the center of each sine curve from the center of the dimensional axis. Step 6: Based on Steps 4 and 5, use the IRadon transform to estimate the x-axis and y-axis coordinates of the scattering point.

2. The three-dimensional imaging method for space spin swarm targets based on Kalman filtering according to claim 1, characterized in that: The instantaneous slant range expression for each scattering point of the space spin swarm target in step one is ΔR. P (t m )=x' p sin(ωt m )+y' p cos(ωt m )+z' p The instantaneous slant distance of each scattering point at each moment forms a sine curve; In the formula, x' p =xsin(φ),y' p =ysin(φ), z' p = zcos(φ), where φ represents the angle between the spin axis of the target's spin motion and the radar line of sight, and x, y, z are the actual coordinates of the scattering point.

3. The three-dimensional imaging method for space spin swarm targets based on Kalman filtering according to claim 2, characterized in that: The one-dimensional distance image S in step one r (r,t m ) contains sine curves with different amplitudes, periods, and initial phases, S r (r,t m ) is an M×N two-dimensional matrix.

4. The three-dimensional imaging method for space spin swarm targets based on Kalman filtering according to claim 3, characterized in that: In step two, setting an appropriate threshold for the one-dimensional distance image S r (r,t m The image is binarized, and then a skeleton is extracted from the binarized image to obtain image S. r (m,n); The specific process is as follows: The skeleton extraction algorithm is represented as: In the formula, This indicates that structuring element B continuously erodes the binarized image A. Second-rate, It represents the number of the last iteration before the binarized image A is eroded to an empty set.

5. The three-dimensional imaging method for space spin swarm targets based on Kalman filtering according to claim 4, characterized in that: In step three, based on image S r (m,n) determines that the number of sine curves is n1. The Kalman filter algorithm is then used to process the image S. r Extract the sine curves from (m,n); the specific process is as follows: Step 3: Based on the principle that adjacent points of a sine curve have similar slopes, extract the first 30 points of each sine curve as prior information for Kalman filtering reassociation. Based on this prior information, obtain the system state value and variance value at time k of the j-th curve. At this point, k = 31, j = 1; the specific process is as follows: Image S r The curves in (m,n) can be considered as being formed by the motion of a target point a1 along the echo number direction in a two-dimensional plane. Using a two-dimensional continuous Wiener acceleration model, the system motion state of the target point a1 at time k can be expressed as: Where, x′ k and y′ k This represents the current position of target point a1 in the coordinate system. This represents the velocity of target point a1 along the two coordinate axes. This represents the acceleration of the target point a1 along the two coordinate axes; The expressions for the measurement matrix and the observation matrix are: and k =[y′ k x′ k ] T Where H represents the measurement matrix of the two-dimensional continuous Wiener acceleration model, y k The observation matrix represents the two-dimensional continuous Wiener acceleration model, and T denotes the transpose; The Kalman filter algorithm consists of two parts: prediction and update. First, the system motion state at the current moment is predicted based on the system motion state at the previous moment, thus obtaining the predicted value of the system motion state at the current moment. The expression for the prediction stage is: in, and A represents the predicted value and variance of the system's motion state at the current moment, respectively. k-1 Let Q represent the system state transition matrix at time k. k-1 This represents the variance of the state noise, before the current system measurements are used; x k-1 P represents the mean of the actual values ​​of the system's motion state at time k-1. k-1 This represents the actual variance of the system's motion state at time k-1; Based on the predicted value of the system's motion state at the current moment and the measured value of the system's motion state at the current moment, y k Update the system state; the current measurement value of the system's motion state is y. k This is manifested in image S r The expression for updating the x-coordinate of the point with a value of 1 in the column (m,n) where n=k is the same as the x-coordinate of the point with a value of 1 is: Among them, v k S represents the estimation deviation of the measured value. k It is the variance of the new information, K k It is the filter gain, x k and P k The updated mean and variance of the system state at time k can be used to predict the system state at time k+1; H k R represents the measurement matrix of the system. k The covariance matrix representing the noise; Step 3.2: Utilize the system state value and variance value at time k-1. Make a prediction at time k to obtain the predicted value of the system state at time k. With the predicted variance Step 33: Search image S r In the matrix (m,n), the x-coordinates of all points with a value of 1 in column n=k are stored in matrix row1. If there are n2 points with a value of 1, then row1 is a matrix of size 1×n2; if there are no points with a value of 1, then row1 = [C(k-1,j)-5,C(k-1,j)-4,...,C(k-1,j)+5]. In the formula, C(k-1,j) represents the coordinate matrix of the j-th curve at time k-1 in the distance dimension; Steps 3 and 4: Using each point in row1 as an observation, predict the value at the current time. Perform an update to obtain the state value after updating the predicted value at the i-th position of the j-th curve at time k. Based on state values Generate matrix X; If the minimum value is located at position n3 in the search matrix X, then (k, row1(n3)) is the point closest to the current curve state. This point is taken as the point of the j-th curve at time k. Let S... r (k,row1(n3))=0; Step 35: If k > N, jump to step 36; otherwise, let k = k + 1 and repeat steps 32 to 35. In the formula, N represents the image S. r The number of columns in (m,n), i.e., the number of pulse accumulations; Step 36: If j > n1, stop the search and output the curve coordinate matrix C; otherwise, let j = j + 1 and repeat steps 32 to 36.

6. The three-dimensional imaging method for space spin swarm targets based on Kalman filtering according to claim 5, characterized in that: In step four, the EMD algorithm is used to perform frequency analysis on each extracted sine curve to obtain the estimated spin frequency of the scattering point corresponding to each sine curve, and scattering points with the same spin frequency are classified into the same sub-target; the specific process is as follows: Step 4: Let j = 1, s(t) = C(:,j); In the formula, j represents the j-th curve, and C(:,j) represents the position vector of the j-th curve at each time step; Step 4.2: Based on the upper envelope v1(t) and lower envelope v2(t) of the signal s(t), use the formula... Find the mean m of the upper envelope v1(t) and lower envelope v2(t) of the signal s(t); Step 43: Let h = s(t) - m, and determine whether h satisfies the conditions of the intrinsic mode function (IMF). If it does, proceed to step 44; otherwise, let s(t) = h and repeat steps 42 to 43. The condition for the intrinsic mode function (IMF) is: The absolute value of the difference between the number of extreme points and the number of zero-crossing points is less than or equal to 1, and the envelopes of the maximum and minimum points are symmetric about the time axis; Step 4: Let the intrinsic mode function IMF1 = h, perform an FFT transform on the signal IMF1, and the frequency value corresponding to the peak point on the positive half axis of the spectrum is the spin frequency w of the scattering point corresponding to the curve. j ; Steps 4 and 5: If j > n1, output the spin frequency of each curve; otherwise, let j = j + 1 and repeat steps 4 and 5.

7. The three-dimensional imaging method for space spin swarm targets based on Kalman filtering according to claim 6, characterized in that: In step five, the z-axis coordinates of the corresponding scattering points are estimated based on the deviation of the center of each sine curve from the center of the dimensional axis; the specific process is as follows: Since the position coordinates of each sine curve at each time are known, the center value of the sine curve can be obtained by averaging the position coordinates of the same sine curve at each time. The distance from the center of the dimension is half the number of samples in a single pulse; The z-axis coordinate of the scattering point corresponding to the sine curve is estimated based on the value of the deviation of the center of the sine curve from the center of the dimension. The formula for estimating the z-axis coordinate value is as follows: In the formula, r j Let z represent the mean of the envelope of the j-th curve. j Let C(i,j) represent the estimated z-axis coordinate of the scattering point corresponding to the j-th curve, and let C(i,j) represent the position vector of the j-th curve at time i. Indicates the distance from the center of the dimension. Let c represent the resolution of the distance dimension, c′ represent the speed of light, and B represent the signal bandwidth.

8. The three-dimensional imaging method for space spin swarm targets based on Kalman filtering according to claim 7, characterized in that: In step six, based on steps four and five, the IRadon transform is used to estimate the x-axis and y-axis coordinates of the scattering point; the specific process is as follows: The IRadon transform is equivalent to a two-dimensional search for values ​​along the x and y axes, and the search formula is: In the formula, S r (r,t m S is the compensated one-dimensional distance image. IRT (x,y) represents the IRadon transform values ​​of x and y within the search range for the sine curve to be searched. j and y j The two-dimensional coordinates of the peak point after applying the IRadon transform to the curve are the estimated values ​​of the scattering point corresponding to the sine curve to be searched in the x and y directions; t m This refers to the pulse signal transmission time, i.e., the slow time.

Images