A distributed radar target velocity measurement and positioning method and device based on iterative adaptive filtering
By using an iterative adaptive filtering method, accurate estimation and relocation of the radial velocity of the target in a space-based distributed multi-frequency multi-baseline radar system were achieved. This solved the problems of clutter suppression and performance degradation of moving target parameter estimation caused by terrain interferometry phase coupling, and improved the accuracy and robustness of velocity measurement and positioning.
Patent Information
- Application Number
- CN202411903678.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-23
- Publication Date
- 2025-12-26
- Estimated Expiration
- 2044-12-23
AI Technical Summary
In space-based distributed multi-frequency multi-baseline radar systems, the coupling between terrain interferometric phase and moving target radial velocity interferometric phase leads to a deterioration in clutter suppression performance and a severe deterioration in moving target parameter estimation performance. Existing technologies struggle to achieve high-precision target radial velocity estimation and relocation.
An iterative adaptive filtering method is adopted, which compensates for the elevation difference of the detected position of the moving target through frequency band separation, clutter suppression, target detection, eigenvalue decomposition, adaptive matched filtering algorithm and iterative processing, so as to achieve accurate estimation and relocation of the radial velocity of the target.
It significantly improves the accuracy of radial velocity estimation, overcomes the influence of terrain elevation coupling, reduces velocity measurement relocation error, solves the mutual coupling problem between target velocity measurement and positioning error and terrain elevation compensation error, and improves the velocity measurement and positioning accuracy and robustness of the system.
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Figure CN119689425B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of radar positioning, and particularly relates to a distributed radar target velocity positioning method and device based on iterative adaptive filtering. BACKGROUND
[0002] With the continuous progress of radar technology and the increasing demand of application, radar system realizes important tasks such as synthetic aperture radar imaging, interferometric measurement, ground moving target indication and moving target velocity positioning by increasing degrees of freedom. The space-based distributed multi-frequency multi-baseline radar system has very rich time-space-frequency domain degrees of freedom, can realize high-resolution synthetic aperture radar imaging, high-precision interferometric measurement and moving target velocity positioning, and has great application prospects.
[0003] In the past two decades, moving target radial velocity estimation and repositioning are the key contents of spaceborne radar research. A single-satellite multi-channel system can realize clutter suppression by using the coherence characteristics between channels, and further combined with an adaptive matched filter, the radial velocity of the target can be estimated. The Gaofen-3 SAR satellite in China has a dual-channel ground moving target indication (abbreviated as: GMTI) mode, which can realize high-precision moving target velocity positioning function. A multi-satellite formation system can flexibly form multiple effective baselines, which is an important way to realize better minimum detectable velocity and higher velocity positioning accuracy. At the same time, the distributed radar adopts frequency division orthogonal waveform to work in a multi-transmit multi-receive mode, which can take into account high-resolution imaging and wide-beam coverage, and maximizes system efficiency. However, for the space-based distributed multi-frequency multi-baseline radar system, the terrain interference phase introduced by the mixed baseline configuration is a key factor restricting the performance of the system GMTI processing. On the one hand, the terrain interference phase makes the spatial distribution of the clutter have an elevation dependence, the non-uniformity of the clutter is prominent, and then leads to the deterioration of the clutter suppression performance. On the other hand, the coupling problem of the terrain interference phase and the radial velocity of the moving target causes the serious deterioration of the moving target parameter estimation performance. For the non-uniformity of the clutter, the related research work has proposed a robust clutter suppression method based on terrain interference phase compensation, which will not be described here. For the moving target parameter estimation problem, the previous person has proposed a multi-channel multi-pixel joint processing method, which uses the coherence information of the target adjacent pixel pairs for height compensation, and can realize target parameter estimation and positioning function, and the velocity measurement accuracy is higher than that of the single-pixel method. However, the radial velocity of the moving target causes the imaging position to shift, and there is a high deviation between the real position of the target and the imaging position, which further leads to the deviation of the radial velocity estimation. Therefore, the previous person has proposed an interference phase decoupling strategy based on a nonlinear array structure and a method for iteratively compensating the target elevation interference phase using DEM information. However, these two methods must meet the nonlinear array system constraint condition, which brings challenges to system design and signal processing.
[0004] Therefore, how to provide a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering to achieve high-precision target radial velocity estimation and repositioning has become a technical problem to be solved at present. SUMMARY
[0005] Embodiments of the present application provide a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering, a distributed radar target velocity measurement and positioning device based on iterative adaptive filtering, an electronic device and a computer storage medium, to solve the problem of target velocity measurement and positioning deviation caused by terrain elevation interference phase coupling under the mixed baseline configuration of the distributed radar system.
[0006] In a first aspect of the embodiments of the present application, a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering is provided, comprising:
[0007] The distributed multi-frequency multi-baseline radar echo completes frequency band separation, and each frequency band echo independently completes SAR imaging;
[0008] Each frequency band independently performs SAR imaging domain clutter suppression and target detection;
[0009] According to the independent target detection results of each frequency band, estimate the target initial velocity jointly in multiple frequency bands, and take the target initial velocity as the iteration initial value;
[0010] According to the clutter suppression and the target detection results, for the central frequency band within the target neighborhood, estimate the clutter elevation directed vector using the eigenvalue decomposition method;
[0011] According to the estimation results of the clutter elevation directed vector, use the target initial velocity estimated jointly in multiple frequency bands to assist in compensating the elevation difference of the moving target detection position, and obtain the compensated target data vector;
[0012] According to the compensated target data vector, estimate the radial velocity of the moving target using the adaptive matched filter algorithm;
[0013] According to the estimation results of the radial velocity, reposition the target;
[0014] According to the difference between the repositioning results of the moving target and the estimation results of the previous time, obtain the repositioning error of the moving target, and judge the repositioning results;
[0015] According to the repositioning results of the moving target, recompensate the elevation difference of the moving target detection position, and obtain the final target radial velocity estimation and repositioning results through iteration processing.
[0016] In a second aspect of the embodiments of the present application, a distributed radar target velocity measurement and positioning device based on iterative adaptive filtering is provided, comprising:
[0017] an imaging module configured to complete band separation by distributed multi-frequency multi-baseline radar echo, and each band echo independently completes SAR imaging;
[0018] a detection module configured to independently perform SAR imaging domain clutter suppression and target detection for each band;
[0019] a first estimation module configured to jointly estimate an initial target velocity according to the independent target detection results of each band, and take the initial target velocity as an initial value of iteration;
[0020] a second estimation module configured to estimate a clutter height direction vector by using an eigenvalue decomposition method within a target neighborhood for a center band according to the clutter suppression and the target detection results;
[0021] a compensation module configured to compensate an elevation difference of a moving target detection position by using the initial target velocity estimated by the multi-band joint estimation according to an estimation result of the clutter height direction vector, to obtain a compensated target data vector;
[0022] a third estimation module configured to estimate a radial velocity of a moving target by using an adaptive matched filtering algorithm according to the compensated target data vector;
[0023] a repositioning module configured to reposition a target according to an estimation result of the radial velocity;
[0024] a decision module configured to obtain a moving target repositioning error by subtracting a previous estimation result from a repositioning result of a moving target, and make a decision on the repositioning result;
[0025] an iteration module configured to recompensate an elevation difference of a moving target detection position according to the repositioning result of the moving target, and obtain a final target radial velocity estimation and repositioning result by iteration processing.
[0026] In a third aspect of the embodiments of the present application, a computing device is provided, comprising:
[0027] a memory and a processor;
[0028] the memory is configured to store computer executable instructions, and the processor is configured to execute the computer executable instructions, so as to implement the steps of the above-mentioned distributed radar target velocity measurement and positioning method based on iterative adaptive filtering.
[0029] According to a fourth aspect of the embodiments of the present application, a computer readable storage medium is provided, which stores computer executable instructions, and the instructions are executed by a processor to implement the steps of the above-mentioned distributed radar target velocity measurement and positioning method based on iterative adaptive filtering.
[0030] The application provides a distributed radar target velocity measurement positioning method based on iterative adaptive filtering, comprising: distributed multi-frequency multi-baseline radar echo completes frequency band separation, each frequency band echo independently completes SAR imaging; each frequency band independently performs SAR imaging domain clutter suppression and target detection; according to the independent target detection results of each frequency band, the initial velocity of the target is estimated by joint multi-band, and the initial velocity of the target is taken as an iterative initial value; according to the clutter suppression and the target detection result, the eigenvalue decomposition method is used to estimate the clutter elevation orientation vector within the target neighborhood for the central frequency band; according to the estimation result of the clutter elevation orientation vector, the initial velocity of the target estimated by the joint multi-band is used to assist in compensating the elevation difference of the moving target detection position, and a compensated target data vector is obtained; according to the compensated target data vector, the radial velocity of the moving target is estimated by using an adaptive matched filtering algorithm; the target is repositioned according to the estimation result of the radial velocity; the repositioning error of the moving target is obtained by subtracting the estimation result of the previous time from the repositioning result of the moving target, and the repositioning result is judged; according to the repositioning result of the moving target, the elevation difference of the moving target detection position is recompensated, and the final target radial velocity estimation and repositioning result are obtained through iterative processing.
[0031] The distributed radar target velocity measurement positioning method based on iterative adaptive filtering provided by the application has the following beneficial effects:
[0032] 1. The application adopts an iterative adaptive matched filtering method to realize the radial velocity estimation and repositioning of the space-based distributed multi-frequency multi-baseline radar moving target. The technical means based on data estimation and target elevation orientation vector compensation can significantly improve the radial velocity estimation accuracy, and overcome the problem of reduced velocity measurement and repositioning accuracy caused by the influence of terrain elevation coupling in the prior art. The target elevation compensation and target positioning are alternately iterated, which solves the problem of mutual coupling of target velocity measurement and positioning error and terrain elevation compensation error. The signal processing process involved in the application is completely based on observation data, which overcomes the dependence on prior information in the prior art, and thus solves the problem of velocity measurement and positioning error caused by inaccurate prior information.
[0033] 2. The application obtains the initial velocity of the target by using the joint estimation method of the target Doppler deviation between the multi-band, and uses it as auxiliary information to obtain the initial value of the terrain phase compensation, which can effectively weaken the terrain elevation coupling, reduce the error of the initial velocity measurement and positioning, accelerate the iterative convergence speed, and avoid the divergence of the iterative result. The application overcomes the problem that the target detection position azimuth deviates greatly when the radial velocity of the target is large, and the iterative processing cannot converge, and the problem of low target velocity measurement and positioning accuracy in the complex geographical scene with rapidly changing terrain undulations.
[0034] The above description is only a summary of the technical solutions of the present application. In order to enable one skilled in the art to better understand the technical means of the present application, the contents of the specification can be implemented, and in order to enable the above and other purposes, characteristics and advantages of the present application to be more obvious and easy to understand, the following specific embodiments of the present application are described. BRIEF DESCRIPTION OF DRAWINGS
[0035] Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The accompanying drawings are included to provide a description of the preferred embodiments, and are not meant to limit the present application. Moreover, the same reference numerals are used throughout the various drawings to designate identical elements. In the drawings:
[0036] Figure 1 A flowchart of a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application;
[0037] Figure 2 A flowchart of another distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application;
[0038] Figure 3 is a SAR image data simulation result graph in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application;
[0039] Figure 4 is a target radial velocity estimation RMSE change curve with target radial velocity in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application;
[0040] Figure 5 is a target repositioning result of a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application;
[0041] Figure 6 is a target radial velocity estimation RMSE change curve with iteration number in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application;
[0042] Figure 7 is an airborne multi-frequency multi-baseline distributed radar measured data SAR image in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application;
[0043] Figure 8A target repositioning result map after processing of measured data of the airborne multi-frequency multi-baseline distributed radar in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application is shown in the figure;
[0044] Figure 9 A structural schematic diagram of a distributed radar target velocity measurement and positioning device based on iterative adaptive filtering provided by an embodiment of the present application is shown in the figure.
[0045] Figure 10 A structural block diagram of a computing device provided by an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION
[0046] Exemplary embodiments of the present disclosure will be described in greater detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be accurately conveyed to those skilled in the art.
[0047] In a mixed baseline configuration of a distributed radar system, the interference phase between channels simultaneously introduces the terrain interference phase and the radial velocity interference phase of a moving target, and the coupling of the two causes serious deterioration of the moving target parameter estimation performance. Therefore, the terrain interference phase of the distributed radar system is a key factor restricting the GMTI processing performance of the system.
[0048] For the problem of moving target parameter estimation of a multi-channel radar system, a multi-channel multi-pixel joint processing method is proposed by the previous person, which uses the coherence information of adjacent pixel pairs of the target for high compensation, and can realize target parameter estimation and positioning function, and the velocity measurement accuracy is higher than that of single pixel method. However, the radial velocity of the moving target causes the imaging position to shift, and there is a high deviation between the real position of the target and the imaging position, which further causes the radial velocity estimation deviation. Therefore, the previous person proposes an interference phase decoupling strategy based on a nonlinear array structure and a method of iteratively compensating the target elevation interference phase using digital terrain elevation map information. However, this method must satisfy the nonlinear array system constraint condition, which brings challenges to system design and signal processing.
[0049] In view of the problem that the interference phase coupling of the distributed radar system leads to inaccurate moving target parameter estimation, the present application provides a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering, which can realize target radial velocity estimation and repositioning in a mixed baseline configuration.
[0050] Referring to Figure 1 , Figure 1 A flowchart of a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by an embodiment of the present application is shown in the figure. Figure 1As shown, specifically comprising the following steps.
[0051] Step S102: The distributed multi-frequency multi-baseline radar echo completes frequency band separation, and each frequency band echo independently completes SAR imaging;
[0052] Step S104: Each frequency band independently performs SAR imaging domain clutter suppression and target detection;
[0053] Step S106: According to the independent target detection results of each frequency band, the initial speed of the target is estimated in a multi-frequency band, and the initial speed of the target is taken as an iteration initial value;
[0054] Step S108: According to the clutter suppression and the target detection result, for the center frequency band in the target neighborhood, the eigenvalue decomposition method is used to estimate the clutter height direction vector;
[0055] Step S110: According to the estimation result of the clutter height direction vector, the initial speed of the target estimated by the multi-frequency band joint estimation is used to assist in compensating the height difference of the moving target detection position, and a compensated target data vector is obtained;
[0056] Step S112: According to the compensated target data vector, the radial velocity of the moving target is estimated by using an adaptive matched filtering algorithm;
[0057] Step S114: According to the estimation result of the radial velocity, the target is relocated;
[0058] Step S116: According to the difference between the moving target relocation result and the previous estimation result, the moving target relocation error is obtained, and the relocation result is judged;
[0059] Step S118: According to the moving target relocation result, the height difference of the moving target detection position is recompensated, and through iterative processing, the final target radial velocity estimation and relocation result are obtained.
[0060] In the embodiments of the present application, the SAR imaging domain clutter suppression and target detection of each frequency band independently includes: under the configuration of the distributed multi-frequency multi-baseline radar system, the terrain interference phase compensation is used to eliminate the terrain dependence of the clutter; according to the interference phase compensation result, the space-time adaptive algorithm in the SAR image domain is used for clutter suppression; after the clutter suppression, the constant false alarm detection method is used for target detection.
[0061] In actual application, under the configuration of the space-based distributed multi-frequency multi-baseline radar system, for the multi-channel SAR image data of each frequency band, the terrain interference phase compensation is used to eliminate the terrain dependence of the clutter.
[0062] It should be noted that the same operation needs to be performed on each frequency band echo for target detection.
[0063] In the embodiment of the present application, the step of estimating the clutter elevation orientation vector in the target neighborhood of the center frequency band by using the eigenvalue decomposition method according to the clutter suppression result and the target detection result comprises:
[0064] The step of estimating the clutter elevation orientation vector in the target neighborhood of the center frequency band by using the eigenvalue decomposition method according to the clutter suppression result and the target detection result based on a first target calculation formula, wherein the first target calculation formula comprises:
[0065]
[0066] wherein, represents the clutter covariance matrix estimated by the target surrounding area clutter sample data; γ 1, …, γ L represents the eigenvalue, and the eigenvector corresponding to the maximum eigenvalue is the elevation interference phase orientation: v 1 … v L represents the eigenvector corresponding to the maximum eigenvalue. T represents the matrix transposition operation.
[0067] In the embodiment of the present application, the step of estimating the target initial velocity based on the independent target detection results of each frequency band and jointly estimating the target initial velocity in multiple frequency bands comprises:
[0068] The target initial velocity is obtained by using a target estimation method based on the relationship among the target velocity, the center wavelength of the frequency band and the target Doppler frequency, wherein the target initial velocity is the eigenvector with the minimum error of the Doppler shift of each frequency band.
[0069] It should be noted that the target estimation method herein can be a least square fitting method, or can be a least square fitting method, or can be replaced by other methods, and the present embodiment is not limited thereto.
[0070] The target velocity can be estimated by using a least square fitting method based on the relationship among the target velocity, the center wavelength of the frequency band and the target Doppler frequency.
[0071] f di = 2v r / λ i
[0072] In the formula, f di represents the Doppler frequency of the target in i frequency bands, v r represents the radial velocity of the target, λ i represents the wavelength of the radar signal of i frequency bands.
[0073] In the embodiment of the application, the estimated result of the clutter height direction vector is used to compensate the height difference of the detection position of the moving target by using the initial target velocity estimated by the multi-band joint estimation, to obtain a compensated target data vector, which comprises:
[0074] According to the initial target velocity information estimated by the multi-band joint estimation, a real position area of the moving target is determined;
[0075] According to the estimated result of the clutter height direction vector, a first height direction vector of the real position of the target is estimated by using the clutter samples corresponding to the surrounding area of the real position area of the moving target;
[0076] According to the first height direction vector of the real position of the target and a second height direction vector of the detection position, a height difference direction vector of the real position and the detection position of the target is calculated;
[0077] According to the height difference direction vector, a compensated data vector is obtained after phase compensation processing of the target data vector.
[0078] Specifically, according to the first height direction vector of the real position of the target and the second height direction vector of the detection position, the height difference direction vector of the real position and the detection position of the target is calculated, which comprises:
[0079] The calculation formula of the height difference direction vector of the real position and the detection position of the target is:
[0080]
[0081] Wherein, represents the height direction of the target detection position; the height direction of the target real position; symbol () * represents the conjugate operation; the symbol represents the Hadamard product.
[0082] Specifically, according to the height difference direction vector, a compensated data vector is obtained after phase compensation processing of the target data vector, which comprises:
[0083] In one embodiment of the application, the height difference direction vector of the real position and the detection position of the target is used to compensate the target data vector, and the compensated data vector is represented as:
[0084]
[0085] Wherein, represents the compensated data vector; z represents the data column vector z = [z1, z2, …, z L ]; represents the height difference direction vector of the real position and the detection position of the target.
[0086] In the embodiments of the present application, the step of estimating the radial velocity of the moving target according to the compensated target data vector by using the adaptive matched filtering algorithm comprises:
[0087] The step of estimating the radial velocity of the moving target according to the compensated target data vector by using the adaptive matched filtering algorithm comprises:
[0088]
[0089] wherein, represents the radial velocity estimation result after the road compensation processing; represents the steering vector containing only the target velocity; represents the compensated data vector.
[0090] In the embodiments of the present application, the step of repositioning the target according to the estimation result of the radial velocity comprises:
[0091]
[0092] wherein, y D represents the azimuth position corresponding to the target detection result; R T represents the target slant range; v a represents the satellite platform flight speed.
[0093] In the embodiments of the present application, the step of obtaining the moving target repositioning error by subtracting the previous estimation result from the repositioning result of the moving target, and judging the repositioning result comprises:
[0094] The step of obtaining the moving target repositioning error by subtracting the previous estimation result from the repositioning result of the moving target, and judging the repositioning result based on the judgment condition, wherein the judgment condition comprises:
[0095]
[0096] wherein, v rn represents the target radial velocity estimation result in the current iteration; v rn-1 represents the target radial velocity estimation result in the previous iteration; y o represents the road centerline position; represents the elevation difference steering vector between the target real position and the detection position in the current iteration; represents the elevation difference steering vector between the target real position and the detection position in the previous iteration; ε1, ε2 are given constants, which can be set according to the system repositioning accuracy.
[0097] In the embodiments of the present application, according to the moving target relocation result, the elevation difference of the moving target detection position is re-compensated, and the final target radial velocity estimation and relocation result are obtained through iterative processing, including:
[0098] The moving target relocation result is brought into the step of "compensating the elevation difference of the moving target detection position with the initial target velocity estimated by the multi-band joint estimation", and the target elevation difference is estimated;
[0099] Through iterative processing, the steps of "compensating the elevation difference of the moving target detection position with the initial target velocity estimated by the multi-band joint estimation", "estimating the radial velocity of the moving target by the adaptive matched filtering algorithm", "relocating the moving target by the radial velocity estimation result", "obtaining the relocation error of the moving target by subtracting the estimation result of the previous time from the relocation result of the moving target, and judging the relocation result" are repeatedly executed, and the final target radial velocity estimation and relocation result are obtained.
[0100] Referring to Figure 2 , Figure 2 Another flowchart of a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by the embodiments of the present application is shown.
[0101] As Figure 2 shown, the method specifically includes the following steps.
[0102] Step S201: inputting the original echo data of the multi-frequency multi-baseline distributed radar;
[0103] Step S202: echo band separation and SAR imaging processing;
[0104] Step S203: clutter suppression and target detection;
[0105] Step S204: joint multi-band estimation of the initial value of the target velocity;
[0106] Step S205: estimation of the elevation direction in the central frequency band;
[0107] Step S206: initial velocity assisted acquisition of the target elevation deviation;
[0108] Step S207: adaptive matched search estimation of the radial velocity;
[0109] Step S208: target relocation;
[0110] Step S209: calculation of the velocity measurement and positioning error of two iterations;
[0111] Step S210: judging whether the target velocity measurement and positioning error converges?
[0112] Step S211: if yes, output the target speed and the relocation result;
[0113] Step S212: if no, iteratively update and re-execute steps S206-S211.
[0114] The effect of the present application is further described below through space-based multi-frequency multi-simulation experiments.
[0115] 1. Simulation conditions.
[0116] In the simulation experiment of the present embodiment, a spaceborne four-star formation SAR-GMTI system is taken as an example, and the simulation parameter configuration is as follows: orbital height 700 km, satellite flight speed 7500 m / s, working wavelength 0.03 m, pulse repetition frequency 4000 Hz, the distributed radar adopts frequency division orthogonal waveform, signal bandwidth 50 MHz, frequency band interval 50 MHz, target signal-to-noise ratio 20 dB, and clutter-to-noise ratio 20 dB. The distributed radar simultaneously contains along-track baselines and vertical track baselines, the along-track baselines are 0, 40, 80 and 120 meters respectively, and the vertical baselines are 0, 30, 60 and 90 meters respectively. The detailed parameters are shown in Table 1:
[0117] Table 1 Spaceborne radar system parameters
[0118]
[0119] In the actual measurement data experiment of the present embodiment, an airborne distributed multi-baseline radar SAR-GMTI system is taken as an example, and in order to verify the performance of the multi-frequency multi-baseline distributed radar system, the echo data is divided into 3 sub-bands during signal processing. The specific system parameter configuration is shown in Table 2:
[0120] Table 2 Airborne radar system parameters
[0121]
[0122] 2. Simulation content and result analysis.
[0123] Simulation content: based on the distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided in the above embodiment one, the present embodiment respectively completes GMTI processing on space-based multi-frequency multi-baseline distributed radar simulation data and airborne multi-frequency multi-baseline distributed radar actual measurement data, so as to verify the target radial velocity estimation and relocation performance of the method of the present application.
[0124] Result analysis: please refer to Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 .
[0125] Specifically,Figure 3 is a simulation result image of a space-based multi-frequency multi-baseline distributed radar SAR image data in a distributed radar target velocity measurement positioning method based on iterative adaptive filtering provided by an embodiment of the present application, wherein Figure 3 (a) is a DEM image of a simulation scene, (b) is an original amplitude image, and (c) is an interference phase image. It can be seen from the interference phase image that the terrain elevation interference phase changes rapidly along the distance and azimuth dimensions. In this type of observation scene, the true position of the target and the position where imaging is located have a large difference in the terrain elevation interference phase, which leads to a target terrain elevation interference phase compensation error, and further affects the radial velocity estimation performance.
[0126] Figure 4 is a curve graph of target radial velocity estimation RMSE changing with target radial velocity in a space-based multi-frequency multi-baseline distributed radar target velocity measurement positioning method based on iterative adaptive filtering provided by an embodiment of the present application. The processing results of the algorithm of the present application (denoted as: I-AMF algorithm) are compared with a one-dimensional adaptive matched filter algorithm (denoted as: 1D-AMF method), a two-dimensional adaptive matched filter algorithm (denoted as: 2D-AMF method), an alternating iterative maximum likelihood estimation method (denoted as: CDML method), and a velocity estimation Cramer-Rao bound (denoted as: CRB). The simulation experiment is performed by setting point targets with different radial velocities, 100 times of Monte Carlo experiments, statistical velocity estimation root mean square error (denoted as: RMSE), and the RMSE estimated by different processing methods and the change curve of the target radial velocity are given. From Figure 4 It can be seen that the AMF method directly used for radial velocity estimation of a moving target under a mixed baseline configuration has a large error, and the greater the target velocity, the greater the RMSE value. This is because the greater the target velocity, the farther the imaging position deviates from the true position, and the greater the terrain elevation interference phase compensation error. From Figure 3 It can be seen from (a) and (c) that the greater the target azimuth position offset, the greater the corresponding terrain height difference under the experimental conditions of the present example. The simulation results prove that the terrain elevation interference phase compensation error of the target leads to a serious deterioration of the performance of the AMF radial velocity estimation method and even failure. Figure 4 In the figure, the blue solid line is the RMSE change curve obtained by using the I-AMF method of the present application, and the black solid line is the radial velocity estimation Cramer-Rao bound. From Figure 4 It can be seen that under the distributed multi-baseline array configuration, the algorithm of the present application can obviously improve the radial velocity estimation accuracy.
[0127] Figure 5is a target repositioning result of a space-based multi-frequency multi-baseline distributed radar in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by the embodiment of the application, the blue circles in the figure mark the detected target positions, and the yellow plus signs mark the real azimuth positions of the target repositioning. From Figure 5 It can be seen that the radial velocity of the moving target causes the azimuth position after imaging to deviate from the highway, and the moving target is repositioned to the highway in the same range gate as the detection position after GMTI processing. In comparison Figure 5 (a-d) It can be seen that the traditional one-dimensional and two-dimensional AMF methods are affected by the height interference phase compensation error, and the velocity measurement and repositioning performance deteriorates, and the I-AMF algorithm provided by the application can obtain higher target radial velocity estimation accuracy.
[0128] Figure 6 is a target radial velocity estimation RMSE change curve with iteration times in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by the embodiment of the application. The application adopts iterative processing to obtain the final target radial velocity estimation and repositioning result, and further reduces the influence of prior information extraction error. From Figure 6 It can be seen that the method has good robustness to road network information error, and can converge after 3 to 4 iterations.
[0129] Figure 7 is an airborne multi-frequency multi-baseline distributed radar SAR image of measured data in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by the embodiment of the application. From Figure 7 It can be seen from the amplitude of that there is a train in the scene, and the imaging position of the target moves.
[0130] Figure 8 is a target repositioning result after data processing of an airborne multi-frequency multi-baseline distributed radar in a distributed radar target velocity measurement and positioning method based on iterative adaptive filtering provided by the embodiment of the application, (a) 1D-AMF method (b) 2D-AMF method (c) CDML method (d) the method of the application. The blue circles mark the detected target positions, and the yellow plus signs mark the real azimuth positions of the target repositioning. In comparison Figure 8 The processing results of (a-d) are obviously visible, the traditional one-dimensional and two-dimensional AMF methods and the CDML method are affected by the height interference phase compensation error, and the velocity measurement and repositioning performance deteriorates, and the repositioning position obviously deviates from the road. After GMTI processing by the I-AMF method provided by the application, the target is repositioned to the rail in the same range gate as the detection position. In particular, from Figure 8As can be seen in (d), the number of target points accurately relocated on the rail is the most, and the result proves that more accurate radial velocity estimation and relocation results can be obtained after the I-AMF algorithm of the application is used.
[0131] As can be seen from the simulation experiment results, the I-AMF method of the application can effectively eliminate the influence of the height interference phase compensation error, and improve the target radial velocity estimation and relocation performance of the space-based multi-frequency multi-baseline distributed radar system in the terrain undulating scene. The application adopts iterative processing to obtain the final target radial velocity estimation and relocation result, and has good convergence and robustness.
[0132] The method provided by the application has the following beneficial effects: 1. The application adopts an iterative adaptive matched filtering method to realize the radial velocity estimation and relocation of the space-based distributed multi-frequency multi-baseline radar moving target. The technical means based on data estimation and target height direction vector compensation can significantly improve the radial velocity estimation accuracy, and overcome the problem of reduced velocity measurement and relocation accuracy caused by the influence of terrain height coupling in the prior art. The target height compensation and target positioning are alternately iterated, which solves the problem of mutual coupling of target velocity measurement and positioning error and terrain height compensation error. The signal processing process involved in the application is completely based on observation data, which overcomes the dependence on prior information in the prior art, and thus solves the problem of velocity measurement and positioning error caused by inaccurate prior information. 2. The application uses the target Doppler deviation joint estimation method to obtain the target initial velocity, and uses it as auxiliary information to obtain the initial value of the terrain phase compensation, which can effectively weaken the terrain height coupling, reduce the initial velocity measurement and positioning error, and accelerate the iterative convergence speed and avoid the divergence of the iterative result. The application overcomes the problem that the target detection position is greatly deviated when the target radial velocity is large, and the iterative processing cannot converge, and the problem that the target velocity measurement and positioning accuracy is low in the complex geographical scene with rapidly changing terrain undulation.
[0133] Corresponding to the method embodiments described above, the specification also provides an embodiment of a distributed radar target velocity measurement and positioning device based on iterative adaptive filtering, Figure 9 A structure diagram of a distributed radar target velocity measurement and positioning device based on iterative adaptive filtering provided by the application embodiment is shown in FIG. 8. Figure 9 As shown in the figure, the device comprises:
[0134] The imaging module 902 is configured to complete frequency band separation of the distributed multi-frequency multi-baseline radar echo, and each frequency band echo independently completes SAR imaging;
[0135] The detection module 904 is configured to independently perform SAR imaging domain clutter suppression and target detection for each frequency band;
[0136] The first estimation module 906 is configured to jointly estimate an initial target velocity of multiple frequency bands according to the independent target detection results of the frequency bands, and take the initial target velocity as an initial value of iteration;
[0137] The second estimation module 908 is configured to estimate a clutter height direction vector in a target neighborhood of a center frequency band by using an eigenvalue decomposition method according to the clutter suppression and the target detection result;
[0138] The compensation module 910 is configured to compensate an elevation difference of a target detection position by using the initial target velocity estimated by the multiple frequency band joint estimation according to an estimation result of the clutter height direction vector, and obtain a compensated target data vector;
[0139] The third estimation module 912 is configured to estimate a radial velocity of a moving target by using an adaptive matched filtering algorithm according to the compensated target data vector;
[0140] The repositioning module 914 is configured to reposition the target according to an estimation result of the radial velocity;
[0141] The decision module 916 is configured to obtain a repositioning error of the moving target by subtracting a previous estimation result from a repositioning result of the moving target, and make a decision on the repositioning result;
[0142] The iteration module 918 is configured to recompensate the elevation difference of the target detection position according to the repositioning result of the moving target, and obtain a final estimation result of the radial velocity of the target and a repositioning result by iteration.
[0143] In an optional embodiment, the detection module 904 is further configured to:
[0144] In a distributed multi-frequency multi-baseline radar system configuration, a terrain interference phase compensation is used to eliminate the terrain dependence of clutter;
[0145] According to an interference phase compensation result, a space-time adaptive algorithm in a SAR image domain is used for clutter suppression;
[0146] After the clutter suppression, a constant false alarm rate detection method is used for target detection.
[0147] In an optional embodiment, the second estimation module 908 is further configured to:
[0148] According to the clutter suppression and the target detection result, a clutter height direction vector in a target neighborhood of a center frequency band is estimated by using an eigenvalue decomposition method based on a first target calculation formula, wherein the first target calculation formula comprises:
[0149]
[0150] wherein, represents the clutter covariance matrix estimated by the target surrounding area clutter sample data; γ1, …, γ L represents the eigenvalue, arranged from large to small, and the eigenvector corresponding to the largest eigenvalue is the height interference phase direction: v1…v L represents the eigenvector corresponding thereto; () T represents the matrix transposition operation.
[0151] In an optional embodiment, the first estimation module 906 is further configured to:
[0152] Using the relationship between the target velocity, the frequency band center wavelength, and the target Doppler frequency, a target estimation method is used to obtain a target initial velocity, wherein the target initial velocity is the eigenvector with the minimum error of each frequency band Doppler shift.
[0153] In an optional embodiment, the compensation module 910 is further configured to:
[0154] According to the target initial velocity information estimated by the multi-band joint estimation, the real position area of the moving target is determined;
[0155] According to the estimation result of the clutter height direction vector, the first height direction vector of the target real position is estimated using the clutter samples corresponding to the surrounding area of the real position area of the moving target;
[0156] According to the first height direction vector of the target real position and the second height direction vector of the detection position, a height difference direction vector of the target real position and the detection position is calculated;
[0157] According to the height difference direction vector, a compensated data vector is obtained after phase compensation processing is performed on the target data vector.
[0158] In an optional embodiment, the third estimation module 912 is further configured to:
[0159] According to the compensated target data vector, the radial velocity of the moving target is estimated using an adaptive matched filtering algorithm, wherein the adaptive matched filtering algorithm comprises:
[0160]
[0161] wherein, represents the radial velocity estimation result after road compensation processing; represents the direction vector containing only the target velocity; represents the compensated data vector.
[0162] In an optional embodiment, the repositioning module 914 is further configured to:
[0163]
[0164] wherein y D represents the target detection result corresponding azimuth position; R T represents the target slant range; v a represents the satellite platform flight speed.
[0165] In an optional embodiment, the iteration module 916 is further configured to:
[0166] Based on the decision condition, the moving target repositioning error is obtained by subtracting the moving target repositioning result from the previous estimation result, and the repositioning result is judged, wherein the decision condition comprises:
[0167]
[0168] wherein v rn represents the target radial velocity estimation result in the current iteration; v rn-1 represents the target radial velocity estimation result in the previous iteration; y o represents the road center line position; represents the elevation difference guide vector of the target real position and the detection position in the current iteration; represents the elevation difference guide vector of the target real position and the detection position in the previous iteration; ε1, ε2 are given constants, which can be set according to the system repositioning accuracy.
[0169] The device provided by the embodiment of the application has the following beneficial effects: 1. The iterative adaptive matching filtering method is adopted to realize the radial velocity estimation and repositioning of a space-based distributed multi-frequency multi-baseline radar moving target. The technology of data-based estimation and target elevation-oriented vector compensation is adopted to significantly improve the radial velocity estimation accuracy and overcome the problem of reduced velocity repositioning accuracy caused by the influence of terrain elevation coupling; the target elevation compensation and target positioning are alternately iterated to solve the problem of mutual coupling of target velocity positioning error and terrain elevation compensation error; the signal processing process involved in the application is completely based on observation data, which overcomes the dependence on prior information in the prior art and solves the problem of velocity positioning error caused by inaccurate prior information. 2. The initial velocity of the target is obtained by using the multi-frequency band target Doppler deviation joint estimation method, and the initial value of the terrain phase compensation is obtained by using the initial velocity as auxiliary information, which can effectively reduce the terrain elevation coupling, reduce the initial velocity positioning error, accelerate the iteration convergence speed and avoid the divergence of the iteration result. The application overcomes the problem that the target detection position is greatly deviated when the radial velocity of the target is large, and the iteration processing cannot converge, and the problem that the target velocity positioning accuracy is low in a complex geographical scene with rapidly changing terrain undulations.
[0170] Each of the embodiments in the specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on the difference from other embodiments. In particular, for the distributed radar target velocity positioning device based on iterative adaptive filtering, since it is basically similar to the distributed radar target velocity positioning method based on iterative adaptive filtering, the description is relatively simple, and the relevant parts can be referred to the part of the description of the distributed radar target velocity positioning method based on iterative adaptive filtering.
[0171] Figure 10 A structural block diagram of a computing device is provided for the embodiment of the application. The components of the computing device 1000 include but are not limited to a memory 1010 and a processor 1020. The processor 1020 is connected with the memory 1010 through a bus 1030, and a database 1050 is used to save data.
[0172] The computing device 1000 also includes an access device 1040 that enables the computing device 1000 to communicate via one or more networks 1060. Examples of such networks include a public switched telephone network (PSTN), a local area network (LAN), a wide area network (WAN), a personal area network (PAN), or a combination of networks such as the Internet. The access device 1040 can include one or more of any type of network interface (for example, a network interface card (NIC)) such as a wired or wireless IEEE 802.11 wireless local area network (WLAN) wireless interface, a Worldwide Interoperability for Microwave Access (Wi-MAX) interface, an Ethernet interface, a Universal Serial Bus (USB) interface, a cellular network interface, a Bluetooth interface, Near Field Communication (NFC).
[0173] In one embodiment of the present specification, the above-mentioned components of the computing device 1000 and other components not shown in the figure can be connected to each other, for example, through a bus. It should be understood that Figure 10 In one embodiment of the present specification, the above-mentioned components of the computing device 1000 and other components not shown in the figure can be connected to each other, for example, through a bus. It should be understood that Figure 10 The computing device structure diagram shown is only for the purpose of example, and is not a limitation on the scope of the present specification. Other components can be added or replaced as needed by those skilled in the art.
[0174] Each embodiment in the present specification is described in a progressive manner, and the same or similar parts between each embodiment can be referred to each other, and each embodiment focuses on the difference from other embodiments. In particular, for the computing device embodiment, since it is basically similar to the distributed radar target velocity positioning method based on iterative adaptive filtering embodiment, the description is relatively simple, and the relevant parts can be referred to the part of the distributed radar target velocity positioning method based on iterative adaptive filtering embodiment.
[0175] An embodiment of the present specification also provides a computer readable storage medium, which stores computer executable instructions, and the computer executable instructions are executed by a processor to implement the steps of the above-mentioned distributed radar target velocity positioning method based on iterative adaptive filtering.
[0176] The various embodiments in the specification are described in progressive manner, and the same or similar parts among the various embodiments can be mutually referred to, and each of the embodiments focuses on the difference from other embodiments. In particular, the computer-readable storage medium embodiment is basically similar to the distributed radar target velocity measurement and positioning method based on iterative adaptive filtering, and thus the description is relatively simple, and the relevant parts can be referred to the description of the distributed radar target velocity measurement and positioning method based on iterative adaptive filtering.
[0177] An embodiment of the specification also provides a computer program, which, when executed in a computer, causes the computer to perform the steps of the above-mentioned distributed radar target velocity measurement and positioning method based on iterative adaptive filtering.
[0178] The various embodiments in the specification are described in progressive manner, and the same or similar parts among the various embodiments can be mutually referred to, and each of the embodiments focuses on the difference from other embodiments. In particular, the computer-readable storage medium embodiment is basically similar to the distributed radar target velocity measurement and positioning method based on iterative adaptive filtering, and thus the description is relatively simple, and the relevant parts can be referred to the description of the distributed radar target velocity measurement and positioning method based on iterative adaptive filtering.
[0179] The above describes specific embodiments of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in a different order than the order in which they are recited and still accomplish desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve the desired results. In certain implementations, multitasking and parallel processing can be advantageous.
[0180] It should be noted that the above describes specific embodiments of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in a different order than the order in which they are recited and still accomplish desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve the desired results. In certain implementations, multitasking and parallel processing can be advantageous. Secondly, those skilled in the art should know that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the embodiments of the specification.
[0181] In the above embodiments, the description of each embodiment focuses on different aspects, and the parts not described in detail in a certain embodiment can be referred to the relevant description of other embodiments.
[0182] The preferred embodiments of the present specification disclosed above are only used to help explain the present specification. Alternative embodiments do not describe all the details and limit the present application to the specific embodiments described. Obviously, many modifications and changes can be made according to the content of the embodiments of the present specification. The present specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the embodiments of the present specification, so that those skilled in the art can well understand and utilize the present specification. The present specification is limited only by the claims and their full scope and equivalents.
Claims
1. A distributed radar target velocity measurement positioning method based on iterative adaptive filtering, characterized in that, The method comprises the following steps: Each frequency band independently completes frequency band separation of distributed multi-frequency multi-baseline radar echo, and independently completes SAR imaging of each frequency band echo; Each frequency band independently performs clutter suppression and target detection in a SAR imaging domain; According to the independent target detection results of each frequency band, an initial target velocity is estimated by joint multi-band, and the initial target velocity is used as an iterative initial value; wherein the initial target velocity is a feature vector with minimum Doppler shift error of each frequency band; According to the clutter suppression and the target detection results, a clutter height direction vector is estimated in a target neighborhood of a center frequency band by using an eigenvalue decomposition method; According to the estimation result of the clutter height direction vector, a target data vector after compensation is obtained by using the initial target velocity estimated by joint multi-band to assist in compensating the height difference of the detection position of the moving target; According to the target data vector after compensation, an adaptive matched filter algorithm is used to estimate the radial velocity of the moving target; According to the estimation result of the radial velocity, the target is repositioned; According to the difference between the repositioning result of the moving target and the estimation result of the previous time, the repositioning error of the moving target is obtained, and the repositioning result is judged; According to the repositioning result of the moving target, the height difference of the detection position of the moving target is recompensated, and the final target radial velocity estimation and repositioning result are obtained through iterative processing.
2. The method of claim 1, wherein, The method that each frequency band independently performs clutter suppression and target detection in a SAR imaging domain comprises the following steps: Under the configuration of a distributed multi-frequency multi-baseline radar system, the terrain-dependent clutter is compensated and eliminated by using terrain interference phase compensation; According to the interference phase compensation result, a space-time adaptive algorithm in a SAR image domain is used for clutter suppression; After clutter suppression, a constant false alarm rate detection method is used for target detection.
3. The method of claim 1, wherein, The method that according to the clutter suppression and the target detection results, a clutter height direction vector is estimated in a target neighborhood of a center frequency band by using an eigenvalue decomposition method comprises the following steps: According to the clutter suppression and the target detection results, a clutter height direction vector is estimated in a target neighborhood of a center frequency band by using an eigenvalue decomposition method based on a first target calculation formula, wherein the first target calculation formula comprises the following steps: wherein, represents the clutter covariance matrix estimated by the target surrounding area clutter sample data; represents the eigenvalues arranged in descending order, and the eigenvector corresponding to the largest eigenvalue is the clutter height orientation vector: ; represents the eigenvector corresponding thereto; represents the matrix transposition operation.
4. The method of claim 1, wherein, The method that according to the independent target detection results of each frequency band, an initial target velocity is estimated by joint multi-band, and the initial target velocity is used as an iterative initial value comprises the following steps: By using the relationship among target velocity, frequency band center wavelength and target Doppler frequency, a target estimation method is used to obtain the initial target velocity.
5. The method of claim 1, wherein, The method that according to the estimation result of the clutter height direction vector, a target data vector after compensation is obtained by using the initial target velocity estimated by joint multi-band to assist in compensating the height difference of the detection position of the moving target comprises the following steps: According to the initial target velocity information estimated by joint multi-band, a real position area of the moving target is determined; According to the estimation result of the clutter height direction vector, a first height direction vector of the real target position is estimated by using the clutter samples corresponding to the surrounding area of the real target position area; According to the first height direction vector of the real target position and a second height direction vector of the detection position, a height difference direction vector of the real target position and the detection position is calculated; According to the elevation difference guided vector, a compensated data vector is obtained after phase compensation processing is performed on a target data vector.
6. The method of claim 1, wherein, The adaptive matched filter algorithm for estimating the radial velocity of the moving target according to the compensated target data vector comprises: The adaptive matched filter algorithm for estimating the radial velocity of the moving target according to the compensated target data vector comprises: wherein, represents a radial velocity estimation result after compensation processing; represents a guidance vector containing only a target velocity; represents a compensated target data vector.
7. The method of claim 6, wherein, The target is relocated according to the estimation result of the radial velocity, and comprises: wherein, represents the azimuth position corresponding to the target detection result; represents the slant range of the target; represents the flight speed of the satellite platform.
8. The method of claim 1, wherein, The relocation error of the moving target is obtained by subtracting the estimation result of the previous time from the relocation result of the moving target, and the relocation result is judged, and comprises: The relocation error of the moving target is obtained by subtracting the estimation result of the previous time from the relocation result of the moving target based on the judgment condition, and the relocation result is judged, wherein the judgment condition comprises: wherein, represents the target radial velocity estimation result in the current iteration; represents the target radial velocity estimation result in the last iteration; represents the elevation difference between the target real position and the detection position in the current iteration; represents the elevation difference between the target real position and the detection position in the last iteration; is a given constant, set according to the system repositioning accuracy.
9. A distributed radar target velocity measurement and localization apparatus based on iterative adaptive filtering, characterized in that, It comprises: The imaging module is configured to complete frequency band separation of distributed multi-frequency multi-baseline radar echoes, and each frequency band echo independently completes SAR imaging; The detection module is configured to independently perform SAR imaging domain clutter suppression and target detection for each frequency band; The first estimation module is configured to estimate the initial velocity of the target based on the independent target detection result of each frequency band, and the initial velocity of the target is used as the initial value of iteration; wherein the initial velocity of the target is the feature vector with the minimum Doppler shift error of each frequency band; The second estimation module is configured to estimate the clutter elevation guided vector in the target neighborhood using eigenvalue decomposition for the center frequency band based on the clutter suppression and the target detection result; The compensation module is configured to compensate the elevation difference of the moving target detection position using the initial velocity of the target estimated by the multi-band joint estimation based on the estimation result of the clutter elevation guided vector, and obtain a compensated target data vector; The third estimation module is configured to estimate the radial velocity of the moving target using the adaptive matched filter algorithm based on the compensated target data vector; The relocation module is configured to relocate the target according to the estimation result of the radial velocity; The judgment module is configured to obtain the relocation error of the moving target by subtracting the estimation result of the previous time from the relocation result of the moving target, and judge the relocation result. The iteration module is configured to re-compensate the elevation difference of the moving target detection position based on the relocation result of the moving target, and obtain the final target radial velocity estimation and relocation result through iteration processing.
10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores an information transmission implementation program, and the program is executed by the processor to implement the steps of the method in any one of claims 1-8.