Phased array radar multi-beam angle measurement method and system based on quantum white whale mechanism

Through the method based on the quantum beluga mechanism, the problem of unsatisfactory multi-beam angle measurement accuracy of phased array radar is solved. By establishing an error curve table and iterative optimization, higher angle measurement accuracy and information utilization are achieved.

CN119105018APending Publication Date: 2024-12-10CHINA ELECTRONIC TECH GRP CORP NO 38 RES INST +1

Patent Information

Application Number
CN202411269600.8
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-11
Publication Date
2024-12-10

AI Technical Summary

Technical Problem

The multi-beam angle measurement accuracy of phased array radar is affected by the beam broadening effect and low beam information utilization, resulting in unsatisfactory angle measurement.

Method used

Using a method based on the quantum beluga mechanism, the distribution information of array elements in phased array radar is determined, the normal and pitch target width are calculated, the error curve table is established, the target optimization function is constructed, and the quantum position of beluga whales is initialized and iteratively updated. Get the global optimal position and weighting process to obtain accurate angle measurement information.

Benefits of technology

The accuracy of multi-beam angle measurement of phased array radar is improved, and the information of five beams is fully utilized, which overcomes the influence of traditional methods by beam broadening effect and achieves higher angle measurement accuracy.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN119105018A_ABST
    Figure CN119105018A_ABST
Patent Text Reader

Abstract

The invention provides a phased array radar multi-beam angle measurement method and system based on a quantum whale mechanism, and relates to the field of radar signal processing, and the method comprises the steps: building an error curve table, and constructing a target optimization function; initializing the quantum position, and calculating a fitness value to obtain a global quantum position; iteratively updating the quantum position of each white whale, calculating an updated fitness function value and updating the global quantum position; and under the condition that the maximum number of iterations is reached, determining an optimal quantum position and mapping the optimal quantum position into a global optimal position so as to determine a target azimuth weighting coefficient and a target pitching weighting coefficient. According to the method, the target azimuth weighting coefficient and the target pitching weighting coefficient are rapidly obtained through the quantum white whale mechanism, and compared with a traditional method that only the maximum beam and the second maximum beam are used for table look-up in the azimuth direction and the pitching direction, information of five beams is completely utilized, and higher angle measurement precision is achieved.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a multi-beam angle measurement method and system for a phased array radar based on a quantum white whale mechanism. Background Art

[0002] Phased array radar is a phase-controlled electronically scanned array radar. It uses a large number of individually controlled small antenna units arranged into an antenna array. Each antenna unit is controlled by an independent phase-shift switch. By controlling the phase of each antenna unit, different phase beams can be synthesized. The electromagnetic waves emitted by each antenna unit of the phased array are synthesized into a nearly straight radar main lobe based on the principle of interference, while the side lobes are caused by the unevenness of each antenna unit. At the same aperture and operating wavelength, the response speed, target update rate, multi-target tracking capability, resolution, versatility, and electronic countermeasure capability of phased array radar are far superior to traditional radars.

[0003] As the core equipment in modern radar, phased array radar is crucial to accurately search, measure and track targets. Target angle measurement, as an important part of its measurement parameters, has a significant impact on the performance indicators of the entire phased array radar, especially the tracking system.

[0004] In related technologies, multi-beam angle measurement methods for phased array radars mostly use methods such as sum and difference beam amplitude ratio and adjacent beam amplitude ratio. Although such methods have good real-time performance and low computational complexity, the angle measurement accuracy will be affected by the beam broadening effect, and all beam information is not fully utilized, resulting in less than ideal angle measurement accuracy. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a phased array radar multi-beam angle measurement method and system based on the quantum Beluga mechanism, which solves the problem that the multi-beam angle measurement accuracy of the phased array radar is not ideal due to factors such as beam broadening effect and low beam information utilization.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0007] In a first aspect, an embodiment of the present application provides a multi-beam angle measurement method for a phased array radar based on a quantum white whale mechanism, the method comprising: determining the distribution information of multiple array elements in the phased array radar, calculating the normal target width and the elevation target width of the phased array radar in the uv space, and determining the beam overlap information to establish an error curve table; obtaining snapshot sampling data of the received signal, and constructing a target optimization function based on the error curve table; initializing and setting parameters for the quantum position of each white whale in the preset quantum white whale mechanism, calculating the fitness values ​​of all white whales through the constructed fitness function, and obtaining the fitness value of all white whales. local quantum position; based on the white whale optimization mechanism, iteratively update the quantum position of each white whale to obtain the target quantum position; map the target quantum position to the physical position, calculate the fitness function value of all white whales after the update, and update the global quantum position; when the maximum number of iterations is reached, determine the current global quantum position as the optimal quantum position, and transform the optimal quantum position mapping into the global optimal position; based on the global optimal position, determine the target azimuth weighting coefficient and the target pitch weighting coefficient, and weight the azimuth angle measurement results and the pitch angle measurement results respectively to obtain accurate angle measurement information.

[0008] According to the first aspect of the embodiment of the present application, in a phased array radar, multiple array elements are distributed in azimuth and elevation respectively. The aforementioned determination of the distribution information of multiple array elements in the phased array radar, calculation of the normal target width and elevation target width of the phased array radar in the uv space, and determination of the beam overlap information to establish an error curve table may specifically include the following steps: determining the first interval of adjacent array elements distributed in azimuth, and the second interval distributed in elevation; based on the first interval and the second interval, calculating the normal azimuth width and elevation beam width of the phased array radar; mapping the normal azimuth width and elevation beam width to the uv space to obtain the normal target width and elevation target width; based on the normal target width and the elevation target width, determining the error functions corresponding to the azimuth and elevation directions, and establishing an error curve table.

[0009] According to the first aspect of the embodiment of the present application, the aforementioned initialization and parameter setting of the quantum position of each beluga whale in the preset quantum beluga mechanism, the fitness values ​​of all beluga whales are calculated by the constructed fitness function, and the global quantum position is obtained, which may specifically include the following steps: setting the number of beluga whales to Q, the maximum number of iterations to G, and in the g-th iteration, the quantum position of the q-th beluga whale in the 2-dimensional search space is When g = 1, each dimension of the quantum position of all beluga whales in the first generation is initialized to a uniform random number between [0, 1]; according to the preset target mapping rule, each dimension of the quantum position of all beluga whales is mapped to the search space range to obtain the physical position of the qth beluga whale in the gth generation; the fitness value of each beluga whale is calculated according to the constructed fitness function, and the quantum position corresponding to the optimal fitness value is determined as the global quantum position corresponding to the gth generation

[0010] According to the first aspect of the embodiment of the present application, the aforementioned target mapping rule satisfies the expression:

[0011]

[0012] In the formula, is the physical location of the qth beluga whale of the gth generation, is the quantum position of the qth beluga whale of the gth generation, u o,max and u o,min are the upper and lower limits of the o-th dimension search space, q=1,2,…,Q, o=1,2; and They correspond to the azimuth weighting coefficient β and the elevation weighting coefficient α respectively.

[0013] According to the first aspect of the embodiment of the present application, the aforementioned iterative updating of the quantum position of each beluga whale based on the beluga optimization mechanism to obtain the target quantum position may specifically include the following steps: in the iterative updating process, for the qth beluga whale of the gth generation, a balance factor is generated; based on the relationship between the balance factor and the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation is determined; according to the initial quantum rotation angle, the quantum position is updated using a simulated quantum rotation gate to obtain the corresponding target quantum position;

[0014] Among them, when the balance factor is less than the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation satisfies the expression: in, is the o-th quantum position of the x-th beluga whale of the g-th generation, x is a random integer between [1,Q] except q, and is a random number uniformly distributed between [0,1];

[0015] When the balance factor is greater than or equal to the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation satisfies the expression:

[0016]

[0017] in, For the gth generation The oth-dimensional quantum position of a white whale, is a random integer between [1,Q] except q, and is a random number uniformly distributed between [0,1]. is the Levy flight coefficient, and is a random number that obeys a Gaussian distribution with a mean of 0 and a variance of 1, μ is a control parameter between [0,2], and Γ represents the Gamma function.

[0018] According to the first aspect of the embodiment of the present application, the balance factor is in, is a random number uniformly distributed between [0,1];

[0019] When the balance factor is less than the preset critical threshold, the target quantum position is Where, q=1,2,…,Q, o=1,2;

[0020] When the balance factor is greater than or equal to the preset critical threshold, the target quantum position is in, is the oth-dimensional global optimal quantum position until the gth generation; the target quantum position is

[0021] According to the first aspect of the embodiment of the present application, the aforementioned mapping of the target quantum position to a physical position, calculating the fitness function values ​​of all beluga whales after the update, and updating the global quantum position may specifically include the following steps: mapping the target quantum position to a physical position, and calculating the fitness function values ​​of all beluga whales; determining the o-th dimensional quantum rotation angle of the q-th beluga whale of the g+1th generation based on the fitness function value of the q-th beluga whale; based on the o-th dimensional quantum rotation angle of the q-th beluga whale of the g+1th generation, using a simulated quantum rotation gate to update the quantum position to obtain the quantum position of the g+1th generation; and updating the global quantum position based on the quantum position of the g+1th generation.

[0022] In the second aspect, the embodiment of the present application provides a phased array radar multi-beam angle measurement system based on the quantum white whale mechanism, the system comprising a calculation module, a construction module, a setting module, an iteration module, a first mapping module, a second mapping module and a weighting module; wherein the calculation module is used to determine the distribution information of multiple array elements in the phased array radar, calculate the normal target width and the pitch target width of the phased array radar in the uv space, and determine the beam overlap information to establish an error curve table; the construction module is used to obtain the snapshot sampling data of the received signal, and construct a target optimization function based on the error curve table; the setting module is used to initialize and set parameters for the quantum position of each white whale in the preset quantum white whale mechanism, and through the constructed fitness function The fitness values ​​of all beluga whales are calculated to obtain the global quantum position; the iteration module is used to iteratively update the quantum position of each beluga whale based on the beluga optimization mechanism to obtain the target quantum position; the first mapping module is used to map the target quantum position to a physical position, calculate the fitness function values ​​of all beluga whales after the update, and update the global quantum position; the second mapping module is used to determine the current global quantum position as the optimal quantum position when the maximum number of iterations is reached, and transform the optimal quantum position mapping into the global optimal position; the weighting module is used to determine the target azimuth weighting coefficient and the target pitch weighting coefficient based on the global optimal position, and weight the azimuth angle measurement results and the pitch angle measurement results respectively to obtain accurate angle measurement information.

[0023] In a third aspect, an embodiment of the present application provides an electronic device, comprising: a processor, a memory, and a program stored in the memory and executable on the processor, wherein when the program is executed by the processor, the phased array radar multi-beam angle measurement method based on the quantum Beluga mechanism in the aforementioned first aspect is implemented.

[0024] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium storing a program or instruction. When the program or instruction is executed by a processor, the phased array radar multi-beam angle measurement method based on the quantum Beluga mechanism in the aforementioned first aspect is implemented.

[0025] The present invention provides a phased array radar multi-beam angle measurement method and system based on the quantum white whale mechanism. Compared with the prior art, it has the following beneficial effects:

[0026] The present application calculates the normal target width and elevation target width of the phased array radar in the uv space, and establishes an error curve table in the uv space to cope with different situations where the central beam points; linear interpolation is used to reduce the quantization error when looking up the table, and weighted processing is performed on the azimuth and elevation angle measurement results respectively; the present application is based on the quantum white whale mechanism, and through initialization of quantum positions, parameter setting, calculation of fitness values ​​of all white whales, iterative update of the quantum position of each white whale, position mapping and other processing, finally when the maximum number of iterations is reached, the optimal quantum position is determined and mapped to the global optimal position, and the global optimal position is used to characterize the estimated values ​​of the azimuth weighting coefficient and the elevation weighting coefficient. The present application quickly obtains the target azimuth weighting coefficient and the target elevation weighting coefficient through the quantum white whale mechanism. Compared with the traditional method of looking up the table using only the largest beam and the second largest beam in the azimuth and elevation directions, the present application method fully utilizes the information of the five beams and has higher angle measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0028] Figure 1 It is a flow chart of a phased array radar multi-beam angle measurement method based on the quantum white whale mechanism provided in an embodiment of the present application;

[0029] Figure 2 yes Figure 1 An exemplary flow chart of S110;

[0030] Figure 3 is a schematic diagram of a normalized error curve in azimuth provided in an embodiment of the present application;

[0031] Figure 4 is a schematic diagram of a normalized error curve in pitch direction provided in an embodiment of the present application;

[0032] Figure 5 is a schematic diagram of a curve showing the relationship between the angle measurement root mean square error and the signal-to-noise ratio provided in an embodiment of the present application;

[0033] Figure 6 It is a structural schematic diagram of a phased array radar multi-beam angle measurement system based on the quantum white whale mechanism provided in an embodiment of the present application;

[0034] Figure 7 It is a structural schematic diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0037] The embodiments of the present application provide a phased array radar multi-beam angle measurement method and system based on the quantum Beluga mechanism, thereby solving the problem of unsatisfactory multi-beam angle measurement accuracy of phased array radar due to factors such as beam broadening effect and low beam information utilization.

[0038] The technical solution in the embodiment of the present application is to solve the above technical problems, and the overall idea is as follows:

[0039] Phased array radar is a phase-controlled electronically scanned array radar. It uses a large number of individually controlled small antenna units arranged into an antenna array. Each antenna unit is controlled by an independent phase-shift switch. By controlling the phase of each antenna unit, different phase beams can be synthesized. The electromagnetic waves emitted by each antenna unit of the phased array are synthesized into a nearly straight radar main lobe based on the principle of interference, while the side lobes are caused by the unevenness of each antenna unit. Phased arrays are divided into passive and active types. The passive type has lower technical performance, while the active type has excellent performance, better development prospects, and higher technical performance.

[0040] Phased array radar solves the various inherent problems of traditional mechanical scanning radar. At the same aperture and operating wavelength, the phased array's response speed, target update rate, multi-target tracking capability, resolution, versatility, electronic countermeasure capability, etc. are far superior to traditional radar. Relatively speaking, phased array radar also comes at the cost of being more expensive, requiring higher technical skills, and having greater power consumption and cooling requirements.

[0041] Phased array radar is the core equipment in modern radar. Whether it can accurately search, measure and track the target is an important basis for determining the performance indicators of a radar. Target angle measurement, as an important part of the measurement parameters of phased array radar, has a significant impact on the performance indicators of the entire phased array radar, especially the tracking system.

[0042] In the related technology, the angle can be measured by the single pulse sum-difference beam amplitude ratio method. This method forms a sum beam, an azimuth difference beam and an elevation difference beam at each wave position. The target angle is estimated by the amplitude ratio and phase difference between the difference beam and the sum beam. In the case of simultaneous multi-beam coverage in a large airspace, even if the sampling rate is low, the amount of data is huge, which is not suitable for the case of a large number of beams. Phased array radar multi-beam angle measurement methods mostly use sum-difference beam amplitude ratio and adjacent beam amplitude ratio methods. Although such methods have good real-time performance and low computational complexity, the angle measurement accuracy will be affected by the beam broadening effect, and all beam information is not fully utilized. Usually only the largest beam and the second largest beam are used, and all beam information is not fully utilized. The angle measurement accuracy needs to be further improved.

[0043] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0044] The following first introduces a phased array radar multi-beam angle measurement method based on the quantum Beluga mechanism provided in an embodiment of the present application.

[0045] The present application embodiment provides a flow chart of a phased array radar multi-beam angle measurement method based on the quantum white whale mechanism, such as Figure 1 As shown, the phased array radar multi-beam angle measurement method may include the following steps S110-S170.

[0046] S110, determining distribution information of multiple array elements in the phased array radar, calculating the normal target width and the elevation target width of the phased array radar in the uv space, and determining beam overlap information to establish an error curve table.

[0047] S120, acquiring snapshot sampling data of the received signal, and constructing a target optimization function based on the error curve table.

[0048] S130, initializing and setting parameters for the quantum position of each beluga whale in the preset quantum beluga mechanism, calculating the fitness values ​​of all beluga whales through the constructed fitness function, and obtaining the global quantum position.

[0049] S140. Iteratively update the quantum position of each beluga whale based on the beluga optimization mechanism to obtain the target quantum position.

[0050] S150, mapping the target quantum position to a physical position, calculating the fitness function values ​​of all updated beluga whales, and updating the global quantum position.

[0051] S160, when the maximum number of iterations is reached, determine the current global quantum position as the optimal quantum position, and transform the optimal quantum position mapping into the global optimal position. It can be understood that in the process of iterative updating, it is determined whether the current corresponding algebra g reaches the maximum number of iterations G. If not, set g = g + 1 and return to S140; if reached, terminate the loop iteration.

[0052] S170. Based on the global optimal position, determine the target azimuth weighting coefficient and the target pitch weighting coefficient, and perform weighted processing on the azimuth angle measurement result and the pitch angle measurement result respectively to obtain accurate angle measurement information.

[0053] The above is a specific implementation method of a phased array radar multi-beam angle measurement method based on the quantum white whale mechanism provided in an embodiment of the present application. The present application calculates the normal target width and the elevation target width of the phased array radar in the uv space, and establishes an error curve table in the uv space to cope with different situations where the center beam points in different directions; when looking up the table, linear interpolation is used to reduce the quantization error and weighted processing is performed on the azimuth angle measurement results and the elevation angle measurement results from the azimuth and elevation directions respectively.

[0054] This application is based on the quantum white whale mechanism. By initializing quantum positions, setting parameters, calculating the fitness values ​​of all white whales, iteratively updating the quantum positions of each white whale, and performing position mapping, the optimal quantum position is finally determined and mapped to the global optimal position when the maximum number of iterations is reached. The global optimal position can characterize the estimated values ​​of the azimuth weighting coefficient and the pitch weighting coefficient. This application uses the quantum white whale mechanism to quickly obtain the target azimuth weighting coefficient and the target pitch weighting coefficient. Compared with the traditional method of only using the largest beam and the second largest beam to look up the table in azimuth and pitch, the method of this application fully utilizes the information of the five beams, is not affected by the beam broadening effect, and can solve the designed azimuth and pitch weighting coefficients with high precision, and quickly and accurately obtain the estimated results.

[0055] In some embodiments, Figure 2 As shown, the aforementioned determination of distribution information of multiple array elements in the phased array radar, calculation of the normal target width and the elevation target width of the phased array radar in the uv space, and determination of beam overlap information to establish an error curve table, that is, the aforementioned S110 may specifically include the following steps:

[0056] S210: Determine a first interval between adjacent array elements distributed along the azimuth direction and a second interval between adjacent array elements distributed along the elevation direction.

[0057] S220. Based on the first interval and the second interval, calculate and obtain the normal azimuth width and elevation beam width of the phased array radar.

[0058] S230 , mapping the normal azimuth width and the elevation beam width to the uv space to obtain the normal target width and the elevation target width.

[0059] S240: Based on the normal target width and the elevation target width, determine the error functions corresponding to the azimuth and elevation directions, and establish an error curve table.

[0060] In the embodiment of the present application, it can be understood that, assuming that the phased array radar is M 1 ×M 2 dimensional and contains M array elements, the number of array elements distributed along the azimuth direction is M 1 , the number of array elements distributed along the pitch direction is M 2 , M=M 1 ×M 2 , then the normal beam width and elevation beam width of the phased array radar are θ 3dB =0.886λM 1 d 1 and Where λ is the signal wavelength, d 1 is the spacing between adjacent array elements distributed along the azimuth direction, d 2 is the spacing between adjacent array elements distributed along the pitch direction; then the normal beam width θ 3dB and elevation beamwidth Convert to uv space to get the normal target width and pitch target width, that is, u and v dimensional beam width and

[0061] It should be noted that, assuming that the azimuth beam patterns of two adjacent beams with 3dB overlap are and in, represents the elevation pointing angles of the two beams, sinc represents the normalized sinc function; assuming that the elevation beam patterns of the other two adjacent beams with 3dB overlap are and in, The error functions in azimuth and elevation are and According to the error function, a normalized error and an error curve table are established in the uv space.

[0062] In some embodiments, in the process of obtaining the snapshot sampling data of the received signal and constructing the target optimization function based on the error curve table, that is, in the aforementioned S120, the maximum number of snapshots can be defined as K, assuming that the beam pointing direction of the central receiving beam of the kth snapshot of the phased array radar is Convert it to uv space to get the uv beam pointing as Then the uv beam pointing directions of two adjacent beams in azimuth are and The uv beam pointing directions of two adjacent beams in the elevation direction are and Then the target echo signals of the center receiving beam and the azimuth and elevation receiving beam are and Among them, x(k)=a(u k ,v k )s(k)+n(k) is the kth snapshot data received by the phased array radar.

[0063] θ k and represents the azimuth and elevation angle of the target in the kth snapshot, Phased array radar Line The position coordinates of the array element where the column is located, s(k) is the received signal, n(k) is an M×1 dimensional complex Gaussian noise vector, k=1,2,…,K, j is a complex unit, T is the transpose, and H is the conjugate transpose.

[0064] Then, the errors of the center beam and the adjacent beams in elevation are calculated respectively, and we get and According to the pitch error curve table, the error corresponding to and Then calculate and Then the pitch angle of the target in the kth snapshot is estimated to be Among them, α is the weighting coefficient in the elevation direction, which is used to calculate the error between the center beam and the adjacent beam in the azimuth direction. and

[0065] According to the azimuth error curve table, the error corresponding to and Then calculate and Then the azimuth of the target in the kth snapshot is estimated to be Among them, β is the azimuth weighting coefficient, and then all the snapshot sampling data are obtained to construct the target optimization function, which satisfies the expression: Here, argmin means finding the variable with the minimum function value. Satisfies the expression: Satisfies the expression:

[0066] In some embodiments, the aforementioned initialization and parameter setting of the quantum position of each beluga whale in the preset quantum beluga mechanism, the fitness values ​​of all beluga whales are calculated by the constructed fitness function to obtain the global quantum position, that is, the aforementioned S130 may specifically include the following steps:

[0067] S310, set the number of white whales to Q, the maximum number of iterations to G, and in the g-th iteration, the quantum position of the q-th white whale in the 2-dimensional search space is When g = 1, each dimension of the quantum position of all beluga whales in the first generation is initialized to a uniform random number between [0, 1].

[0068] S320. According to a preset target mapping rule, each dimension of the quantum positions of all beluga whales is mapped into the search space to obtain the physical position of the qth beluga whale of the gth generation.

[0069] S330, calculate the fitness value of each beluga whale according to the constructed fitness function, and determine that the quantum position corresponding to the optimal fitness value is the global quantum position corresponding to the g-th generation

[0070] In one example, the fitness function of the qth beluga whale of the gth generation satisfies the expression:

[0071] The target mapping rule satisfies the expression:

[0072]

[0073] In the formula, is the physical location of the qth beluga whale of the gth generation, is the quantum position of the qth beluga whale of the gth generation, u o,max and u o,min are the upper and lower limits of the o-th dimension search space, q=1,2,…,Q, o=1,2; and They correspond to the azimuth weighting coefficient β and the elevation weighting coefficient α respectively.

[0074] In some embodiments, the aforementioned iterative update of the quantum position of each beluga whale based on the beluga optimization mechanism to obtain the target quantum position, that is, the aforementioned S140 may specifically include the following steps:

[0075] S410. During the iterative update process, a balance factor is generated for the qth beluga whale of the gth generation.

[0076] S420. Based on the relationship between the balance factor and the preset critical threshold, determine the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation.

[0077] S430, according to the initial quantum rotation angle, using a simulated quantum rotation gate to update the quantum position to obtain a corresponding target quantum position.

[0078] Among them, when the balance factor is less than the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation satisfies the expression:

[0079] in, is the o-th quantum position of the x-th beluga whale of the g-th generation, x is a random integer between [1,Q] except q, and is a random number uniformly distributed between [0,1]. When the balance factor is greater than or equal to the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation satisfies the expression:

[0080]

[0081] in, For the gth generation The oth-dimensional quantum position of a white whale, is a random integer between [1,Q] except q, and is a random number uniformly distributed between [0,1]. is the Levy flight coefficient, and is a random number that obeys a Gaussian distribution with a mean of 0 and a variance of 1, μ is a control parameter between [0,2], and Γ represents the Gamma function.

[0082] In the embodiment of the present application, it can be understood that the global optimal quantum position is updated to the g+1th generation. When the fitness function value of the qth beluga whale is not improved, the oth-dimensional quantum rotation angle of the qth beluga whale of the g+1th generation is determined as in, and is a random number uniformly distributed between [0,1]. For the gth generation The oth-dimensional quantum position of a white whale, is a random integer between [1,Q] except q. Based on the o-th quantum rotation angle of the q-th beluga whale in the g+1th generation, the quantum position can be updated using a simulated quantum rotation gate to obtain the target quantum position of the g+1th generation; the target quantum position of the g+1th generation satisfies the expression: q=1,2,…,Q,o=1,2.

[0083] In some embodiments, the balance factor is in, is a random number uniformly distributed between [0,1]; when the balance factor is less than the preset critical threshold, the target quantum position is Where q = 1, 2, ..., Q, o = 1, 2; when the balance factor is greater than or equal to the preset critical threshold, the target quantum position is in, is the oth-dimensional global optimal quantum position until the gth generation; the target quantum position is

[0084] In the embodiments of the present application, it can be understood that the present application executes a corresponding update strategy to update the quantum rotation angle based on the relationship between the balance factor and the preset critical threshold to obtain a target quantum rotation angle; then, based on the White Whale optimization mechanism, a simulated quantum rotation gate is used to update the quantum position to obtain a target quantum position; the preset critical threshold can be 0.5.

[0085] In one example, the aforementioned mapping of the target quantum position to the physical position, calculating the fitness function values ​​of all white whales after the update, and updating the global quantum position, that is, the aforementioned S150 may specifically include the following steps:

[0086] S510, mapping the target quantum position to a physical position, and calculating the fitness function values ​​of all beluga whales.

[0087] S520. Determine the o-th dimensional quantum rotation angle of the q-th beluga whale of the g+1-th generation based on the fitness function value of the q-th beluga whale.

[0088] S530. Based on the o-th dimensional quantum rotation angle of the q-th beluga whale of the g+1-th generation, the quantum position is updated using a simulated quantum rotation gate to obtain the quantum position of the g+1-th generation.

[0089] S540, updating the global quantum position based on the quantum position of the g+1th generation.

[0090] It should also be noted that the present application has verified the technical effect of the phased array radar multi-beam angle measurement method based on the quantum white whale mechanism proposed in the present application through experiments. Figure 3 , Figure 4 and Figure 5 The phased array radar multi-beam angle measurement method based on the quantum Beluga mechanism designed in this application is denoted as QBWO-MBAE, and the traditional multi-beam amplitude comparison method in the prior art is denoted as MBAC.

[0091] In the simulation experiment, the number of array elements of the phased array radar distributed along the azimuth direction is M. 1 =100, the number of array elements distributed along the pitch direction is M 2 =100, the total number of array elements is M=M 1 ×M 2 =10000, Phased Array Radar Line The position coordinates of the array element where the column is located are The azimuth and pitch angles of the target at the kth snapshot are The beam pointing direction of the center receiving beam of the kth snapshot is ω k , and is a random angle uniformly distributed between [0°, 1°], k = 1, 2, ..., K, the number of snapshots K = 120, the signal frequency is 100 MHz, and the pitch pointing angle when the table is created

[0092] The parameters of the quantum white whale mechanism are set as follows: G = 50, Q = 10, μ = 1.5, [u 1,min ,u 1,max ]=[u 2,min ,u 2,max ]=[0,1]. The simulation results show the relationship curve between the error and u, v established in the uv space, simulate the change curve of the root mean square error of angle measurement with the signal-to-noise ratio, and give the estimation results of the azimuth weighting coefficient and the pitch weighting coefficient in the absence of noise: It can be seen from the simulation diagram that the phased array radar multi-beam angle measurement method based on the quantum Beluga mechanism designed in this application shows an estimation performance that is superior to the traditional method.

[0093] In some embodiments, Figure 6 As shown, the present application provides a phased array radar multi-beam angle measurement system based on the quantum white whale mechanism, which may include the following modules:

[0094] The calculation module 610 is used to determine the distribution information of multiple array elements in the phased array radar, calculate the normal target width and the elevation target width of the phased array radar in the uv space, and determine the beam overlap information to establish an error curve table;

[0095] A construction module 620, for acquiring snapshot sampling data of the received signal and constructing a target optimization function based on the error curve table;

[0096] The setting module 630 is used to initialize and set parameters of the quantum position of each beluga whale in the preset quantum beluga mechanism, calculate the fitness value of all beluga whales through the constructed fitness function, and obtain the global quantum position;

[0097] Iteration module 640, used for iteratively updating the quantum position of each beluga whale based on the beluga optimization mechanism to obtain a target quantum position;

[0098] A first mapping module 650 is used to map the target quantum position to a physical position, calculate the fitness function values ​​of all white whales after the update, and update the global quantum position;

[0099] A second mapping module 660 is used to determine that the current global quantum position is the optimal quantum position when the maximum number of iterations is reached, and map the optimal quantum position to the global optimal position;

[0100] The weighting module 670 is used to determine the target azimuth weighting coefficient and the target pitch weighting coefficient based on the global optimal position, and perform weighted processing on the azimuth angle measurement result and the pitch angle measurement result respectively to obtain accurate angle measurement information.

[0101] According to an embodiment of the present application, any multiple modules among the calculation module 610, the construction module 620, the setting module 630, the iteration module 640, the first mapping module 650, the second mapping module 660 and the weighting module 670 can be combined into one module for implementation, or any one of the modules can be split into multiple modules. Alternatively, at least part of the functions of one or more of these modules can be combined with at least part of the functions of other modules and implemented in one module.

[0102] In some embodiments, the calculation module 610 may be specifically used to:

[0103] Determine a first interval between adjacent array elements distributed in the azimuth direction and a second interval between adjacent array elements distributed in the elevation direction;

[0104] Based on the first interval and the second interval, the normal azimuth width and the elevation beam width of the phased array radar are calculated;

[0105] Map the normal azimuth width and the elevation beam width to the uv space to obtain the normal target width and the elevation target width;

[0106] Based on the normal target width and the elevation target width, the error functions corresponding to the azimuth and elevation directions are determined, and an error curve table is established.

[0107] In some embodiments, the setting module 630 may be specifically used to:

[0108] Assume the number of beluga whales is Q, the maximum number of iterations is G, and in the g-th iteration, the quantum position of the q-th beluga whale in the 2D search space is When g = 1, each dimension of the quantum position of all white whales in the first generation is initialized to a uniform random number between [0, 1];

[0109] According to the preset target mapping rules, each dimension of the quantum positions of all beluga whales is mapped into the search space to obtain the physical position of the qth beluga whale of the gth generation;

[0110] The fitness value of each beluga whale is calculated according to the constructed fitness function, and the quantum position corresponding to the optimal fitness value is determined as the global quantum position corresponding to the gth generation.

[0111] In some embodiments, the iteration module 640 may be specifically configured to:

[0112] During the iterative update process, for the qth beluga whale in the gth generation, a balance factor is generated;

[0113] Based on the relationship between the balance factor and the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation is determined;

[0114] According to the initial quantum rotation angle, the quantum position is updated using a simulated quantum rotation gate to obtain the corresponding target quantum position.

[0115] In some embodiments, the first mapping module 650 may be specifically used to:

[0116] Map the target quantum position to the physical position and calculate the fitness function values ​​of all beluga whales;

[0117] Based on the fitness function value of the qth beluga whale, determine the oth-dimensional quantum rotation angle of the qth beluga whale of the g+1th generation;

[0118] Based on the o-th dimensional quantum rotation angle of the q-th beluga whale in the g+1th generation, the quantum position is updated using a simulated quantum rotation gate to obtain the quantum position of the g+1th generation;

[0119] The global quantum position is updated based on the quantum position of the g+1th generation.

[0120] Figure 6 Each module in the system shown has the function of implementing each step in the aforementioned phased array radar multi-beam angle measurement method based on the quantum Beluga mechanism, and can achieve its corresponding technical effect. For the sake of concise description, it will not be repeated here.

[0121] In some embodiments, the present application provides an electronic device, the structural diagram of the electronic device is as follows Figure 7 shown.

[0122] The electronic device may include a processor 710 and a memory 720 storing computer program instructions.

[0123] Specifically, the processor 710 may include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or may be configured to implement one or more integrated circuits of the embodiments of the present application.

[0124] The memory 720 may include a large capacity memory for data or instructions. By way of example and not limitation, the memory 720 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a universal serial bus (USB) drive or a combination of two or more of these. In appropriate cases, the memory 720 may include a removable or non-removable (or fixed) medium. In appropriate cases, the memory 720 may be inside or outside the integrated gateway disaster recovery device. In a specific embodiment, the memory 720 is a non-volatile solid-state memory.

[0125] The memory 720 may include a read-only memory (ROM), a random access memory (RAM), a disk storage medium device, an optical storage medium device, a flash memory device, an electrical, optical or other physical / tangible memory storage device. Therefore, generally, the memory 720 includes one or more tangible (non-transitory) computer-readable storage media (e.g., a memory device) encoded with software including computer executable instructions, and when the software is executed (e.g., by one or more processors), it can perform the operations described in any of the above-mentioned embodiments of the phased array radar multi-beam angle measurement method based on the quantum white whale mechanism.

[0126] The processor 710 reads and executes the computer program instructions stored in the memory 720 to implement any one of the phased array radar multi-beam angle measurement methods based on the quantum Beluga mechanism in the above embodiments.

[0127] In one example, the electronic device may further include a communication interface 730 and a bus 700. Figure 7 As shown, the processor 710, the memory 720, and the communication interface 730 are connected via a bus 700 and communicate with each other.

[0128] The communication interface 730 is mainly used to implement communication between various modules, devices, units and / or equipment in the embodiments of the present application.

[0129] Bus 700 includes hardware, software or both, and the parts of online data flow billing equipment are coupled to each other. For example, but not limitation, bus may include accelerated graphics port (AGP) or other graphics bus, enhanced industrial standard architecture (EISA) bus, front-end bus (FSB), hypertransport (HT) interconnection, industrial standard architecture (ISA) bus, infinite bandwidth interconnection, low pin count (LPC) bus, memory bus, micro channel architecture (MCA) bus, peripheral component interconnection (PCI) bus, PCI-Express (PCI-X) bus, serial advanced technology attachment (SATA) bus, video electronics standard association local (VLB) bus or other suitable bus or two or more of these combinations. In appropriate cases, bus 700 may include one or more buses. Although the present application embodiment describes and shows a specific bus, the present application considers any suitable bus or interconnection.

[0130] In addition, in combination with the multi-beam angle measurement method of phased array radar based on the quantum white whale mechanism in the above embodiment, the embodiment of the present application can provide a computer storage medium for implementation. The computer storage medium stores computer program instructions; when the computer program instructions are executed by the processor, any one of the multi-beam angle measurement methods of phased array radar based on the quantum white whale mechanism in the above embodiment is implemented.

[0131] It should be clear that the present application is not limited to the specific configuration and processing described above and shown in the figures. For the sake of simplicity, a detailed description of the known method is omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present application is not limited to the specific steps described and shown, and those skilled in the art can make various changes, modifications and additions, or change the order between the steps after understanding the spirit of the present application.

[0132] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, it can be, for example, an electronic circuit, an application specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present application are programs or code segments that are used to perform the required tasks. The program or code segment can be stored in a machine-readable medium, or transmitted on a transmission medium or a communication link by a data signal carried in a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, optical fiber media, radio frequency (RF) links, etc. The code segment can be downloaded via a computer network such as the Internet, an intranet, etc.

[0133] It should also be noted that the exemplary embodiments mentioned in this application describe some methods or systems based on a series of steps or devices. However, this application is not limited to the order of the above steps, that is, the steps can be performed in the order mentioned in the embodiment, or in a different order from the embodiment, or several steps can be performed simultaneously.

[0134] Aspects of the present disclosure are described above with reference to the flowchart and / or block diagram of the method, device (system) and computer program product according to the embodiment of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device to produce a machine so that these instructions executed by the processor of the computer or other programmable data processing device enable the implementation of the function / action specified in one or more boxes of the flowchart and / or block diagram. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field programmable logic circuit. It can also be understood that each box in the block diagram and / or flowchart and the combination of boxes in the block diagram and / or flowchart can also be implemented by dedicated hardware that performs a specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0135] In summary, compared with the prior art, this application has the following beneficial effects:

[0136] 1. This application calculates the normal target width and elevation target width of the phased array radar in the uv space, and establishes an error curve table in the uv space to cope with different situations where the central beam points. When looking up the table, linear interpolation is used to reduce the quantization error, and the azimuth angle measurement results and the elevation angle measurement results can be weighted in the azimuth and elevation directions respectively.

[0137] 2. Based on the quantum Beluga mechanism, the present application can quickly obtain the target azimuth weighting coefficient and the target elevation weighting coefficient, and then perform weighted processing on the azimuth angle measurement results and the elevation angle measurement results respectively, so as to quickly and accurately obtain the estimation results; compared with the traditional method of only using the largest beam and the second largest beam to look up the table in the azimuth and elevation directions, the method of the present application fully utilizes the information of the five beams and has higher angle measurement accuracy.

[0138] 3. This application proves the effectiveness of the proposed phased array radar multi-beam angle measurement method and system based on the quantum Beluga mechanism through simulation experiments, overcoming the problems of traditional methods being affected by the beam broadening effect and not making full use of all beam information, and has higher accuracy than traditional solution methods.

[0139] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A phased array radar multi-beam angle measurement method based on quantum white whale mechanism, characterized in that: include: Determine the distribution information of multiple array elements in the phased array radar, calculate the normal target width and the elevation target width of the phased array radar in the uv space, and determine the beam overlap information to establish an error curve table; Acquire snapshot sampling data of the received signal, and construct a target optimization function based on the error curve table; Initialize the quantum position and set the parameters of each beluga whale in the preset quantum beluga mechanism, calculate the fitness values ​​of all beluga whales through the constructed fitness function, and obtain the global quantum position; Iteratively update the quantum position of each beluga based on the beluga optimization mechanism to obtain the target quantum position; Mapping the target quantum position to a physical position, calculating the fitness function values ​​of all beluga whales after the update, and updating the global quantum position; When the maximum number of iterations is reached, determining the current global quantum position as the optimal quantum position, and mapping and transforming the optimal quantum position into a global optimal position; Based on the global optimal position, a target azimuth weighting coefficient and a target pitch weighting coefficient are determined, and weighted processing is performed on the azimuth angle measurement result and the pitch angle measurement result respectively to obtain accurate angle measurement information.

2. The phased array radar multi-beam angle measurement method based on the quantum white whale mechanism according to claim 1, characterized in that: In the phased array radar, the plurality of array elements are distributed in azimuth and elevation directions respectively; The determining of distribution information of a plurality of array elements in the phased array radar, calculating the normal target width and the elevation target width of the phased array radar in the uv space, and determining beam overlap information to establish an error curve table includes: Determine a first interval between adjacent array elements distributed along the azimuth direction and a second interval between adjacent array elements distributed along the elevation direction; Based on the first interval and the second interval, a normal azimuth width and an elevation beam width of the phased array radar are calculated; Mapping the normal azimuth width and the elevation beam width to uv space to obtain a normal target width and an elevation target width; Based on the normal target width and the elevation target width, error functions corresponding to the azimuth and elevation directions are determined, and an error curve table is established.

3. The phased array radar multi-beam angle measurement method based on the quantum white whale mechanism as claimed in claim 1, characterized in that: The quantum position of each beluga whale in the preset quantum beluga mechanism is initialized and parameters are set, and the fitness values ​​of all beluga whales are calculated by constructing a fitness function to obtain the global quantum position, including: Assume the number of beluga whales is Q, the maximum number of iterations is G, and in the g-th iteration, the quantum position of the q-th beluga whale in the 2D search space is When g = 1, each dimension of the quantum position of all white whales in the first generation is initialized to a uniform random number between [0, 1]; According to the preset target mapping rules, each dimension of the quantum positions of all beluga whales is mapped into the search space to obtain the physical position of the qth beluga whale of the gth generation; The fitness value of each beluga whale is calculated according to the constructed fitness function, and the quantum position corresponding to the optimal fitness value is determined as the global quantum position corresponding to the gth generation.

4. The phased array radar multi-beam angle measurement method based on the quantum white whale mechanism as claimed in claim 3, characterized in that: The target mapping rule satisfies the expression: In the formula, is the physical location of the qth beluga whale of the gth generation, is the quantum position of the qth beluga whale of the gth generation, u o,max and u o,min are the upper and lower limits of the o-th dimension search space, q=1,2,…,Q, o=1,2; and They correspond to the azimuth weighting coefficient β and the elevation weighting coefficient α respectively.

5. The phased array radar multi-beam angle measurement method based on the quantum white whale mechanism as claimed in claim 3, characterized in that: The iterative updating of the quantum position of each beluga whale based on the beluga optimization mechanism to obtain the target quantum position includes: During the iterative update process, for the qth beluga whale in the gth generation, a balance factor is generated; Based on the relationship between the balance factor and the preset critical threshold, determining the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation; According to the initial quantum rotation angle, the quantum position is updated using a simulated quantum rotation gate to obtain a corresponding target quantum position; Wherein, when the balance factor is less than the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation satisfies the expression: in, is the o-th quantum position of the x-th beluga whale of the g-th generation, x is a random integer between [1,Q] except q, and is a random number uniformly distributed between [0,1]; When the balance factor is greater than or equal to the preset critical threshold, the target quantum rotation angle of the oth dimension of the qth beluga whale of the g+1th generation satisfies the expression: in, For the g generation The oth-dimensional quantum position of a white whale, is a random integer between [1,Q] except q, and is a random number uniformly distributed between [0,1]. is the Levy flight coefficient, and is a random number that obeys a Gaussian distribution with a mean of 0 and a variance of 1, μ is a control parameter between [0,2], and Γ represents the Gamma function.

6. The phased array radar multi-beam angle measurement method based on the quantum white whale mechanism as claimed in claim 5, characterized in that: The balance factor is in, is a random number uniformly distributed between [0,1]; When the balance factor is less than the preset critical threshold, the target quantum position is Where, q=1,2,…,Q, o=1,2; When the balance factor is greater than or equal to the preset critical threshold, the target quantum position is in, is the o-th dimension global optimal quantum position until the g-th generation; the target quantum position is 7. The phased array radar multi-beam angle measurement method based on the quantum white whale mechanism according to claim 1, characterized in that: The mapping of the target quantum position to a physical position, calculating the fitness function values ​​of all white whales after the update, and updating the global quantum position include: Mapping the target quantum position to a physical position, and calculating the fitness function values ​​of all beluga whales; Based on the fitness function value of the qth beluga whale, determine the oth-dimensional quantum rotation angle of the qth beluga whale of the g+1th generation; Based on the o-th dimensional quantum rotation angle of the q-th beluga whale of the g+1-th generation, the quantum position is updated using a simulated quantum rotation gate to obtain the quantum position of the g+1-th generation; The global quantum position is updated based on the quantum position of the g+1th generation.

8. A phased array radar multi-beam angle measurement system based on the quantum white whale mechanism, characterized in that: include: A calculation module, used to determine the distribution information of multiple array elements in the phased array radar, calculate the normal target width and the elevation target width of the phased array radar in the uv space, and determine the beam overlap information to establish an error curve table; A construction module, used to obtain snapshot sampling data of the received signal and construct a target optimization function based on the error curve table; The setting module is used to initialize and set parameters of the quantum position of each beluga whale in the preset quantum beluga mechanism, calculate the fitness values ​​of all beluga whales through the constructed fitness function, and obtain the global quantum position; An iteration module is used to iteratively update the quantum position of each beluga whale based on the beluga optimization mechanism to obtain the target quantum position; A first mapping module is used to map the target quantum position to a physical position, calculate the fitness function values ​​of all beluga whales after the update, and update the global quantum position; A second mapping module is used to determine that the current global quantum position is the optimal quantum position when the maximum number of iterations is reached, and map the optimal quantum position to a global optimal position; The weighting module is used to determine the target azimuth weighting coefficient and the target pitch weighting coefficient based on the global optimal position, and perform weighted processing on the azimuth angle measurement result and the pitch angle measurement result respectively to obtain accurate angle measurement information.

9. An electronic device, characterized in that: include: A processor, a memory, and a program stored in the memory and executable on the processor, wherein when the program is executed by the processor, the multi-beam angle measurement method for phased array radar based on the quantum white whale mechanism as described in any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a program or instruction, and when the program or instruction is executed by the processor, the phased array radar multi-beam angle measurement method based on the quantum white whale mechanism as described in any one of claims 1 to 7 is implemented.

Citation Information

Patent Citations

  • Optimum design method for double-constraint lobe array antenna based on cosecant square and combined phases

    CN108920767A

  • Near field source direction finding method based on quantum whale optimization mechanism

    CN108983142A

  • Antenna array element sparse method and device, electronic equipment and storage medium

    CN117933094A

  • Positioning method and system, node, storage medium and product

    CN118382057A

  • Ultrasonic focusing method and system based on quantum whale mechanism

    CN119838165A

Cited By

  • Angle measurement method suitable for radar with any subarray architecture

    CN120468765A