CN115421157B - Method and device for constructing radar array based on undirected adjacency graph - Google Patents

Method and device for constructing radar array based on undirected adjacency graph Download PDF

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CN115421157B
CN115421157B CN202211298872.1A CN202211298872A CN115421157B CN 115421157 B CN115421157 B CN 115421157B CN 202211298872 A CN202211298872 A CN 202211298872A CN 115421157 B CN115421157 B CN 115421157B
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array
sub
radar
virtual
elements
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CN115421157A (en
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李强
龙天尧
黄磊
周汉飞
王伟
梁磊
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Shenzhen University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/88—Lidar systems specially adapted for specific applications
    • G01S17/89—Lidar systems specially adapted for specific applications for mapping or imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention relates to the technical field of radars, in particular to a method and a device for constructing a radar array based on a non-directional adjacency graph. The method comprises the steps of firstly simulating a receiving signal of the radar, then constructing a virtual array by using the simulated receiving signal of the radar, then processing the virtual array to obtain an undirected adjacent matrix, and judging whether undirected graphs of the undirected adjacent matrix are communicated or not, wherein the undirected graphs are communicated to show that the position of a hollow array element in the virtual array can be used for placing the radar. If the undirected graph is connected, the position of the hollow array element in the virtual array is suitable for placing the radar. And obtaining a subarray which is formed by the minimum array elements and can enable the undirected graph to be non-connected through traversal, and replacing the hollow array elements in the array to be supplemented with the non-hollow array elements to obtain the final target radar array. The invention can balance the problem between the aperture of the radar array and the accuracy of the reference data provided by the radar array.

Description

Method and device for constructing radar array based on undirected adjacency graph
Technical Field
The invention relates to the technical field of radars, in particular to a method and a device for constructing a radar array based on a non-directional adjacency graph.
Background
The realization of obstacle avoidance of unmanned driving, autonomous robots and unmanned aerial vehicles all requires three-dimensional modeling of external complex environments. The unmanned system mainly relies on a laser radar point cloud image to construct an environment three-dimensional model. The laser radar has accurate distance measurement and high spatial resolution, and is an ideal environment sensor for automatic driving. However, as the wavelength range of the laser radar is in the nm level, when the laser radar encounters dust in the air, macromolecular aerosols such as water vapor and raindrops can generate refraction or scattering phenomena, and the laser radar cannot be used in severe weather such as rainstorm, snowstorm, haze and sand storm. In order to reduce the influence of the above natural phenomena on the lidar so that the lidar can provide necessary reference data for the unmanned technology, the prior art often adopts increasing the number of radars to increase the accuracy of the reference data provided by the array of radars. For example, an array of radars can provide reference data of the angle of arrival for the unmanned technology, and the resolution of the angle of arrival is larger when the aperture (the aperture is the size of the space occupied by the radars in the array) of the radar array is larger, so that the higher the resolution of the angle of arrival is, the safer the unmanned technology can perform. Conversely, the smaller the aperture of the radar array, the greater the resolution of the angle of arrival. And the radar array with large aperture increases the difficulty of using the radar. Therefore, it is necessary to balance the resolution of the radar array aperture and the angle of arrival, i.e. to improve the resolution of the angle of arrival (reference data) under the premise of limited radar array aperture, or to make a compromise between the radar array aperture and the quality of the reference data provided by the radar array difficult.
In summary, the prior art is difficult to balance the problem of the radar array aperture and the quality of the reference data provided by the radar array.
Thus, there is a need for improvements and enhancements in the art.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method and a device for constructing a radar array based on a non-directional adjacency graph, and solves the problem that in the prior art, the aperture of the radar array and the quality of reference data provided by the radar array are difficult to balance.
In order to achieve the purpose, the invention adopts the following technical scheme:
in a first aspect, the present invention provides a method for constructing a radar array based on an undirected adjacency graph, wherein the method includes:
generating a Hankel matrix by taking array elements in a virtual array as elements in the matrix and taking virtual receiving signals corresponding to the array elements as element values in the matrix, wherein the array elements are used for representing a radar, and the virtual receiving signals are used for simulating receiving signals of the radar;
setting a non-zero element value in the Hankel matrix as one and a zero element value as zero to obtain an undirected adjacency matrix;
when an undirected graph corresponding to the undirected adjacency matrix has connectivity, selecting the array elements from the virtual array to form a sub-array, and taking the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as an array to be supplemented;
and according to a convex optimization algorithm, filling the cavity array elements covered by the array to be filled with non-cavity array elements to obtain a target radar array, wherein the positions of the non-cavity array elements in the array to be filled before filling are used for placing the radar, and the positions of the cavity array elements in the array to be filled before filling are not placed with the radar.
In one implementation, the virtual array and the method for generating the virtual received signal include:
respectively endowing each array element in two preset arrays with simulation receiving signals, wherein the array elements are used for representing a radar, and the simulation receiving signals are used for simulating receiving signals of the radar;
and subtracting the array elements in the two preset arrays in pairs to obtain virtual arrays and virtual receiving signals corresponding to the virtual arrays, wherein the subtraction is to subtract the position of the array element of one of the preset arrays in one of the preset arrays by the position of the array element of the other preset array in the other preset array, and subtract the simulated receiving signals of the array elements of the one of the preset arrays by the simulated receiving signals of the array elements of the other preset array.
In one implementation manner, the total number of the array elements covered by one of the two preset arrays and the total number of the array elements covered by the other preset array are mutually prime numbers, where the array element pitch of one of the preset arrays is equal to the total number of the array elements of the other preset array multiplied by a wavelength, the array element pitch of the other preset array is equal to the total number of the array elements of one of the preset arrays multiplied by a wavelength, and the wavelength is a wavelength of a signal to be received by the radar.
In one implementation, the method for generating the simulated received signal includes:
setting a pitching angle when the radar receives a transmission signal of a signal source, wherein the signal source is used for transmitting the signal to the radar;
setting noise information of the environment where the radar is located;
and generating the simulation receiving signal according to the pitching angle, the transmitting signal, the noise information and the position of the array element in the preset array.
In one implementation, when an undirected graph corresponding to the undirected adjacency matrix has connectivity, selecting the array elements from the virtual array to form a sub-array, and using the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as an array to be complemented includes:
forming sub-arrays by using the array elements at the head end and the tail end of the virtual array, and if the undirected graphs corresponding to the sub-arrays have connectivity, adding the array elements except the array elements at the head end and the tail end to the sub-arrays one by one until the undirected graphs corresponding to the sub-arrays after the array elements are added have non-connectivity to obtain target sub-arrays;
and obtaining an array to be compensated according to the target subarray.
In an implementation manner, the forming a sub-array with the array elements at the head and the tail of the virtual array, and if the undirected graph corresponding to the sub-array has connectivity, adding the array elements except the array elements at the head and the tail to the sub-array one by one until the undirected graph corresponding to the sub-array after the addition of the array elements has non-connectivity, to obtain a target sub-array includes:
forming a first sub-array in the sub-arrays by using the array elements at the head end and the tail end of the virtual array;
forming the array elements except the array elements at the head end and the tail end in the virtual array into a second sub array in the sub arrays, wherein the second sub array and the first sub array are relatively prime arrays;
if the undirected graphs corresponding to the virtual sub-arrays formed by the first sub-array and the second sub-array have connectivity, the array elements of the virtual arrays are respectively added to the second sub-array and the first sub-array one by one until the undirected graphs corresponding to the virtual sub-arrays formed by the second sub-array and the first sub-array after the array elements are added have non-connectivity, and the second sub-array and the first sub-array after the array elements are added are taken as target sub-arrays.
In one implementation, the method for completing a hole array element covered by an array to be completed as a non-hole array element according to a convex optimization algorithm to obtain a target radar array, where a position of the non-hole array element in the array to be completed before completion is used for placing the radar, and a position of the hole array element in the array to be completed before completion is not placed with the radar includes:
adding unknown parameters to the non-cavity array elements in the array to be compensated to obtain virtual non-cavity array elements, wherein the unknown parameters are used for representing the cavity array elements in the array to be compensated;
generating the Hankel matrix corresponding to the virtual non-cavity array element according to the position of the virtual non-cavity array element in the array to be compensated and the simulation received signal corresponding to the virtual non-cavity array element;
generating an estimation matrix corresponding to the virtual non-hollow array element according to the Hankel matrix corresponding to the virtual non-hollow array element;
establishing a constraint condition according to the F norm of the difference between the estimation matrix and the Hankel matrix corresponding to the virtual non-cavity array element being less than a set value;
calculating a parameter value corresponding to the unknown parameter when the kernel norm of the estimation matrix takes the minimum value under the constraint condition;
obtaining the cavity array elements to be completed according to the parameter values;
and placing the radar at the position of the cavity array element to be completed in the array to be completed to obtain a target radar array.
In a second aspect, an embodiment of the present invention further provides an apparatus for constructing a radar array based on an undirected adjacency graph, where the apparatus includes the following components:
the device comprises a Hankel matrix generation module, a receiving module and a processing module, wherein the Hankel matrix generation module is used for generating a Hankel matrix by taking array elements in a virtual array as elements in the matrix and taking virtual receiving signals corresponding to the array elements as element values in the matrix, the array elements are used for representing a radar, and the virtual receiving signals are used for simulating receiving signals of the radar;
the undirected adjacency matrix construction module is used for setting a non-zero element value in the Hankel matrix as one and a zero element value as zero to obtain an undirected adjacency matrix;
a to-be-supplemented array construction module, configured to select the array elements from the virtual array to form a sub-array when an undirected graph corresponding to the undirected adjacency matrix has connectivity, and use the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as a to-be-supplemented array;
and the array element completion module is used for completing the cavity array elements covered by the array to be completed into non-cavity array elements according to a convex optimization algorithm to obtain a target radar array, the positions of the non-cavity array elements in the array to be completed before completion are used for placing the radars, and the positions of the cavity array elements in the array to be completed before completion are not placed with the radars.
In a third aspect, an embodiment of the present invention further provides a terminal device, where the terminal device includes a memory, a processor, and a program stored in the memory and executable on the processor and used for constructing a radar array based on a directed adjacency graph, and when the processor executes the program for constructing a radar array based on a directed adjacency graph, the steps of the method for constructing a radar array based on a directed adjacency graph are implemented.
In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, where a program for constructing a radar array based on a non-directional adjacency graph is stored on the computer-readable storage medium, and when the program for constructing a radar array based on a non-directional adjacency graph is executed by a processor, the steps of the method for constructing a radar array based on a non-directional adjacency graph described above are implemented.
Has the advantages that: the method comprises the steps of firstly simulating a receiving signal of a radar, then constructing a virtual array by using the simulated receiving signal of the radar, then processing the virtual array to obtain an undirected adjacent matrix, and judging whether undirected graphs of the undirected adjacent matrix are communicated, wherein the undirected graphs are communicated to show that the position of a cavity array element in the virtual array can be used for placing the radar, namely the cavity array element is expanded into a non-cavity array element. If the undirected graph is connected, the position of the hollow array element in the virtual array is suitable for placing the radar. Traversing the subarrays of the virtual arrays communicated by the undirected graph, finding the subarrays (to-be-complemented arrays) which can make the undirected graph be non-communicated and consist of the minimum array elements, and then replacing the hollow array elements in the to-be-complemented arrays with the non-hollow array elements to obtain the final target radar array. The invention adopts a one-by-one traversal method to obtain the minimum radar number (the radar number corresponds to the radar aperture) required by the array when the undirected graph is not connected, and the radar array corresponding to the undirected graph can provide accurate reference data when the undirected graph is not connected. Therefore, the invention can balance the problem between the aperture of the radar array and the accuracy of the reference data provided by the radar array, namely, the invention can provide the reference data with the precision under the condition that the aperture of the radar array is smaller.
Drawings
FIG. 1 is an overall flow diagram of the present invention;
FIG. 2 is a schematic diagram of a virtual array in an embodiment of the invention;
FIG. 3 is a co-prime array in an embodiment of the invention;
FIG. 4 is a schematic illustration of a non-communication in an embodiment of the present invention;
FIG. 5 is a schematic illustration of connectivity in an embodiment of the present invention;
FIG. 6 is a schematic diagram of the physical array element positions of the MCCA in the embodiment of the present invention;
FIG. 7 is a schematic diagram of a virtual array element position according to an embodiment of the present invention;
FIG. 8 is a graph comparing FFT spatial spectra in an embodiment of the present invention;
FIG. 9 is a graph illustrating deviation from a noise-free full aperture received signal in accordance with an embodiment of the present invention;
fig. 10 is a schematic block diagram of an internal structure of a terminal device according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is clearly and completely described below by combining the embodiment and the attached drawings of the specification. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Research shows that the realization of obstacle avoidance of unmanned driving, autonomous robots and unmanned aerial vehicles requires three-dimensional modeling of external complex environments. The unmanned system mainly relies on a laser radar point cloud image to construct an environment three-dimensional model. The laser radar has accurate distance measurement and high spatial resolution, and is an ideal environment sensor for automatic driving. However, as the wavelength range of the laser radar is in the nm level, when the laser radar encounters dust in the air, macromolecular aerosols such as water vapor and raindrops can generate refraction or scattering phenomena, and the laser radar cannot be used in severe weather such as rainstorm, snowstorm, haze and sand storm. In order to reduce the influence of the above natural phenomena on the lidar so that the lidar can provide necessary reference data for the unmanned technology, the prior art often adopts the method of increasing the number of radars so as to increase the accuracy of the reference data provided by the array of radars. For example, an array of radars can provide reference data of the angle of arrival for the unmanned technology, and the resolution of the angle of arrival is larger when the aperture (the aperture is the size of the space occupied by the radars in the array) of the radar array is larger, so that the higher the resolution of the angle of arrival is, the safer the unmanned technology can perform. Conversely, the smaller the aperture of the radar array, the greater the resolution of the angle of arrival. And the radar array with large aperture increases the difficulty of using the radar. Therefore, it is necessary to equalize the radar array aperture and the resolution of the angle of arrival, i.e. to improve the resolution of the angle of arrival (reference data) with a limited radar array aperture.
In order to solve the technical problems, the invention provides a method and a device for constructing a radar array based on a non-directional adjacency graph, and solves the problem that in the prior art, the aperture of the radar array and the accuracy of reference data provided by the radar array are difficult to balance. When the method is implemented specifically, a virtual array is established by using a radar and a virtual receiving signal thereof, then the virtual array is converted into a Hankel matrix, the Hankel matrix is converted into an undirected adjacent matrix, whether an undirected graph of the undirected adjacent matrix has connectivity is judged, if the undirected graph has connectivity, array elements are selected from the virtual array to form a sub-array, the sub-array is the minimum array element required by enabling the undirected graph corresponding to the sub-array to be non-connected, and finally, the screened hole array elements serving as an array to be supplemented are supplemented to be non-hole array elements. The embodiment can take account of the problem between the radar array aperture and the accuracy of the reference data provided by the radar array.
For example, in the virtual array shown in fig. 2, the position of each solid circle in fig. 2 represents that radar should be placed at the position, and each dotted circle represents that radar is not placed at the position temporarily. Generating a Hankel matrix according to each radar position in the virtual array and a radar signal, then converting the Hankel matrix into a non-directional adjacent matrix, judging whether the non-directional adjacent matrix has connectivity, when the non-directional adjacent matrix has connectivity, selecting radar to form a sub-array from the virtual array of FIG. 2, sequentially converting each sub-array into a corresponding Hankel matrix, a non-directional adjacent matrix and a non-directional graph, if the sub-array A formed by 20 array elements of P-12 (P represents the position), P-11, P-10, P-7 to P7, P11 and P12 in FIG. 2 is a non-connected graph, and if the number of the array elements contained in the sub-array corresponding to other non-connected graphs is more than 20, the sub-array A is a completeable array (to-be-completed array), finally completing the radar at P-11 in the sub-array A (adding a radar at the position) through a convex optimization algorithm, and finally forming 19 radar positions by the radar array of P-12, P-11, P-10, P-7 to P-7 and P12 (without P11) and the radar signal) to form a target.
Exemplary method
The method for constructing the radar array based on the undirected adjacency graph can be applied to terminal equipment, and the terminal equipment can be terminal products with a computing function, such as a computer and the like. In this embodiment, as shown in fig. 1, the method for constructing a radar array based on a non-directional adjacency graph specifically includes the following steps:
s100, generating a Hankel matrix by taking array elements in a virtual array as elements in the matrix and taking virtual receiving signals corresponding to the array elements as element values in the matrix, wherein the array elements are used for representing a radar, and the virtual receiving signals are used for simulating receiving signals of the radar.
The virtual array in this embodiment is composed of non-cavity array elements and cavity array elements, the cavity array elements are without radars, and the non-cavity array elements are with radars. And simulating a real radar array by using the virtual array, and constructing the real radar array by establishing the virtual array. The radar array constructed by the embodiment can provide high-quality reference data (DOA resolution).
In one embodiment, the method for constructing the virtual array and the simulation received signal includes the following steps S101 and S102:
and S101, respectively endowing each array element in the two preset arrays with simulation receiving signals, wherein the array elements are used for representing the radar, and the simulation receiving signals are used for simulating the receiving signals of the radar.
As shown in FIG. 3, the number of array elements of the first predetermined array is
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The number of array elements of the second predetermined array is ^ 5>
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And
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are prime numbers of each other, and the spacing between the array elements in the first predetermined array is ^ greater than or equal to ^ greater than>
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And the spacing between the array elements in the second predetermined array is->
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，/>
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The position of the array element is the position where the radar is supposed to be located, so that the radar actually needs to receive the half wavelength of the signal. The simulation received signal is given to each array element so that the array elements simulate radar received signals.
In one embodiment, the array element position is expressed as follows:
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in this embodiment, generating the simulated received signal includes the steps of:
s1011, setting the pitching angle when the radar receives the emission signal of the signal source
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The source is configured to transmit a signal to the radar.
S1012, setting noise information of the environment where the radar is located.
And S1013, generating the simulation receiving signal according to the pitching angle, the transmitting signal, the noise information and the position of the array element in the preset array.
If a radar can be from different angles during the period t
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(Angle relative to horizontal, i.e. pitch angle) </or >>
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Number (& lt & gt)>
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Is relatively->
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The number of the smaller number is,
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then each preset array->
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Is greater than or equal to>
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Simulated received signal of
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：
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In the formula (I), the compound is shown in the specification,
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is the pitch angle of the radar is->
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A received transmitting signal (a receiving signal from the radar perspective) from a source, and>
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is the first->
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A predetermined number of first/second predetermined arrays>
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Position of the array element (relative to one of the ends of the predetermined array), ->
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For emission of a signal wavelength>
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Which is noise information of the environment in which the radar is located (white gaussian noise in this embodiment).
And S102, subtracting the array elements in the two preset arrays by two to obtain virtual arrays and virtual receiving signals corresponding to the virtual arrays, wherein the subtraction is to subtract the position of the array element of one preset array in one preset array by the position of the array element of the other preset array in the other preset array, and subtract the simulated receiving signal of the array element of the one preset array by the simulated receiving signal of the array element of the other preset array.
In this embodiment, the first position of each of the two predetermined arrays is zero, and the distance between adjacent positions in each array is half a wavelength
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(present embodiment is +>
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Is 1), such as in FIG. 3, a first position in a first predetermined array +>
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And the second position is->
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And the third position is->
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Up to the fifteenth position->
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（/>
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Is 5, based on>
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Multiply by->
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Equal to 5, i.e. the spacing between array elements in the first predetermined array is 5, there are 3 array elements in the first predetermined array, 3x5 is equal to 15), and likewise each position of the second predetermined array is obtained, and the maximum position of the second predetermined array is ≥ h>
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。/>
First position of first preset array
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Minus the first position of the second predetermined array>
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Equal to 0 (at position 0 in FIG. 2), due to the first preset array and the second preset array->
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There is radar, so the radar should be set at the position of the virtual array 0 in fig. 2. Position 8 in FIG. 2 is a first predetermined array of +>
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Less a second predetermined array>
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Due to the ^ of the first predetermined array>
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And a second predetermined array of +>
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There is no radar, so no radar is set at the position of the virtual array 8 in fig. 2 for the time being. Position 9 in FIG. 2 is a first predetermined array->
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Less a second predetermined array>
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Due to the ^ of the first predetermined array>
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There is a radar, so the radar should be set at the position of the virtual array 9 in fig. 2 (the solid line in fig. 2 indicates that the radar is set, and the broken line indicates that the radar is not set for the moment). Subtracting the other positions of the first preset array and the second preset array in turn can obtain whether all the positions of the virtual array in fig. 2 are provided with radars (only a part of the virtual array in the embodiment is shown in fig. 2).
After the virtual array is obtained, the virtual received signal of the cavity array element (the dotted line is the cavity array element, corresponding to the position where the radar is not set for the moment) in the virtual array is zero, and the virtual received signal of the non-cavity array element (the solid line is the non-cavity array element, corresponding to the position where the radar is set) is the result of subtracting the simulated received signals of the two corresponding array elements in the two preset arrays.
In one embodiment, generating a Hankel matrix (Hankel matrix) from a virtual array is prior art, provided that the virtual array comprises sequentially arranged array elements
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。
Then the hankel matrix is:
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the generation of the virtual array and the hankerr matrix in step S100 is based on the following principle:
setting a sub-array element number as
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And &>
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And the spacing between the array elements is->
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And
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in which is->
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Is half wavelength. All physical array element positions of the cross-prime array>
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：
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（1）
The physical array element arrangement of the co-prime array is shown in fig. 1, two sub-arrays share the first array element and share the first array element
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A physical array element. The difference covariance array is a virtual array which performs difference extension expression on received array element signals, and the specific array element position relationship can be expressed as follows:
Figure 983081DEST_PATH_IMAGE036
（2）
from the properties of the co-prime numbers and equation (2), the difference covariance array of the co-prime array can be deduced (Virtual array) has an aperture of
Figure 71123DEST_PATH_IMAGE037
. For example, the number of sub-array elements is ^ 4>
Figure 338156DEST_PATH_IMAGE038
、/>
Figure 740319DEST_PATH_IMAGE039
A schematic diagram of the co-prime array and its difference co-array (virtual array) is shown in fig. 2. As can be seen from fig. 2, if only the continuous array element part in the middle of the virtual array is used, part of the aperture will be lost and the maximum aperture cannot be reached. And then, the holes in the virtual array are approximately completed through a matrix completion method.
Next assume that the co-prime array is from a different angle
Figure 251940DEST_PATH_IMAGE040
Receive->
Figure 510883DEST_PATH_IMAGE041
（/>
Figure 468475DEST_PATH_IMAGE041
Is a relatively small number L) of mutually incoherent narrow-band far-field target signals, and a difference co-array is generated, the data at the holes in the virtual array is represented as 0, which can be represented as:
Figure 736645DEST_PATH_IMAGE042
（3）
wherein
Figure 587927DEST_PATH_IMAGE043
Represented as a collection of received signals, and,
Figure 17771DEST_PATH_IMAGE044
is greater than or equal to>
Figure 462659DEST_PATH_IMAGE045
The individual steering vectors can be expressed as:
Figure 268941DEST_PATH_IMAGE046
（4）
will have a size of
Figure 725461DEST_PATH_IMAGE047
Receive signal of>
Figure 591786DEST_PATH_IMAGE048
Folded along an anti-diagonal into a Hankel matrix->
Figure 258391DEST_PATH_IMAGE049
：
Figure 868364DEST_PATH_IMAGE050
（5）
Wherein
Figure 428658DEST_PATH_IMAGE051
，/>
Figure 669146DEST_PATH_IMAGE052
Indicating an upward integer.
S200, setting the non-zero element value in the Hankel matrix H as one and the zero element value as zero to obtain an undirected adjacent matrix
Figure 885364DEST_PATH_IMAGE053
(adjacency matrix of undirected graph):
Figure 345033DEST_PATH_IMAGE054
（6）
s300, when the undirected graph corresponding to the undirected adjacency matrix has connectivity, selecting the array elements from the virtual array to form a sub-array, and taking the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as an array to be supplemented.
In this embodiment, it is the prior art to generate an undirected graph from an undirected adjacency matrix.
For example, the following non-directional adjacency matrix
Figure 963096DEST_PATH_IMAGE055
And undirected adjacency matrix->
Figure 108907DEST_PATH_IMAGE056
To illustrate the connectivity of an undirected graph: />
Figure 812421DEST_PATH_IMAGE057
Matrix array
Figure 826513DEST_PATH_IMAGE055
In (A)>
Figure 299083DEST_PATH_IMAGE058
(first row, third column) maps the first and third points in an undirected graph (FIG. 4), and { (R) }>
Figure 615795DEST_PATH_IMAGE058
Is a non-zero value, so mapping into an undirected graph is: there is a connection between the first point and the third point, and since there is a connection between one point and none of the points in FIG. 4, there is no way to neighbor matrix->
Figure 150812DEST_PATH_IMAGE055
Undirected graph of (a) is unconnected.
By way of example, FIG. 4 is
Figure 578382DEST_PATH_IMAGE055
In the undirected graph of (a), generates->
Figure 171038DEST_PATH_IMAGE055
Is based on the following principle:
an undirected graph only considers whether the elements in the undirected adjacency matrix that are off-diagonal are zero, e.g.
Figure 517706DEST_PATH_IMAGE055
In>
Figure 195812DEST_PATH_IMAGE058
(first row and third column) are mapped to the first and third points in the undirected graph as @>
Figure 427073DEST_PATH_IMAGE058
Is non-zero and therefore there is a line between the first point and the third point. And->
Figure 874235DEST_PATH_IMAGE055
The first point and the second point in the undirected graph of element mappings of the first row and the second column in (a) because £ is @>
Figure 906650DEST_PATH_IMAGE055
Is zero, and thus there is no connection between the first point and the second point in the undirected graph, it is likewise known that £ is £ r @>
Figure 806473DEST_PATH_IMAGE055
There is no connection line between the second point and the third point in the undirected graph. Accordingly, is present>
Figure 575846DEST_PATH_IMAGE055
Undirected graphs are unconnected.
FIG. 5 is
Figure 143094DEST_PATH_IMAGE059
Generates an undirected graph of->
Figure 97143DEST_PATH_IMAGE059
Is based on the following principle:
matrix array
Figure 687525DEST_PATH_IMAGE059
In>
Figure 322905DEST_PATH_IMAGE060
(first row, second column) is mapped to a first point and a second point in an undirected graph (FIG. 5), and +>
Figure 557709DEST_PATH_IMAGE060
Is a non-zero value, so mapping into an undirected graph is: there is a connection between the first point and the second point, and, similarly, a non-zero value->
Figure 620343DEST_PATH_IMAGE061
(second row, third column) maps the second and third points in the undirected graph (fig. 5), so the mapping into the undirected graph is: there is a connection between the second point and the third point, and, in sum, no direction adjacency matrix->
Figure 229178DEST_PATH_IMAGE059
Undirected graph of (a) is connected.
In one embodiment, when the undirected graph corresponding to the undirected adjacency matrix does not have connectivity, the virtual array at this time is the array to be complemented (the complemented array).
In another embodiment, when the undirected graph corresponding to the undirected adjacency matrix has connectivity, an array element needs to be selected from the virtual array to form each sub-array, and then a sub-array which can be used as an array to be complemented is selected from each sub-array. The embodiment includes the following steps S301, S302, S303, and S304:
s301, the array elements at the head end and the tail end of the virtual array form a first sub-array in the sub-arrays.
S302, the array elements except the array elements at the head end and the tail end in the virtual array form a second sub array in the sub arrays, and the second sub array and the first sub array are relatively prime arrays.
S303, if the undirected graph corresponding to the virtual sub-array formed by the first sub-array and the second sub-array has connectivity, adding the array elements of the virtual array to the second sub-array and the first sub-array one by one until the undirected graph corresponding to the virtual sub-array formed by the second sub-array and the first sub-array after the addition of the array elements has non-connectivity, and using the second sub-array and the first sub-array after the addition of the array elements as a target sub-array MCCA (minimum complementary co-prime array).
And S304, obtaining an array to be compensated according to the target subarray.
The detailed process of S301 to S304 is illustrated:
if the undirected graph corresponding to the virtual array in FIG. 2 is not connected, p is added 12 And p -12 Is (p) 12 And p -12 At the head and tail ends) to form a first sub-array, and then randomly selecting p 1 、p 9 、p 10 And the array elements form a second sub-array, whether undirected graphs corresponding to a new virtual array formed by the first sub-array and the second sub-array are communicated or not is calculated, at the moment, one traversal is completed, and the number of the array elements contained in the first sub-array and the second sub-array is mutually equal in each traversal. And if the undirected graph obtained by the traversal is communicated, performing the traversal for the next time, respectively adding an array element in the first subarray and the second subarray traversed for the next time, and judging whether the undirected graph corresponding to the virtual array generated by the first subarray and the second subarray after the addition of the array element has connectivity or not until the undirected graph corresponding to the virtual array formed by the first subarray and the second subarray generated after the addition of the array element one by one does not have connectivity, wherein the first subarray and the second subarray after the addition of the array element are the finally required target MCCA. And generating a final array to be compensated by the two target sub-arrays. (two target sub-arrays are differenced to obtain an array to be complemented, the form of the array to be complemented is the same as that of the virtual array in the figure 2, and the array comprises a cavity array element and a non-cavity array element).
The generation of the two target sub-arrays MCCA in steps S301 to S304 is based on the following principle:
in order not to destroy the maximum aperture of the differencing array (virtual array), the first and last array elements of the physical array are fixed. Then, the number of antennas (array elements) is from small to large (because the antennas at two fixed ends are included, the number of the MCCA antennas is increased from 3 upwards), the other antennas except the antennas at two ends are subjected to position combination traversal to generate sub-arrays of a co-prime array, the connectivity of an undirected graph corresponding to the co-prime array is judged, and the minimum number of antennas is obtained and conforms to the non-connectivity MCCA.
And S400, according to a convex optimization algorithm, completing the hollow array elements covered by the array to be completed into non-hollow array elements to obtain a target radar array, wherein the positions of the non-hollow array elements in the array to be completed before completing are used for placing the radars, and the positions of the hollow array elements in the array to be completed before completing are not used for placing the radars.
Step S300 obtains a to-be-supplemented array formed by two target sub-arrays MCCA, and when the to-be-supplemented array includes a cavity array element, it needs to be considered whether to supplement each cavity array element included in the array, that is, whether to set a radar at a position where the cavity array element is located, so that the supplemented radar array can provide high-quality reference data (such as a wave arrival angle) for the unmanned technology. Step S400 includes the following steps:
s401, adding unknown parameters to the non-cavity array elements in the array to be compensated to obtain virtual non-cavity array elements, wherein the unknown parameters are used for representing the cavity array elements in the array to be compensated.
Because it is not known which cavity array element and how many cavity array elements need to be complemented to enable the radar array corresponding to the array after completion to provide a high-quality arrival angle, the cavity array element needing to be complemented is used as an unknown parameter to be solved. The method comprises the steps of firstly assuming a hollow array element as a non-hollow array element, and forming a set serving as an observation element by the assumed non-hollow array element and an original real non-hollow array element of an array to be compensated
Figure 605933DEST_PATH_IMAGE062
The virtual non-hole array element.
S402, generating the Hankel matrix H corresponding to the virtual non-cavity array element according to the position of the virtual non-cavity array element in the array to be compensated and the simulation received signal corresponding to the virtual non-cavity array element.
In this embodiment, the hankel matrix H corresponding to the virtual non-cavity array element is calculated by using formula (5).
And S403, generating an estimation matrix X corresponding to the virtual non-hollow array element according to the Hankel matrix corresponding to the virtual non-hollow array element.
S404, establishing a constraint condition by using the F norm of the difference between the estimation matrix and the Hankel matrix corresponding to the virtual non-cavity array element to be less than a set value:
Figure 944511DEST_PATH_IMAGE063
Figure 178046DEST_PATH_IMAGE064
represents the F norm (Frobenius-norm).
Set value in the present embodiment
Figure 477440DEST_PATH_IMAGE065
Noise information for characterizing the environment in which the radar is located, i.e. the greater the noise, the greater the->
Figure 454623DEST_PATH_IMAGE065
The larger and vice versa>
Figure 896975DEST_PATH_IMAGE065
The smaller.
In one embodiment, the error parameter
Figure 301412DEST_PATH_IMAGE065
Related to noise power and array sparsity.
S405, calculating a parameter value corresponding to the unknown parameter when the kernel norm of the estimation matrix X takes the minimum value under the constraint condition.
And S406, obtaining the cavity array element needing to be completed according to the parameter values.
S407, placing the radar at the position of the cavity array element to be completed in the array to be completed to obtain a target radar array.
Namely, it is
Figure 88102DEST_PATH_IMAGE066
When the virtual non-hollow array elements are established, after the specific virtual non-hollow array elements are obtained, the known non-hollow array elements which are the hollow array elements corresponding to the unknown parameters are removed, and the cavity array elements which need to be complemented into the non-hollow array elements are solved.
In one embodiment, the constraints are derived using the following principles
Figure 868976DEST_PATH_IMAGE067
And a target function->
Figure 916567DEST_PATH_IMAGE066
：
Hankel matrix formed by received signals
Figure 491904DEST_PATH_IMAGE068
Is a rank is->
Figure 765891DEST_PATH_IMAGE069
According to the theory of completion by matrix:
Figure 84877DEST_PATH_IMAGE070
wherein
Figure 3285DEST_PATH_IMAGE071
Representative of matrix rank operation, <' > based on a predetermined number of bits>
Figure 749524DEST_PATH_IMAGE072
Is->
Figure 510807DEST_PATH_IMAGE068
Is collected and selected>
Figure 367905DEST_PATH_IMAGE073
Then it is the approximation generated>
Figure 390087DEST_PATH_IMAGE072
In a predetermined evaluation matrix, and->
Figure 572807DEST_PATH_IMAGE074
For observing the set of elements, i.e. ->
Figure 555806DEST_PATH_IMAGE075
Is->
Figure 793759DEST_PATH_IMAGE073
The observation projection matrix of (2):
Figure 873710DEST_PATH_IMAGE076
due to the fact that
Figure 899435DEST_PATH_IMAGE077
The minimization matrix rank of (c) belongs to the non-convex problem of NP-Hard, so the optimization problem is relaxed: />
Figure 432047DEST_PATH_IMAGE078
Wherein
Figure 958844DEST_PATH_IMAGE079
Represents the nuclear norm (nuclear-norm). The matrix is destroyed to some extent due to the presence of noise
Figure 893302DEST_PATH_IMAGE080
Low rank specialThereby affecting the outcome of the optimization. In order to improve the optimization effect and remove noise, the distance with error parameters is characterized by the constraint conditions:
Figure 89928DEST_PATH_IMAGE081
the number of sub-arrays is
Figure 188465DEST_PATH_IMAGE082
、/>
Figure 191056DEST_PATH_IMAGE083
The target radar array constructed by the invention can provide high-quality arrival angles, namely the arrival angles have higher resolution.
The above co-prime array and the physical and virtual array element positions of 17 MCCAs are shown in fig. 6 and 7, wherein the 0 th line is a co-prime array. The number of virtual array elements of the co-prime array in fig. 7 is 45, and the number of virtual array elements of the MCCA in the other 17 rows is 23 except for row 2, which is 19. Virtual array
Figure 917704DEST_PATH_IMAGE084
The sparsity of (a) is defined as:
Figure 613127DEST_PATH_IMAGE085
wherein is
Figure 448228DEST_PATH_IMAGE086
Represents the number of arrays, <' > based on>
Figure 926614DEST_PATH_IMAGE087
Representing a completion operation. The higher the sparsity is, the more the number of the array elements of the holes of the array is, and the more sparse the array is. The sparsity of the coprime array is about 0.26, while the sparsity of the second row of MCCAs is about 0.69, with the sparsity of the remaining MCCAs being about 0.63.
Next, a simulation experiment link is performed,according to the power of noise and the sparsity of the array, complementing the error parameters of the optimization algorithm by the co-prime array low-rank matrix
Figure 835664DEST_PATH_IMAGE088
Set to 0.8 and MCCA to 0.2. Taking the second row of MCCA with the highest sparsity and all virtual arrays (Coprime Array, CA) of the initial Coprime Array, continuous virtual apertures (CA-continuous) of the Coprime Array and Full-Aperture arrays (Full-Aperture) columns with noise as experimental objects, and respectively complementing the MCCA and the CA into MCCA-completed and CA-completed of the Full-Aperture arrays by using a low-rank matrix method.
Experiment one: fast Fourier Transform (FFT) spatial spectrum
Setting a single snapshot of dual target signals with array incidence angles of
Figure 747994DEST_PATH_IMAGE089
And &>
Figure 742495DEST_PATH_IMAGE090
The Signal-to-Noise Ratio (SNR) was set to 20dB. As shown in FIG. 8, MCCA-completed, CA-completed and Full-Aperture can form peaks accurately, and the other methods have different degrees of angle ambiguity.
Experiment two: deviation comparison with noiseless full aperture received signal
MCCA-completed and CA-completed, full-Aperture and noiseless Full Aperture arrays
The variation trend of the deviation value of the received signal with SNR is shown in fig. 9, where the deviation is defined as:
Figure 24572DEST_PATH_IMAGE091
/>
wherein
Figure 788128DEST_PATH_IMAGE092
Represents a fifth->
Figure 153251DEST_PATH_IMAGE093
Acceptance signal for a submonol test>
Figure 307151DEST_PATH_IMAGE094
Then it is a noise-free full aperture received signal,
Figure 533864DEST_PATH_IMAGE095
representing a 1-norm operation. The experimental result is shown in fig. 9, the MCCA and CA after completion can eliminate partial noise, and the noise reduction effect of MCCA is better than that of CA.
In summary, the method includes firstly simulating a receiving signal of the radar, then constructing a virtual array by the simulated receiving signal of the radar, then processing the virtual array to obtain an undirected adjacent matrix, and judging whether undirected graphs of the undirected adjacent matrix are communicated or not, wherein the undirected graphs are communicated to show that the position of a cavity array element in the virtual array can be used for placing the radar, namely the cavity array element is expanded into a non-cavity array element. If the undirected graph is connected, the position of the hollow array element in the virtual array is suitable for placing the radar. Traversing the subarrays of the virtual arrays communicated by the undirected graph, finding the subarrays (to-be-complemented arrays) which can make the undirected graph be non-communicated and consist of the minimum array elements, and then replacing the hollow array elements in the to-be-complemented arrays with the non-hollow array elements to obtain the final target radar array. The invention adopts a one-by-one traversal method to obtain the minimum radar number (the radar number corresponds to the radar aperture) required by the array when the undirected graph is not connected, and the radar array corresponding to the undirected graph can provide accurate reference data when the undirected graph is not connected. Therefore, the invention can balance the problem between the aperture of the radar array and the accuracy of the reference data provided by the radar array, namely the invention can provide the reference data with draft precision under the condition of smaller aperture of the radar array.
In addition, the invention takes the vehicle-mounted millimeter wave radar as a research platform and designs a minimum complementable co-prime linear array according to the connectivity of the covariance matrix of the received signals. Firstly, setting an initial co-prime linear array and generating a covariance matrix of a received signal; then, traversing and judging the subarray of the array through a discriminator, and screening a completeable subarray with the least array elements as MCCA; and finally, completing the sparse array obtained in the last step into a uniform array by a convex optimization method, and realizing the aperture expansion of the array without the angle ambiguity.
Exemplary devices
The embodiment also provides a device for constructing a radar array based on the undirected adjacency graph, which comprises the following components:
the device comprises a Hankel matrix generation module, a receiving module and a processing module, wherein the Hankel matrix generation module is used for generating a Hankel matrix by taking array elements in a virtual array as elements in the matrix and taking virtual receiving signals corresponding to the array elements as element values in the matrix, the array elements are used for representing a radar, and the virtual receiving signals are used for simulating receiving signals of the radar;
the undirected adjacency matrix construction module is used for setting a non-zero element value in the Hankel matrix as one and a zero element value as zero to obtain an undirected adjacency matrix;
a to-be-supplemented array construction module, configured to select the array elements from the virtual array to form a sub-array when an undirected graph corresponding to the undirected adjacency matrix has connectivity, and use the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as a to-be-supplemented array;
and the array element completion module is used for completing the cavity array elements covered by the array to be completed into non-cavity array elements according to a convex optimization algorithm to obtain a target radar array, the positions of the non-cavity array elements in the array to be completed before completion are used for placing the radars, and the positions of the cavity array elements in the array to be completed before completion are not placed with the radars.
Based on the above embodiments, the present invention further provides a terminal device, and a schematic block diagram thereof may be as shown in fig. 10. The terminal equipment comprises a processor, a memory, a network interface, a display screen and a temperature sensor which are connected through a system bus. Wherein the processor of the terminal device is configured to provide computing and control capabilities. The memory of the terminal equipment comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operating system and the computer program to run on the non-volatile storage medium. The network interface of the terminal device is used for connecting and communicating with an external terminal through a network. The computer program is executed by a processor to implement a method of constructing a radar array based on an undirected adjacency graph. The display screen of the terminal equipment can be a liquid crystal display screen or an electronic ink display screen, and the temperature sensor of the terminal equipment is arranged in the terminal equipment in advance and used for detecting the operating temperature of the internal equipment.
It will be understood by those skilled in the art that the block diagram of fig. 10 is only a block diagram of a part of the structure related to the solution of the present invention, and does not constitute a limitation to the terminal device to which the solution of the present invention is applied, and a specific terminal device may include more or less components than those shown in the figure, or may combine some components, or have different arrangements of components.
In one embodiment, a terminal device is provided, where the terminal device includes a memory, a processor, and a program stored in the memory and executable on the processor for constructing a radar array based on a directed adjacency graph, and when the processor executes the program for constructing a radar array based on a directed adjacency graph, the following operation instructions are implemented:
generating a Hankel matrix by taking array elements in a virtual array as elements in the matrix and taking virtual receiving signals corresponding to the array elements as element values in the matrix, wherein the array elements are used for representing a radar, and the virtual receiving signals are used for simulating receiving signals of the radar;
setting a non-zero element value in the Hankel matrix as one and a zero element value as zero to obtain an undirected adjacency matrix;
when an undirected graph corresponding to the undirected adjacency matrix has connectivity, selecting the array elements from the virtual array to form a sub-array, and taking the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as an array to be supplemented;
and according to a convex optimization algorithm, filling the cavity array elements covered by the array to be filled with non-cavity array elements to obtain a target radar array, wherein the positions of the non-cavity array elements in the array to be filled before filling are used for placing the radar, and the positions of the cavity array elements in the array to be filled before filling are not placed with the radar.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, databases, or other media used in embodiments provided herein may include non-volatile and/or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), rambus (Rambus) direct RAM (RDRAM), direct Rambus Dynamic RAM (DRDRAM), and Rambus Dynamic RAM (RDRAM), among others.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, and not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (8)

1. A method for constructing a radar array based on an undirected adjacency graph is characterized by comprising the following steps:
generating a Hankel matrix by taking array elements in a virtual array as elements in the matrix and taking virtual receiving signals corresponding to the array elements as element values in the matrix, wherein the array elements are used for representing a radar, and the virtual receiving signals are used for simulating receiving signals of the radar;
setting a non-zero element value in the Hankel matrix as one and a zero element value as zero to obtain an undirected adjacency matrix;
when an undirected graph corresponding to the undirected adjacency matrix has connectivity, selecting the array elements from the virtual array to form a sub-array, and taking the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as an array to be supplemented;
according to a convex optimization algorithm, filling the cavity array elements covered by the array to be filled with non-cavity array elements to obtain a target radar array, wherein the positions of the non-cavity array elements in the array to be filled before filling are used for placing the radars, and the positions of the cavity array elements in the array to be filled before filling are not placed with the radars;
when an undirected graph corresponding to the undirected adjacency matrix has connectivity, selecting the array elements from the virtual array to form a sub-array, and taking the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as an array to be complemented, including:
forming a first sub-array in the sub-arrays by using the array elements at the head end and the tail end of the virtual array;
forming the array elements except the array elements at the head end and the tail end in the virtual array into a second sub-array in the sub-arrays, wherein the second sub-array and the first sub-array are relatively prime arrays;
if the undirected graphs corresponding to the virtual sub-arrays formed by the first sub-array and the second sub-array have connectivity, adding the array elements of the virtual arrays to the second sub-array and the first sub-array one by one until the undirected graphs corresponding to the virtual sub-arrays formed by the second sub-array and the first sub-array after the array elements are added have non-connectivity, and taking the second sub-array and the first sub-array after the array elements are added as target sub-arrays;
and obtaining an array to be compensated according to the target subarray.
2. The method for constructing a radar array based on a non-directional adjacency graph according to claim 1, wherein the virtual array and the method for generating the virtual received signals comprise:
respectively endowing each array element in two preset arrays with simulation receiving signals, wherein the array elements are used for representing a radar, and the simulation receiving signals are used for simulating receiving signals of the radar;
and subtracting the array elements in the two preset arrays in pairs to obtain virtual arrays and virtual receiving signals corresponding to the virtual arrays, wherein the subtraction is to subtract the position of the array element of one of the preset arrays in one of the preset arrays by the position of the array element of the other preset array in the other preset array, and subtract the simulated receiving signals of the array elements of the one of the preset arrays by the simulated receiving signals of the array elements of the other preset array.
3. The method as claimed in claim 2, wherein the total number of the array elements covered by one of the two predetermined arrays and the total number of the array elements covered by the other of the two predetermined arrays are mutually prime numbers, the array element pitch of one of the predetermined arrays is equal to the total number of the array elements of the other of the predetermined arrays multiplied by a wavelength, and the array element pitch of the other of the predetermined arrays is equal to the total number of the array elements of one of the predetermined arrays multiplied by a wavelength, and the wavelength is a wavelength of a signal to be received by the radar.
4. The method for constructing a radar array based on an undirected adjacency graph according to claim 2, wherein the method for generating the simulated received signals comprises:
setting a pitching angle when the radar receives a transmission signal of a signal source, wherein the signal source is used for transmitting the signal to the radar;
setting noise information of the environment where the radar is located;
and generating the simulation receiving signal according to the pitching angle, the transmitting signal, the noise information and the position of the array element in the preset array.
5. The method according to claim 4, wherein the method for constructing a radar array based on the undirected adjacency graph includes the following steps of completing the hole array elements covered by the array to be completed into non-hole array elements according to a convex optimization algorithm to obtain a target radar array, wherein the positions of the non-hole array elements in the array to be completed before completing are used for placing the radars, and the positions of the hole array elements in the array to be completed before completing are not used for placing the radars, including:
adding unknown parameters to the non-cavity array elements in the array to be compensated to obtain virtual non-cavity array elements, wherein the unknown parameters are used for representing the cavity array elements in the array to be compensated;
generating the Hankel matrix corresponding to the virtual non-cavity array element according to the position of the virtual non-cavity array element in the array to be compensated and the simulation received signal corresponding to the virtual non-cavity array element;
generating an estimation matrix corresponding to the virtual non-hollow array element according to the Hankel matrix corresponding to the virtual non-hollow array element;
establishing a constraint condition according to the F norm of the difference between the estimation matrix and the Hankel matrix corresponding to the virtual non-cavity array element being less than a set value;
calculating a parameter value corresponding to the unknown parameter when the kernel norm of the estimation matrix takes the minimum value under the constraint condition;
obtaining the cavity array elements to be completed according to the parameter values;
and placing the radar at the position of the cavity array element to be completed in the array to be completed to obtain a target radar array.
6. An apparatus for constructing a radar array based on an undirected adjacency graph, the apparatus comprising:
the device comprises a Hankel matrix generation module, a receiving module and a processing module, wherein the Hankel matrix generation module is used for generating a Hankel matrix by taking array elements in a virtual array as elements in the matrix and taking virtual receiving signals corresponding to the array elements as element values in the matrix, the array elements are used for representing a radar, and the virtual receiving signals are used for simulating receiving signals of the radar;
the undirected adjacency matrix construction module is used for setting a non-zero element value in the Hankel matrix as one and a zero element value as zero to obtain an undirected adjacency matrix;
a to-be-supplemented array construction module, configured to select the array elements from the virtual array to form a sub-array when an undirected graph corresponding to the undirected adjacency matrix has connectivity, and use the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as a to-be-supplemented array;
the array element completion module is used for completing the cavity array elements covered by the array to be completed into non-cavity array elements according to a convex optimization algorithm to obtain a target radar array, the positions of the non-cavity array elements in the array to be completed before completion are used for placing the radars, and the positions of the cavity array elements in the array to be completed before completion are not placed with the radars;
when an undirected graph corresponding to the undirected adjacency matrix has connectivity, selecting the array elements from the virtual array to form a sub-array, and taking the sub-array formed by the minimum array elements corresponding to the undirected graph having the non-connectivity as an array to be complemented, including:
forming a first sub-array in the sub-arrays by using the array elements at the head end and the tail end of the virtual array;
forming the array elements except the array elements at the head end and the tail end in the virtual array into a second sub array in the sub arrays, wherein the second sub array and the first sub array are relatively prime arrays;
if the undirected graphs corresponding to the virtual sub-arrays formed by the first sub-array and the second sub-array have connectivity, adding the array elements of the virtual array to the second sub-array and the first sub-array one by one until the undirected graphs corresponding to the virtual sub-arrays formed by the second sub-array and the first sub-array after the array elements are added have non-connectivity, and taking the second sub-array and the first sub-array after the array elements are added as target sub-arrays;
and obtaining an array to be compensated according to the target subarray.
7. A terminal device, characterized in that the terminal device comprises a memory, a processor and a program stored in the memory and executable on the processor for constructing a radar array based on a directed adjacency graph, and the processor implements the steps of the method for constructing a radar array based on a directed adjacency graph according to any one of claims 1 to 5 when executing the program for constructing a radar array based on a directed adjacency graph.
8. A computer-readable storage medium, on which a program for constructing a radar array based on a undirected adjacency graph is stored, which program, when executed by a processor, performs the steps of the method for constructing a radar array based on a undirected adjacency graph as claimed in any one of claims 1 to 5.
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