CN112230214B - MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation - Google Patents

MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation Download PDF

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CN112230214B
CN112230214B CN202010984810.0A CN202010984810A CN112230214B CN 112230214 B CN112230214 B CN 112230214B CN 202010984810 A CN202010984810 A CN 202010984810A CN 112230214 B CN112230214 B CN 112230214B
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angle
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CN112230214A (en
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邹林
李婧
张美茹
刘德旭
汪学刚
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University of Electronic Science and Technology of China
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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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/42—Simultaneous measurement of distance and other co-ordinates
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • G01S13/32—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated
    • G01S13/34—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal
    • 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
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/35—Details of non-pulse systems
    • G01S7/352—Receivers
    • 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
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/35—Details of non-pulse systems
    • G01S7/352—Receivers
    • G01S7/354—Extracting wanted echo-signals
    • 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
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects

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Abstract

The invention discloses an MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation, belongs to the technical field of signal processing, and particularly relates to the technical field of radar virtual aperture measurement direction of arrival. The existing interpolation method is to find the relation between the actual manifold matrix and the expected manifold matrix by using virtual transformation, then to perform corresponding transformation on the beating baseband signal matrix, so as to approximately simulate the missing beating baseband signal, and then to perform spatial smoothing on the interpolated beating baseband signal matrix. The method has higher requirement on the array type, and the array type is required to meet the invariance of the subarray shift, namely the subarray configuration is the same, but the subarray configuration is not applicable when the subarray configuration is different. According to the method, through the relation between the actual manifold matrix and the expected manifold matrix, approximate simulation is carried out on the beat baseband signal data which is missing in the virtual antenna area array, so that high side lobes and grating lobes can be effectively restrained; in a proper range, the number of the longitudinally-interpolated antennas is increased, and the angle resolution in the pitching direction can be effectively improved.

Description

MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to the technical field of radar virtual aperture measurement direction of arrival.
Background
With the wide global application of intelligent transportation systems, the unmanned technology as a product of informatization and industrialization fusion brings subversive changes to the whole automobile industry, and an Advanced Driving Assistance System (ADAS) as a basis of the unmanned technology is rapidly developed in the global scope. The MIMO millimeter wave radar is less affected by severe weather, has a long action distance and strong penetration capability, has the characteristics of miniaturization, large bandwidth and narrow beam, and becomes the standard configuration of an ADAS system.
The radar transmitter generates a continuous high frequency constant amplitude wave, the transmit frequency varying linearly with time, also known as a fast ramp mode LFMCW waveform. Through analyzing the millimeter wave radar beat baseband signal, the distance, the speed and the direction of the target can be obtained, the potential danger is pre-judged, especially, the blind area of the visual field can be detected and pre-warned, and the driving safety is effectively improved.
The angle resolution is the minimum angle difference between two targets which can be identified by the radar, and when the target directions are close, the improvement of the angle resolution is particularly important for effectively and accurately identifying the surrounding static environment and dynamic targets.
The MIMO radar virtual aperture angle measurement technology is characterized in that a wave path difference is generated by using a distance difference of receiving antennas, a phase difference is obtained through the wave path difference, two-dimensional fast Fourier transform is carried out on a beat baseband signal phase of each receiving antenna to obtain target azimuth-pitching angle information, and the more the receiving antennas are, the better the angular resolution is. In fact, due to the limitation of cost and resources, a large-aperture virtual antenna area array can be obtained by adopting an equivalent MIMO system method, and in most cases, the area array is a sparse area array. For a conventional sparse area array type, in an angle measurement technology, the processing of an antenna beat baseband signal generally combines a zero padding method or an interpolation method with spatial smoothing, and then target angle estimation can be realized through two-dimensional Fourier transform.
The zero filling method is to set a beat baseband signal at a position without an antenna array element in a virtual sparse area array to be 0, and then realize azimuth-elevation angle estimation by using 2-FFT (fast Fourier transform), so that the angle resolution is improved to a certain extent, but the improvement of the angle resolution is limited, and high side lobes and grating lobes exist. The interpolation method is that the relation between the actual manifold matrix and the expected manifold matrix is found out by utilizing virtual transformation, then the corresponding transformation is carried out on the beat baseband signal, the missing beat baseband signal can be simulated approximately, and then the spatial smoothing is carried out on the interpolated beat baseband signal matrix. To solve the problem, a MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation is provided.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: for a conventional sparse area array type, the processing of the antenna beat baseband signal in the angle measurement technology generally combines a zero padding method or an interpolation method with spatial smoothing. The zero filling method is to set a beat baseband signal at the position without an antenna array element in a virtual sparse area array to be 0, and then realize azimuth-elevation angle estimation by using 2-FFT (fast Fourier transform), so that the angle resolution is improved to a certain extent, but the degree is limited, and the problems of high sidelobe and grating lobe exist. The interpolation method is that the relation between the actual manifold matrix and the expected manifold matrix is found by utilizing virtual transformation, then the corresponding transformation is carried out on the matrix of the beat baseband signal, the missing beat baseband signal can be simulated approximately, and then the spatial smoothing is carried out on the interpolated matrix of the beat baseband signal. The method has higher requirement on the array type, and the array type is required to meet the invariance of the subarray shift, namely the subarray configuration is the same, but the subarray configuration is not applicable when the subarray configuration is different.
On the premise of ensuring that the angle measurement error is within an acceptable range, the invention provides a MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation, which is improved on the basis of an interpolation method for improving the angle resolution of a sparse area array type MIMO radar and effectively inhibiting high side lobes and grating lobes, and comprises the following steps:
step 1: a sparse area array is placed in a three-dimensional coordinate plane, and the position coordinate of the ith antenna array element is
Figure BDA0002688866280000021
P far-field targets are incident into a sparse area array, and the narrow-band signal set is s k (t)}K =1,2,3 \8230 \8230p, two-dimensional angle set of
Figure BDA0002688866280000022
θ k And &>
Figure BDA0002688866280000023
Respectively represents the azimuth angle and the pitch angle of the kth target, the position vector of the kth target relative to the reference point is->
Figure BDA0002688866280000024
Wherein->
Figure BDA0002688866280000025
Each part in the position vector respectively represents a direction vector of the target relative to the reference point in positive directions of x, y and z; the beat baseband signal of the ith virtual array antenna can be obtained by utilizing the MIMO radar virtual aperture angle measurement technology:
Figure BDA0002688866280000026
wherein e is i (t) is zero-mean complex white gaussian noise uncorrelated with the signal, and the antenna phase difference function due to angle is:
Figure BDA0002688866280000027
wherein, λ represents the wavelength of the radar antenna, and defines the observation vector corresponding to each antenna as the vector formed by the phase difference function of different angles
Figure BDA0002688866280000028
Step 2: forming a sparse beat baseband signal matrix by beat baseband signal data of each antenna at the same time, carrying out zero filling on the matrix, carrying out estimation on an observation region of a target angle through 2-FFT (fast Fourier transform), uniformly dividing the matrix after setting a step length, and arranging the matrix according to rows to obtain an observation set;
and step 3: the observation vectors corresponding to the actual antenna array form an actual observation vector matrix, and the observation vectors corresponding to the expected antenna array form an expected observation vector matrix; partitioning the antenna array according to the characteristics of the array, and processing the actual observation vector matrix and the beat baseband signal matrix of part of the antennas by using a space smoothing method to obtain a new actual observation vector matrix and a new beat baseband signal matrix;
and 4, step 4: under the condition that the observation area of the target angle is known, obtaining observation vectors corresponding to the actual array antenna and the expected array antenna according to the formula (2); arranging the actual and expected observation vector matrixes according to rows to obtain an actual manifold matrix A and an expected manifold matrix
Figure BDA0002688866280000031
Finding the relation between the two by solving an interpolation function B, wherein the interpolation function satisfies the formula (3);
Figure BDA0002688866280000032
and 5: arranging the block-smoothed beat baseband signal matrix according to rows, multiplying the interpolation function B by the rows, reversely arranging the block-smoothed beat baseband signal matrix according to the previous arrangement mode to obtain an interpolated beat baseband signal matrix, and calculating target two-bit angle information through 2-FFT.
The angle measurement flow chart is shown in fig. 1.
The invention has the beneficial effects that:
through the relation between the actual manifold matrix and the expected manifold matrix, approximate simulation is carried out on the beat baseband signal data missing in the virtual antenna area array, and therefore high side lobes and grating lobes can be effectively restrained.
In a proper range, the number of longitudinally-inserted antennas is increased, and the angle resolution in the pitching direction can be effectively improved.
Drawings
FIG. 1 is a flow chart of MIMO radar virtual sparse area array angle measurement based on block smooth interpolation;
FIG. 2 is an antenna arrangement for a virtual sparse area array radar;
FIG. 3 is a schematic diagram of a sparse area array and target location information;
FIG. 4 is a schematic diagram of two-dimensional observation block regions arranged in rows
FIG. 5 is a schematic diagram of the construction of an actual manifold matrix and a desired manifold matrix;
FIG. 6 is a pitch pattern with vertical nulling and vertical interpolation of 7, 14, 21 antennas;
FIG. 7 is a plot of pitch pattern main lobe width versus number of longitudinally interpolated antennas;
FIG. 8 is a plot of pitch pattern main and side lobe ratios versus number of longitudinally interpolated antennas;
FIG. 9 is a plot of azimuth absolute value error versus signal-to-noise ratio;
FIG. 10 is a graph of absolute value error of pitch angle versus signal-to-noise ratio;
FIG. 11 is a diagram of absolute value error in azimuth versus number of longitudinally interpolated antennas;
fig. 12 is a graph of absolute pitch angle error versus number of longitudinally interpolated antennas.
Detailed Description
Step 1: the invention adopts a cascade MIMO radar, the virtual area array type of which is a sparse area array is equivalent to 86 array antennas in the transverse direction and 7 array antennas in the longitudinal direction, so that the azimuth angle resolution is higher and is 1.33 degrees, and the pitch angle resolution is lower and is 16.38 degrees. The distance between the array elements in the horizontal direction and the vertical direction is integral multiple of d, wherein d = lambda/2, and lambda is the wavelength of the radar antenna. The number of the antennas in the rows is 1,2, 4 and 7, the first row is a uniform linear array, the number of the antennas is 86, the 2 nd, 4 th and 7 th rows are 16 antennas, the antennas are arranged in a staggered manner, the number of the antennas in the second row is {10, 11, 12, 13, 21, 22, 23, 24, 56, 57, 58, 59, 60, 61, 62 and 63}, fig. 2 shows the antenna arrangement of a radar virtual sparse area array, the side length of a square is the array element interval, and black dots represent array elements. The original point is taken as an antenna reference point, the sparse area array is positioned on an xOz plane, and the position coordinate of the nth row and mth column antenna array element is
Figure BDA0002688866280000041
Fig. 3 is a schematic diagram of sparse area array and target position information, and black dots represent array elements. P far-field targets are incident into a sparse area array, and the narrow-band signal set is s k (t) }, a two-dimensional set of angles being +>
Figure BDA0002688866280000042
Wherein k =1,2, \8230;, P, θ k And &>
Figure BDA0002688866280000043
Respectively represents the azimuth angle and the pitch angle of the kth target, the position vector of the kth target relative to the reference point is->
Figure BDA0002688866280000044
Wherein
Figure BDA0002688866280000045
Each part in the position vector respectively represents a direction vector of the target relative to the reference point in positive directions of x, y and z; . The beating baseband signal of the virtual array antenna can thus be expressed as:
Figure BDA0002688866280000046
wherein, (n, m) represents the position coordinates of the virtual array antenna; e.g. of a cylinder n,m (t) is zero-mean complex white gaussian noise uncorrelated with the signal, and the antenna phase difference function due to angle is:
Figure BDA0002688866280000047
defining observation vectors corresponding to each antenna as vectors formed by phase difference functions of different angles
Figure BDA0002688866280000048
And 2, step: each antenna being at the same timeAnd forming a beat baseband signal matrix by the beat baseband signal data of the points, filling zero in the sparse matrix, and estimating an azimuth-pitch angle observation area through 2-FFT. If the observation signal is located in a certain two-dimensional observation region { (Θ, Ψ) | [ Θ ] E [ θ [ ] 1 ,θ r ],
Figure BDA0002688866280000049
In the method, theta represents the observation range of the target azimuth angle, psi represents the observation range of the target pitch angle, wherein theta 1 、/>
Figure BDA00026888662800000410
Is the left boundary, θ r 、/>
Figure BDA00026888662800000411
Is the right boundary, the image is uniformly divided, and the dividing step length is set to be delta theta and/or greater than or equal to>
Figure BDA00026888662800000412
And then arranging the observation regions in rows to obtain an observation set O, wherein FIG. 4 is a schematic diagram of the arrangement of the two-dimensional observation regions in rows.
And step 3: and the observation vectors corresponding to the actual antenna array form an actual observation vector matrix, and the observation vectors corresponding to the expected antenna array form an expected observation vector matrix. For the sparse area array type, because the first row of antennas is dense, the other rows of antennas are fewer in number and similar in structure, the area array is partitioned, the first row is a first part, and the other antennas are used as a second part. And processing the actual observation vector matrix and the beat baseband signal matrix of the first part of antennas in a spatial smoothing mode, setting the size of a subarray selected by spatial smoothing to be 1 multiplied by 30, and adopting an averaging mode for smooth data processing. The second part of antennas are not processed to obtain a new actual observation vector matrix and a beat baseband signal matrix.
And 4, step 4: assuming a true antenna array size of N M, the desired antenna array size is
Figure BDA0002688866280000051
When the observation region where the target angle is located is known, according to equation (5), obtaining observation vectors corresponding to the actual array antenna and the expected array antenna as follows:
Figure BDA0002688866280000052
the actual observation vector matrix is divided into blocks and smoothed and is arranged with the expected observation vector matrix according to rows respectively to obtain an actual manifold matrix A and an expected manifold matrix
Figure BDA0002688866280000053
Fig. 4 is a schematic structural diagram of an actual manifold matrix and an expected manifold matrix, in the diagram, the actual array size is 3 × 4, the expected array size is 4 × 4, and black dots represent array elements. The relationship between the actual flow pattern matrix and the desired flow pattern matrix is found by solving an interpolation function B, which satisfies equation (7).
Figure BDA0002688866280000054
Arranging the block-smoothed beat baseband signal matrixes according to the mode of figure 4, then, carrying out left multiplication on an interpolation function B to obtain interpolated signal vectors, carrying out reverse arrangement on the interpolated signal vectors according to the arrangement method to obtain interpolated beat baseband signal matrixes, and estimating target angle information through two-dimensional Fourier transform.
And 5: the vertical null-filling and the interpolation method based on block smoothing are considered, the vertical interpolation is respectively carried out for 7, 14 and 21 antennas, and the improvement of the angle resolution and the suppression degree of the side lobe and the grating lobe are analyzed through the pitching directional diagram. The number of points after the longitudinal zero padding is 680, as shown in fig. 6, when the number of the direct longitudinal zero padding and the number of the longitudinal interpolation antennas are 7, the width of the main lobe is 15.32 degrees, and when the number of the interpolation antennas is more than 7, the width of the main lobe is obviously reduced, and the angular resolution is improved; when the direct longitudinal zero compensation is carried out, the number of the longitudinal equivalent antennas is 7, but the number of the actual antennas is only 4, the directional diagram has high side lobes and grating lobes, the ratio of the main lobe to the side lobe is smaller and is 2.19dB, the side lobes and the grating lobes are greatly reduced after interpolation, and the ratio of the main lobe to the side lobe is improved. Fig. 7 is a diagram of a relationship between a main lobe width of a pitch directional diagram and the number of longitudinally interpolated antennas, and as the number of longitudinally interpolated antennas increases, the main lobe width decreases first and then tends to be stable, which can reach 4.37 degrees at the lowest, and the angular resolution can be increased to about 3.51 times at the highest. FIG. 8 is a relationship diagram of the main lobe ratio and the side lobe ratio of a pitching directional diagram and the number of longitudinally interpolated antennas, the main lobe ratio and the side lobe ratio are linearly increased and then tend to be stable along with the increase of the number of the longitudinally interpolated antennas, the main lobe ratio and the side lobe ratio are both higher and are increased by about 10dB-11dB within the range of 12.65dB-13.45 dB. The comprehensive analysis shows that the number of the longitudinally interpolated antennas is within 26, the larger the number of the longitudinally interpolated antennas is, the higher the angle resolution is, and meanwhile, the high side lobes and grating lobes are effectively inhibited.
And 6: assume that there is a target, 20 degrees on the right front, with a pitch angle of 2 degrees. When the number of the longitudinally interpolated antennas is 7, 14 and 21 respectively, the change of absolute value errors of the azimuth angle and the pitch angle along with the signal-to-noise ratio is considered, and the comparison is carried out with a longitudinal zero padding method. Fig. 9 and 10 are graphs of absolute errors of azimuth angle and pitch angle and signal-to-noise ratio, respectively, and as the signal-to-noise ratio is improved, the angle measurement error is reduced and then becomes stable. The number of the longitudinally interpolated antennas is 14, when the signal-to-noise ratio is greater than 5dB, the azimuth angle measurement error is within 0.1 degree, the pitch angle measurement error is within 0.2 degree, and finally the angle approaches to 0 degree. The comprehensive analysis shows that when the signal-to-noise ratio is low, the anti-noise performance of the interpolation method is weaker than that of the zero filling method, and the angle measurement error is larger, but when the signal-to-noise ratio is high, the angle measurement errors corresponding to the zero filling method and the interpolation method are close.
And 7: when the signal-to-noise ratio is respectively 5dB, 10dB, 15dB and 20dB, the change of absolute value errors of azimuth angles and pitching angles along with the number of longitudinally interpolated antennas is considered. Fig. 11 and 12 are diagrams showing the relationship between the absolute errors of the azimuth angle and the pitch angle and the number of longitudinally interpolated antennas, respectively, and as the number of the interpolated antennas increases, the angle measurement error becomes larger after stabilizing in a lower range. When the signal-to-noise ratio is 10dB and the number of the longitudinally interpolated antennas is less than 18, the azimuth angle measurement error is stabilized within the range of 0.1 degree, and the pitch angle measurement error is stabilized within the range of 0.2 degree. The comprehensive analysis can obtain that the requirement on the signal-to-noise ratio is higher when the number of the interpolation antennas is larger.
TABLE 1 comparison of zero padding method with the present method
Figure BDA0002688866280000061
Experiments prove that under the condition of a certain signal-to-noise ratio, the number of the longitudinally interpolated antennas is properly selected, so that the absolute value error of azimuth angle measurement is within 0.1 degree, the absolute value error of pitch angle measurement is within 0.3 degree, and the test indexes are met. According to the table 1, the method and the traditional method keep the same azimuth angle measurement precision, the pitch angle measurement precision is improved to 2 times of the original pitch angle measurement precision, the pitch angle resolution is improved to 2-3 times, meanwhile, high side lobes and grating lobes are effectively restrained, and the main lobe-side lobe ratio is improved by about 11dB. Therefore, the new MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation is superior to the traditional method.

Claims (1)

1. A MIMO radar virtual sparse area array angle measurement method based on block smooth interpolation is improved on the basis of an interpolation method for improving the angle resolution of a sparse area array type MIMO radar and effectively inhibiting high sidelobes and grating lobes on the premise of ensuring that an angle measurement error is within an acceptable range, and comprises the following steps:
step 1: a sparse area array is placed in a three-dimensional coordinate plane, and the position coordinate of the ith antenna array element is
Figure FDA0003878026740000011
P far-field targets are incident into a sparse area array, and the narrow-band signal set is s k (t) }, k =1,2,3 \ 8230; 8230p, two-dimensional angle set is->
Figure FDA0003878026740000012
θ k And &>
Figure FDA0003878026740000013
Respectively represent the k-th itemTarget azimuth angle and pitch angle, the position vector of the kth target relative to the reference point is
Figure FDA0003878026740000014
Wherein->
Figure FDA0003878026740000015
Each part in the position vector respectively represents a direction vector of the target relative to the reference point in positive directions of x, y and z; the beat baseband signal of the ith virtual array antenna can be obtained by utilizing the MIMO radar virtual aperture angle measurement technology:
Figure FDA0003878026740000016
wherein e is i (t) is zero-mean complex white gaussian noise uncorrelated with the signal, and the antenna phase difference function due to angle is:
Figure FDA0003878026740000017
wherein, λ represents the wavelength of the radar antenna, and defines the observation vector corresponding to each antenna as the vector formed by the phase difference function of different angles
Figure FDA0003878026740000018
Step 2: forming a sparse beat baseband signal matrix by beat baseband signal data of each antenna at the same time, carrying out zero filling on the matrix, carrying out estimation on a target angle observation region through 2D-FFT, uniformly dividing the matrix after setting a step length, and arranging the matrix according to rows to obtain an observation set;
and step 3: the observation vectors corresponding to the actual antenna array form an actual observation vector matrix, and the observation vectors corresponding to the expected antenna array form an expected observation vector matrix; for the sparse area array type, because the first row of antennas are dense, the other rows of antennas are fewer in number and similar in structure, the area array is partitioned, the first row is a first part, and the other antennas are used as a second part; processing the actual observation vector matrix and the beat baseband signal matrix of the first part of antennas in a space smoothing mode, setting the size of a subarray selected by the space smoothing to be 1 multiplied by 30, and adopting an averaging mode for the smooth data processing mode; the second part of antennas do not process to obtain a new actual observation vector matrix and a beat baseband signal matrix;
and 4, step 4: under the condition that the observation area of the target angle is known, obtaining observation vectors corresponding to the actual array antenna and the expected array antenna according to the formula (2); arranging the actual and expected observation vector matrixes according to rows to obtain an actual manifold matrix A and an expected manifold matrix
Figure FDA0003878026740000019
Finding the relation between the two by solving an interpolation function B, wherein the interpolation function satisfies the formula (3);
Figure FDA0003878026740000021
and 5: arranging the beat baseband signal matrixes subjected to block smoothing according to rows, multiplying the interpolated function B by the left side, then reversely arranging the beat baseband signal matrixes according to the previous arrangement mode to obtain interpolated beat baseband signal matrixes, and calculating target two-bit angle information through 2-FFT.
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