CN112612010A - Meter-wave radar low elevation height measurement method based on lobe splitting pretreatment - Google Patents

Meter-wave radar low elevation height measurement method based on lobe splitting pretreatment Download PDF

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CN112612010A
CN112612010A CN202011373744.XA CN202011373744A CN112612010A CN 112612010 A CN112612010 A CN 112612010A CN 202011373744 A CN202011373744 A CN 202011373744A CN 112612010 A CN112612010 A CN 112612010A
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target
matrix
array
wave
low elevation
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宋玉伟
胡国平
郑桂妹
陈晨
王鸿帧
彭加强
主钦宇
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Air Force Engineering University of PLA
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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
    • 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
    • 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
    • G01S13/42—Simultaneous measurement of distance and other co-ordinates

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Abstract

The invention discloses a meter-wave radar low elevation height measurement method based on lobe splitting preprocessing, which comprises the steps of firstly, utilizing a lobe splitting phenomenon of a meter-wave radar to establish an error curve graph and an angle coding value in advance, calculating an error value after receiving target information, and then obtaining an angle estimation initial value through comparison; then, obtaining an angle estimation range by utilizing the wave beam width of the meter-wave radar on the basis of the initial value; and after the received data is subjected to real-value processing, the angle measurement precision is improved by utilizing a generalized MUSIC algorithm or a maximum likelihood algorithm. The method is simple and practical, can quickly obtain the target low elevation angle, and has higher angle measurement and height measurement precision.

Description

Meter-wave radar low elevation height measurement method based on lobe splitting pretreatment
Technical Field
The invention relates to the field of low elevation angle estimation of a meter-wave radar, in particular to a low elevation angle height measurement method of the meter-wave radar based on lobe splitting preprocessing.
Background
The meter-wave radar has the advantages of anti-stealth, anti-radiation missile resistance and the like due to the long wavelength, and the meter-wave radar is concerned by scholars at home and abroad today when stealth is used. However, the wave beam of the meter-wave radar is wide, and serious multipath effect exists in a low elevation angle area, so that the low elevation angle estimation of the meter-wave radar becomes a big problem. The existing low elevation angle estimation algorithm mostly utilizes a decorrelation algorithm such as spatial smoothing and matrix reconstruction to process and then utilizes a conventional super-resolution algorithm to estimate the low elevation angle, but the algorithm is large in calculation amount, array aperture is lost, and the method is difficult to implement in practical application.
Disclosure of Invention
The invention aims to improve the low elevation angle height measurement accuracy of the meter wave radar while reducing the implementation difficulty of the low elevation angle height measurement of the meter wave radar, and provides a lobe splitting preprocessing-based low elevation angle height measurement method of the meter wave radar, which is simple and practical, can quickly obtain a target low elevation angle, and has higher angle measurement and high accuracy measurement.
In order to achieve the purpose, the invention is implemented according to the following technical scheme:
a meter-wave radar low elevation height measurement method based on lobe splitting preprocessing comprises the following steps:
s1, establishing an error curve graph and an elevation angle coding value by utilizing a lobe splitting phenomenon of a meter wave radar, calculating an error amplitude of a subarray wave beam after receiving a target echo signal, and obtaining a target low elevation angle coarse estimation value by comparing the error curve graph;
s2, narrowing the spectrum peak searching range by using the half beam width of the conventional array radar and the low elevation rough estimation value of the target obtained in the S1;
s3, carrying out real value processing on the received data by using a unitary matrix;
s4, performing spectral peak search in the narrowed spectral peak search range by utilizing a generalized MUSIC algorithm or a maximum likelihood estimation algorithm to obtain a target low elevation precise estimation value;
and S5, converting the target low elevation angle fine estimation value into target height data by using the geometric relation.
Further, the specific step of S1 is:
s101, assuming a vertically placed meter-wave radar, and constructing a meter-wave radar multi-path propagation model with M receiving array elements, namely receiving antennas;
the data received by the mth array element at time t is represented as:
Figure BDA0002807601650000021
s(t)+nm(t) (1)
in the formula (1), λ is a wavelength; rho is a reflection coefficient and is set to be-1; s (t) is the signal complex envelope; n ism(t) is additive white gaussian noise; thetadIs the target direct wave signal incidence angle; thetasIs the target reflected multipath signal incident angle; the alpha is 2 pi delta R/lambda is the phase difference generated by the time delay difference of the reflected wave and the direct wave; Δ R ═ Ri-RdIs the wave path difference; r is the horizontal distance between the antenna and the target; rdIs a direct wave path; riThe multipath reflection distance from the target to the receiving antenna after the target is reflected by the ground; the direct wave path and the reflected wave path are represented by a geometrical relationship as follows:
Figure BDA0002807601650000022
Figure BDA0002807601650000023
in the formulae (2) and (3), haAnd htRespectively the height of a receiving antenna of the meter-wave radar and the height of a target;
in practical cases, R > haAnd R >＞htTherefore, equation (2) and equation (3) are simplified by quadratic development, and the equation of the path difference obtained by discarding the higher-order terms is as follows:
Figure BDA0002807601650000024
substituting the formula (4) into the phase difference formula to obtain the phase difference alpha-4 pi hthaa/R lambda; the direct wave incident angle theta is obtained by geometric relationshipdIncident angle theta with reflected wavesThe relation of (1):
Figure BDA0002807601650000031
the geometric relational expression can reduce the search of the generalized MUSIC spectral peak from the search of a two-dimensional spectral peak to the search of a one-dimensional spectral peak;
the data received by the entire array at time t is represented as:
Figure BDA0002807601650000032
wherein
Figure BDA0002807601650000033
Representing a multipath fading coefficient; n (t) is an additive white Gaussian noise vector; l is the number of fast beats, a (θ)d),a(θs) The steering vector representing the direct and reflected waves is written as:
Figure BDA0002807601650000034
Figure BDA0002807601650000035
A＝[a(θd),a(θs)]compounding a guide vector for the signal;
s102, obtained by formula (6):
X(θd)＝[x1(θd),...xm(θd),...x13(θd)]T (9)
then, carrying out sub-array beam forming on the array by using a sub-array selection matrix, wherein different sub-arrays comprise as many array elements as possible by using the sub-array synthesis matrix, and the larger the center distance of the sub-arrays is, the better the array elements are;
obtaining the sub-array synthesized beam by using the formula (9) and the sub-array selection matrix as follows:
Figure BDA0002807601650000036
after subarray synthesis, three subarray synthesized beams exist, phase coding is obtained by utilizing phase comparison processing to determine an elevation angle range, phase difference is obtained by conducting phase comparison processing on the ith synthesized beam and the jth synthesized beam, and the following formula is obtained:
Figure BDA0002807601650000037
in equation (12), Φ represents the phase, and the following mathematical processing is performed on the subarray synthesized beam phase difference:
Figure BDA0002807601650000041
c is to be1,2C1,3C2,3Defining as elevation angle code, and determining target elevation angle interval by using the code;
s103, after the target low elevation angle interval is determined, amplitude comparison processing is utilized, namely the error amplitude value of the subarray wave beam is obtained according to the following formula:
Figure BDA0002807601650000042
s104, establishing an error curve graph, namely a coding curve in advance according to the prior conditions of S101-S103;
s105, after receiving the target echo signal, calculating the error amplitude of the subarray wave beam by using the echo signal, and comparing the error amplitude with an error curve chart established in advance to obtain a target low elevation coarse estimation value thetarough。
Further, the specific step of S2 is:
s201, according to the target low elevation angle rough estimation value thetaroughDefining a new spectrum peak search range as theta ═ thetarough-θ1,θrough+θ1) Wherein theta1Is the conventional array radar half beamwidth.
Further, the specific step of S3 is:
s301, equation (6) is an M × L dimensional array received signal matrix, and its covariance matrix is expressed as:
RXX＝E[X(t)XH(t)] (15)
s302, performing real-valued processing on the received data by using a unitary matrix, and defining the unitary matrix as follows:
Figure BDA0002807601650000044
Figure BDA0002807601650000045
II thereinKK x K switching matrix with 1 element on the anti-diagonal and 0, IKA K multiplied by K unit array;
the unitary matrix changes the Centro-Hermitian matrix into a real matrix by a unitary transformation, but RXXIt is not a Centro-Hermitian matrix, so it is transformed into a Centro-Hermitian matrix by a bi-directional smoothing:
Figure BDA0002807601650000051
then, unitary transformation is carried out on the real matrix to obtain a real matrix:
Figure BDA0002807601650000052
similarly, unitary transformation is also performed on the composite steering vector a to obtain a real-valued composite steering vector:
AU＝[UHa(θd),UHa(θs)] (19)。
further, the generalized MUSIC algorithm in S4 has the following calculation formula:
Figure BDA0002807601650000053
in the formula: un is a pair-real covariance matrix RUAnd (3) performing feature decomposition to obtain a real noise subspace, and defining a real value space projection matrix as follows:
Figure BDA0002807601650000054
further, the calculation formula of the maximum likelihood estimation algorithm in S4 is as follows:
Figure BDA0002807601650000055
trace is the trace operator.
Compared with the prior art, firstly, an error curve graph and an angle coding value are established in advance by utilizing a lobe splitting phenomenon of a meter wave radar, and after target information is received, an error value is calculated and compared to obtain an angle estimation initial value; then, obtaining an angle estimation range by utilizing the wave beam width of the meter-wave radar on the basis of the initial value; and after the received data is subjected to real-value processing, the angle measurement precision is improved by utilizing a generalized MUSIC algorithm or a maximum likelihood algorithm. The method is simple and practical, can quickly obtain the target low elevation angle, and has higher angle measurement and height measurement precision.
Drawings
Fig. 1 is a multi-path propagation model of a meter-wave radar constructed according to an embodiment of the invention.
Fig. 2 is a graph of error curves established by an embodiment of the present invention.
Fig. 3 is a spectrum peak search diagram of a lobe splitting preprocessing real-valued generalized MUSIC algorithm and a lobe splitting preprocessing real-valued maximum likelihood estimation algorithm of a simulation example.
Fig. 4 is a graph of the root mean square error value of the lobe splitting preprocessing real-valued generalized MUSIC algorithm and the lobe splitting preprocessing real-valued maximum likelihood algorithm as a function of the signal-to-noise ratio in the simulation example: (a) a graph of height RMSE as a function of signal to noise ratio; (b) low elevation angle RMSE is plotted as a function of signal to noise ratio.
Fig. 5 is a running time diagram of conventional generalized MUSIC, maximum likelihood estimation algorithm, lobe splitting pre-processing real-valued generalized MUSIC based on lobe splitting, and real-valued maximum likelihood estimation algorithm as an array element changes for simulation examples.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. The specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
Assuming a vertically placed linear array radar, the number of receiving array elements is M. As shown in fig. 1, haAnd htRespectively the transmit array antenna height and the target height. Wherein B is the reflection point, R is the horizontal distance between the antenna and the target, RdIs the direct wave path, RiThe multipath reflection distance from the target to the receiving antenna after the target is reflected by the ground. ThetadIs the target direct wave signal incident angle, thetasIs the target reflected multipath signal angle of incidence.
When the meter-wave radar detects a low elevation target, a multipath reflection phenomenon exists, namely, signals received by a receiving array come from four reflection paths: radar-target-radar, radar-target-reflection point-radar, radar-reflection point-target-reflection point-radar. However, when the conventional phased array meter wave radar carries out low elevation height measurement, the distance difference between the target and the mirror image relative to the radar is small, and the target and the mirror image are located in a distance unit. Thus, only the receive multipath may be considered as two reflection paths, namely radar-target-radar, radar-target-reflection point-radar. The data received by the mth array element at time t can be expressed as:
Figure BDA0002807601650000071
s(t)+nm(t) (1)
in the formula (1), λ is wavelength, ρ is reflection coefficient, which is generally-1, s (t) is signal complex envelope, nm(t) is additive white gaussian noise, α ═ 2 π Δ R/λ is the phase difference due to the delay difference between the reflected wave and the direct wave, Δ R ═ Ri-RdIs the wave path difference. The direct wave path and the reflected wave path can be represented by the geometrical relationship as follows:
Figure BDA0002807601650000072
Figure BDA0002807601650000073
in practical cases, R > haAnd R > htTherefore, the equation (2) and (3) are simplified by quadratic expansion, and the equation of the path difference obtained by discarding the higher order term is as follows:
Figure BDA0002807601650000074
substituting formula (4) into the phase difference formula yields a phase difference of 4 pi hthaand/R lambda. Similarly, the incident angle theta of the direct wave can be easily obtained from the geometrical relationshipdIncident angle theta with reflected wavesThe relation of (1):
Figure BDA0002807601650000075
the generalized MUSIC spectral peak search can be reduced from two-dimensional spectral peak search to one-dimensional spectral peak search by utilizing the geometric relational expression.
The data received by the entire array at time t can be expressed as:
Figure BDA0002807601650000076
wherein
Figure BDA0002807601650000077
Representing the multipath fading coefficient, N (t) is an additive white Gaussian noise vector, L is the snapshot number, a (theta)d),a(θs) The steering vector representing the direct and reflected waves is written as:
Figure BDA0002807601650000081
Figure BDA0002807601650000082
A＝[a(θd),a(θs)]the steering vector is compounded for the signal.
Assuming that the number M of receiving antennas is 13, the radar operating frequency is 240MHz, the array element spacing is 0.5M, and the bottom antenna height is 4M. Then, from equation (6):
X(θd)＝[x1(θd),...xm(θd),...x13(θd)]T (9)
and then carrying out sub-array beam synthesis on the beam by using the sub-array selection matrix. The sub-array synthesis matrix is to make different sub-arrays contain as many array elements as possible, and the larger the center distance of the sub-arrays is, the better the array is. The present embodiment selects the matrix as follows:
Figure BDA0002807601650000083
the sub-array synthesized beam can be obtained by using the equations (9) and (10) as follows:
Figure BDA0002807601650000084
after the subarray synthesis, three subarray synthesis beams exist, and at the moment, the low elevation coarse estimation can be performed by utilizing the lobe splitting phenomenon according to the subarray synthesis beams. Because of the 'multi-valued phenomenon' of the error curve, the phase encoding obtained by the phase comparison processing is needed to determine the elevation angle range. And performing phase comparison processing on the ith synthetic beam and the jth synthetic beam to obtain a phase difference as follows:
Figure BDA0002807601650000085
in the formula (12), Φ represents the sampling phase. In practical cases, the phase difference phii,jThere are in-phase and anti-phase phenomena. The elevation range can be determined from this phenomenon. The following mathematical processing is carried out on the subarray synthesized beam phase difference:
Figure BDA0002807601650000091
c is to be1,2C1,3C2,3Defined as the elevation angle code, and the target elevation angle interval can be determined by the code as shown in the table 1.
TABLE 1
C12 C13 C23 Interval of elevation angle
1 1 1 0.5°～4°
1 0 0 4°～5.14°
0 0 1 5.14°～7.2°
After the target low elevation angle interval is determined, amplitude comparison processing is utilized, namely an error amplitude value of the subarray wave beam is obtained according to the following formula:
Figure BDA0002807601650000092
assuming that the number M of the receiving antennas is 13, the radar operating frequency is 240MHz, the array element spacing is 0.5M, the bottom antenna height is 4M, and the ground reflection coefficient rho is-0.95. An error curve graph, i.e., a coding curve, can be established in advance according to the prior condition as shown in fig. 2.
It can be seen from fig. 2 that the error curve is a single value within the determined elevation angle range, so that after receiving the target echo signal, the error amplitude of the subarray beam is calculated by using the echo signal, and then the result is compared with the error curve established in advance to obtain the target low elevation angle coarse estimation value thetarough。
Obtaining a coarse estimation value theta of a target angle through a lobe splitting algorithmroughThen, according to thetaroughDefining a new spectrum peak search range as theta ═ thetarough-θ1,θrough+θ1) Wherein theta1Is the conventional array radar half beamwidth because if the target power is outside the radar beamwidth, the radar will not detect the target.
Equation (6) is an M × L dimensional array received signal matrix, and its covariance matrix can be expressed as:
RXX＝E[X(t)XH(t)] (15)
the equation (15) is a complex matrix, and in order to further reduce the computational complexity of the algorithm, the unitary matrix can be used to perform real-valued processing on the received data. Defining a unitary matrix as follows:
Figure BDA0002807601650000101
Figure BDA0002807601650000102
II thereinKK x K switching matrix with 1 element on the anti-diagonal and 0, IKIs a unit matrix of K multiplied by K.
Depending on the nature of the unitary matrix, the unitary matrix can be transformed from a Centro-Hermitian matrix to a real matrix by a unitary transformation, but RXXIt is not a Centro-Hermitian matrix, so it needs to be bi-directionally smoothed once to convert it into a Centro-Hermitian matrix:
Figure BDA0002807601650000103
then, unitary transformation is carried out on the matrix to obtain a real matrix:
Figure BDA0002807601650000104
similarly, unitary transformation can be performed on the composite steering vector a to obtain a real-valued composite steering vector:
AU＝[UHa(θd),UHa(θs)] (19)
after the real value processing, the low elevation angle fine estimation can be performed by using a maximum likelihood estimation algorithm or a generalized MUSIC algorithm, and it should be noted that the generalized MUSIC algorithm and the maximum likelihood estimation algorithm are widely known and are not described herein. The real-valued generalized MUSIC spectral peak search formula is as follows:
Figure BDA0002807601650000105
in the formula, Un is a real covariance matrix RUAnd (3) performing characteristic decomposition to obtain a real noise subspace, and defining a real value space projection matrix as follows:
Figure BDA0002807601650000106
then the real-valued maximum likelihood estimation spectral peak search formula is as follows:
Figure BDA0002807601650000111
trace is the trace operator. After the target low elevation angle is obtained through spectral peak searching, the target height can be obtained by utilizing the geometric relation.
Simulation example
In order to verify the feasibility of the above embodiment, a computer simulation experiment was performed, which specifically includes the following steps:
assuming a vertically placed meter-wave radar array, the number M of receiving antennas is 13, the radar operating frequency is 240MHz, the array element spacing is 0.5M, the height of the bottom receiving antenna is 4M, and the height h of the transmitting antenna isaThe ground reflection coefficient rho is-0.95 and the target direct wave incidence angle is theta at 7md4.5 degrees. The root mean square error is defined as follows:
Figure BDA0002807601650000112
in the formula (23), K is the Monte Carlo test frequency,
Figure BDA0002807601650000113
is the k-th measurementAnd obtaining the target elevation angle.
Fig. 3 is a spectrum peak search diagram of the lobe splitting preprocessing real-valued generalized MUSIC algorithm and the lobe splitting preprocessing real-valued maximum likelihood algorithm, where the SNR is 10dB, and the snap number snap is 50, as can be found from fig. 3, the algorithm provided in the above embodiment can correctly estimate the target low elevation angle, and greatly reduce the spectrum peak search range.
Fig. 4 is a graph of the root mean square error value of the lobe splitting preprocessing real-valued generalized MUSIC algorithm and the lobe splitting preprocessing real-valued maximum likelihood algorithm provided herein, which varies with the signal-to-noise ratio, the snap number snap is 10, and the monte carlo experiment frequency K is 500.
The following fig. 5 shows the running time of the conventional generalized MUSIC, the maximum likelihood estimation algorithm, the real-valued generalized MUSIC based on lobe splitting preprocessing and the maximum likelihood estimation algorithm based on lobe splitting preprocessing, which varies with the array element, wherein the snapshot number snap 100 can be found from fig. 5, and the running time is obviously reduced after the lobe splitting preprocessing.
Computer simulation results show that the algorithm provided by the invention has lower complexity and still has good angle measurement precision under the conditions of low snapshot and low signal-to-noise ratio.
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.

Claims (6)

1. A meter-wave radar low elevation height measurement method based on lobe splitting pretreatment is characterized by comprising the following steps:
s1, establishing an error curve graph and an elevation angle coding value by utilizing a lobe splitting phenomenon of a meter wave radar, calculating an error amplitude of a subarray wave beam after receiving a target echo signal, and obtaining a target low elevation angle coarse estimation value by comparing the error curve graph;
s2, reducing a spectrum peak searching range by using the half beam width of the conventional array radar and the target low elevation rough estimation value obtained by S1;
s3, carrying out real value processing on the received data by using a unitary matrix;
s4, performing spectral peak search in the narrowed spectral peak search range by utilizing a generalized MUSIC algorithm or a maximum likelihood estimation algorithm to obtain a target low elevation precise estimation value;
and S5, converting the target low elevation angle fine estimation value into target height data by using the geometric relation.
2. The meter-wave radar low elevation height measurement method based on lobe splitting preprocessing as claimed in claim 1, wherein the specific steps of S1 are:
s101, assuming a vertically placed meter-wave radar, and constructing a meter-wave radar multi-path propagation model, wherein the number of receiving array elements, namely receiving antennas, is M;
the data received by the mth array element at time t is represented as:
Figure FDA0002807601640000011
s(t)+nm(t) (1)
in the formula (1), λ is a wavelength; rho is a reflection coefficient and is set to be-1; s (t) is the signal complex envelope; n ism(t) is additive white gaussian noise; thetadIs the target direct wave signal incidence angle; thetasIs the target reflected multipath signal incident angle; the alpha is 2 pi delta R/lambda is the phase difference generated by the time delay difference of the reflected wave and the direct wave; Δ R ═ Ri-RdIs the wave path difference; r is the horizontal distance between the antenna and the target; rdIs a direct wave path; riThe multipath reflection distance from the target to the receiving antenna after the target is reflected by the ground; the direct wave path and the reflected wave path are represented by a geometrical relationship as follows:
Figure FDA0002807601640000012
Figure FDA0002807601640000021
in the formulae (2) and (3), haAnd htRespectively the height of a receiving antenna of the meter-wave radar and the height of a target;
in practical cases, R > haAnd R > htTherefore, equation (2) and equation (3) are simplified by quadratic expansion, and the equation of the path difference obtained by discarding the higher order terms is as follows:
Figure FDA0002807601640000022
substituting the formula (4) into the phase difference formula to obtain the phase difference alpha-4 pi hthaa/R lambda; the direct wave incidence angle theta is obtained by geometric relationshipdIncident angle theta with reflected wavesThe relation of (1):
Figure FDA0002807601640000023
the geometric relational expression can reduce the search of the generalized MUSIC spectral peak from the search of a two-dimensional spectral peak to the search of a one-dimensional spectral peak;
the data received by the entire array at time t is represented as:
Figure FDA0002807601640000024
wherein
Figure FDA0002807601640000025
Representing a multipath fading coefficient; n (t) is an additive white Gaussian noise vector; l is the number of snapshots, a (θ)d),a(θs) The steering vector representing the direct and reflected waves is written as:
Figure FDA0002807601640000026
Figure FDA0002807601640000027
A＝[a(θd),a(θs)]compounding a guide vector for the signal;
s102, obtained by formula (6):
X(θd)＝[x1(θd),...xm(θd),...x13(θd)]T (9)
then, carrying out sub-array beam forming on the array by using a sub-array selection matrix, wherein different sub-arrays comprise as many array elements as possible by using the sub-array synthesis matrix, and the larger the center distance of the sub-arrays is, the better the array elements are;
obtaining the sub-array synthesized beam by using the formula (9) and the sub-array selection matrix as follows:
Figure FDA0002807601640000031
after subarray synthesis, three subarray synthesized beams exist, phase encoding is obtained by utilizing phase comparison processing to determine an elevation angle range, and phase difference is obtained by conducting phase comparison processing on the ith synthesized beam and the jth synthesized beam according to the following formula:
Figure FDA0002807601640000032
in equation (12), Φ represents the phase, and the following mathematical processing is performed on the subarray synthesized beam phase difference:
Figure FDA0002807601640000033
c is to be1,2C1,3C2,3Defining as elevation angle code, and determining target elevation angle interval by using the code;
s103, after the target low elevation angle interval is determined, amplitude comparison processing is utilized, namely the error amplitude value of the subarray wave beam is obtained according to the following formula:
Figure FDA0002807601640000034
s104, establishing an error curve graph, namely a coding curve in advance according to the prior conditions of S101-S103;
s105, after receiving the target echo signal, calculating the error amplitude of the subarray wave beam by using the echo signal, and comparing the error amplitude with an error curve chart established in advance to obtain a target low elevation coarse estimation value thetarough。
3. The meter-wave radar low elevation height measurement method based on lobe splitting preprocessing as claimed in claim 2, wherein the specific steps of S2 are:
s201, according to the target low elevation angle rough estimation value thetarouDefining a new spectrum peak search range as theta ═ thetarough-θ1,θrough+θ1) Wherein theta1Is the conventional array radar half beamwidth.
4. The meter-wave radar low elevation height measurement method based on lobe splitting preprocessing as claimed in claim 1, wherein the specific steps of S3 are:
s301, equation (6) is an M × L dimensional array received signal matrix, and its covariance matrix is expressed as:
RXX＝E[X(t)XH(t)] (15)
s302, performing real-valued processing on the received data by using a unitary matrix, and defining the unitary matrix as follows:
Figure FDA0002807601640000041
Figure FDA0002807601640000042
II thereinKK x K switching matrix with 1 element on the anti-diagonal and 0, IKA K multiplied by K unit array;
the unitary matrix changes the Centro-Hermitian matrix into a real matrix by a unitary transformation, but RXXIt is not a Centro-Hermitian matrix, so it is transformed into a Centro-Hermitian matrix by a bi-directional smoothing:
Figure FDA0002807601640000043
then, unitary transformation is carried out on the real matrix to obtain a real matrix:
Figure FDA0002807601640000044
similarly, unitary transformation is also performed on the composite steering vector a to obtain a real-valued composite steering vector:
AU＝[UHa(θd),UHa(θs)] (19)。
5. the metric-wave radar low elevation height finding method based on lobe splitting preprocessing as claimed in claim 4, wherein the generalized MUSIC algorithm in S4 is calculated as follows:
Figure FDA0002807601640000045
in the formula: un is a pair-real covariance matrix RUAnd (3) performing characteristic decomposition to obtain a real noise subspace, and defining a real value space projection matrix as follows:
Figure FDA0002807601640000051
6. the metric-wave radar low elevation height finding method based on lobe splitting preprocessing as claimed in claim 4, wherein the maximum likelihood estimation algorithm in S4 has the following calculation formula:
Figure FDA0002807601640000052
trace is the trace operator.
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