CN108535698A - The low elevation estimate method of metre wave radar based on beam space - Google Patents

The low elevation estimate method of metre wave radar based on beam space Download PDF

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CN108535698A
CN108535698A CN201810293295.4A CN201810293295A CN108535698A CN 108535698 A CN108535698 A CN 108535698A CN 201810293295 A CN201810293295 A CN 201810293295A CN 108535698 A CN108535698 A CN 108535698A
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CN108535698B (en
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赵永波
霍炯
刘宏伟
苏洪涛
何学辉
陈�胜
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Xidian 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
    • 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
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques

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Abstract

The invention discloses a kind of low elevation estimate methods of metre wave radar based on beam space, mainly solve when array number is larger, the existing problem larger based on the RML algorithm operation quantities in array element space, and implementation step is：1) the metre wave radar Signal reception model x for including multipath signal is established；2) construction beam forming matrix Q；3) it finds out through the transformed reception signal y of beam forming matrix Q and transformed compound direction vector b；4) target elevation estimation is carried out using the method for accurate maximum likelihood RML to transformed reception signal y, finds out the estimated value of target elevationThe present invention is compared with the existing RML algorithms based on array element space, in the case where angle measurement accuracy is essentially identical, can substantially reduce operand, save operation time, convenient for the real-time processing of signal, be conducive to engineer application, can be used under the low elevation angle there are when multipath reflection interference target elevation measurement.

Description

The low elevation estimate method of metre wave radar based on beam space
Technical field
The invention belongs to Radar Technology field, the low elevation estimate method of specifically a kind of metre wave radar can be used for low There are target elevation measurements when multipath reflection interference under the elevation angle.
Background technology
Along with the continuous development of antiradiation missile and target stealth technology, metre wave radar is gradually by the height of countries in the world Degree is paid attention to.When carrying out low-angle tracking, the existing target direct signal of metre wave radar received signal, and have mirror-reflection and overflow anti- Penetrate equal multipath signals and ambient noise.The presence of multipath signal will cause the beam split of radar vertical plane and upwarp, no The detection to echo signal is only influenced, the measurement of elevation of target is also seriously affected.
It is a kind of important means for improving elevation estimate performance using array super resolution technology comprising multiple signal classification MUSIC algorithms and maximum likelihood ML class algorithms etc..But in low signal-to-noise ratio and limited number of snapshots, the former angle measurement performance can be big Amplitude declines, thus using limited in actual radar system.The latter generally requires to carry out multi-dimensional search, and operand is opposite It is larger.But it is not high to radar pulse resource requirement, and suitable for coherent source and single snap the case where.Seemingly such as accurate maximum Right RML algorithms, E.Bosse, R.M.Turner, M.Lecours, " Tracking swerling fluctuating targets at low altitude over the sea,”IEEE Transactions on Aerospace and Electronic Systems,1991,27(5):The prior information of reflectance factor ρ is utilized in 806-822.RML algorithms, is used in combination under multipath conditions multiple Steering vector is closed instead of the conventional steering vector in free space, then arrival angular direction DOA estimations are carried out with maximum likelihood method. Algorithm parameter to be estimated is few, and estimated accuracy is high.But the deficiency of this method is：When the more hour operation quantity of array number can be unfavorable very greatly In Project Realization.
Invention content
Present invention aims at the defect for above-mentioned prior art, propose that a kind of metre wave radar based on beam space is low Elevation estimate method is convenient for Project Realization under the premise of ensureing angle measurement accuracy, to reduce operand.
To achieve the above object, the technical solution adopted by the present invention includes as follows：
(1) the metre wave radar Signal reception model x for including multipath signal is established；
(2) construction beam forming matrix Q；
About 0 ° of symmetrical 3 continuous wave beam, it is respectively-θ to enable its beam position for design0、0°、θ0, the Wave beam forming of foundation Matrix Q ∈ CN×33 column vectors be represented sequentially as：
Q(:, 1) and=exp (j2 π dvsin (- θ0)/λ),
Q(:, 2) and=exp (j2 π dvsin (0)/λ),
Q(:, 3) and=exp (j2 π dvsin (θ0)/λ),
Wherein, Q (:, 1) indicate Q first row, Q (:, 2) indicate Q secondary series, Q (:, 3) and indicate that the third of Q arranges, this 3 Each row of a column vector are directed toward different directions, form wave cover space, and exp () is indicated using natural constant e the bottom of as Exponent arithmetic, j indicate that imaginary unit, d indicate that the array element spacing of radar antenna, λ indicate wavelength, v=[- (N-1):2:N-1]T/ 2, N indicate that bay number, T indicate transposition, sin (θ0) indicate to seek θ0Sine value, θ0Size adjusted according to actual conditions It is whole；
(3) utilize beam forming matrix Q=[Q (:,1)Q(:,2)Q(:, 3)], realize receive signal x from array element space to The conversion of beam space obtains transformed reception signal y=QHX and transformed steering vector b=QHW, wherein w indicate base Compound direction vector in array element space；
(4) target elevation estimation is carried out using the method for accurate maximum likelihood RML to transformed reception signal y, found out The estimated value of target elevation
Wherein L (θ) indicates likelihood function value,Pb=b [bHb]-1bH, H expression conjugate transpositions.
The invention has the advantages that：
1. the present invention under the premise of ensureing angle measurement accuracy, reduces operand compared with prior art.
The existing RML algorithms based on array element space are that the docking collection of letters number carries out a DOA estimations directly in array element grade, work as battle array First more hour operation quantity of number is larger.
And the present invention be by construct beam forming matrix, several wave beams of array element space combination, then to synthesis after The data of Beam Domain carry out DOA estimations using RML algorithms, since transformed wave beam port number is much smaller than array element channel before Number, thus operand can be greatly reduced.
2. saving operation time.
Simulation result shows the present invention relative to the existing RML algorithms based on array element space, although angle measurement accuracy can be slightly Loss, but be not much different, especially in the case of high s/n ratio, the two angle measurement accuracy is essentially identical.But when array number increases When, program execution time of the invention is much smaller, and array number is bigger, and advantage of the invention is more apparent, and operation is greatly saved Time.
Description of the drawings
Fig. 1 is the multipath geometrical model under the metre wave radar low-angle tracking environment that the present invention uses；
Fig. 2 is the implementation flow chart of the present invention；
Fig. 3 be with the present invention with the existing RML algorithms based on array element space, to target elevation estimation root-mean-square error with Signal-to-noise ratio changes comparison diagram；
Fig. 4 is single program execution when estimating target elevation with the present invention and the existing RML algorithms based on array element space Time changes comparison diagram with array number.
Specific implementation mode
For convenience, we are by taking uniform line-array as an example, but the present invention is not limited to uniform line-array.Referring to Fig.1, the present invention uses Metre wave radar low-angle tracking environment under multipath geometrical model, including a uniform line-array being disposed vertically and a height be htTarget.Wherein, reception antenna of the uniform line-array as radar, the array number of antenna are N, and array element spacing is d, in antenna Heart height is hr, the air line distance of target and radar is Rd, the multipath distance formed by reflection is Rm, the direct wave letter of target Number it is respectively θ with the direction of multipath signal1And θ2, it is assumed that direction of arrival more than horizontal direction is the positive direction of angle.
With reference to Fig. 2, the multipath geometrical model of present invention combination Fig. 1 carries out the low elevation angle target direction of arrival of metre wave radar and estimates Meter realizes that steps are as follows：
Step 1, the metre wave radar Signal reception model x for including multipath signal is established.
When carrying out low-angle tracking, the existing target direct signal of metre wave radar received signal, and have multipath return, And ambient noise.For convenience, present invention assumes that it is single goal model, and the case where be mirror-reflection.Wherein target is through Signal can use θ1Steering vector a (θ on direction1) and θ1Complex envelope S on direction1Product obtains；Same mirror signal can Use θ2Steering vector a (θ on direction2) and θ2Complex envelope S on direction2Product obtains.I.e.：
X=a (θ1)s1+a(θ2)s2+n
Due in the geometrical model of Fig. 1, θ2With θ1There are geometrical relationships：θ2=-arcsin (sin (θ1)+2hr/Rd), Sin () expressions ask sine operation, arcsin () to indicate negate sine operation, and θ2With θ1Complex envelope on direction meets：s2 =ρ e-jψs1, ρ expression reflectance factors, ψ is direct-path signal and multipath signal in the phase difference of array reference point, the π Δs of ψ=2 R/ λ, Δ R indicate the range difference of through distance and multipath distance, therefore x can be reduced to following form：
X=ws+n
Wherein w=a (θ1)+ρe-jψa(-arcsin(sin(θ1)+2hr/Rd)) indicate compound direction vector, a (- arcsin (sin(θ1)+2hr/Rd)) indicate multipath return steering vector a (θ2), s indicates the multiple packet in target direct-path signal direction Network s1；n∈CN×1Indicate that zero-mean justifies white Gaussian noise, and, noise variance Var (n)=σ uncorrelated to signal2I, wherein σ2 Indicate that its variance yields size, I indicate unit matrix.
Step 2, construction beam forming matrix Q.
The building method of beam forming matrix has very much, and the angle measurement accuracy of distinct methods can be variant.Usually, using 3 The RML algorithms of a continuous wave beam, performance are further added by wave beam number, angle measurement already close to the RML algorithms based on array element space The improvement of energy is less apparent, but corresponding operand can greatly improve.
About 0 ° of symmetrical 3 continuous wave beam, it is respectively-θ to enable its beam position for present invention design0、0°、θ0, establish wave beam Form matrix Q ∈ CN×33 column vectors be represented sequentially as：
Q(:, 1) and=exp (j2 π dvsin (- θ0)/λ)；
Q(:, 2) and=exp (j2 π dvsin (0)/λ)；
Q(:, 3) and=exp (j2 π dvsin (θ0)/λ)；
Wherein Q (:, 1) indicate Q first row, Q (:, 2) indicate Q secondary series, Q (:, 3) and indicate that the third of Q arranges, this 3 Each row of column vector are directed toward different directions, form wave cover space, and exp () is indicated using natural constant e as the finger at bottom Number operation, j indicate that imaginary unit, d indicate that the array element spacing of radar antenna, λ indicate wavelength,N Indicate that bay number, T indicate transposition, θ0Size can be adjusted according to actual conditions, to keep beam position space special Fixed region；
Beam forming matrix is obtained by 3 column vectors：Q=[Q (:,1) Q(:,2) Q(:,3)].
Step 3, it finds out through the transformed reception signal y of beam forming matrix and transformed compound direction vector b.
Collection of letters x is docked by beam forming matrix Q to be converted, and transformed reception signal is obtained：Y=QHx；
Compound direction vector w is converted by beam forming matrix Q, obtains transformed compound direction vector：B= QHw；
Pass through the conversion of above-mentioned beam forming matrix Q, so that it may realize that receive signal turns from array element space to beam space It changes.
Step 4, target elevation estimation is carried out using the method for accurate maximum likelihood RML to transformed reception signal y, asked Go out the estimated value of target elevation
RML algorithms are a kind of effective target elevation methods of estimation, it is based on traditional maximum likelihood ML algorithms. The prior information of reflectance factor ρ is utilized in RML algorithms, and compound direction vector under multipath conditions is used in combination to replace routine in free space Steering vector, then target elevation is estimated with ML algorithms, by taking the reception signal of single snap as an example, specific implementation process is such as Under：
(4a) utilizes the Signal reception model x=ws+n that step 1 is established, and obtains preliminary log likelihood function expression formula：
Under the conditions of the signal model of step 1, x can be regarded as obey mean value be ws, covariance matrix σ2The N-dimensional of I Gaussian vectors can obtain the following expression of conditional probability：
According to the thought for seeking maximum likelihood, to formula<4-1>Logarithm is taken, and removes constant, preliminary log likelihood function can be obtained Expression formula is：
(4b) is to the noise variance value σ in preliminary log likelihood function2Estimated, obtains new likelihood function formula：
Maximum value is obtained to preliminary log likelihood function, then to formula<4-2>Derivation is carried out, and it is 0 to enable its derivative, is acquired Noise variance value σ2Estimated value：
By formula<4-3>Obtained σ2Estimated value substitutes into formula<4-2>In, and remove the likelihood function that constant term can obtain newly and be：
(4c) estimates the complex envelope s in direct-path signal direction, obtains the final likelihood function formula of RML algorithms：
Use formula<4-4>Conjugation local derviation is asked to s, and order is null vector, the estimated value for obtaining s is：
S=[wHw]-1wHx <4-5>
By formula<4-5>Substitution formula<4-4>In can obtain：
To formula<4-6>Simultaneously abbreviation is arranged, removes constant term therein, can obtain the final likelihood function of RML algorithms is：
Wherein, Pw=w [wHw]-1wH；
(4d) seeks the target elevation estimated value of the RML algorithms based on beam space：
Pass through the transformed reception signal y of beam forming matrix Q and transformed composite guide by what is obtained in step 3 Formula is substituted into vector b<4-7>In, it obtains：
Wherein, Pb=b [bHb]-1bH；
When L (θ) being enabled to obtain maximum value corresponding θ value sizes are exactly the estimated value of target elevation, therefore target elevation is estimated EvaluationIt is represented by：
The effect of the present invention can be further illustrated by following Computer Simulation：
One, simulated conditions
Using vertical uniform uniform line-array, if array number N=15, wavelength X=2m, array element spacing d=1m, the high h of antenna holderr =12m, object height ht=4000m, target and radar antenna distance Rd=100km, reflectance factor ρ=0.9ejπ, array element noise It is -5dB~15dB than value range, the beam position of beam forming matrix takes -3 °, 0 °, 3 ° respectively.
Assuming that the reception noise of each array element is independent identically distributed zero-mean circle white Gaussian noise.Target elevation is estimated Counting definition of accuracy is For the estimated value that n-th is tested, θ is target elevation Actual value, MC is the total degree of Monte-Carlo experiments, in emulation experiment, MC=500.RMSE is smaller, represents elevation estimate Error is smaller.
Two, emulation content
Emulation 1：Under above-mentioned simulated conditions, with the angle measurement of the invention obtained with the existing RML algorithms based on array element space Precision is compared with signal-to-noise ratio change curve, as a result such as Fig. 3.
As seen from Figure 3, in low signal-to-noise ratio, with the present invention compared with the existing RML algorithms based on array element space, Though angle measurement accuracy is slightly lost, difference is less than 0.045 °；And with the increase of signal-to-noise ratio, angle measurement accuracy of the invention is gradual Close to the angle measurement accuracy of the RML algorithms based on array element space.
Emulation two：Under above-mentioned simulated conditions, setting array element signal-to-noise ratio be 10dB, bay number value range be 10~ 55, it is carried out pair with array number change curve with the existing RML algorithm single program execution times based on array element space with the present invention Than as a result such as Fig. 4.
As seen from Figure 4, when array number is smaller, it is little that two kinds of algorithm routines execute time phase difference；With array number Increase, the existing RML algorithm routines execution time based on array element space sharply increases, and the present procedure execution time then changes Very little.When array number is larger, advantage of the invention is more apparent, has been greatly saved operation time, easily facilitates engineer application.

Claims (2)

1. a kind of low elevation estimate method of metre wave radar based on beam space, including：
(1) the metre wave radar Signal reception model x for including multipath signal is established；
(2) construction beam forming matrix Q；
About 0 ° of symmetrical 3 continuous wave beam, it is respectively-θ to enable its beam position for design0、0°、θ0, the beam forming matrix of foundation Q∈CN×33 column vectors be represented sequentially as：
Q(:, 1) and=exp (j2 π dvsin (- θ0)/λ),
Q(:, 2) and=exp (j2 π dvsin (0)/λ),
Q(:, 3) and=exp (j2 π dvsin (θ0)/λ),
Wherein, Q (:, 1) indicate Q first row, Q (:, 2) indicate Q secondary series, Q (:, 3) and indicate that the third of Q arranges, this 3 row Each row of vector are directed toward different directions, form wave cover space, and exp () is indicated using natural constant e as the index at bottom Operation, j indicate that imaginary unit, d indicate that the array element spacing of radar antenna, λ indicate wavelength, v=[- (N-1):2:N-1]T/ 2, N table Show that bay number, T indicate transposition, sin (θ0) indicate to seek θ0Sine value, θ0Size be adjusted according to actual conditions；
(3) utilize beam forming matrix Q=[Q (:,1) Q(:,2) Q(:, 3)], it realizes and receives signal x from array element space to wave The conversion in beam space obtains transformed reception signal y=QHX and transformed steering vector b=QHW, wherein w expression are based on The compound direction vector in array element space；
(4) target elevation estimation is carried out using the method for accurate maximum likelihood RML to transformed reception signal y, finds out target The estimated value at the elevation angle
Wherein L (θ) indicates likelihood function value,Pb=b [bHb]-1bH, H expression conjugate transpositions.
2. according to the method described in claim 1, the metre wave radar signal comprising multipath signal that wherein step (1) is established receives Model x is indicated as follows：
X=ws+n
Wherein x ∈ CN×1Indicate that the data that radar antenna array single snap receives, N indicate that bay number, w indicate composite guide To vector, w=a (θ1)+ρe-jψa(-arcsin(sin(θ1)+2hr/Rd)), wherein a (θ1) indicate that the guiding of direct-path signal is sweared Amount, a (- arcsin (sin (θ1)+2hr/Rd)) indicating the steering vector of multipath signal, arcsin () expressions are negated sinusoidal fortune It calculates, ρ indicates that reflectance factor, ψ are direct-path signal and multipath signal in the phase difference of array reference point, the π Δ R/ λ of ψ=2, Δ R tables Show the range difference of through distance and multipath distance；S indicates the complex envelope of target direct-path signal, n ∈ CN×1Indicate that zero-mean circle is high This white noise, it is uncorrelated to signal, and noise variance Var (n)=σ2I, wherein σ2Indicate that its variance yields size, I indicate unit square Battle array.
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