CN108535698B - Meter-wave radar low elevation angle estimation method based on beam space - Google Patents

Meter-wave radar low elevation angle estimation method based on beam space Download PDF

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CN108535698B
CN108535698B CN201810293295.4A CN201810293295A CN108535698B CN 108535698 B CN108535698 B CN 108535698B CN 201810293295 A CN201810293295 A CN 201810293295A CN 108535698 B CN108535698 B CN 108535698B
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赵永波
霍炯
刘宏伟
苏洪涛
何学辉
陈�胜
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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
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Abstract

The invention discloses a method for estimating a low elevation angle of a meter-wave radar based on a beam space, which mainly solves the problem that the operation amount of the prior RML algorithm based on the array element space is large when the number of array elements is large, and comprises the following implementation steps: 1) establishing a meter-wave radar signal receiving model x containing multipath signals; 2) constructing a beam forming matrix Q; 3) solving a receiving signal y converted by the beam forming matrix Q and a converted composite steering vector b; 4) estimating the target elevation angle of the converted received signal y by adopting a method of accurate maximum likelihood (RML), and solving the estimated value of the target elevation angle
Figure DDA0001618141230000011
Compared with the prior RML algorithm based on the array element space, the method can greatly reduce the operation amount, save the operation time, facilitate the real-time processing of signals, be beneficial to engineering application and be used for target elevation angle measurement when multipath reflection interference exists under low elevation angles under the condition that the angle measurement precision is basically the same.

Description

Meter-wave radar low elevation angle estimation method based on beam space
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a low elevation angle estimation method for a meter wave radar, which can be used for target elevation angle measurement when multipath reflection interference exists under a low elevation angle.
Background
With the continuous development of anti-radiation missiles and target stealth technologies, the meter-wave radar is gradually paid high attention from all countries in the world. When low-angle tracking is carried out, signals received by the meter-wave radar not only have target direct signals, but also multipath signals such as mirror reflection, diffuse reflection and the like, and background noise. The existence of multipath signals can cause lobe splitting and upwarping of a radar vertical plane, which not only affects the detection of target signals, but also seriously affects the elevation angle measurement of the target.
The adoption of the array super-resolution technology is an important means for improving the elevation estimation performance, and comprises a multi-signal classification MUSIC algorithm, a maximum likelihood ML algorithm and the like. However, at low signal-to-noise ratio and limited fast beat number, the angle measurement performance of the former is greatly reduced, and thus the application in a practical radar system is limited. The latter often requires multidimensional searching and is relatively computationally expensive. But it has low requirement on radar pulse resources and is suitable for coherent sources and single snapshot situations. For example, the precise maximum likelihood RML algorithm, e.bosse, r.m.turner, m.lecours, "Tracking switching deflecting target at low arrival over the sea," IEEE Transactions on aeronautics and Electronic Systems,1991,27(5):806-822.RML algorithm uses the prior information of the reflection coefficient ρ, replaces the conventional steering vector in free space with the composite steering vector under multipath conditions, and estimates the direction of arrival DOA using the maximum likelihood method. The algorithm has few parameters to be estimated and high estimation precision. But the disadvantages of the method are: when the number of array elements is large, the calculation amount is large, and the engineering realization is not facilitated.
Disclosure of Invention
The invention aims to provide a method for estimating the low elevation angle of the meter-wave radar based on the beam space, aiming at overcoming the defects of the prior art, so that the calculation amount is reduced on the premise of ensuring the angle measurement precision, and the engineering realization is facilitated.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) establishing a meter-wave radar signal receiving model x containing multipath signals;
(2) constructing a beam forming matrix Q;
3 continuous beams symmetrical about 0 DEG are designed, and the beam directions are respectively-theta0、0°、θ0The established beamforming matrix Q ∈ CN×3The 3 column vectors are sequentially represented as:
Q(:,1)＝exp(j2πdvsin(-θ0)/λ)，
Q(:,2)＝exp(j2πdvsin(0)/λ)，
Q(:,3)＝exp(j2πdvsin(θ0)/λ)，
wherein Q (: 1) represents a first column of Q, Q (: 2) represents a second column of Q, Q (: 3) represents a third column of Q, each column of the 3 column vectors points in a different direction to form a beam coverage space, exp (·) represents an exponential operation with a natural constant e as the base, j represents an imaginary unit, d represents an array element pitch of the radar antenna, λ represents a wavelength, v [ - (N-1):2: N-1)]TN denotes the number of antenna elements, T denotes the transposition, sin (theta)0) Expression of finding theta0Sine value, θ0The size of the pressure sensor is adjusted according to the actual situation;
(3) using a beamforming matrix Q ═ Q (: 1) Q (: 2) Q (: 3)]Realizing the conversion of the received signal x from the array element space to the beam space, and obtaining the converted received signal y as QHx and the transformed steering vector b ═ QHw, wherein w represents a composite steering vector based on an array element space;
(4) estimating the target elevation angle of the converted received signal y by adopting a method of accurate maximum likelihood (RML), and solving the estimated value of the target elevation angle
Figure BDA0001618141210000021
Figure BDA0001618141210000022
Where L (theta) represents the likelihood function values,
Figure BDA0001618141210000023
Pb＝b[bHb]-1bHand H denotes a conjugate transpose.
The invention has the following advantages:
1. compared with the prior art, the invention reduces the calculation amount on the premise of ensuring the angle measurement precision.
The existing RML algorithm based on the array element space directly performs DOA estimation on a received signal at the array element level, and when the number of array elements is large, the calculation amount is large.
The invention synthesizes array element space into a plurality of wave beams by constructing a wave beam forming matrix, and then adopts an RML algorithm to carry out DOA estimation on the data of the synthesized wave beam domain.
2. The operation time is saved.
Simulation results show that compared with the existing RML algorithm based on the array element space, the angle measurement precision is slightly lost, but the difference is not large, and particularly under the condition of high signal-to-noise ratio, the angle measurement precision of the two is basically the same. However, when the number of array elements is increased, the program execution time of the invention is much smaller, and the advantage of the invention is more obvious when the number of array elements is larger, thereby greatly saving the operation time.
Drawings
FIG. 1 is a multi-path geometric model in a low-angle tracking environment of a meter-wave radar used in the invention;
FIG. 2 is a flow chart of an implementation of the present invention;
FIG. 3 is a graph comparing the RMS error of target elevation estimation with the signal-to-noise ratio using the present invention and the prior array element space based RML algorithm;
fig. 4 is a comparison graph of the single program execution time with the array element number variation when estimating the target elevation angle by using the present invention and the existing RML algorithm based on the array element space.
Detailed Description
For convenience, we take equidistant linear arrays as an example, but the invention is not limited to equidistant linear arrays. Ginseng radix (Panax ginseng C.A. Meyer)Referring to fig. 1, the multi-path geometric model under the low-angle tracking environment of the meter-wave radar used by the invention comprises an equidistant linear array vertically arranged and a height htThe object of (1). The equidistant linear array is used as a receiving antenna of the radar, the number of array elements of the antenna is N, the spacing between the array elements is d, and the center height of the antenna is hrThe linear distance between the target and the radar is RdThe multipath distance due to reflection is RmThe directions of the direct wave signal and the multipath signal of the target are theta1And theta2The direction of arrival above the horizontal direction is assumed to be the positive direction of the angle.
Referring to fig. 2, the method performs the estimation of the direction of arrival of the low elevation angle target of the meter-wave radar by combining the multipath geometric model of fig. 1, and the implementation steps are as follows:
step 1, establishing a meter-wave radar signal receiving model x containing multipath signals.
When low-angle tracking is carried out, signals received by the meter-wave radar have not only target direct signals, but also multipath reflected signals and background noise. For convenience, the present invention assumes that it is a single object model, and is the case of specular reflection. Where the direct target signal can be theta1Directional vector a (theta) in the direction1) And theta1Complex envelope S in direction1Obtaining a product; the same mirror reflection signal can be used2Directional vector a (theta) in the direction2) And theta2Complex envelope S in direction2The product is obtained. Namely:
x＝a(θ1)s1+a(θ2)s2+n
since in the geometric model of FIG. 1, θ2And theta1There is a geometric relationship: theta2＝-arcsin(sin(θ1)+2hr/Rd) Sin (-) denotes sine calculation, arcsin (-) denotes arcsine calculation, and θ2And theta1The complex envelope in the direction satisfies: s2＝ρe-jψs1Where ρ represents a reflection coefficient, ψ is a phase difference between a direct wave signal and a multipath signal at an array reference point, ψ is 2 π Δ R/λ, Δ R represents a distance difference between a direct distance and a multipath distance, and thus x can be simplified as inThe following forms:
x＝ws+n
where w ═ a (θ)1)+ρe-jψa(-arcsin(sin(θ1)+2hr/Rd) Denotes a composite steering vector, a (-arcsin (sin (θ)1)+2hr/Rd) A steering vector a (theta) representing a multipath reflected signal2) And s represents the complex envelope s of the target direct wave signal direction1；n∈CN×1Representing zero mean round white gaussian noise, and being uncorrelated with the signal, with a noise variance var (n) ═ σ2I, where σ2The variance value is shown, and I is an identity matrix.
And 2, constructing a beam forming matrix Q.
There are many methods for constructing the beam forming matrix, and the angle measurement accuracy of different methods is different. Generally, the performance of the RML algorithm adopting 3 continuous beams is already close to that of the RML algorithm based on the array element space, and then the number of the beams is increased, so that the improvement of the angle measurement performance is not obvious, but the corresponding operand is greatly improved.
The invention designs 3 continuous wave beams symmetrical about 0 degree, and the wave beam directions are respectively theta0、0°、θ0Establishing a beamforming matrix Q ∈ CN×3The 3 column vectors are sequentially represented as:
Q(:,1)＝exp(j2πdvsin(-θ0)/λ)；
Q(:,2)＝exp(j2πdvsin(0)/λ)；
Q(:,3)＝exp(j2πdvsin(θ0)/λ)；
wherein Q (: 1) represents a first column of Q, Q (: 2) represents a second column of Q, Q (: 3) represents a third column of Q, each column of the 3 column vectors points in a different direction forming a beam coverage space, exp (·) represents an exponential operation with a natural constant e as the base, j represents an imaginary unit, d represents an array element pitch of the radar antenna, λ represents a wavelength,
Figure BDA0001618141210000041
n denotes the number of antenna elements, T denotes the transposition, theta0Can be adjusted according to the actual situation, thereby leading the beam to point to the nullA specific region;
the beamforming matrix is derived from 3 column vectors: q ═ Q (: 1) Q (: 2) Q (: 3) ].
And 3, obtaining the received signal y converted by the beam forming matrix and the converted composite steering vector b.
Converting the received signal x by the beam forming matrix Q to obtain a converted received signal: y is QHx；
Converting the composite steering vector w through the beam forming matrix Q to obtain a converted composite steering vector: b is QHw；
By switching the beam forming matrix Q, the received signal can be switched from the array element space to the beam space.
Step 4, carrying out target elevation estimation on the converted received signal y by adopting a precise maximum likelihood (RML) method, and solving an estimated value of the target elevation
Figure BDA0001618141210000051
The RML algorithm is an efficient target elevation estimation method, which is based on the traditional maximum likelihood ML algorithm. The RML algorithm utilizes prior information of a reflection coefficient rho, replaces a conventional guide vector in a free space with a composite guide vector under a multipath condition, estimates a target elevation angle by using an ML algorithm, takes a received signal of a single snapshot as an example, and concretely realizes the following processes:
(4a) and (2) obtaining an initial log-likelihood function expression by using the signal receiving model x which is established in the step 1 as ws + n:
under the signal model condition of step 1, x can be regarded as obeying mean value ws and covariance matrix σ2An N-dimensional gaussian vector of I, the following expression of conditional probability can be obtained:
Figure BDA0001618141210000052
according to the idea of solving the maximum likelihood, taking the logarithm of the formula <4-1>, and removing the constant, the expression of the obtained initial log-likelihood function is as follows:
Figure BDA0001618141210000053
(4b) for the noise variance value sigma in the initial log-likelihood function2Estimating to obtain a new likelihood function formula:
if the initial log-likelihood function is to obtain the maximum value, the equation is obtained<4-2>The derivative is calculated and the derivative is 0 to obtain the noise variance value sigma2Estimated value of (a):
Figure BDA0001618141210000054
general formula<4-3>Obtained sigma2Substitution of estimated values into<4-2>And the new likelihood function obtained by removing the constant term is as follows:
Figure BDA0001618141210000055
(4c) estimating a complex envelope s of the direction of the direct wave signal to obtain a final likelihood function formula of an RML algorithm:
the conjugate bias is calculated for s by the equation <4-4> and is made to be a zero vector, and the estimated value of s is obtained as:
s＝[wHw]-1wHx <4-5>
the formula <4-4> can be substituted by the formula <4-5 >:
Figure BDA0001618141210000061
and (3) clearing and simplifying the formula <4-6>, and removing constant terms in the formula to obtain the final likelihood function of the RML algorithm as follows:
Figure BDA0001618141210000062
wherein，Pw＝w[wHw]-1wH；
(4d) Solving a target elevation angle estimated value of the beam space-based RML algorithm:
substituting the received signal y after being converted by the beam forming matrix Q and the converted composite steering vector b obtained in the step 3 into an expression <4-7>, so as to obtain:
Figure BDA0001618141210000063
wherein, Pb＝b[bHb]-1bH；
Let the theta value corresponding to the maximum L (theta) be the estimated value of the target elevation angle, so the estimated value of the target elevation angle
Figure BDA0001618141210000064
Can be expressed as:
Figure BDA0001618141210000065
the effects of the present invention can be further illustrated by the following computer simulation:
first, simulation condition
Vertical uniform equidistant linear array is used, the number of array elements N is 15, the wavelength lambda is 2m, the distance d between the array elements is 1m, and the height h of the antenna framer12m, target height ht4000m, target to radar antenna distance Rd100km, reflection coefficient ρ 0.9ejπThe array element signal-to-noise ratio value range is-5 dB-15 dB, and the beam directions of the beam forming matrix are respectively-3 degrees, 0 degrees and 3 degrees.
The received noise of each array element is assumed to be independent and equally distributed zero-mean circular white Gaussian noise. The accuracy of the estimation of the target elevation angle is defined as
Figure BDA0001618141210000066
Figure BDA0001618141210000067
Is as followsAnd (3) obtaining an estimated value in n times of experiments, wherein theta is a true value of the target elevation angle, MC is the total times of Monte-Carlo experiments, and in the simulation experiment, MC is 500. The smaller the RMSE, the smaller the error representing the elevation angle estimate.
Second, simulation content
Simulation 1: under the simulation conditions, the angle measurement precision along with the signal-to-noise ratio change curve obtained by the method and the prior RML algorithm based on the array element space are compared, and the result is shown in figure 3.
As seen from fig. 3, under the condition of low signal-to-noise ratio, compared with the conventional RML algorithm based on the array element space, the angle measurement accuracy is slightly lost, but the difference is less than 0.045 °; and with the increase of the signal-to-noise ratio, the angle measurement precision of the method gradually approaches the angle measurement precision of the RML algorithm based on the array element space.
Simulation II: under the simulation conditions, the signal-to-noise ratio of the array element is set to be 10dB, the value range of the antenna array element number is 10-55, the single program execution time of the method is compared with the single program execution time of the existing RML algorithm based on the array element space along with the change curve of the array element number, and the result is shown in FIG. 4.
As seen from fig. 4, when the number of array elements is small, the execution times of the two algorithm programs are not much different; with the increase of the number of the array elements, the execution time of the existing RML algorithm program based on the array element space is increased sharply, and the change of the execution time of the program of the invention is small. When the array element number is larger, the method has more obvious advantages, greatly saves the operation time and is more convenient for engineering application.

Claims (2)

1. A method for estimating a low elevation angle of a meter-wave radar based on a beam space comprises the following steps:
(1) establishing a meter-wave radar signal receiving model x containing multipath signals;
(2) constructing a beam forming matrix Q;
3 continuous beams symmetrical about 0 DEG are designed, and the beam directions are respectively-theta0、0°、θ0The established beamforming matrix Q ∈ CN×3The 3 column vectors are sequentially represented as:
Q(:,1)＝exp(j2πdvsin(-θ0)/λ)，
Q(:,2)＝exp(j2πdvsin(0)/λ)，
Q(:,3)＝exp(j2πdvsin(θ0)/λ)，
wherein Q (: 1) represents a first column of Q, Q (: 2) represents a second column of Q, Q (: 3) represents a third column of Q, each column of the 3 column vectors points in a different direction to form a beam coverage space, exp (·) represents an exponential operation with a natural constant e as the base, j represents an imaginary unit, d represents an array element pitch of the radar antenna, λ represents a wavelength, v [ - (N-1):2: N-1)]TN denotes the number of antenna elements, T denotes the transposition, sin (theta)0) Expression of finding theta0Sine value, θ0The size of the pressure sensor is adjusted according to the actual situation;
(3) using a beamforming matrix Q ═ Q (: 1) Q (: 2) Q (: 3)]Realizing the conversion of the received signal x from the array element space to the beam space, and obtaining the converted received signal y as QHx and the transformed steering vector b ═ QHw, wherein w represents a composite steering vector based on an array element space;
(4) estimating the target elevation angle of the converted received signal y by adopting a method of accurate maximum likelihood (RML), and solving the estimated value of the target elevation angle
Figure FDA0001618141200000011
Figure FDA0001618141200000012
Where L (theta) represents the likelihood function values,
Figure FDA0001618141200000013
Pb＝b[bHb]-1bHand H denotes a conjugate transpose.
2. The method of claim 1, wherein the metric-wave radar signal reception model x containing the multipath signals established in step (1) is represented as follows:
x＝ws+n
wherein x ∈ CN×1Data received by the radar antenna array in single snapshot is represented, N represents the number of antenna elements, w represents a composite steering vector, and w is a (theta)1)+ρe-jψa(-arcsin(sin(θ1)+2hr/Rd) Wherein a (theta)1) Denotes a steering vector of the direct wave signal, a (-arcsin (sin (θ)1)+2hr/Rd) Representing a guide vector of a multipath signal, arcsin (·) representing inverse sine operation, ρ representing a reflection coefficient, ψ is a phase difference between a direct wave signal and the multipath signal at an array reference point, ψ is 2 pi Δ R/λ, Δ R represents a distance difference between a direct distance and the multipath distance; s represents the complex envelope of the target direct wave signal, n is equal to CN×1Represents zero mean round white gaussian noise, is uncorrelated with the signal, and has a noise variance var (n) ═ σ2I, where σ2The variance value is shown, and I is an identity matrix.
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