CN106291499B - Wave arrival direction estimating method based on least variance method vector correlation - Google Patents
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- 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
本发明属于雷达信号处理技术领域，公开了一种基于最小方差法矢量相关性的波达方向估计方法，包括：设定雷达均匀线阵，根据雷达均匀线阵得到雷达接收数据，并根据雷达均匀线阵确定第一导向矢量和第二导向矢量；根据雷达接收数据，计算雷达接收数据的协方差矩阵，并对其求逆，得到雷达接收数据的协方差逆矩阵，从而确定雷达接收数据的协方差逆矩阵的算术平方根；根据第一导向矢量、第二导向矢量和雷达接收数据的协方差逆矩阵的算术平方根计算第一相关矢量和第二相关矢量，并构造空间谱函数；根据空间谱函数，对波达方向进行最大似然估计，得到波达方向的估计值；以提高角度分辨率和测向性能的稳健性。
The invention belongs to the technical field of radar signal processing, and discloses a method for estimating direction of arrival based on minimum variance method vector correlation, comprising: setting a radar uniform linear array, obtaining radar received data according to the radar uniform linear array, and The linear array determines the first steering vector and the second steering vector; according to the radar received data, calculate the covariance matrix of the radar received data, and inverse it to obtain the inverse covariance matrix of the radar received data, thereby determining the covariance matrix of the radar received data. The arithmetic square root of the inverse variance matrix; calculate the first correlation vector and the second correlation vector according to the arithmetic square root of the first steering vector, the second steering vector and the inverse covariance matrix of the radar received data, and construct a spatial spectral function; according to the spatial spectral function , the maximum likelihood estimation of the direction of arrival is carried out, and the estimated value of the direction of arrival is obtained; in order to improve the angular resolution and the robustness of the direction finding performance.
Description
Technical field
The invention belongs to Radar Signal Processing Technology fields more particularly to a kind of based on least variance method vector correlation
Wave arrival direction estimating method can be used for target positioning and tracking.
Background technique
It is signal wave by the subspace class algorithm of representative of multiple signal classification MUSIC and invariable rotary subspace ESPRIT
One of the most important method estimated up to direction DOA.This kind of algorithm is empty using signal subspace and noise according to known information source number
Between between orthogonality estimate DOA.Due to signal subspace and noise subspace be under noiseless model it is completely orthogonal, because
It can unlimited close two realizations of goal resolution in this subspace class theory of algorithm.
Although there is subspace class algorithm excellent super-resolution to estimate performance, they are almost required to known information source number and make
For prior information, by Eigenvalues Decomposition, then DOA estimation is carried out.In Estimation Methods for Source Number, information theory criterion AIC and most
Small description length criteria MDL is relatively effective, however due to the limitation of number of sampling points in practical application, estimate performance with
The reduction of Signal to Noise Ratio (SNR) and reduce, error probability is increase accordingly, eventually lead to DOA estimation method failure.
Capon proposes minimum variance Power estimation algorithm MVDR, avoids the estimation of information source number.Capon algorithm makes noise
And the power that any signal on non-information source direction is contributed is minimum, while keeping the signal power on information source direction
It is constant, but its angular resolution is lower.
However, the super-resolution Measure direction performance of above-mentioned super resolution algorithm be all based on array manifold it is accurately known under the premise of
It obtains.But in actual engineer application, true array manifold is often with weather, environment and device itself
Change and a degree of deviation occurs.Such as each array element electromagnetic property of antenna is likely to occur between inconsistent, array element and exists
There are deviations etc. for coupling, the actual position of array element and nominal position.At this point, the performance of these super-resolution Direction Finding Algorithms can be serious
Deteriorate, or even failure.
Summary of the invention
For the deficiency of above-mentioned prior art, the purpose of the present invention is to provide one kind to be based on least variance method vector correlation
The Wave arrival direction estimating method of property, to improve the robustness of angular resolution and Measure direction performance.
The technical principle that the present invention realizes is: the present invention utilizes vector on the direction θAnd its θ ' closed on is square
Upward vectorCorrelation indicate vector on the direction θVariation.Utilize vectorChange
Change to construct space spectral function, the estimation of direction of arrival is carried out using the spectrum peak position of space spectral function, improves its angle point
The robustness of resolution and Measure direction performance.
In order to achieve the above objectives, the embodiment of the present invention, which adopts the following technical scheme that, is achieved.
A kind of Wave arrival direction estimating method based on least variance method vector correlation, described method includes following steps:
Step 1, radar even linear array is set, radar is obtained according to the radar even linear array and receives data, and according to institute
It states radar even linear array and determines the first steering vector a (θ) and the second steering vector a (θ ')；The relational expression of θ and θ ' are as follows: sin θ=
Sin θ '+ρ, ρ ∈ [10-8, 10-4]；
Step 2, data are received according to the radar, calculates radar and receive the covariance matrix of data, and invert to it, obtains
The covariance inverse matrix of data is received to radar, so that it is determined that radar receives the arithmetic square root of the covariance inverse matrix of data；
Step 3, the arithmetic square root that the covariance inverse matrix of data is received according to the first steering vector and radar calculates the
One dependent vector；The second phase is calculated according to the arithmetic square root that the second steering vector and radar receive the covariance inverse matrix of data
Close vector；
Step 4, according to the first dependent vector of arithmetic and the second dependent vector, space spectral function is constructed；
Step 5, according to the space spectral function, maximal possibility estimation is carried out to direction of arrival, obtains estimating for direction of arrival
Evaluation.
The invention has the following advantages over the prior art: the present invention is due to the vector phase that is utilized in Capon algorithm
Guan Xinglai constructs new space spectral function, and the robustness of Measure direction performance, Er Qieshi are not only increased compared with traditional Capon algorithm
Higher angle resolution and angle measurement accuracy are showed；The present invention does not need to determine information source number and Eigenvalues Decomposition in advance, with MUSIC
Algorithm is compared, can be to avoid the influence due to estimation mistake because of information source number to Mutual coupling performance.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of Wave arrival direction estimating method based on least variance method vector correlation provided in an embodiment of the present invention
Flow diagram；
Fig. 2 is when array is error free, to Capon algorithm, MUSIC algorithm and the present invention in Signal to Noise Ratio (SNR)=5dB
Spatial spectrum emulates schematic diagram；
Fig. 3 is influence of the signal-to-noise ratio to Capon algorithm, MUSIC algorithm and inventive algorithm performance when array is error free
Emulate schematic diagram；
Fig. 4 is when array element is mutually disturbed there are Random amplitude, to Capon algorithm, MUSIC algorithm and the present invention in signal-to-noise ratio
Spatial spectrum when SNR=5dB emulates schematic diagram；
Fig. 5 is when array element is mutually disturbed there are Random amplitude, and signal-to-noise ratio is to Capon algorithm, MUSIC algorithm and inventive algorithm
The influence of performance emulates schematic diagram.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The embodiment of the present invention provides a kind of Wave arrival direction estimating method based on least variance method vector correlation, such as Fig. 1
Shown, described method includes following steps:
Step 1, radar even linear array is set, radar is obtained according to the radar even linear array and receives data, and according to institute
It states radar even linear array and determines the first steering vector a (θ) and the second steering vector a (θ ')；The relational expression of θ and θ ' are as follows: sin θ=
Sin θ '+ρ, ρ ∈ [10-8, 10-4]。
Step 1 specifically includes:
(1a) sets the reception data of each array element in radar even linear array as xi(t), i=1 ..., N, wherein N is radar
The element number of array that even linear array includes；The reception data of all array elements are arranged successively in radar even linear array, form entire radar
The reception data x (t) of even linear array；
(1b) determines the first steering vector a (θ) and the second steering vector a (θ ') according to radar even linear array；Wherein, a
(θ)=[1, ejκdsinθ..., ejκ(N-1)d sinθ]T, a (θ ')=[1, ejκdsinθ..., ejκ(N-1)d sinθ]T；
Wherein, θ is scanning angle, and θ ' closes on direction, the relational expression of θ and θ ' for θ's are as follows: sin θ=sin θ '+ρ, ρ ∈
[10-8, 10-4], a (θ) be angle be θ when array steering vector, a (θ ') be angle be θ ' when array steering vector, N table
Show that array number, κ are wave number, d is array element spacing, and j is imaginary unit, and e is natural constant, and subscript T indicates transposition.
Step 2, data are received according to the radar, calculates radar and receive the covariance matrix of data, and invert to it, obtains
The covariance inverse matrix of data is received to radar, so that it is determined that radar receives the arithmetic square root of the covariance inverse matrix of data.
Step 2 specifically includes:
(2a) receives data x (t) according to radar, obtains the covariance matrix that radar receives data using maximal possibility estimationWherein subscript H indicates conjugate transposition, x (tl) it is the l times sampled data, l=1,2 ... L, L are snap
Number；
(2b) receives the covariance matrix of data to radarIt inverts, obtains the covariance inverse matrix that radar receives dataAnd then obtain the arithmetic square root that radar receives the covariance inverse matrix of data
Step 3, the arithmetic square root that the covariance inverse matrix of data is received according to the first steering vector and radar calculates the
One dependent vector；The second phase is calculated according to the arithmetic square root that the second steering vector and radar receive the covariance inverse matrix of data
Close vector.
Step 3 specifically includes:
(3a) receives the arithmetic square root of the covariance inverse matrix of data according to the first steering vector a (θ) and radarMeter
The first dependent vector Ψ is calculated,
(3b) receives the arithmetic square root of the covariance inverse matrix of data according to the second steering vector a (θ ') and radar
The second dependent vector Γ is calculated,
Wherein, subscript H indicates conjugate transposition.
Step 4, according to the first dependent vector of arithmetic and the second dependent vector, space spectral function is constructed.
Step 4 specifically:
(4a) calculates normalizated correlation coefficient α according to the first dependent vector Ψ and the second dependent vector Γ:
(4b) obtains space spectral function P (θ) according to mathematical normalization related coefficient α:
Wherein, | | | |2Indicate 2 norms, the array steering vector that a (θ) is angle when being θ, a (θ ') is angle when being θ '
Array steering vector,The covariance inverse matrix of data is received for radar, subscript H indicates conjugate transposition.
Step 5, according to the space spectral function, maximal possibility estimation is carried out to direction of arrival, obtains estimating for direction of arrival
Evaluation.
Step 5 specifically: according to space spectral function P (θ), maximal possibility estimation is carried out to direction of arrival, obtains Bo Dafang
To estimated value
Effect of the invention can be further illustrated by following Computer Simulation:
The good resolving power of Power estimation algorithm is reflected on the spectral curve of space: in the information source that two spaces orientation is spaced closely together
Sharp spectral peak is formed at orientation, and at non-information source orientation, the amplitude of space spectral curve is answered between especially two information source orientation
When low as far as possible.Therefore, defining two angle of arrival is respectively θ1、θ2Information source, to Mr. Yu's single experiment, if normalized space
Spectrum obtains two spectral peaks, and the corresponding estimation orientation of two spectral peaksMeetAndWhen, then claim this time experiment information source that can successfully differentiate.It is special by covering for further verification algorithm performance
The influence of noise alignment algorithm super-resolution performance is investigated in Carlow experiment, i.e., main to investigate the letter closely spaced to two incident angles
Number resolution situation.Experiment repeats 500 times, and the root mean square for counting information source success resoluting probability and the estimation of information source orientation misses
Difference.Success resoluting probability, which refers to, successfully differentiates the percentage that number accounts for experiment sum.
Simulated conditions: array is the equidistant even linear array that array element spacing is half-wavelength, array number N=16, number of snapshots snap
=50；There are two the noncoherent targets of constant power, and angle of arrival is respectively 0 ° and 4 °；Parameter ρ=10-7。
Emulation 1: performance comparison when array is error free
1.1) the Mutual coupling performance for verifying the method for the present invention when array is error free, by the method for the present invention and now
There is space spectrogram of the Capon and MUSIC algorithm in Signal to Noise Ratio (SNR)=5dB to be emulated, as a result as shown in Figure 2.
1.2) error free in array with three kinds of methods, and influence to performance is imitated when signal-to-noise ratio is changing value
Very, as a result as shown in figure 3, wherein Fig. 3 (a) is the successful resoluting probability of information source under different signal-to-noise ratio, Fig. 3 (b) is different noises
Estimate root-mean-square error in orientation than lower information source.
As shown in Figure 2, spectral peak of the invention is more sharp.
By Fig. 3 (a) it is found that the method for the present invention resolution ratio ratio MUSIC algorithm and Capon algorithm are high.It can by Fig. 3 (b)
Know, in the case where low signal-to-noise ratio, the angle measurement accuracy of three kinds of algorithms is not high, but the precision outline of MUSIC algorithm is better.
Emulation 2: performance comparison when array element is mutually disturbed there are Random amplitude
Since array element amplitude phase error, element position disturbance and array element mutual coupling error factors can cause array element width mutually to be disturbed at random
Dynamic problem.
2.1) the Mutual coupling performance for verifying the method for the present invention when array element is mutually disturbed there are Random amplitude, is sent out with this
Bright method and existing Capon and MUSIC algorithm rely on Random amplitude there are 10% orientation and mutually disturb in Signal to Noise Ratio (SNR)=5dB
Space spectrogram when [note: when it is 10% that width, which mutually disturbs, indicating that amplitude relative error is 10% and phase error is 0.1 π rad]
It is emulated, as a result as shown in Figure 4.
2.2) with three kinds of methods when there are 10% orientation dependence Random amplitudes mutually to disturb, and signal-to-noise ratio is changing value
Influence to performance emulates, as a result as shown in figure 5, wherein Fig. 5 (a) is that the successful resolution of information source under different signal-to-noise ratio is general
Rate, Fig. 5 (b) are that root-mean-square error is estimated in the orientation of information source under different signal-to-noise ratio.
As shown in Figure 4, when array element is mutually disturbed there are Random amplitude, the method for the present invention spectral peak is still sharp, secondary lobe still compared with
It is low.
By Fig. 5 (a) and Fig. 5 (b) it is found that for being divided into 4 ° of incoherent signal between two angles, although this 3 kinds of algorithms
Can all improve with the raising of signal-to-noise ratio, comparatively, the method for the present invention influenced by array error it is smaller.In lesser battle array
Under conditions of column error, MUSIC algorithm and Capon algorithm performance can deteriorate, they are difficult the two signals in close proximity
It fully differentiates and opens, and the method for the present invention has very high resolution ratio, while higher angle measurement essence is able to maintain after successfully differentiating
Degree, shows that the present invention has good robustness and engineer application.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (4)
1. a kind of Wave arrival direction estimating method based on least variance method vector correlation, which is characterized in that the method includes
Following steps:
Step 1, radar even linear array is set, radar is obtained according to the radar even linear array and receives data, and according to the thunder
The first steering vector a (θ) and the second steering vector a (θ ') are determined up to even linear array；θ is scanning angle, and θ ' is the side of closing on of θ
To the relational expression of θ and θ ' are as follows: sin θ=sin θ '+ρ, ρ ∈ [10-8, 10-4]；
Step 2, data are received according to the radar, calculates radar and receive the covariance matrix of data, and invert to it, obtains thunder
Up to the covariance inverse matrix for receiving data, so that it is determined that radar receives the arithmetic square root of the covariance inverse matrix of data；
Step 3, the arithmetic square root that the covariance inverse matrix of data is received according to the first steering vector and radar calculates the first phase
Close vector；The second related arrow is calculated to the arithmetic square root for the covariance inverse matrix that radar receives data according to the second steering vector
Amount；
Wherein, step 3 specifically includes:
(3a) receives the arithmetic square root of the covariance inverse matrix of data according to the first steering vector a (θ) and radarCalculate the
One dependent vector Ψ,
(3b) receives the arithmetic square root of the covariance inverse matrix of data according to the second steering vector a (θ ') and radarIt calculates
Second dependent vector Γ,
Wherein, subscript H indicates conjugate transposition；
Step 4, according to the first dependent vector of arithmetic and the second dependent vector, space spectral function is constructed；
Wherein, step 4 specifically includes:
(4a) calculates normalizated correlation coefficient α according to the first dependent vector Ψ and the second dependent vector Γ:
(4b) obtains space spectral function P (θ) according to mathematical normalization related coefficient α:
Wherein, | | | |2Indicate 2 norms, the array steering vector that a (θ) is angle when being θ, the battle array that a (θ ') is angle when being θ '
Column steering vector,The covariance inverse matrix of data is received for radar, subscript H indicates conjugate transposition；
Step 5, according to the space spectral function, maximal possibility estimation is carried out to radar target direction of arrival, obtains radar target
The estimated value of direction of arrival.
2. a kind of Wave arrival direction estimating method based on least variance method vector correlation according to claim 1, special
Sign is that step 1 specifically includes:
(1a) sets the reception data of each array element in radar even linear array as xi(t), i=1 ..., N, wherein N is radar uniform line
The element number of array that battle array includes；The respective reception data of array element N number of in radar even linear array are arranged successively, radar uniform line is formed
The reception data x (t) of battle array；
(1b) determines the first steering vector a (θ) and the second steering vector a (θ ') according to radar even linear array；Wherein, a (θ)=
[1, ejκdsinθ..., ejκ(N-1)dsinθ]T, a (θ ')=[1, ejκdsinθ..., ejκ(N-1)dsinθ]T；
Wherein, θ is scanning angle, and θ ' closes on direction, the relational expression of θ and θ ' for θ's are as follows: sin θ=sin θ '+ρ, ρ ∈ [10-8,
10-4], a (θ) be angle be θ when array steering vector, a (θ ') be angle be θ ' when array steering vector, N indicate radar
The element number of array that even linear array includes, κ are wave number, and d is array element spacing, and j is imaginary unit, and e is natural constant, and subscript T is indicated
Transposition.
3. a kind of Wave arrival direction estimating method based on least variance method vector correlation according to claim 1, special
Sign is that step 2 specifically includes:
(2a) receives data x (t) according to radar, obtains the covariance matrix that radar receives data using maximal possibility estimationWherein subscript H indicates conjugate transposition, x (tl) it is the l times sampled data, l=1,2 ... L, L are snap
Number；
(2b) receives the covariance matrix of data to radarIt inverts, obtains the covariance inverse matrix that radar receives dataInto
And obtain the arithmetic square root that radar receives the covariance inverse matrix of data
4. a kind of Wave arrival direction estimating method based on least variance method vector correlation according to claim 1, special
Sign is, step 5 specifically:
According to space spectral function P (θ), maximal possibility estimation is carried out to radar target direction of arrival, obtains radar target wave up to side
To estimated value SymbolExpression corresponding θ value when asking P (θ) maximum.
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