CN105572629A - Two-dimensional direction measuring method of low operation complexity and applicable to any array structure - Google Patents

Abstract

The invention provides a two-dimensional direction measuring method of low operation complexity and applicable to any array structure. The method comprises the steps of: calculating a sampling matrix [gamma] by means of 2-D IDFT; constructing a covariance matrix shown in the specification, and obtaining a noise characteristic vector En and a matrix shown in the specification; calculating the sum of block matrixes, obtaining a matrix D, then calculating the sum of all elements along each diagonal of the matrix D, and constructing a matrix C based on the sum of all elements; applying 2-D IDFT conversion to the matrix C so as to realize crude searching on DOA; carrying out fined DOA searching on each time of DOA crude searching by a 2-D MUSIC method, searching for a target, and completing direction measurement. According to the invention, the calculation amount of the case in which root-MUSIC or MUSIC is singly used is substantially reduced, the identical DOA estimation effect is achieved, and the method is easier to realize by hardware.

Description

A kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure

Technical field

The present invention relates to array signal processing method, especially relate to a kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure.

Background technology

Within nearest 30 years, be that array signal develops swift and violent period, occurred a large amount of outstanding array signal processing method.DOA algorithm for estimating based on second-order statistic mainly contains maximum likelihood (ML, MaximumLikelihood) method, linear prediction (LP) method, multiple signal classification (MUSIC, MUltipleSIgnalClassification) method and invariable rotary subspace (ESPRIT) method etc.Wherein ML method has optimum estimated performance, but its calculated amount is very large, and MUSIC algorithm has started the beginning of subspace class Array Signal Processing algorithm research, is a milestone in Array Signal Processing algorithm research.

Arrival direction estimation generally adopts face battle array or vector sensor to realize the estimation of two-dimensional parameter, most efficient 2-d DOA algorithm for estimating is on the basis of one dimension DOA algorithm for estimating, directly propose for space two-dimensional spectrum, as two-dimentional MUSIC algorithm and various two dimensional ESPRIT algorithms etc.Two dimension MUSIC algorithm is the typical algorithm of arrival direction estimation, and this method can produce progressive unbiased esti-mator, but will at two-dimensional parameter space search spectrum peak, and its calculated amount is quite large.

At document [1] M.Landmann, A.Richter, andR.S.Thoma, " DoAresolutionlimitsinMIMOchannelsounding; " inInternationalSymposiumonAntennasandPropagationandUSNC/ URSINationalRadioScienceMeeting, in 2004, propose the concept of effective pore sife distribution function (EADF, EffectiveApertureDistributionFunction).

At document [2] M.Costa, A.Richter, andV.Koivunen, " Lowcomplexityazimuthandelevationestimationforarbitraryar rayconfigurations; " IEEEInt.Conf.Acoust.SpeechSignalProcess (ICASSP), pp.2185 – 2188, in 2009, utilize the EADF method of document [1], 2-D direction-finding method is improved.Document hypothesis has P incoherent narrow band signal source, and 1 array having N number of sensor, the angle of pitch and the position angle parameter of each sensor are as follows: (θ, φ)={ (θ ₁, φ ₁) ..., (θ _p, φ _p), wherein θ is the angle of pitch of sensor and meets θ ∈ [0,180 °], φ be position angle and meet φ ∈ [0,360 °), so, the data of acquisition can be provided by following formula: X=A (θ, φ) S+N, wherein represent array manifold (also can be described as guiding vector) matrix, signal matrix, represent measurement noises, this noise is second order traversal zero mean Gaussian white noise, represent a plural number set, N, P, K are positive integer, represent matrix line number or columns, and K is the fast umber of beats of sampling.

Suppose that the array manifold matrix of n-th antenna from calculation matrix gained is wherein angle parameter when representative is measured, n is positive integer, represents n-th antenna, Q _erepresent the total number of sample points on an angle of pitch, Q _arepresent the total number of sample points on a position angle, represent real number set.

Target is split by author on two-dimentional spatial domain, and the angle of pitch and position angle are divided into 60 i.e. Q separately _e=Q _a=60 carry out data acquisition, carry out the collection of 60 × 60=3600 secondary data altogether, obtain array manifold due to θ ∈ [0,180 °], not with 360 ° for the cycle, do not meet the requirement of FFT, therefore need periodization.For meeting the periodicity requirements of FFT, special Α _n(θ _c, φ _c) translation 180 ° overturns again, and cut out head and the tail two row, construct following matrix:

${\tilde{A}}_n(\mathrm{\θ},\mathrm{\φ})=\left[\begin{array}{c}{A}_n({\mathrm{\θ}}_c,{\mathrm{\φ}}_c)\\ A_n^r({\mathrm{\θ}}_c,{\mathrm{\φ}}_c)\end{array}\right]$

R represents and carries out matrix transpose operation to matrix.Right carry out 2-DIDFT change and just obtain sampling matrix Γ.

After obtaining sampling matrix Γ, can by array manifold model writing as shown in the formula a (θ, φ)=Γ d (θ, φ)+ε (M _e, M _a), wherein Γ is sampling matrix, and d (θ, φ) represents position angle and pitch position vector, M _erepresent the modulus on the angle of pitch, M _arepresent the modulus on position angle. in formula represent existence and unigueness computing, ε (M in formula _e, M _a) representative model error.Above process is off-line operation, and only needs execution once just can in the hope of the sampling matrix Γ of given aerial array.When array starts direction finding work, collect K snap to construct covariance matrix feature decomposition is carried out to it, obtains noise feature vector E _nand matrix along every bar diagonal line of matrix B, calculate partitioned matrix and, obtain matrix D, then along every bar diagonal line of matrix D, calculate each element sum, and with this structural matrix C.The cost function of 2-DMUSIC can write following binary polynomial:

p(ζ，ω)＝p(ζ) ^TCp(ω)＝0

Wherein, ζ=e ^{j φ}, ω=e ^{j θ}, d _e=2M _e-2, d _a=2M _a-2.Finally by the root solving this binary polynomial, to estimate the angle of pitch and position angle.As can be seen from above step, when array aperture becomes very large, the exponent number of this binary polynomial also can become very large, causes the computation complexity of rooting process very high, and is also not easy to realize on the hardware such as FPGA.

Summary of the invention

The object of the invention is to: for prior art Problems existing, a kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure is provided, solve existing two-dimentional direction-finding method calculated amount quite large, be not easy to the problem carrying out realizing on the hardware such as FPGA.

Goal of the invention of the present invention is achieved through the following technical solutions:

Be applicable to a two-dimentional direction-finding method for the low computational complexity of General Cell structure, it is characterized in that, the method comprises:

1) in some orientation, measure array element response, and carry out calculating sampling matrix Γ by 2-DIDFT;

2) collect snap and construct covariance matrix feature decomposition is carried out to it, obtains noise feature vector E _nand matrix

3) along every bar diagonal line of matrix B, calculate partitioned matrix and, obtain matrix D, then along every bar diagonal line of matrix D, calculate each element sum, and with this structural matrix C;

4) 2-DFFT conversion is used to carry out coarse search to DOA to Matrix C;

5) in a very little angular regions, meticulous DOA search is carried out to each DOA coarse search application 2-DMUSIC method, looks for target, complete direction finding.

As further technical scheme, for given array, step 1) perform once.

As further technical scheme, step 3) comprise the following steps:

First, matrix be expressed as follows by partitioned matrix form:

wherein, each block matrix is a M _a× M _amatrix;

Secondly, all 2M are calculated _eon-1 diagonal line block element and, obtain vector: $D=\left[\begin{array}{cccc}{D}_1& D_2& ...& D_{2M_e-1}\end{array}\right]$ , wherein, similarly, to i-th column vector of C, all 2M are calculated _eon-1 diagonal line block element and can obtain: ${\[c\]}_{i,q}=\underset{\∀M_a-(m-n)=q}{\overset{n}{\Σ}}{\[D_i\]}_{m,n};$

Then, will $\mathrm{\θ}=\frac{2\mathrm{\π}}{N_1}{n}_1$ With $\mathrm{\φ}=\frac{2\mathrm{\π}}{N_2}{n}_2$ Substitute into following formula

$p(\mathrm{\θ},\mathrm{\φ})=d{(\mathrm{\θ},\mathrm{\φ})}^H\left({\mathrm{\Γ}}^H{E}_n{E}_n^H\mathrm{\Γ}\right)d(\mathrm{\θ},\mathrm{\φ})=p{\left(\mathrm{\θ}\right)}^{T}Cp\left(\mathrm{\φ}\right)$

Rewriting spatial spectrum is as follows:

$p(n_1,n_2)=\underset{k_2=0}{\overset{d_e}{\Σ}}\underset{k_1=0}{\overset{d_a}{\Σ}}C(k_1,k_2)e^{i\frac{2\mathrm{\π}}{N_1}{n}_1{k}_1}{e}^{i\frac{2\mathrm{\π}}{N_2}{n}_2{k}_2},$ Wherein, $p\left(\mathrm{\θ}\right)={\[{z_{\mathrm{\θ}}}^{2M_a-2},{z_{\mathrm{\θ}}}^{2M_a-3},...,1\]}^T,$ $p\left(\mathrm{\φ}\right)={\[{z_{\mathrm{\φ}}}^{2M_e-2},{z_{\mathrm{\φ}}}^{2M_e-3},...,1\]}^T,$ d _a＝2M _a-2,d _e＝2M _e-2， $C(k_1,k_2)={\[C\]}_{d_a+1-k_1,d_e+1-k_2},$ Symbol [C] _m,nrepresent (m, n) individual element of C.

As further technical scheme, step 4) comprising: first to the 2M of Matrix C _e-1 row carries out N ₁the FFT of individual point calculates, then to obtained N ₁individual row carries out N ₂the FFT of individual point calculates, and then carries out minimum value search, corresponding to the coarse search of DOA to this thick spatial spectrum.

As further technical scheme, step 5) comprising: step 4) the DOA coarse search result (θ that obtains in coarse search ₁, φ ₁), at angle θ ∈ [θ ₁-Δ θ, θ ₁+ Δ θ], φ ∈ [φ ₁-Δ φ, φ ₁+ Δ φ] scope in, be divided into some grids, carry out meticulous down scale 2-DMUSIC and search for, wherein Δ θ and Δ φ is detection range.

As further technical scheme, carry out grid subdivision to angular regions near each coarse search DOA result, Local grid number value is Q ₁=Q ₂=69, each mesh spacing is degree is within the scope of Δ θ=Δ φ ≈ 3 ° at angular range, and all (θ, φ) values of 69 × 69 two-dimensional grids are substituted into following formula

$p(\mathrm{\θ},\mathrm{\φ})=d{(\mathrm{\θ},\mathrm{\φ})}^H\left({\mathrm{\Γ}}^H{E}_n{E}_n^H\mathrm{\Γ}\right)d(\mathrm{\θ},\mathrm{\φ})=p{\left(\mathrm{\θ}\right)}^{T}Cp\left(\mathrm{\φ}\right)$ In, carry out meticulous 2-DMUSIC search, look for target, complete direction finding.

Compared with prior art, the present invention mainly utilizes the mixed method based on MUSIC, first carry out high range DOA search, down scale DOA search is carried out again after determining target area, thus the operand decreased when being used alone root-MUSIC or MUSIC, achieve identical DOA estimation effect, and the easy hardware implementing of the method.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is root-mean-square error and the input signal-to-noise ratio graph of a relation of position angle estimation;

Fig. 3 is the root-mean-square error of angle of pitch estimation and the graph of a relation of input signal-to-noise ratio;

Fig. 4 is the root-mean-square error of position angle estimation and fast umber of beats graph of a relation;

Fig. 5 is the root-mean-square error of angle of pitch estimation and the graph of a relation of fast umber of beats.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Embodiment

The present invention carries out method enforcement according to the flow process of accompanying drawing 1.

First suppose that two signals from different angles incide on aerial array, and, emulate all stochastic generation DOA at every turn.

Step one, for realizing the object of calibration, some orientation being measured array element response, and carrys out calculating sampling matrix Γ by 2-DIDFT.It should be noted that, for given array, this off-line procedure only needs to perform once.

Step 2, collection snap construct covariance matrix feature decomposition is carried out to it, obtains noise feature vector E _nand matrix

Step 3, calculate B diagonal element and, obtain matrix D, then calculate each diagonal element in D and, and with this structural matrix C.Concrete operations are as follows:

First, matrix be expressed as follows by partitioned matrix form:

Wherein, each block matrix is a M _a× M _amatrix, M _a=M _e=51.

Secondly, all 2M are calculated _eon-1 diagonal line block element and as follows vector:

$D=\left[\begin{array}{cccc}{D}_1& D_2& ...& D_{2M_e-1}\end{array}\right]$

Wherein, similarly, to i-th column vector of C, all 2M are calculated _eon-1 diagonal line block element and can obtain: ${\[c\]}_{i,q}=\underset{\∀M_a-(m-n)=q}{\overset{n}{\Σ}}{\[D_i\]}_{m,n}.$

Then, will $\mathrm{\θ}=\frac{2\mathrm{\π}}{N_1}{n}_1$ With $\mathrm{\φ}=\frac{2\mathrm{\π}}{N_2}{n}_2$ Substitute into following formula

$p(\mathrm{\θ},\mathrm{\φ})=d{(\mathrm{\θ},\mathrm{\φ})}^H\left({\mathrm{\Γ}}^H{E}_n{E}_n^H\mathrm{\Γ}\right)d(\mathrm{\θ},\mathrm{\φ})=p{\left(\mathrm{\θ}\right)}^{T}Cp\left(\mathrm{\φ}\right)$

Can spatial spectrum be rewritten as follows:

$p(n_1,n_2)=\underset{k_2=0}{\overset{d_e}{\Σ}}\underset{k_1=0}{\overset{d_a}{\Σ}}C(k_1,k_2)e^{i\frac{2\mathrm{\π}}{N_1}{n}_1{k}_1}{e}^{i\frac{2\mathrm{\π}}{N_2}{n}_2{k}_2}$

Wherein, $p\left(\mathrm{\θ}\right)={\[{z_{\mathrm{\θ}}}^{2M_a-2},{z_{\mathrm{\θ}}}^{2M_a-3},...,1\]}^T,p\left(\mathrm{\φ}\right)={\[{z_{\mathrm{\φ}}}^{2M_e-2},{z_{\mathrm{\φ}}}^{2M_e-3},...,1\]}^T,$ The two is all Vandermonde structure vectors.D _a=2M _a-2, d _e=2M _e-2, symbol [C] _m,nrepresent (m, n) individual element of C.

Step 4, to Matrix C use 2-DFFT conversion.First to the 2M of Matrix C _e-1 row carries out N ₁the FFT of individual point calculates, then to obtained N ₁individual row carries out N ₂the FFT of individual point calculates.N ₁and N ₂a suitable value can be got, as 256.Then minimum value search is carried out, corresponding to the coarse search of DOA to this thick spatial spectrum.

Step 5, in a very little angular regions, meticulous DOA search is carried out to each DOA coarse search application 2-DMUSIC method.Such as, in step 4) certain DOA coarse search result (θ of obtaining in coarse search ₁, φ ₁), at angle θ ∈ [θ ₁-Δ θ, θ ₁+ Δ θ], φ ∈ [φ ₁-Δ φ, φ ₁+ Δ φ] (wherein Δ θ and Δ φ is detection range) scope in, be divided into some grids, carry out meticulous down scale 2-DMUSIC and search for, look for target, complete direction finding.

For step 5), this example provides a kind of specific embodiment: carry out grid subdivision to angular regions near each coarse search DOA result, Local grid number value is Q ₁=Q ₂=69.Each mesh spacing is degree is within the scope of Δ θ=Δ φ ≈ 3 ° at angular range, and all (θ, φ) values of 69 × 69 two-dimensional grids are substituted into following formula $p(\mathrm{\θ},\mathrm{\φ})=d{(\mathrm{\θ},\mathrm{\φ})}^H\left({\mathrm{\Γ}}^H{E}_n{E}_n^H\mathrm{\Γ}\right)d(\mathrm{\θ},\mathrm{\φ})=p{\left(\mathrm{\θ}\right)}^{T}Cp\left(\mathrm{\φ}\right)$ In carry out meticulous 2-DMUSIC search, look for target, complete direction finding.

Fig. 2 and Fig. 3 investigated when input signal-to-noise ratio (SNR) from-10dB change to 20dB and fast umber of beats get 200 time, root-mean-square error (RMSE) performance between the estimated value of DOA and actual value.Fig. 4 and Fig. 5, illustrates under signal to noise ratio (S/N ratio) is 10dB condition, the relation between the root-mean-square error that DOA estimates and fast umber of beats.As can be seen from four width figure, be N in value ₁=N ₂when=4096, the mixed method that this patent proposes can realize the estimation effect about the same with 2-Droot-MUSIC method, and to be better than in value be N ₁=N ₂effect when=256.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, it should be pointed out that all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (6)

1. be applicable to a two-dimentional direction-finding method for the low computational complexity of General Cell structure, it is characterized in that, the method comprises:

1) in some orientation, measure array element response, and carry out calculating sampling matrix Γ by 2-DIDFT;

2) collect snap and construct covariance matrix feature decomposition is carried out to it, obtains noise feature vector E _nand matrix

3) along every bar diagonal line of matrix B, calculate partitioned matrix and, obtain matrix D, then along every bar diagonal line of matrix D, calculate each element sum, and with this structural matrix C;

4) 2-DFFT conversion is used to carry out coarse search to DOA to Matrix C;

5) in a very little angular regions, meticulous DOA search is carried out to each DOA coarse search application 2-DMUSIC method, looks for target, complete direction finding.

2. a kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure according to claim 1, is characterized in that, for given array, and step 1) perform once.

3. a kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure according to claim 1, is characterized in that, step 3) comprise the following steps:

First, matrix be expressed as follows by partitioned matrix form:

wherein, each block matrix is a M _a× M _amatrix;

Secondly, all 2M are calculated _eon-1 diagonal line block element and, obtain vector: $D=\left[\begin{array}{cccc}{D}_1& D_2& ...& D_{2M_e-1}\end{array}\right]$ , wherein, similarly, to i-th column vector of C, all 2M are calculated _eon-1 diagonal line block element and can obtain: ${\[C\]}_{i,q}=\underset{\∀M_a-(m-n)=q}{\overset{n}{\Σ}}{\[D_i\]}_{m,n};$

Then, will $\mathrm{\θ}=\frac{2\mathrm{\π}}{N_1}{n}_1$ With $\mathrm{\φ}=\frac{2\mathrm{\π}}{N_2}{n}_2$ Substitute into following formula

$p(\mathrm{\θ},\mathrm{\φ})=d{(\mathrm{\θ},\mathrm{\φ})}^H\left({\mathrm{\Γ}}^H{E}_n{E}_n^H\mathrm{\Γ}\right)d(\mathrm{\θ},\mathrm{\φ})=p{\left(\mathrm{\θ}\right)}^{T}Cp\left(\mathrm{\φ}\right)$

Rewriting spatial spectrum is as follows:

$p(n_1,n_2)=\underset{k_2=0}{\overset{d_e}{\Σ}}\underset{k_1=0}{\overset{d_a}{\Σ}}C(k_1,k_2)e^{i\frac{2\mathrm{\π}}{N_1}{n}_1{k}_1}{e}^{i\frac{2\mathrm{\π}}{N_2}{n}_2{k}_2},$ Wherein, $p\left(\mathrm{\θ}\right)={\[{z_{\mathrm{\θ}}}^{2M_a-2},{z_{\mathrm{\θ}}}^{2M_a-3},...,1\]}^T,$ $p\left(\mathrm{\φ}\right)={\[{z_{\mathrm{\φ}}}^{2M_e-2},{z_{\mathrm{\φ}}}^{2M_e-3},...,1\]}^T,$ d _a＝2M _a-2,d _e＝2M _e-2， $C(k_1,k_2)={\[C\]}_{d_a+1-k_1,d_e+1-k_2},$ Symbol [C] _m,nrepresent (m, n) individual element of C.

4. a kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure according to claim 1, is characterized in that, step 4) comprising: first to the 2M of Matrix C _e-1 row carries out N ₁the FFT of individual point calculates, then to obtained N ₁individual row carries out N ₂the FFT of individual point calculates, and then carries out minimum value search, corresponding to the coarse search of DOA to this thick spatial spectrum.

5. a kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure according to claim 1, is characterized in that, step 5) comprising: step 4) the DOA coarse search result (θ that obtains in coarse search ₁, φ ₁), at angle θ ∈ [θ ₁-Δ θ, θ ₁+ Δ θ], φ ∈ [φ ₁-Δ φ, φ ₁+ Δ φ] scope in, be divided into some grids, carry out meticulous down scale 2-DMUSIC and search for, wherein Δ θ and Δ φ is detection range.

6. a kind of two-dimentional direction-finding method being applicable to the low computational complexity of General Cell structure according to claim 5, is characterized in that, carry out grid subdivision to angular regions near each coarse search DOA result, Local grid number value is Q ₁=Q ₂=69, each mesh spacing is degree is within the scope of Δ θ=Δ φ ≈ 3 ° at angular range, and all (θ, φ) values of 69 × 69 two-dimensional grids are substituted into following formula

$p(\mathrm{\θ},\mathrm{\φ})=d{(\mathrm{\θ},\mathrm{\φ})}^H\left({\mathrm{\Γ}}^H{E}_n{E}_n^H\mathrm{\Γ}\right)d(\mathrm{\θ},\mathrm{\φ})=p{\left(\mathrm{\θ}\right)}^{T}Cp\left(\mathrm{\φ}\right)$ In, carry out meticulous 2-DMUSIC search, look for target, complete direction finding.