CN102841344B - Method for estimating parameters of near-field broadband signal resources by utilizing less array elements - Google Patents

Abstract

The invention provides a method for estimating parameters of DOA (direction of arrival) and a distance of more near-field broadband signal resources by utilizing less array elements. The method comprises the following steps of: fully making use of characteristics of broadband signals, constructing a Toeplitz matrix by utilizing mutual correlation of outputs of array elements in a family of frequency on condition that array elements are less, wherein the Toeplitz matrix meets the conventional narrowband MUSIC algorism and comprises information about the DOA and the distance parameter; at last, estimating the DOA and the distance parameter by utilizing the MUSIC algorithm, thus realizing location of more near-field broadband signal resources. According to the method disclosed by the invention, location of more near-filed broadband signal resources can be realized by utilizing less array elements without parameter pairing, angle pre-estimation and broadband focusing, therefore, the method is lower in computational load and convenient for a practical application.

Description

A kind of few array element near field wideband signal source method for parameter estimation

Technical field

The present invention is applied to broadband, the near field Technology for Target Location in Array Signal Processing field.

Background technology

Radiation source location based on sensor array is an important research content of Array Signal Processing, and it is at radar, sonar, radio communication, all has a wide range of applications in the various fields such as seismology and radioastronomy.Under normal circumstances, when information source position and receiving array distant time, objective emission signal can be regarded as a plane wave at receiving end, the position of target can be determined by the position angle of information source (DOA).Traditional high resolution DOA estimation method all obtains based under the model of far field.But, when more namely information source is positioned at Near Field scope to information source distance receiving array, the hypothesis of plane wave is no longer set up, signal passes through array with the form of spherical wave, the DOA and the distance parameter that now need to estimate information source could realize location simultaneously, no longer valid based on the method obtained under the assumed condition of far field.Therefore in recent years, the research of estimation of parameters of near field sources is caused gradually to the concern of Chinese scholars, to become in Array Signal Processing field a new focus.In the past for over ten years, MUSIC(Multiple Signal Classification Multiple Signal Classification) algorithm, maximum likelihood (MLE), the methods such as second-order statistic and weighted linear prediction are all used to locate near field narrowband target.

Along with the development of modern signal processing technology, the application of broadband signal in array signal processing system is more and more general.So far, there have been many scholars to estimate to be studied to the DOA of broadband signal, and achieved significant achievement in research.In recent years, the various countries scholar that is correlated with also proposes a series of localization method in succession for broadband, near field orientation of information source problem, as maximum likelihood method, and two-dimentional MUSIC algorithm, path tracking algorithm, higher-order ESPRIT etc.These algorithms more or less also exist some shortcomings, although such as maximum likelihood method has best estimated performance, calculated amount is very large, limit its application in Practical Project.ISSM algorithm estimated performance under Low SNR in two dimension MUSIC algorithm is poor, and calculated amount is large, coherent signal source can not be estimated, CSSM class algorithm, by application focussing matrix, focuses on the data of different frequency point, obtains the data of single-frequency point (reference frequency point), thus calculate signal covariance matrix, apply traditional narrow subspace method again and calculate position angle, but this algorithm needs to estimate information source position, and final positioning result is responsive to discreet value.Higher-order ESPRIT calculated amount is comparatively large, and often there is the problems such as parameter pairing or aperture loss.

Above-mentioned broadband, near field signal source locating method is all based upon under element number of array number is more than or equal to a signal source said conditions.Such as, MUSIC algorithm is by transforming to frequency domain by Received signal strength, heart frequency in the estimation, and broadband signal is focused on (to form arrowband) in center frequency point, obtaining an autocorrelation matrix by receiving vector again, obtaining signal subspace and noise subspace by this autocorrelation matrix thus calculating the position angle DOA of information source.The order of the autocorrelation matrix of MUSIC algorithm construction needs the number equaling signal source, like this, just needs element number of array number to be more than or equal to signal source number.

Obviously require that element number of array number is more than or equal to signal source number and cannot be suitable in the environment such as the growing mobile communication of user, user is now far longer than element number of array in general, and consider from physical condition or financial cost, array number is also more limited usually.But when information source number is greater than array number, array manifold matrix no longer Line independent between respectively arranging, order can be there is and wane in information source covariance matrix, then now the large eigenwert number of array signal covariance matrix is less than information source number, can not form signal subspace, traditional subspace method cannot re-use.

Summary of the invention

Technical matters to be solved by this invention is, provides a kind of method utilizing less array element to estimate the DOA of more near field wideband signal source and distance parameter.

The present invention is that in receiving array, the quantity of array element is at least 5 for solving the problems of the technologies described above provided technical scheme, and the array element at receiving array center is set to reference array element, comprises the following steps:

(1) the Received signal strength x of each array element in pair array _pt () is carried out discrete Fourier transformation and is obtained the array signal model X of near field wideband signal source in frequency field _pf (), enters step (two) and step (five) afterwards;

$X_p\left(f\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{S}_k\left(f\right)e^{{\mathrm{j\τ}}_{\mathrm{pk}}\left(f\right)}+N_p\left(f\right)$

Wherein, p represents the numbering of each array element, reference array element be numbered p=0, and being left negative direction centered by reference array element, is to the right positive dirction; K is the number of the irrelevant wideband signal source near field, S _kf () represents the frequency spectrum of a kth signal in frequency f, N _pf () represents p additional noise in frequency f, additional noise N _pf () is incoherent zero-mean space white noise with signal, τ _pkf () represents that a kth signal incides reference array element relative to the phase differential of p array element in frequency f;

(2) frequency bandwidth [f of nearly field width band signal _min, f _max] resolving into 2N+1 frequency race, N is the maximal value of positive frequencies hop count, the cross-correlation r containing azimuth information that the array element be centrosymmetric in calculated rate race exports _p(f ₀+ n Δ f):

$r_p\left(n\right)\stackrel{\mathrm{\Δ}}{=}{r}_p(f_0+\mathrm{n\Δf})=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{X}_p(f_0+\mathrm{n\Δf},l)X_{-p}^{*}(f_0+\mathrm{n\Δf},l);$

Wherein, p=1,2; N=-N ... ,-1,0,1 ..., N; L=1,2 ... L, L represent the fast umber of beats of frequency domain; () ^*represent complex conjugate computing; f ₀centered by frequency, Δ f is frequency interval, x _p(f ₀+ n Δ f, l) represent observation time is divided into L subsegment, then to frequency f ₀the array received signal at+n Δ f place carries out the frequency-region signal that discrete Fourier transformation obtains, expression is defined as;

(3) (2N+1) the individual cross-correlation calculated in step (two) is utilized structure Toeplitz matrix R _{p, 1};

(4) the Toeplitz matrix R that step (three) obtains is utilized _{p, 1}, use MUSIC algorithm to calculate the position angle parameter of the irrelevant wideband signal source near field;

(5) frequency bandwidth [f of nearly field width band signal _min, f _max] resolving into 2N+1 frequency race, N is the maximal value of positive frequencies hop count, the cross-correlation r containing the information of position angle and distance parameter that the array element be centrosymmetric in calculated rate race exports _p(n Δ f):

$r_{\mathrm{p\Δf}}\left(n\right)\stackrel{\mathrm{\Δ}}{=}{r}_p\left(\mathrm{n\Δf}\right)=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{X}_p(f_0+\mathrm{n\Δf},l)X_{-p}^{*}(f_0-\mathrm{n\Δf},l);$

(6) (2N+1) the individual cross-correlation calculated in step (five) is utilized structure Toeplitz matrix R _{p, 2};

(7) the Toeplitz matrix R that step (six) obtains is utilized _{p, 2}and the position angle parameter that step (four) obtains, use MUSIC algorithm to calculate the distance parameter of the irrelevant wideband signal source near field.

The present invention makes full use of the feature of broadband signal, provide a kind of few array element near field broadband signal source azimuth angle and distance two-dimensional parameter Combined estimator new method, when less array element (minimum 5 array elements), the cross-correlation that utilizes array element in frequency race to export constructs and meets existing arrowband MUSIC algorithm, Toeplitz matrix (Toeplitz matrix) containing position angle and distance parameter information, finally adopt MUSIC algorithm to estimate position angle and distance parameter, realize positioning more near field wideband signal source.

The invention has the beneficial effects as follows, less array element can be utilized to position more near field wideband signal source, and do not need parameter to match, angle is estimated and Wideband Focusing, and operand is less, is convenient to practical application.

Accompanying drawing explanation

Fig. 1: the inventive method process flow diagram.

Fig. 2: near field broadband signal receiving array model.

The root-mean-square error (RMSE) of Fig. 3: two near field broadband signal source azimuth angle DOA is with signal to noise ratio (S/N ratio) change curve.

The normalization root-mean-square error (RNMSE) of Fig. 4: two near field wideband signal source distance parameters is with signal to noise ratio (S/N ratio) change curve.

Fig. 5: the inventive method is to the estimated capacity analogous diagram of multiple signal source.Fig. 5 (a) and (b) provide the pseudo-spectrogram that five and six near field its incident angles of irrelevant wideband signal source are respectively [-20 °-10 ° 0 ° 10 ° 20 °] and [-30 °-20 °-10 ° 0 ° 10 ° 20 °] respectively.

Embodiment

The present invention is set forth further below in conjunction with the drawings and specific embodiments.These embodiments are interpreted as only being not used in for illustration of the present invention limiting the scope of the invention.After the content of having read the present invention's record, those skilled in the art can make various changes or modifications the present invention, and these equivalence changes and modification fall into the scope of the claims in the present invention equally.

Embodiment 1

DOA of the present invention and the emulation of distance parameter estimated performance:

The method of embodiment 1 as shown in Figure 1, receiving array is the Nonuniform Linear Array be made up of 5 array elements as shown in Figure 2, and the position at array center place is set to the phase reference point of receiving array, position angle parameter and the distance parameter of 2 uncorrelated near field broadband signals are respectively [θ ₁, r ₁], [θ ₂, r ₂], wherein [θ ₁, r ₁]=[-10 °, 4], [θ ₂, r ₂]=[5 °, 2], broadband signal [f _min, f _max] relative to centre frequency normalized spatial spectrum scope be [0.8,1.2], i.e. frequency f centered by its bandwidth ₀40%, wideband signal source is divided into 21 frequency races (2N+1), i.e. the maximal value N=10 of forward (or oppositely) frequency hop count, the difference between side frequency race is center array element is reference array element, the 1st array element on the right of reference array element and the spacing d of reference array element ₁and the spacing d of the 2nd array element on the right of reference array element and reference array element ₂be respectively d ₂=c/2 Δ f.Wherein, r _min=min{r ₁, r ₂}=2, c are the velocity of propagation in signal propagation medium.

The information source number K=2 of the irrelevant broadband signal near field, observation time is divided into L time subsegment, L=16.Signal to noise ratio snr changes from-3dB to 15dB, carries out 1000 Monte Carlo experiments.

The estimated performance of embodiment 1 middle distance parameter is weighed by normalization root-mean-square error (RNMSE), and the estimated performance of position angle DOA then uses root-mean-square error (RMSE) to weigh, and the arrowband subspace method of employing is spectrum MUSIC method.

DOA and distance parameter method of estimation comprise the following steps:

(1) pair array Received signal strength x _pt () is carried out discrete Fourier transformation (DFT) and is obtained the array signal model X of near field wideband signal source in frequency field _p(f) be:

$X_p\left(f\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{S}_k\left(f\right)e^{{\mathrm{j\τ}}_{\mathrm{pk}}\left(f\right)}+N_p\left(f\right)$

Wherein, the present embodiment frequency domain exports corresponding p=0, and ± 1, ± 2, p=0 represents reference array element, and p=-1, p=1 are illustrated respectively in reference array element the right and left the 1st array element, and p=-2, p=2 are illustrated respectively in reference array element the right and left the 2nd array element, S _kf () represents kth the signal spectrum of array element p in frequency f, N _pf () represents p the additional noise in f frequency race, and be incoherent zero-mean space white noise with signal, τ _pkf () represents that a kth signal incides reference array element relative to the phase differential of p array element on frequency race f, to phase differential τ _pkf () carries out Fresnel(Fresnel) approximate after, neglect quadratic term and can obtain τ _pk(f) ≈ ω _pk(f)+φ _pk(f), wherein ω _pkf () is the electrical angle parameter only containing position angle parameter, θ _pkf () is the electrical angle parameter simultaneously containing position angle and distance parameter.

${\mathrm{\ω}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}-p2\mathrm{\πf}{d}_1\sin \left({\mathrm{\θ}}_k\right)/c& p=\±1\\ -\mathrm{p\πf}{d}_2\sin \left({\mathrm{\θ}}_k\right)/c& p=\±2\\ 0& p=0\end{array}\right.$

${\mathrm{\φ}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}\mathrm{\πf}{d}_1^2{\cos }^2\left({\mathrm{\θ}}_k\right)/c{r}_k\left(f\right)& p=\±1\\ \mathrm{\πf}{d}_2^2{\cos }^2\left({\mathrm{\θ}}_k\right)/{\mathrm{cr}}_k\left(f\right)& p=\±2\\ 0& p=0\end{array}\right.$

In formula, c is the velocity of propagation in signal propagation medium, θ _kthe position angle DOA of a kth signal, as shown in Figure 2, d ₁and d ₂be respectively the 1st array element on the right of reference array element and the 2nd relative distance between array element position and reference array element, r _k(f)=r _kc/f, wherein r _kfor the distance parameter of a kth information source on frequency race f.

(2) suppose that broadband signal has identical power spectrum in given normalized frequency bandwidth [0.8,1.2], and about centre frequency f ₀symmetry, wherein normalization centre frequency namely S is had _k(f ₀+ n Δ f)=S _k(f ₀-n Δ f) k=1 ..., K, n=1 ..., N, K are information source sum, and N is the maximal value of forward (or reverse) frequency hop count.Without loss of generality, assuming that each broadband signal can resolve into 2N+1 frequency race, the frequency phase-difference between it is adjacent is Δ f=0.02.

Based on above hypothesis, calculate and centre frequency f ₀frequency domain after the Received signal strength of symmetrical array element carries out DFT exports X ₁(f ₀+ n Δ f) and X _-1(f ₀+ n Δ f) and X ₂(f ₀+ n Δ f) and X _-2(f ₀+ n Δ f) between cross-correlation be:

$r_p(f_0+\mathrm{n\Δf})\stackrel{\mathrm{\Δ}}{=}E\left\{X_p(f_0+\mathrm{n\Δf})X_{-p}^{*}(f_0+\mathrm{n\Δf})\right\}$

$=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_k(f_0+\mathrm{n\Δf})e^{j2{\mathrm{\ω}}_{\mathrm{pk}}(f_0+\mathrm{n\Δf})}$ p=1,2；n=-N,…,-1,0,1,…,N

Wherein E{} and () ^*represent mathematical expectation and complex conjugate computing respectively.P _k(f ₀+ n Δ f) be that a kth signal is at frequency race f ₀the power spectrum at+n Δ f place.This shows, the identical i.e. P of power spectrum signal in interested frequency band _k(f ₀+ n Δ f) have nothing to do with frequency race f, therefore cross-correlation r _p(f ₀+ n Δ f) can be rewritten as:

$r_p\left(n\right)\stackrel{\mathrm{\Δ}}{=}{r}_p(f_0+\mathrm{n\Δf})=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_{k{f}_0}{e}^{j2{\mathrm{\ω}}_{\mathrm{pk}}\left(\mathrm{n\Δf}\right)}\stackrel{\mathrm{\Δ}}{=}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_{k{f}_0}{e}^{\mathrm{jn}{\mathrm{\α}}_{\mathrm{pk}}};$ P=1,2; N=-N ... ,-1,0,1 ..., in N formula, cross-correlation r can be regarded as _pn the amplitude of (), containing the parameter of azimuth information ${\mathrm{\α}}_{\mathrm{pk}}\stackrel{\mathrm{\Δ}}{=}2{\mathrm{\ω}}_{\mathrm{pk}}\left(\mathrm{\Δf}\right),$ expression is defined as.

(3) forward 2(p=1 is utilized, 2) cross-correlation of (2N+1) individual frequency race of individual array element the Toeplitz Toeplitz matrix R be constructed as follows _{p, 1}:

Wherein, matrix A _{p, 1}=[a _{p, 1}(θ ₁), a _{p, 1}(θ ₂) ..., a _{p, 1}(θ _k)] be the generalized circular matrix that (N+1) × K ties up, so work as θ _i≠ θ _jtime (i ≠ j), A _{p, 1}be the sequency spectrum matrix of linear independence between column vector and its kth row can be expressed as a _{p, 1}(θ _k)=[1, exp (-j α _pk) ..., exp (-jN α _pk)] ^t; $D\left(P\right)\stackrel{\mathrm{\Δ}}{=}\mathrm{diag}\left(P\right)=\mathrm{diag}\{P_{1f_0},P_{2f_0},\·\·\·,P_{K{f}_0}\}$ It is a diagonal matrix.By k=1,2 ..., K, can find out so the order of D (P) is K.Known by describing above, matrix R _{p, 1}order equal the number of near field wideband signal source.

(4) Toeplitz matrix R required in step (three) is utilized _{p, 1}, application arrowband MUSIC algorithm tries to achieve DOA, and method is as follows:

First to matrix R _{p, 1}carry out svd (SVD), then (N+1) × (N+1-K) i.e. that the left singular vector that zero singular value is corresponding is formed be (11 × 9) dimension matrix U _n1for matrix R _{p, 1}noise subspace.

Secondly, the position angle DOA that following spectrum peak search obtains signal is carried out:

$P_1\left({\mathrm{\θ}}_k\right)=\frac{1}{a_{p,1}^H\left({\mathrm{\θ}}_k\right)U_{N1}{U}_{N1}^H{a}_{p,1}\left({\mathrm{\θ}}_k\right)}$

Wherein a _{p, 1}(θ _k)=[1, exp (-j α _pk) ..., exp (-jN α _pk)] ^t, containing the parameter of azimuth information ω _pkas described in step (), Δ f is frequency interval, () ^t() ^hrepresent transposition and conjugate transpose respectively, P ₁(θ) be power spectrum.

(5) calculate and centre frequency f ₀frequency domain after the Received signal strength of symmetrical array element carries out DFT exports X ₁(f ₀+ n Δ f) and X _-1(f ₀-n Δ f) or X ₂(f ₀+ n Δ f) and X _-2(f ₀-n Δ f) between cross-correlation be:

$r_p\left(\mathrm{n\Δf}\right)\stackrel{\mathrm{\Δ}}{=}E\left\{X_p(f_0+\mathrm{n\Δf})X_{-p}^{*}(f_0-\mathrm{n\Δf})\right\}$

$=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_k\left(\mathrm{n\Δf}\right)e^{j2{\mathrm{\ω}}_{\mathrm{pk}}\left(f_0\right)}{e}^{\mathrm{j\π}{d}_p^2{\cos }^2\left({\mathrm{\θ}}_k\right)4f_0\mathrm{n\Δf}/c^2{r}_k}$ P=1,2n=-N ... ,-1,0,1 ..., E{} and () in N formula ^*represent mathematical expectation and complex conjugate computing respectively, f ₀centered by frequency, Δ f is frequency interval, is had nothing to do, namely have by step (two) known power spectrum and frequency $P_k\left(\mathrm{n\Δf}\right)\stackrel{\mathrm{\Δ}}{=}E\left\{S_k(f_0+\mathrm{n\Δf})S_k^{*}(f_0-\mathrm{n\Δf})\right\}=P_k(f_0+\mathrm{n\Δf})=P_k(f_0-\mathrm{n\Δf})=P_k,$ Then above cross-correlation can be rewritten as

$r_{\mathrm{p\Δf}}\left(n\right)\stackrel{\mathrm{\Δ}}{=}{r}_p\left(\mathrm{n\Δf}\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_{k{f}_0}{e}^{\mathrm{j\π}{d}_p^2{\cos }^2\left({\mathrm{\θ}}_k\right)4f_0\mathrm{n\Δf}/c^2{r}_k}\stackrel{\mathrm{\Δ}}{=}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_{k{f}_0}{e}^{\mathrm{jn}{\mathrm{\β}}_{\mathrm{pk}}};$ P=1,2; N=-N ... ,-1,0,1 ..., N wherein

$P_{k{f}_0}\stackrel{\mathrm{\Δ}}{=}{P}_k{e}^{j2{\mathrm{\ω}}_{\mathrm{pk}}\left(f_0\right)},$ ${\mathrm{\β}}_{\mathrm{pk}}\stackrel{\mathrm{\Δ}}{=}\mathrm{\π}{d}_p^2{\cos }^2\left({\mathrm{\θ}}_k\right)4f_0\mathrm{\Δf}/c^2{r}_k,$ D in formula _prepresent the relative distance between p array element position and reference array element, c is the velocity of propagation in signal propagation medium, θ _kthe position angle DOA of a kth signal, r _kfor the distance parameter of a kth information source.

(6) forward 2(p=1, the 2) cross-correlation of (2N+1) individual frequency race of individual array element the Toeplitz matrix R be constructed as follows _{p, 2}:

A in formula _{p, 2}=[a _{p, 2}(θ ₁, r ₁), a _{p, 2}(θ ₂, r ₂) ..., a _{p, 2}(θ _k, r _k)];

a _p，2(θ _k,r _k)=[1,exp(-jβ _pk),…,exp(-jNβ _pk)] ^T， ${\mathrm{\β}}_{\mathrm{pk}}\stackrel{\mathrm{\Δ}}{=}\mathrm{\π}{d}_p^2{\cos }^2\left({\mathrm{\θ}}_k\right)4f_0\mathrm{\Δf}/c^2{r}_k,$ $D\left(P\right)\stackrel{\mathrm{\Δ}}{=}\mathrm{diag}\left(P\right)=\mathrm{diag}\{P_{1f_0},P_{2f_0},\·\·\·,P_{K{f}_0}\};$

Wherein θ _kthe position angle DOA of a kth signal, r _kfor the distance parameter of a kth information source, β _pkfor comprising the parameter at position angle and range information, d _prepresent the relative distance between p array element position and reference array element, c is the velocity of propagation in signal propagation medium, f ₀centered by frequency, Δ f is frequency interval, represent cross-correlation r _{p Δ f}the amplitude of (n).

(7) required in integrating step (six) Toeplitz matrix R _{p, 2}and the position angle DOA tried to achieve in step (four), application arrowband MUSIC algorithm can try to achieve the distance parameter of near field wideband signal source, and method is as follows:

(1) to matrix R _{p, 2}carry out svd (SVD), then (N+1) × (N+1-K) that the left singular vector that zero singular value is corresponding is formed ties up matrix U _n2for matrix R _{p, 2}noise subspace.

(2) carry out following spectrum peak search to obtain

$P_2\left({\mathrm{\β}}_{\mathrm{pk}}\right)=\frac{1}{a_{p,2}^H\left({\mathrm{\β}}_{\mathrm{pk}}\right)U_{N2}{U}_{N2}^H{a}_{p,2}\left({\mathrm{\β}}_{\mathrm{pk}}\right)}$

P=1 in formula, 2, P ₂(β _pk) be power spectrum, a kth column vector a _{p, 2}(β _pk)=[1, exp (-j β _pk) ..., exp (-jN β _pk)] ^t, wherein, β _pkfor comprising the parameter at position angle and range information, () ^t() ^hrepresent transposition and conjugate transpose respectively, K is near field wideband signal source number.

(3) following formula is utilized to calculate the distance parameter of near field wideband signal source:

$r_k=4\mathrm{\π}{d}_p^2{\cos }^2\left({\mathrm{\θ}}_k\right)f_0\mathrm{\Δf}/c^2{\mathrm{\β}}_{\mathrm{pk}}$

P=1 in formula, 2, d _prepresent the relative distance between p array element position and reference array element, c is the velocity of propagation in signal propagation medium, θ _kthe position angle DOA of a kth information source, f ₀centered by frequency, Δ f is frequency interval, r _kfor the distance parameter of a kth information source.

Fig. 3 represents that the RMSE of position angle DOA is with SNR=-3dB to SNR=15dB change curve.Fig. 4 represents that the RNMSE of distance parameter is with SNR=-3dB to SNR=15dB change curve.As can be seen from Figure 3, even if the RMSE of DOA is also very little when signal to noise ratio (snr) is very low, such as, as SNR=-2dB, RMSE only 0.2 °.As can be seen from Figure 4, distance parameter is less, and RNMSE is lower, and namely estimated performance is better.

Embodiment 2:

The present invention is for the estimated capacity of multiple signal source:

The method of embodiment 2 as shown in Figure 1, 5 near field its incident angles of irrelevant wideband signal source are respectively [-20 °-10 ° 0 ° 10 ° 20 °], SNB=5dB, 6 near field its incident angles of irrelevant wideband signal source are respectively [-30 °-20 °-10 ° 0 ° 10 ° 20 °], SNB=10dB, all the other simulated conditions are identical with embodiment 1, the step again performing embodiment 1 after changing simulated conditions can obtain Fig. 5, wherein Fig. 5 (a) and (b) sets forth the pseudo-spectrogram that five and six near field its incident angles of irrelevant wideband signal source are respectively [-20 °-10 ° 0 ° 10 ° 20 °] and [-30 °-20 °-10 ° 0 ° 10 ° 20 °].As can be seen from Figure 5 carried algorithm can be estimated to exceed the near field broadband signal of element number of array, and this be traditional near field broadband spatial spectrum algorithm is be beyond one's reach.

Claims (4)

1. few array element near field wideband signal source method for parameter estimation, it is characterized in that, in receiving array, the quantity of array element is at least 5, and the array element at receiving array center is set to reference array element, comprises the following steps:

(1) the Received signal strength x of each array element in pair array _pt () is carried out discrete Fourier transformation and is obtained the array signal model X of near field wideband signal source in frequency field _pf (), enters step (two) and step (five) afterwards;

$X_p\left(f\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{S}_k\left(f\right)e^{j{\mathrm{\τ}}_{\mathrm{pk}}\left(f\right)}+N_p\left(f\right)$

Wherein, p represents the numbering of each array element, reference array element be numbered p=0, being left negative direction centered by reference array element, is to the right positive dirction; K is the number of the irrelevant wideband signal source near field, S _kf () represents the frequency spectrum of signal in frequency f of a kth signal source, N _pf () represents p additional noise in frequency f, additional noise N _pf () is incoherent zero-mean space white noise with signal, τ _pkf () represents that the signal of a kth signal source incides reference array element relative to the phase differential of p array element in frequency f;

(2) frequency bandwidth [f of nearly field width band signal _min, f _max] resolving into 2N+1 frequency race, N is the maximal value of positive frequencies hop count, the cross-correlation r containing azimuth information that the array element be centrosymmetric in calculated rate race exports _p(f ₀+ n Δ f):

$r_p\left(n\right)\stackrel{\mathrm{\Δ}}{=}{r}_p(f_0+\mathrm{n\Δf})=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{X}_p(f_0+\mathrm{n\Δf},l)X_{-p}^{*}(f_0+\mathrm{n\Δf},l);$

Wherein, p=1,2; N=-N ... ,-1,0,1 ..., N; L=1,2...L, L represent the fast umber of beats of frequency domain; () ^*represent complex conjugate computing; f ₀centered by frequency, Δ f is frequency interval, x _p(f ₀+ n Δ f, l) represent observation time is divided into L subsegment, then to frequency f ₀the array received signal at+n Δ f place carries out the frequency-region signal that discrete Fourier transformation obtains, expression is defined as;

(3) (2N+1) the individual cross-correlation calculated in step (two) is utilized structure Toeplitz matrix R _{p, 1}:

(4) the Toeplitz matrix R that step (three) obtains is utilized _{p, 1}, use MUSIC algorithm to calculate the position angle parameter of the irrelevant wideband signal source near field;

(5) frequency bandwidth [f of nearly field width band signal _min, f _max] resolving into 2N+1 frequency race, N is the maximal value of positive frequencies hop count, the cross-correlation r containing the information of position angle and distance parameter that the array element be centrosymmetric in calculated rate race exports _p(n Δ f), p=1,2:

$r_{\mathrm{p\Δf}}\left(n\right)\stackrel{\mathrm{\Δ}}{=}{r}_p\left(\mathrm{n\Δf}\right)=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{X}_p(f_0+\mathrm{n\Δf},l)X_{-p}^{*}(f_0-\mathrm{n\Δf},l);$

(6) (2N+1) the individual cross-correlation calculated in step (five) is utilized structure Toeplitz matrix R _{p, 2}:

(7) the Toeplitz matrix R that step (six) obtains is utilized _{p, 2}and the position angle parameter that step (four) obtains, use MUSIC algorithm to calculate the distance parameter of the irrelevant wideband signal source near field.

2. one lacks array element near field wideband signal source method for parameter estimation as claimed in claim 1, it is characterized in that, in step (), the signal of a kth signal source incides reference array element relative to the phase differential τ of p array element in frequency f _pkf () calculates by the following method:

τ _pk(f)=ω _pk(f)+φ _pk(f), wherein, ω _pkf () is the electrical angle parameter only containing position angle parameter, φ _pkf () is the electrical angle parameter simultaneously containing position angle and distance parameter;

${\mathrm{\ω}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}-p2\mathrm{\πf}{d}_1\sin \left({\mathrm{\θ}}_k\right)/c& p=\±1\\ -\mathrm{p\πf}{d}_2\sin \left({\mathrm{\θ}}_k\right)/c& p=\±2\\ 0& p=0\end{array}\right.$

${\mathrm{\φ}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}\mathrm{\πf}{d}_1^2{\cos }^2\left({\mathrm{\θ}}_k\right)/{\mathrm{cr}}_{\mathrm{kf}}& p=\±1\\ \mathrm{\πf}{d}_2^2{\cos }^2\left({\mathrm{\θ}}_k\right)/{\mathrm{cr}}_{\mathrm{kf}}& p=\±2\\ 0& p=0\end{array}\right.$

Wherein, c is the velocity of propagation of signal in propagation medium, θ _kthe position angle of a kth signal source, r _kf=r _kc/f, wherein r _kfor the distance parameter of a kth signal source, d ₁and d ₂be respectively the 1st array element and the 2nd relative distance between array element position and reference array element of positive dirction.

3. a kind of few array element near field wideband signal source method for parameter estimation as claimed in claim 2, it is characterized in that, the method using MUSIC algorithm to calculate the position angle parameter of the irrelevant wideband signal source near field in step (four) is:

First to matrix R _{p, 1}carry out svd, (N+1) × (N+1-K) utilizing left singular vector corresponding to zero singular value to form ties up matrix U _n1for matrix R _{p, 1}noise subspace;

Again to power spectrum P ₁(θ _k) carry out the position angle that spectrum peak search obtains signal source

$P_1\left({\mathrm{\θ}}_k\right)=\frac{1}{a_{p,1}^H\left({\mathrm{\θ}}_k\right)U_{N1}{U}_{N1}^H{a}_{p,1}\left({\mathrm{\θ}}_k\right)}$

Wherein, p=1,2, a _{p, 1}(θ _k)=[1, exp (-j α _pk) ..., exp (-jN α _pk)] ^t, α _pk=2 ω _pk(Δ f), ω _pkfor the electrical angle parameter only containing position angle parameter of a kth signal source, Δ f is frequency interval, () ^trepresent transposition, () ^hrepresent conjugate transpose.

4. a kind of few array element near field wideband signal source method for parameter estimation as claimed in claim 3, it is characterized in that, the method using MUSIC algorithm to calculate the distance parameter of the irrelevant wideband signal source near field in step (seven) is:

First to matrix R _{p, 2}carry out svd, (N+1) × (N+1-K) utilizing left singular vector corresponding to zero singular value to form ties up matrix U _n2for matrix R _{p, 2}noise subspace;

Again to power spectrum P ₂(β _pk) carry out spectrum peak search and obtain

$P_2\left({\mathrm{\β}}_{\mathrm{pk}}\right)=\frac{1}{a_{p,2}^H\left({\mathrm{\β}}_{\mathrm{pk}}\right)U_{N2}{U}_{N2}^H{a}_{p,2}\left({\mathrm{\β}}_{\mathrm{pk}}\right)}$

Wherein, p=1,2, a _{p, 2}(β _pk)=[1, exp (-j β _pk) ..., exp (-jN β _pk)] ^t, wherein β _pkfor comprising the parameter at position angle and range information, () ^t() ^hrepresent transposition and conjugate transpose respectively, K is the irrelevant wideband signal source number near field;

Position angle parameter is finally utilized to calculate the distance parameter of the irrelevant wideband signal source near field:

$r_k=4\mathrm{\π}{d}_p^2{\cos }^2\left({\mathrm{\θ}}_k\right)f_0\mathrm{\Δf}/c^2{\mathrm{\β}}_{\mathrm{pk}}$

Wherein, p=1,2, d _prepresent the relative distance between expression p array element position and reference array element, c is the velocity of propagation of signal in propagation medium, θ _kthe position angle of a kth signal source, f ₀centered by frequency, Δ f is frequency interval, r _kfor the distance parameter of a kth signal source.