CN102841344A - 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 target localization technology in Array Signal Processing field.

Background technology

Based on the radiation source of sensor array location is a research content of Array Signal Processing, and it is at radar, sonar, and radio communication all has a wide range of applications in the various fields such as seismology and radioastronomy.Generally, when information source position and receiving array distance is far away, can target be transmitted at receiving end and to regard a plane wave as, the position of target can be confirmed through the position angle (DOA) of information source.Traditional high resolution DOA estimation method all is based on and obtains under the model of far field.Yet; When information source is nearer apart from receiving array is that information source is when being positioned at the Near Field scope; The hypothesis of plane wave is no longer set up; Signal passes through array with the form of spherical wave, and the DOA and the distance parameter that need estimate information source this moment simultaneously could be realized the location, based on the method no longer valid that obtains under the assumed condition of far field.Therefore in recent years, the research of estimation of parameters of near field sources is caused gradually the concern of Chinese scholars become new focus in the Array Signal Processing field.In the past for over ten years, MUSIC (Multiple Signal Classification Multiple Signal Classification) algorithm, maximum likelihood (MLE), methods such as second-order statistic and weighted linear prediction all are used to arrowband, near field target localization.

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 that the DOA of broadband signal is estimated to study, and obtained significant achievement in research.In recent years, the relevant scholar in various countries has also proposed a series of localization method in succession to broadband, near field information source orientation problem, like maximum likelihood method, and two-dimentional MUSIC algorithm, path trace algorithm, high-order ESPRIT algorithm etc.These algorithms more or less exist some shortcomings, though for example maximum likelihood method has best estimated performance, calculated amount is very big, have limited it in actual application in engineering.ISSM algorithm estimated performance under the low signal-to-noise ratio condition in the two dimension MUSIC algorithm is relatively poor, and calculated amount is big, can not estimate the coherent signal source; CSSM class algorithm is through using focussing matrix, and the data of different frequency point are focused on, and obtains the data of single-frequency point (reference frequency point); Thereby calculate signal covariance matrix; Use the traditional narrow subspace method again and calculate the position angle, but this algorithm need estimate the information source position, and final positioning result is responsive to discreet value.High-order ESPRIT algorithm computation amount is bigger, and often has problems such as parameter pairing or aperture loss.

Above-mentioned broadband, near field signal source locating method all is based upon the element number of array number more than or equal under the signal source said conditions.Such as; The MUSIC algorithm will be through receiving signal transformation to frequency domain; Estimating center frequency point; And broadband signal focused on the center frequency point (to form the arrowband), obtain an autocorrelation matrix through receiving vector again, thereby obtain the position angle DOA that signal subspace and noise subspace calculate information source through this autocorrelation matrix.The order of the autocorrelation matrix of MUSIC algorithm construction need equal the number of signal source, like this, just needs the element number of array number more than or equal to the signal source number.

Obviously require the element number of array number can't be suitable in the growing environment such as mobile communication of user more than or equal to the signal source number; The user of this moment is far longer than element number of array in general; And from physical condition or financial cost consideration, array number also is more limited usually.Yet when information source number during greater than array number; No longer linear independent between each row of array flow pattern matrix; Order can take place and wane in the information source covariance matrix; Then the big eigenwert number of array signal covariance matrix can not constitute signal subspace less than information source number at this moment, and traditional subspace method can't re-use.

Summary of the invention

Technical matters to be solved by this invention is, provides a kind of and utilizes less array element that the DOA and the distance parameter of more near field wideband signal source carried out estimation approach.

The present invention solves the problems of the technologies described above the technical scheme that is provided to be, the quantity of array element is at least 5 in the receiving array, and the array element at receiving array center is made as reference array element, may further comprise the steps:

(1) the reception signal x of each array element in the array _p(t) carry out discrete Fourier transformation and obtain the array signal model X of near field wideband signal source in frequency field _p(f), get into 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 representes the numbering of each array element, reference array element be numbered p=0, with reference array element be that the center is negative direction left, be to the right positive dirction; K is the number of the irrelevant wideband signal source near field, S _k(f) frequency spectrum of k signal of expression on frequency f, N _p(f) be illustrated in p additional noise on the frequency f, additional noise N _p(f) be and the incoherent zero-mean of signal space white noise, τ _Pk(f) k signal of expression incides reference array element with respect to the phase differential of p array element on frequency f;

(2) frequency bandwidth [f of broadband signal nearly _Min, f _Max] resolving into 2N+1 frequency family, N is the maximal value of positive frequencies hop count, the simple crosscorrelation r that contains azimuth information of the array element that is centrosymmetric in calculated rate family output _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; () ^*The computing of expression complex conjugate; f ₀Be centre frequency,

Δ f is a frequency interval, X _p(f ₀+ n Δ f, l) expression is divided into L section with observation time, 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) utilize (2N+1) the individual simple crosscorrelation that calculates in the step (two)

Structure Toeplitz matrix R _{P, 1}

(4) the Toeplitz matrix R that utilizes step (three) to obtain _{P, 1}, the position angle parameter of the irrelevant wideband signal source in use MUSIC algorithm computation near field;

(5) frequency bandwidth [f of broadband signal nearly _Min, f _Max] resolving into 2N+1 frequency family, N is the maximal value of positive frequencies hop count, the simple crosscorrelation r of the information that contains position angle and distance parameter of the array element that is centrosymmetric in calculated rate family output _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) utilize (2N+1) the individual simple crosscorrelation that calculates in the step (five)

Structure Toeplitz matrix R _{P, 2}

(7) the Toeplitz matrix R that utilizes step (six) to obtain _{P, 2}And the position angle parameter that obtains of step (four), use the distance parameter of the irrelevant wideband signal source in MUSIC algorithm computation near field.

The present invention makes full use of the characteristics of broadband signal; A kind of few wideband signal source position angle, array element near field is provided and has united the estimation new method apart from two-dimensional parameter; Under the situation of less array element (minimum 5 array elements); Utilize the simple crosscorrelation of the output of array element in the frequency family to construct to satisfy existing arrowband MUSIC algorithm; Contain the Toeplitz matrix (Toeplitz matrix) of position angle and distance parameter information, adopt the MUSIC algorithm to estimate position angle and distance parameter at last, realize more near field wideband signal source is positioned.

The invention has the beneficial effects as follows that less array element capable of using positions more near field wideband signal source, and do not need the parameter pairing, angle is estimated with the broadband and is focused on, and operand is littler, is convenient to practical application.

Description of drawings

Fig. 1: the inventive method process flow diagram.

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

Fig. 3: the root-mean-square error (RMSE) of two near fields wideband signal source position angle DOA is with the signal to noise ratio (S/N ratio) change curve.

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

Fig. 5: the inventive method is to the estimated capacity analogous diagram of a plurality of signal sources.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

Further set forth the present invention below in conjunction with accompanying drawing and specific embodiment.These embodiment are interpreted as only being used to the present invention is described and are not used in restriction protection scope of the present invention.After the content of having read the present invention's record, those skilled in the art can do various changes or modification to the present invention, and these equivalences change and modify and fall into claim of the present invention institute restricted portion equally.

Embodiment 1

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

The method of embodiment 1 is shown in accompanying drawing 1; Receiving array is the non-homogeneous linear array of being made up of 5 array elements shown in accompanying drawing 2; And the position at array center place is made as the phase reference point of receiving array, and the position angle parameter and the distance parameter of 2 uncorrelated near field broadband signals are respectively [θ ₁, r ₁], [θ ₂, r ₂], [θ wherein ₁, r ₁]=[-10 °, 4], [θ ₂, r ₂5 ° of]=[, 2], broadband signal [f _Min, f _Max] with respect to centre frequency The normalization spectral range be [0.8,1.2], promptly its bandwidth is centre frequency f ₀40%, wideband signal source is divided into 21 frequency families (2N+1), i.e. the maximal value N=10 of forward (or reverse) frequency hop count, between the side frequency family differ for Center array element is reference array element, the 1st array element on reference array element the right and the spacing d of reference array element ₁And the spacing d of the 2nd array element on reference array element the right and reference array element ₂Be respectively

d ₂=c/2 Δ f.Wherein, r _Min=min{r ₁, r ₂}=2, c is the velocity of propagation in the signal propagation medium.

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

The estimated performance of embodiment 1 middle distance parameter is weighed with 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 may further comprise the steps:

(1) array receives signal x _p(t) carry out discrete Fourier transformation (DFT) and obtain 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 is exported corresponding p=0, and ± 1, ± 2, p=0 representes reference array element, and p=-1, p=1 are illustrated respectively in the 1st array element of reference array element the right and left, and p=-2, p=2 are illustrated respectively in the 2nd array element of reference array element the right and left, S _k(f) k the signal spectrum of expression array element p on frequency f, N _p(f) be illustrated in p additional noise of f frequency family, and be and the incoherent zero-mean of signal space white noise, τ _Pk(f) k signal of expression incides reference array element with respect to the phase differential of p array element on the f of frequency family, to phase differential τ _Pk(f) carry out Fresnel (Fresnel) approximate after, neglect quadratic term and can obtain τ _Pk(f) ≈ ω _Pk(f)+φ _Pk(f), ω wherein _Pk(f) for only containing the electrical angle parameter of position angle parameter, θ _Pk(f) for containing the electrical angle parameter of position angle and distance parameter simultaneously.

${\mathrm{\&omega;}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}-\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">p</figure-callout>}2\mathrm{\&pi;<figure-callout\; id="1"\; label="f\; d"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">f</figure-callout>}{d}_{}{}_1\sin \left({\mathrm{\&theta;}}_k\right)/c& p=\&PlusMinus;1\\ -\mathrm{p\&pi;<figure-callout\; id="2"\; label="f\; d"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">f</figure-callout>}{d}_{}{}_2\sin \left({\mathrm{\&theta;}}_k\right)/c& p=\&PlusMinus;2\\ 0& p=0\end{array}\right.$

${\mathrm{\&phi;}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}\mathrm{\&pi;<figure-callout\; id="1"\; label="f\; d"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">f</figure-callout>}{d}_{}^{}{}_1^2{\cos }^2\left({\mathrm{\&theta;}}_k\right)/c{r}_k\left(f\right)& p=\&PlusMinus;1\\ \mathrm{\&pi;<figure-callout\; id="2"\; label="f\; d"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">f</figure-callout>}{d}_{}^{}{}_2^2{\cos }^2\left({\mathrm{\&theta;}}_k\right)/{\mathrm{cr}}_k\left(f\right)& p=\&PlusMinus;2\\ 0& p=0\end{array}\right.$

In the formula, c is the velocity of propagation in the signal propagation medium, θ _kBe the position angle DOA of k signal, shown in accompanying drawing 2, d ₁And d ₂Be respectively the 1st array element on reference array element the right and the relative distance between the 2nd array element position and the reference array element, r _k(f)=r _kC/f, wherein r _kDistance parameter for last k the information source of the f of frequency family.

(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

S is promptly arranged _k(f ₀+ n Δ f)=S _k(f ₀-n Δ f) k=1 ..., K, n=1 ..., N, K are the information source sum, N is the maximal value of forward (or reverse) frequency hop count.Be without loss of generality, suppose that each broadband signal can resolve into 2N+1 frequency family, the frequency between it is adjacent differs and is Δ f=0.02.

Based on above hypothesis, calculate and centre frequency f ₀The reception signal of the array element of symmetry carries out the frequency domain output X behind the DFT 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) simple crosscorrelation between is:

$r_p(f_0+\mathrm{n\&Delta;f})\stackrel{\mathrm{\&Delta;}}{=}E\left\{X_p(f_0+\mathrm{n\&Delta;f})X_{-p}^{*}(f_0+\mathrm{n\&Delta;f})\right\}$

$=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{P}_k(f_0+\mathrm{n\&Delta;f}){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$ 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 k signal is at the f of frequency family ₀The power spectrum at+n Δ f place.This shows, in interested frequency band power spectrum signal identical be P _k(f ₀+ n Δ f) irrelevant with the f of frequency family, so simple crosscorrelation r _p(f ₀+ n Δ f) can be rewritten as:

$r_p\left(n\right)\stackrel{\mathrm{\&Delta;}}{=}{r}_p({\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0+\mathrm{N\&Delta;\; f})=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{P}_{k{f}_0}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\stackrel{\mathrm{\&Delta;}}{=}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{P}_{k{f}_0}{e}^{\mathrm{Jn}{\mathrm{\&alpha;}}_{\mathrm{Pk}}};$ P=1,2; N=-N ... ,-1,0,1 ..., in the N formula,

Can regard simple crosscorrelation r as _p(n) amplitude contains the parameter of azimuth information ${\mathrm{\&alpha;}}_{\mathrm{Pk}}\stackrel{\mathrm{\&Delta;}}{=}2{\mathrm{\&omega;}}_{\mathrm{Pk}}\left(\mathrm{\&Delta;\; f}\right),$

Expression is defined as.

(3) utilize the simple crosscorrelation of (2N+1) individual frequency family of the individual array element of forward 2 (p=1,2)

Construct following Toeplitz Toeplitz matrix R _{P, 1}:

Wherein, matrix A _{P, 1}=[a _{P, 1}(θ ₁), a _{P, 1}(θ ₂) ..., a _{P, 1}(θ _K)] be the Fan Demeng matrix of (N+1) * K dimension, so work as θ _i≠ θ _j(during i ≠ j), A _{P, 1}The row non-singular matrix and its k row that are linear independence between the column vector can be expressed as a _{P, 1}(θ _k)=[1, exp (j α _Pk) ..., exp (jN α _Pk)] ^T $D\left(P\right)\stackrel{\mathrm{\&Delta;}}{=}\mathrm{Diag}\left(P\right)=\mathrm{Diag}\{P_{1{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0},P_{2{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0},\&CenterDot;\&CenterDot;\&CenterDot;,P_{K{f}_0}\}$ It is a diagonal matrix.By

k=1; 2; K can find out

so the order of D (P) is K.Can know matrix R through above description _{P, 1}Order equal the number of near field wideband signal source.

(4) utilize the Toeplitz matrix R that is asked in the step (three) _{P, 1}, to use arrowband MUSIC algorithm and try to achieve DOA, method is following:

At first to matrix R _{P, 1}Carry out svd (SVD), then (N+1) * (N+1-K) of the left singular vector formation of zero singular value correspondence is (11 * 9) dimension matrix U _N1Be matrix R _{P, 1}Noise subspace.

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

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

A wherein _{P, 1}(θ _k)=[1, exp (j α _Pk) ..., exp (jN α _Pk)] ^T, contain the parameter of azimuth information

ω _PkDescribed in step (), Δ f is a frequency interval, () ^T() ^HRepresent transposition and conjugate transpose respectively, P ₁(θ) be power spectrum.

(5) calculate and centre frequency f ₀The reception signal of the array element of symmetry carries out the frequency domain output X behind the DFT 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) simple crosscorrelation between is:

$r_p\left(\mathrm{n\&Delta;f}\right)\stackrel{\mathrm{\&Delta;}}{=}E\left\{X_p(f_0+\mathrm{n\&Delta;f})X_{-p}^{*}(f_0-\mathrm{n\&Delta;f})\right\}$

$=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{P}_k\left(\mathrm{N\&Delta;\; f}\right){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j{e}^{\mathrm{J\&pi;}{\mathrm{<figure-callout\; id="2"\; label="d\; p"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">d</figure-callout>}}_p^{}{\mathrm{Cos}}^2\left({\mathrm{\&theta;}}_k\right)4{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\mathrm{N\&Delta;\; f}/c^2{r}_k}$ P=1,2n=-N ... ,-1,0,1 ..., E{} and () in the N formula ^*Represent mathematical expectation and complex conjugate computing respectively, f ₀Be centre frequency, Δ f is a frequency interval, and (two) can know power spectrum and frequency-independent by step, promptly have $P_k\left(\mathrm{N\&Delta;\; f}\right)\stackrel{\mathrm{\&Delta;}}{=}E\left\{S_k({\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0+\mathrm{N\&Delta;\; f})S_k^{*}(f_0-\mathrm{N\&Delta;\; f})\right\}=P_k(f_0+\mathrm{N\&Delta;\; f})=P_k(f_0-\mathrm{N\&Delta;\; f})=P_k,$ Then above simple crosscorrelation can be rewritten as

$r_{\mathrm{P\&Delta;\; f}}\left(n\right)\stackrel{\mathrm{\&Delta;}}{=}{r}_p\left(\mathrm{N\&Delta;\; f}\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{P}_{k{f}_0}{e}^{\mathrm{J\&pi;}{\mathrm{<figure-callout\; id="2"\; label="d\; p"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">d</figure-callout>}}_p^{}{\mathrm{Cos}}^2\left({\mathrm{\&theta;}}_k\right)4{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\mathrm{N\&Delta;\; f}/c^2{r}_k}\stackrel{\mathrm{\&Delta;}}{=}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{P}_{k{f}_0}{e}^{\mathrm{Jn}{\mathrm{\&beta;}}_{\mathrm{Pk}}};$ P=1,2; N=-N ... ,-1,0,1 ..., N wherein

${\mathrm{<figure-callout\; id="0"\; label="P\; k\; f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">P</figure-callout>}}_{k{f}_{}}\stackrel{\mathrm{\&Delta;}}{=}{P}_{\mathrm{<figure-callout\; id="2"\; label="k\; e\; j"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">k</figure-callout>}}{e}^j{2{\mathrm{\&omega;}}_{\mathrm{Pk}}\left(f_0\right)}^{},$ ${\mathrm{\&beta;}}_{\mathrm{Pk}}\stackrel{\mathrm{\&Delta;}}{=}\mathrm{\&pi;}{\mathrm{<figure-callout\; id="2"\; label="d\; p"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">d</figure-callout>}}_p^{}{\mathrm{Cos}}^2\left({\mathrm{\&theta;}}_k\right)4{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\mathrm{\&Delta;\; f}/c^2{r}_k,$ D in the formula _pRepresent the relative distance between p array element position and the reference array element, c is the velocity of propagation in the signal propagation medium, θ _kBe the position angle DOA of k signal, r _kIt is the distance parameter of k information source.

(6) simple crosscorrelation of (2N+1) individual frequency family of the individual array element of forward 2 (p=1,2)

Construct following Toeplitz matrix R _{P, 2}:

A in the 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， ${\mathrm{\&beta;}}_{\mathrm{pk}}\stackrel{\mathrm{\&Delta;}}{=}\mathrm{\&pi;}{\mathrm{<figure-callout\; id="2"\; label="d\; p"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">d</figure-callout>}}_p^{}{\cos }^2\left({\mathrm{\&theta;}}_k\right)4{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\mathrm{\&Delta;f}/c^2{r}_k,$ $D\left(P\right)\stackrel{\mathrm{\&Delta;}}{=}\mathrm{diag}\left(P\right)=\mathrm{diag}\{P_{1{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0},P_{2{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0},\&CenterDot;\&CenterDot;\&CenterDot;,P_{K{f}_0}\};$

θ wherein _kBe the position angle DOA of k signal, r _kBe the distance parameter of k information source, β _PkFor comprising the parameter of position angle and range information, d _pRepresent the relative distance between p array element position and the reference array element, c is the velocity of propagation in the signal propagation medium, f ₀Be centre frequency, Δ f is a frequency interval,

Expression simple crosscorrelation r _{P Δ f}(n) amplitude.

(7) the Toeplitz matrix R that is asked in the integrating step (six) _{P, 2}And the position angle DOA that tries to achieve in the step (four), use the distance parameter that arrowband MUSIC algorithm can be tried to achieve the near field wideband signal source, method is following:

(1) to matrix R _{P, 2}Carry out svd (SVD), then (N+1) * (N+1-K) dimension matrix U of the left singular vector formation of zero singular value correspondence _N2Be matrix R _{P, 2}Noise subspace.

(2) carry out following spectrum peak search and obtain

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

P=1 in the formula, 2, P ₂(β _Pk) be power spectrum, k column vector a _{P, 2}(β _Pk)=[1, exp (j β _Pk) ..., exp (jN β _Pk)] ^T, wherein, β _PkFor comprising the parameter of position angle and range information,

() ^T() ^HRepresent transposition and conjugate transpose respectively, K is a near field wideband signal source number.

(3) utilize the distance parameter of computes near field wideband signal source:

$r_k=4\mathrm{\&pi;}{\mathrm{<figure-callout\; id="2"\; label="d\; p"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">d</figure-callout>}}_p^{}{\cos }^2\left({\mathrm{\&theta;}}_k\right){\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002131763100021.png,HDA00002131763100022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\mathrm{\&Delta;f}/{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002131763100012.png,HDA00002131763100021.png"\; state="\{\{state\}\}">c</figure-callout>}}^2{\mathrm{\&beta;}}_{\mathrm{pk}}$

P=1 in the formula, 2, d _pRepresent the relative distance between p array element position and the reference array element, c is the velocity of propagation in the signal propagation medium, θ _kBe the position angle DOA of k information source, f ₀Be centre frequency, Δ f is a frequency interval, r _kIt is the distance parameter of k information source.

Fig. 3 representes that the RMSE of position angle DOA arrives the SNR=15dB change curve with SNR=-3dB.Fig. 4 representes that the RNMSE of distance parameter arrives the SNR=15dB change curve with SNR=-3dB.As can beappreciated from fig. 3, even the RMSE of DOA is also very little under the very low situation of signal to noise ratio (snr), for example, and when SNR=-2dB, only 0.2 ° of RMSE.As can beappreciated from fig. 4, distance parameter is more little, and RNMSE is low more, and promptly estimated performance is good more.

Embodiment 2:

The present invention is for the estimated capacity of a plurality of signal sources:

The method of embodiment 2 is shown in accompanying drawing 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, and all the other simulated conditions are identical with embodiment's 1; Change the step of carrying out embodiment 1 after the simulated conditions once more and can obtain Fig. 5, wherein Fig. 5 (a) and (b) provided 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.As can be seen from Figure 5 the algorithm of carrying can estimate to surpass the near field broadband signal of element number of array, and this is that traditional broadband, near field spatial spectrum algorithm is to be beyond one's reach.

Claims (5)

1. few array element near field wideband signal source method for parameter estimation is characterized in that the quantity of array element is at least 5 in the receiving array, and the array element at receiving array center is made as reference array element, may further comprise the steps:

(1) the reception signal x of each array element in the array _p(t) carry out discrete Fourier transformation and obtain the array signal model X of near field wideband signal source in frequency field _p(f), get into step (two) and step (five) afterwards;

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

Wherein, p representes the numbering of each array element, reference array element be numbered p=0, with reference array element be that the center is negative direction left, be to the right positive dirction; K is the number of the irrelevant wideband signal source near field, S _k(f) frequency spectrum of k signal of expression on frequency f, N _p(f) be illustrated in p additional noise on the frequency f, additional noise N _p(f) be and the incoherent zero-mean of signal space white noise, τ _Pk(f) k signal of expression incides reference array element with respect to the phase differential of p array element on frequency f;

(2) frequency bandwidth [f of broadband signal nearly _Min, f _Max] resolving into 2N+1 frequency family, N is the maximal value of positive frequencies hop count, the simple crosscorrelation r that contains azimuth information of the array element that is centrosymmetric in calculated rate family output _p(f ₀+ n Δ f):

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

Wherein, p=1,2; N=-N ... ,-1,0,1 ..., N; L=1,2 ... L, L represent the fast umber of beats of frequency domain; () ^*The computing of expression complex conjugate; f ₀Be centre frequency, Δ f is a frequency interval,

X _p(f ₀+ n Δ f, l) expression is divided into L section with observation time, 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) utilize (2N+1) the individual simple crosscorrelation that calculates in the step (two)

Structure Toeplitz matrix R _{P, 1}

(4) the Toeplitz matrix R that utilizes step (three) to obtain _{P, 1}, the position angle parameter of the irrelevant wideband signal source in use MUSIC algorithm computation near field;

(5) frequency bandwidth [f of broadband signal nearly _Min, f _Max] resolving into 2N+1 frequency family, N is the maximal value of positive frequencies hop count, the simple crosscorrelation r of the information that contains position angle and distance parameter of the array element that is centrosymmetric in calculated rate family output _p(n Δ f):

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

(6) utilize (2N+1) the individual simple crosscorrelation that calculates in the step (five)

Structure Toeplitz matrix R _{P, 2}

(7) the Toeplitz matrix R that utilizes step (six) to obtain _{P, 2}And the position angle parameter that obtains of step (four), use the distance parameter of the irrelevant wideband signal source in MUSIC algorithm computation near field.

2. a kind of according to claim 1 few array element near field wideband signal source method for parameter estimation is characterized in that k signal incides reference array element with respect to the phase differential τ of p array element on frequency f in the step () _Pk(f) calculate through following method:

τ _Pk(f)=ω _Pk(f)+φ _Pk(f), wherein, ω _Pk(f) for only containing the electrical angle parameter of position angle parameter, φ _Pk(f) for containing the electrical angle parameter of position angle and distance parameter simultaneously;

${\mathrm{\&omega;}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}-p2\mathrm{\&pi;}{\mathrm{fd}}_1\sin \left({\mathrm{\&theta;}}_k\right)/c& p=\&PlusMinus;1\\ -\mathrm{p\&pi;}{\mathrm{fd}}_2\sin \left({\mathrm{\&theta;}}_k\right)/c& p=\&PlusMinus;2\\ 0& p=0\end{array}\right.$

${\mathrm{\&phi;}}_{\mathrm{pk}}\left(f\right)=\left\{\begin{array}{cc}\mathrm{\&pi;}{\mathrm{fd}}_1^2{\cos }^2\left({\mathrm{\&theta;}}_k\right)/{\mathrm{cr}}_{\mathrm{kf}}& p=\&PlusMinus;1\\ \mathrm{\&pi;}{\mathrm{fd}}_2^2{\cos }^2\left({\mathrm{\&theta;}}_k\right)/{\mathrm{cr}}_{\mathrm{kf}}& p=\&PlusMinus;2\\ 0& p=0\end{array}\right.$

Wherein, c is the velocity of propagation in the signal propagation medium, θ _kBe the position angle of k signal, r _Kf=r _kC/f, wherein r _kBe the distance parameter of k information source, d ₁And d ₂Be respectively the 1st array element of positive dirction and the relative distance between the 2nd array element position and the reference array element, r _k(f)=r _kC/f, wherein r _kDistance parameter for last k the information source of the f of frequency family.

3. like the said a kind of few wideband signal source position angle, array element near field of claim 2 with apart from the two-dimensional parameter combined estimation method, it is characterized in that step (three) is utilized simple crosscorrelation Structure Toeplitz matrix R _{P, 1}Concrete grammar be:

Utilize simple crosscorrelation in the step (six)

Structure Toeplitz matrix R _{P, 2}Concrete grammar be:

4. like the said a kind of few wideband signal source position angle, array element near field of claim 3 with apart from the two-dimensional parameter combined estimation method, it is characterized in that, use the method for the position angle parameter of the irrelevant wideband signal source in MUSIC algorithm computation near field to be in the step (four):

At first to matrix R _{P, 1}Carry out svd, (N+1) * (N+1-K) dimension matrix U of utilizing the corresponding left singular vector of zero singular value to constitute _N1Be 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

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

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 _PkBe the electrical angle parameter that only contains the position angle parameter of k information source, Δ f is a frequency interval, () ^TThe expression transposition, () ^HThe expression conjugate transpose.

5. like the said a kind of few wideband signal source position angle, array element near field of claim 4 with apart from the two-dimensional parameter combined estimation method, it is characterized in that, use the method for the distance parameter of the irrelevant wideband signal source in MUSIC algorithm computation near field to be in the step (seven):

At first to matrix R _{P, 2}Carry out svd, (N+1) * (N+1-K) dimension matrix U of utilizing the corresponding left singular vector of zero singular value to constitute _N2Be matrix R _{P, 2}Noise subspace;

Again to power spectrum P ₂(β _Pk) carry out spectrum peak search and get

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

Wherein, p=1,2, a _{P, 2}(β _Pk)=[1, exp (j β _Pk) ..., exp (jN β _Pk)] ^T, β wherein _PkFor comprising the parameter of position angle and range information, () ^T() ^HRepresent transposition and conjugate transpose respectively, K is the irrelevant wideband signal source number near field;

Utilize the distance parameter of the irrelevant wideband signal source in calculation of parameter near field, position angle at last:

$r_k=4\mathrm{\&pi;}{d}_p^2{\cos }^2\left({\mathrm{\&theta;}}_k\right)f_0\mathrm{\&Delta;f}/c^2{\mathrm{\&beta;}}_{\mathrm{pk}}$

Wherein, p=1,2, d _pRelative distance between p array element position of expression expression and the reference array element, c is the velocity of propagation in the signal propagation medium, θ _kBe the position angle of k information source, f ₀Be centre frequency, Δ f is a frequency interval, r _kIt is the distance parameter of k information source.

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