CN101644760B - Rapid and robust method for detecting information source number suitable for high-resolution array - Google Patents

Abstract

The invention discloses a rapid and robust method for detecting information source number for a high-resolution array, belonging to the signal processing field and comprising the following steps: establishing a received data model of an array antenna, utilizing a multi-level Wiener filter to carry out step-by-step filtration on received data, obtaining the minimum mean square error of each level, and then calculating the maximum likelihood function by using the minimum mean square error, meanwhile, utilizing free parameters referred to calculate the maximum likelihood function to determine the number of unknown free parameters in the model, and finally obtaining an improved minimum description length method, thereby realizing the detection of the number of unknown information sources in airspace. The invention solves the problems of high computational complexity, sensitivity to non-uniform noise and the like in the traditional information source number detection technology. Compared with the prior art, the invention can obtain the information source number in the airspace rapidly and robustly, which provides necessary guarantees for a phase array radar and a communication system applied to practice to carry out target/user trace, direction-of-arrival estimation (DOA ), self-adaptive filtration processing and the like.

Description

A kind of method for detecting information source number that is applicable to the fast robust of high-resolution array

Technical field

The present invention relates to the method that a kind of information source number detects, the phased-array radar that is particularly suitable under the environment complicated and changeable carries out the detection of fast robust with the communication system that adopts intelligent antenna technology to information source number, belongs to the signal processing technology field.

Background technology

Background has a wide range of applications in array signal process technique modern radars and the wireless communication technology.For example, phased-array radar is owing to have data transfer rate height, multi-functional, multiple goal intercepting and capturing, tracking, remarkable advantage such as anti-interference, thereby caused the great attention of various countries.Yet; Phased-array radar is when carrying out the high-resolution location and following the tracks of to a plurality of targets, the target number can't know in advance, needs to detect; Especially in actual environment complicated and changeable; Tend to occur disturbing more, multipath serious situation,, can have influence on location, the detection and tracking of phased-array radar target if the target number estimation is inaccurate.This just requires at first can carry out the detection of fast robust to the target number.

In wireless communication field, intelligent antenna technology is owing to have remarkable advantages with aspects such as suppressing interference improving power system capacity, so become in the mobile communication technology one of active research field the most.As the gordian technique of smart antenna, direction of arrival is estimated and wave beam forms by broad research.Yet, when direction of arrival being carried out the high-resolution estimation, at first need confirm the number of user and interference.For a practical communication system, real-time and sane direction of arrival estimation and beam-forming technology are necessary often, and this just requires system at first can carry out the detection of fast robust to information source number.

Be the detection method of example brief account tradition information source number below with the phased-array radar:

If phased-array radar adopts linear array, signal model can be by accompanying drawing 1 expression.Element number of array is N, to echoed signal at t _lConstantly carry out 1 snap sampling, the observation data of deleting last array element output is designated as:

X(t _l)＝[x ₁(t _l)，x ₂(t _l)，…，x _M(t _l)] ^T

M=N-1 wherein, [ ] ^TThe representing matrix transposition, x _i(t _l) represent that i array element is at t _lReception echo data constantly.Echoed signal is got L snap sampling, then observe echo data be designated as $X={\left\{X\left(t_l\right)\right\}}_{l=1}^L.$

If the probability model of observation data is p (X| Θ), the unknown parameter vector in the Θ representation model wherein, so, the minimum description length of this observation space can approximate representation be:

Wherein K representes the number of unknown free parameter among the Θ.First on above-mentioned equality the right is called log-likelihood function.

Because observation echo data X is steady Gaussian random vector again independently, and average is 0, and their joint probability density function is:

$p\left(X\right|\mathrm{\&Theta;})=\underset{l=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">L</figure-callout>}}{\mathrm{\&Pi;}}}\frac{1}{{\mathrm{\&pi;}}^q\det \left(R_x\right)}\exp \{-X{\left(t_l\right)}^H{R}_x^{-1}X\left(t_l\right)\}---\left(2\right)$

Wherein determinant, R are got in det () expression _xBe echo data covariance matrix, R _x=E [X (t _l) X ^H(t _l)], hope in E [ ] expression peek term, () ^HExpression Hermitian transposition.Then log-likelihood function can be written as:

The mark of tr representing matrix wherein.So (1) formula can be expressed as:

Traditional method is the sample estimates covariance matrix and it is carried out characteristic value decomposition; Utilizing equal this characteristic of minimal eigenvalue to carry out information source number detects; For example M.Wax and T.Kailath were in the method in " Detection of signals by information theoretic criteria " literary composition proposition in 1985; But this method is a complete failure under non-homogeneous noise background, and non-homogeneous noise certainly exists in actual radar system and communication system applications.The method that people such as E.Fishler proposed at " Estimationof the number of sources in unbalanced array via information theoretic criteria " literary composition in 2005 can be used for non-homogeneous noise background; But still need the sample estimates covariance matrix and it is carried out characteristic value decomposition; And often repeatedly iteration is carried out in requirement; Needed computation complexity is quite high, can't real-time implementation in radar and communication system.

The method for detecting information source number that this patent proposes---based on the minimum description length method of least mean-square error; Traditional minimum description length method is improved; Be used for the least mean-square error of multistage wiener filter the calculating of minimum description length; Thereby make this method not need sample estimates covariance matrix and characteristic value decomposition thereof just can detect the number of unknown information source; Solve the difficulty that classic method is run in real system is used effectively, it is simple that promptly the new method of this patent has calculating, to the advantage of non-homogeneous noise robustness.

Describe content of the present invention for ease, at first do following terminological interpretation:

1, about multistage wiener filter (MSWF) principle:

Multistage wiener filter is a kind of effective ways that solve linear filtering problem, and it solves the problem of inverting of covariance matrix through the mode of iteration step by step.

Multistage wiener filter algorithm concrete steps are following:

* explanation: the variable subscript i in forward recursive and the backward recursive is its corresponding progression

Summary of the invention

The purpose of this invention is to provide a kind of robust that is applicable to high-resolution array method for detecting information source number fast; It utilizes the least mean-square error of multistage wiener filter to calculate minimum description length; Thereby the computation complexity that solves traditional information source number detection algorithm in actual radar/communication system is high, to problems such as non-homogeneous ground unrest sensitivities.

The method for detecting information source number of the described fast robust of technical scheme of the present invention is realized through following steps:

(I), element number of array be the array antenna received of N to the fast beat of data of L, according to the multistage wiener filter principle, obtain multistage wiener filter least mean-square error at different levels, making the least mean-square error of multistage wiener filter j level is ρ _j, wherein, j=1,2 ..., M, M=N-1;

(II), the least mean-square error ρ at different levels that obtain in the step (I) _jThe substitution following formula obtains the relation of information source number k of minimum description length mMDL (k) and supposition:

$\mathrm{mMDL}\left(k\right)=L(M-k)\ln \left(\frac{1/(M-k){\mathrm{\&Sigma;}}_{j=k+1}^M{\mathrm{\&rho;}}_j}{{\left({\mathrm{\&Pi;}}_{j=k+1}^M{\mathrm{\&rho;}}_j\right)}^{1/(M-k)}}\right)+\frac{1}{2}k(2M-k-1)\ln L$

(III), make integer k from 0 incremental variations to M-1; The minimum value of search minimum description length mMDL (k), the pairing k value of this minimum value this moment is detected information source number

promptly:

$\hat{q}=\arg \underset{k=\mathrm{0,1},...,M-1}{\min }\mathrm{mMDL}\left(k\right)$

In the method for detecting information source number of the described fast robust of technical scheme of the present invention, the method that obtains multistage wiener filter least mean-square error at different levels in the step (I) is following:

1. utilize following formula to confirm initial reference signal d ₀(t _l) and initial observation data X ₀(t _l):

Initial reference signal: d ₀(t _l)=x _M+1(t _l);

Initial observation data: X ₀(t _l)=[x ₁(t _l) ..., x _M(t _l)] ^T

Wherein, d ₀(t _l) and X ₀(t _l) be respectively the initial reference signal and the initial observation data of multistage wiener filter, x _i(t _l) represent that i array element is at t _lThe echo data that constantly receives;

2. forward recursive: make i=1, and carry out following a～f step, behind each execution of step f, make i increase by 1, repeat a～f, carry out a～f step for the last time, obtain the simple crosscorrelation of observation datas at different levels and reference signal successively up to i=M

Two norm δ _i, matched filter h _iVariance with reference signal

A. the simple crosscorrelation of (i-1) level observation data and reference signal: $r_{x_{i-1}{d}_{i-1}}=E\left[X_{i-1}\left(t_l\right)d_{i-l}^{*}\left(t_l\right)\right];$

B. two norms of the simple crosscorrelation of (i-1) level observation data and reference signal: ${\mathrm{\&delta;}}_i={\left|\right|r_{x_{i-1}{d}_{i-1}}\left|\right|}_2;$

C. i level matched filter: $h_i=r_{x_{i-1}{d}_{i-1}}/{\mathrm{\&delta;}}_i;$

D. i level reference signal: $d_i\left(t_l\right)=h_i^H{X}_{i-1}\left(t_l\right);$

E. the variance of i level reference signal: ${\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="d\; i"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">d</figure-callout>}}_i}^2=E\left[{\left|d_i\left(t_l\right)\right|}^2\right];$

F. i level observation data: X _i(t _l)=X _I-1(t _l)-h _id _i(t _l);

3. backward recursive: at first according to computes M level least mean-square error ρ _M:

ρ _M＝E[|d _M(t _l)| ²]

Next utilizes ρ _MCarry out recurrence step by step with substitution as a result following (*) formula of step in 2., obtain multistage wiener filter least mean-square errors at different levels, said (*) formula is:

${\mathrm{\&rho;}}_{i-1}={\mathrm{\&sigma;}}_{d_{i-1}}^2-{\left|{\mathrm{\&delta;}}_i\right|}^2/{\mathrm{\&rho;}}_i---(*)$

Specifically, utilize in 3. backward recursive to obtain multistage wiener filter least mean-square error methods at different levels to be: make i=M, carry out (*) formula, obtain ρ _M-1Make i=M-1 again, carry out (*) formula, obtain ρ _M-2By that analogy, promptly make i subtract 1 after execution (*) formula at every turn, carry out (*) formula once more, carry out (*) formula for the last time up to i=2 and obtain ρ ₁Till, thereby obtain multistage wiener filter least mean-square error ρ at different levels _j, j=1 wherein, 2 ..., M.

Provide the principle analysis of technical scheme of the present invention below:

With the covariance matrix that receives echo data

R in expression (3) formula _x, $R_{x_0}=E\left[X_0\left(t_l\right)X_0^H\left(t_l\right)\right],$ X ₀(t _l)=[x ₁(t _l) ..., x _M(t _l)] ^T, x wherein _i(t _l) represent that i array element is at t _lReception echo data constantly.Receive the covariance matrix of echo data

Determinant be: $\mathrm{Det}\left(R_{x_0}\right)=\mathrm{Det}\left(R_e\right)=\underset{i=1}{\overset{M}{\mathrm{\&Pi;}}}{\mathrm{\&rho;}}_i,$ Wherein determinant, R are got in det () expression _e=diag ([ρ ₁, ρ ₂, ρ _M] ^T) ${\mathrm{\&rho;}}_1\&GreaterEqual;{\mathrm{\&rho;}}_2...>{\mathrm{\&rho;}}_{q+1}={\mathrm{\&rho;}}_{q+2}={\mathrm{\&rho;}}_{q+3}...={\mathrm{\&rho;}}_M={\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2,$ ρ _i(i=1,2 ..., M) be multistage wiener filter least mean-square error at different levels, ${\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2=1/(M-k){\mathrm{\&Sigma;}}_{i=k+2}^M{\mathrm{\&rho;}}_i.$ Suppose that the information source number in the spatial domain to be measured is k, then (3) formula becomes:

Multistage wiener filter least mean-square error ρ at different levels _i(i=1 ..., k) with ${\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2=\frac{1}{M-k}\underset{i=k+2}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i$ Substitution formula (5) is ignored the irrelevant constant term with information source number k

The expression that obtains log-likelihood function is:

According to the characteristic of multistage wiener filter, the covariance matrix that receives echo data can be expressed as $R_{x_0}=H{\left(W^H\right)}^{-1}{R}_e{W}^{-1}{H}^H,$ Wherein H and W's is expressed as respectively

H＝[h ₁，…h _M]

So the free parameter vector that can obtain thus in the model is: ${\mathrm{\&Theta;}}^T=\left[{\mathrm{\&rho;}}_1,{\mathrm{\&rho;}}_2,...{\mathrm{\&rho;}}_k,{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2,{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">w</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">w</figure-callout>}}_2,...,w_k,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">h</figure-callout>}}_2,...,h_k\right].$ Yet not every free parameter all is independent of each other among the Θ.Obviously, w _iAnd ρ _iAll depend on through matched filter h _iThe resulting reference signal d of filtering _i(t _l), promptly $d_i\left(t_l\right)=h_i^H{x}_0\left(t_l\right).$ That is to say w _iAnd ρ _iBy h _iConfirm.So, the free parameter vector can be reduced to: ${\mathrm{\&Theta;}}^T=[{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,...,h_k].$ Notice that simultaneously matched filter is the vector of orthonomalization, it is individual that orthonomalization can make that free parameter reduces (2k+2 (1/2) k (k-1)).So the free parameter number of Θ is calculated as:

K＝2Mk+1-2k-2(1/2)k(k-1)＝k(2M-k-1)+1 (7)

Minimum description length with the free parameter number K substitution formula (4) of the log-likelihood function F (k) of formula (6) and formula (7) obtains a new minimum description length computing formula:

$\mathrm{MMDL}\left(k\right)=L(M-k)\mathrm{Ln}\left(\frac{1/(M-k){\mathrm{\&Sigma;}}_{i=k+1}^M{\mathrm{\&rho;}}_i}{{\left({\mathrm{\&Pi;}}_{i=k+1}^M{\mathrm{\&rho;}}_i\right)}^{1/(M-k)}}\right)+\frac{1}{2}k(2M-k-1)\mathrm{Ln}L---\left(8\right)$ The minimum value of search minimum description length mMDL (k), the pairing k of this minimum value this moment is detected information source number

Promptly

$\hat{q}=\arg \underset{k=\mathrm{0,1},...,M-1}{\min }\mathrm{mMDL}\left(k\right)$

Compared with prior art, beneficial effect of the present invention is:

Technical scheme according to the invention is directly utilized multistage wiener filter algorithm computation least mean-square error under the situation that does not need Estimation of covariance matrix and characteristic value decomposition thereof, use least mean-square error to calculate minimum description length then.On the one hand, owing to need not to calculate sample covariance matrix and characteristic value decomposition thereof, the method for this patent has the simple advantage of calculating; On the other hand, because non-homogeneous noise only can produce serious disturbance to the eigenwert of covariance matrix, and can not influence the least mean-square error of multistage wiener filter, so the method for this patent has the advantage of robustness under non-homogeneous noise.This makes it in practical application, have computation complexity non-homogeneous noise low, that unfavorable hardware factor is brought can detect target/advantages such as user's number fast robust, can be used in the wireless communication system of phased-array radar/employing intelligent antenna technology target number/user's number being detected.

Description of drawings

The signal model that Fig. 1-the present invention adopted, (a) array structure, (b) relation of electromagnetic wave propagation direction and array; Wherein, d is the spacing of adjacent two array elements, and N is the element number of array of array, and θ is the direction of arrival of signal source;

Fig. 2-spatial domain time domain is the probability that correctly detects target/user's number in the white noise environment;

Comparison computing time of Fig. 3-three kind of method;

Correctly detect the probability of target/user's number in Fig. 4-non-homogeneous noise circumstance.

Embodiment

Below in conjunction with accompanying drawing and embodiment, technical scheme of the present invention is done further explanation.

An embodiment who uses technical scheme according to the invention in field of radar is, adopts the linear array with 10 array elements, and wherein array element distance is a half-wavelength.The direction that incides the arrowband information source (target that radar is to be detected) of two constant powers of this array is respectively [θ ₁, θ ₂=[2.5 °, 7.8 °], signal to noise ratio (snr) is-3dB.This moment, we had N=10, M=9.

The practical implementation step is described below:

(I), element number of array be the array antenna received of N to the fast beat of data of L, according to the multistage wiener filter principle, obtain multistage wiener filter least mean-square error at different levels, making the least mean-square error of multistage wiener filter j level is ρ _j, wherein, j=1,2 ..., M, M=N-1;

The method of the least mean-square error that said acquisition multistage wiener filter is at different levels is following:

1. utilize following formula to confirm initial reference signal d ₀(t _l) and initial observation data X ₀(t _l):

Initial reference signal: d ₀(t _l)=x _M+1(t _l);

Initial observation data: X ₀(t _l)=[x ₁(t _l) ..., x _M(t _l)] ^TWherein, d ₀(t _l) and X ₀(t _l) be respectively the initial reference signal and the initial observation data of multistage wiener filter, x _i(t _l) represent that i array element is at t _lThe echo data that constantly receives;

2. forward recursive: make i=1, and carry out following a～f step, behind each execution of step f, make i increase by 1, repeat a～f, carry out a～f step for the last time, obtain the simple crosscorrelation of observation datas at different levels and reference signal successively up to i=M

Two norm δ _i, matched filter h _iVariance with reference signal

A. the simple crosscorrelation of (i-1) level observation data and reference signal: $r_{x_{i-1}{d}_{i-1}}=E\left[X_{i-1}\left(t_l\right)d_{i-l}^{*}\left(t_l\right)\right];$

B. two norms of the simple crosscorrelation of (i-1) level observation data and reference signal: ${\mathrm{\&delta;}}_i={\left|\right|r_{x_{i-1}{d}_{i-1}}\left|\right|}_2;$

C. i level matched filter: $h_i=r_{x_{i-1}{d}_{i-1}}/{\mathrm{\&delta;}}_i;$

D. i level reference signal: $d_i\left(t_l\right)=h_i^H{X}_{i-1}\left(t_l\right);$

E. the variance of i level reference signal: ${\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="d\; i"\; filenames="H2009100917467E00011.png"\; state="\{\{state\}\}">d</figure-callout>}}_i}^2=E\left[{\left|d_i\left(t_l\right)\right|}^2\right];$

F. i level observation data: X _i(t _l)=X _I-1(t _l)-h _id _i(t _l);

3. backward recursive: at first according to computes M level least mean-square error ρ _M:

ρ _M＝E[|d _M(t _l)| ²]

Next utilizes ρ _MCarry out recurrence step by step with substitution as a result following (*) formula of step in 2., obtain multistage wiener filter least mean-square errors at different levels.Said (*) formula is:

${\mathrm{\&rho;}}_{i-1}={\mathrm{\&sigma;}}_{d_{i-1}}^2-{\left|{\mathrm{\&delta;}}_i\right|}^2/{\mathrm{\&rho;}}_i---(*)$

Specifically, utilize in 3. backward recursive to obtain multistage wiener filter least mean-square error methods at different levels to be: make i=M, carry out (*) formula, obtain ρ _M-1Make i=M-1 again, carry out (*) formula, obtain ρ _M-2By that analogy, promptly make i subtract 1 after execution (*) formula at every turn, carry out (*) formula once more, carry out (*) formula for the last time up to i=2 and obtain ρ ₁Till, thereby obtain multistage wiener filter least mean-square error ρ at different levels _j, j=1 wherein, 2 ..., M.

(II), the least mean-square error ρ at different levels that obtain in the step (I) _jThe substitution following formula obtains the relation of information source number k of minimum description length mMDL (k) and supposition:

$\mathrm{mMDL}\left(k\right)=L(M-k)\ln \left(\frac{1/(M-k){\mathrm{\&Sigma;}}_{j=k+1}^M{\mathrm{\&rho;}}_j}{{\left({\mathrm{\&Pi;}}_{j=k+1}^M{\mathrm{\&rho;}}_j\right)}^{1/(M-k)}}\right)+\frac{1}{2}k(2M-k-1)\ln L$

(III), make integer k from 0 incremental variations to M-1; The minimum value of search minimum description length mMDL (k), the pairing k value of this minimum value this moment is detected information source number

promptly:

$\hat{q}=\arg \underset{k=\mathrm{0,1},...,M-1}{\min }\mathrm{mMDL}\left(k\right)$

Adopt matlab emulation, the simulation result that obtains after the process above-mentioned steps is shown in accompanying drawing 2～4, and accompanying drawing 2 is a Gauss model with the information source that accompanying drawing 3 adopts, and has adopted the information source of Gauss model and the information source of laplace model in the accompanying drawing 4 respectively; MMDL in the accompanying drawing 2～4 is the method that the present invention proposes, and cMDL is the method that M.Wax and T.Kailath proposed in 1985, and rMDL is the method that people such as E.Fishler proposed in 2005.

Can be found out by accompanying drawing 2, adopt method of the present invention, less when the fast umber of beats of sampling, the correct performance that detects is situated between between cMDL and the rMDL method.When the fast umber of beats of sampling was tending towards infinity, for the information source of Gaussian distribution and laplacian distribution, correct detection probability all was tending towards probability 1, explains that method of the present invention is correct in theory.

Accompanying drawing 3 is found out owing to do not need the covariance matrix and the eigenwert of calculating covariance matrix of sample estimates data; Comparing the needed time of mMDL method proposed by the invention with the rMDL method with the cMDL method significantly reduces; Especially when element number of array increases; The used time of mMDL method is almost 1/100 of rMDL method, satisfies real-time treatment requirement in radar and the communication system easily.

Accompanying drawing 4 finds out in the non-homogeneous noise circumstance no matter information source is Gauss model or laplace model, and the cMDL method is meeting complete failure when fast umber of beats is big, and rMDL method and mMDL method performance are all fine; When fast umber of beats seldom the time, though mMDL method performance is inferior to the rMDL method a little, correct detection probability is all greater than 0.6, and along with array number increases, the performance of two kinds of methods much at one.

This shows that method of the present invention can detect the target/user signal source number in the spatial domain to be measured effectively, and have weak point computing time, the advantage of robust in non-homogeneous background noise environment.Therefore, in actual radar and communication system applications, method of the present invention is a kind of than rMDL and the more effective information source number detection technique of cMDL method.

Above-described specific descriptions; Purpose, technical scheme and beneficial effect to invention have carried out further explain, and institute it should be understood that the above is merely specific embodiment of the present invention; And be not used in qualification protection scope of the present invention; All within spirit of the present invention and principle, any modification of being made, be equal to replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1. a method for detecting information source number that is applicable to the fast robust of high resolution ratio array is characterized in that, comprises the steps:

(I), element number of array be the array antenna received of N to the fast beat of data of L, according to the multistage wiener filter principle, obtain multistage wiener filter least mean-square error at different levels, making the least mean-square error of multistage wiener filter j level is ρ _j, wherein, j=1,2 ..., M, M=N-1;

(II), the least mean-square error ρ at different levels that obtain in the step (I) _jThe substitution following formula obtains the relation of information source number k of minimum description length mMDL (k) and supposition:

$\mathrm{mMDL}\left(k\right)=L(M-k)\ln \left(\frac{1/(M-k){\mathrm{\&Sigma;}}_{j=k+1}^M{\mathrm{\&rho;}}_j}{{\left({\mathrm{\&Pi;}}_{j=k+1}^M{\mathrm{\&rho;}}_j\right)}^{1/(M-k)}}\right)+\frac{1}{2}k(2M-k-1)\ln L$

(III), make integer k from 0 incremental variations to M-1; The minimum value of search minimum description length mMDL (k), this moment this minimum value pairing k value be detect information source number

promptly:

$\hat{q}=\arg \underset{k=\mathrm{0,1},...,M-1}{\min }\mathrm{mMDL}\left(k\right)$

Wherein, it is following to obtain the method for multistage wiener filter least mean-square error at different levels in the said step (I):

1. utilize following formula to confirm initial reference signal d ₀(t _l) and initial observation data X ₀(t _l):

Initial reference signal: d ₀(t _l)=x _M+1(t _l);

Initial observation data: X ₀(t _l)=[x ₁(t _l) ..., x _M(t _l)] ^T

Wherein, d ₀(t _l) and X ₀(t _l) be respectively the initial reference signal and the initial observation data of multistage wiener filter, x _i(t _l) represent that i array element is at t _lConstantly receive echo data;

2. forward recursive: make i=1, and carry out following a～f step, behind each execution of step f, make i increase by 1, repeat a～f, carry out a～f step for the last time, obtain the simple crosscorrelation of observation datas at different levels and reference signal successively up to i=M

Two norm δ _i, matched filter h _iVariance with reference signal

The simple crosscorrelation of a, (i-1) level observation data and reference signal:

Two norms of the simple crosscorrelation of b, (i-1) level observation data and reference signal:

C, i level matched filter:

D, i level reference signal:

The variance of e, i level reference signal:

F, i level observation data: X _i(t _l)=X _I-1(t _l)-h _id _i(t _l);

3. backward recursive: at first according to computes M level least mean-square error ρ _M:

ρ _M＝E[|d _M(t _l)| ²]

Next utilizes ρ _MCarry out recurrence step by step with substitution as a result following (*) formula of step in 2., obtain multistage wiener filter least mean-square errors at different levels, said (*) formula is:

${\mathrm{\&rho;}}_{i-1}={\mathrm{\&sigma;}}_{d_{i-1}}^2-{\left|{\mathrm{\&delta;}}_i\right|}^2/{\mathrm{\&rho;}}_i---(*)$

Specifically, utilize in 3. backward recursive to obtain multistage wiener filter least mean-square error methods at different levels to be: make i=M, carry out (*) formula, obtain ρ _M-1Make i=M-1 again, carry out (*) formula, obtain ρ _M-2By that analogy, promptly make i subtract 1 after execution (*) formula at every turn, carry out (*) formula once more, carry out (*) formula for the last time up to i=2 and obtain ρ ₁Till, thereby obtain multistage wiener filter least mean-square error ρ at different levels _j, j=1 wherein, 2 ..., M.

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