CN104459635B - Self adaptation air filter filtering method based on iterative shrinkage Weighted Fusion - Google Patents

Abstract

The invention discloses a kind of self adaptation air filter filtering method based on iterative shrinkage Weighted Fusion, it is realized process and is：Signal model is set up by array antenna received data, obtains the sample covariance matrix of receiving data；Online updating priori covariance matrix by the way of adaptive iteration；Calculate the weight coefficient of sample covariance matrix and priori covariance matrix according to minimum mean-squared error criterion, and obtain the covariance matrix estimated using contraction weighting fusion treatment method；Finally calculate self adaptation weight vector and carry out air filter filtering.The present invention can estimate covariance matrix with degree of precision under Small Sample Size, priori and current data model mismatch problems can effectively be alleviated, avoid the determination of subspace dimension, there is the high advantage with fast convergence rate of output Signal to Interference plus Noise Ratio simultaneously, be that the practical application of self adaptation air filter filtering provides a kind of effective processing method.

Description

Self adaptation air filter filtering method based on iterative shrinkage Weighted Fusion

Technical field

The invention belongs to field of signal processing, it is related to array signal process technique, specifically one kind is added using contraction The self adaptation air filter filtering method that power is merged and updated based on iteration, for estimating association side with degree of precision under condition of small sample Difference matrix, improves the Signal to Interference plus Noise Ratio of aerial array output.

Background technology

Array Signal Processing is one of field of signal processing hot research direction, in radar, sonar, communication, earthquake The fields such as monitoring are applied widely, and the filtering of self adaptation air filter is an important research content of Array Signal Processing, its purpose It is suppression interference and noise while strengthening echo signal power, thus improving the Signal to Interference plus Noise Ratio of array antenna output.Adaptive Air filter filtering essence is answered to be each array element to be carried out adaptive weighted, array weight vector determines the performance of array antenna, and weighs arrow Amount is largely dependent upon signal covariance matrix, and therefore signal covariance matrix estimated accuracy directly affects self adaptation air filter The performance of filtering, and under condition of small sample, there is larger estimation difference in signal covariance matrix, leads to array suppression interference Ability drastically decline, therefore, research condition of small sample under air filter filtering method, there is important actual application value.

At present, calculate self adaptation weight vector algorithm have multiple.Covariance matrix invert (SMI) algorithm be a kind of conventional effectively Algorithm, but when containing desired signal in array data, SMI algorithm can lead to the signal to noise ratio degradation exporting；Subspace is thrown The shadow class algorithm environment stronger to desired signal, filter effect is preferable, but such algorithm needs accurately to estimate signal subspace And noise subspace, and limited by subspace estimation precision under condition of small sample；Diagonal loading algorithm adds on covariance matrix Pair of horns matrix, can effectively overcome the little eigenvalue disturbance of array covariance matrix and the array pattern distortions that cause, but How to choose diagonal loading amount to be not easy to determine；Griffiths et al. is in the IEEE Trans.on Antennas of nineteen eighty-two The article delivered on and Propagation《An alternative approach to linearly constrained adaptive beamforming》In it is proposed that Generalized Sidelobe Canceller (GSC), it can overcome desired signal in SMI algorithm to contain The signal cancellation problem causing in covariance matrix, but the presence due to antenna array error, when signal to noise ratio is higher, also can go out Existing signal cancellation problem, leads to export Signal to Interference plus Noise Ratio decline；Goldstein et al. was in the IEEE of 1998 The article delivered on Trans.Information theory《A multistage representation of the wiener filter based on orthogonal projections》In it is proposed that be based on Generalized Sidelobe Canceller framework Contraction multistage wiener filter, the method do not need to carry out Eigenvalues Decomposition, and computational complexity is low, but the method it needs to be determined that The dimension of processor, and under condition of small sample, the estimated accuracy of processor dimension is not high.

Content of the invention

It is an object of the invention to overcoming the shortcomings of above-mentioned prior art, one kind is provided using contraction Weighted Fusion and to be based on The self adaptation air filter filtering method that iteration updates, effectively alleviates priori and current data model mismatch problems, avoids simultaneously Subspace dimension determines a difficult problem, improves under condition of small sample the estimated accuracy of signal covariance matrix and the letter of output is dry makes an uproar Than.

Realize the object of the invention technical scheme, comprise the steps：

(1) signal model is set up by receiving data X (k) in array antenna k moment, and calculate the sampling association side of receiving data Difference matrix

(2) the initialization energy spectral density of angle of aspect θ is obtained using the sample covariance matrix of receiving dataAnd just Beginningization priori covariance matrix

(3) according to the priori covariance matrix having obtained, using least square method, obtain the optimum power in angle of aspect space W (θ), updates the energy spectral density in angle of aspect spaceAnd update priori covariance matrixRepeat step (3), online Update priori covariance matrix, until obtaining a stable priori covariance matrix R₀；

(4) priori covariance matrix R₀Sample covariance matrix with receiving dataCarry out shrinking at Weighted Fusion Reason, calculates weight coefficient using minimum mean-squared error criterion, obtains the covariance matrix R estimating_E；

(5) calculate the optimum weight vector w of self adaptation air filter filtering_opt, processed using the optimum weight vector obtaining and receive number According to thus obtaining the useful signal of height output Signal to Interference plus Noise Ratio.

The present invention compared with prior art, has advantages below：

(1) online updating priori covariance matrix by the way of iteration self-adapting, can effectively alleviate priori and work as Front data model mismatch problems, obtain the higher priori covariance matrix of estimated accuracy；

(2) sample covariance matrix and priori covariance matrix are processed by the way of shrinking Weighted Fusion, and according to Little mean-square error criteria calculates weight coefficient, can obtain higher signal covariance estimated accuracy under small sample, improves battle array Array antenna exports Signal to Interference plus Noise Ratio, avoids the determination of subspace dimension simultaneously.

The purpose of the present invention, feature, advantage can be described in detail by drawings described below and example.

Brief description

Fig. 1 is the flow chart of the present invention；

Fig. 2 is the schematic diagram of self adaptation air filter filtering of the present invention；

Fig. 3 is the relation being changed with fast umber of beats using distinct methods simulation data Signal to Interference plus Noise Ratio in independent non-time-varying information source Curve chart；

Fig. 4 is the relation being changed with fast umber of beats using distinct methods simulation data Signal to Interference plus Noise Ratio in relevant non-time-varying information source Curve chart；

Fig. 5 is the variation relation curve chart of emulation reconstruct priori covariance matrix error and iterationses.

Specific embodiment

With reference to Fig. 1, the present invention to realize step as follows：

Step 1. sets up signal model according to k reception data X (k), and calculates the covariance matrix of receiving data

1a) set X (k) as k moment array received data, wherein k=1 ..., L, L are fast umber of beats of sampling；If a₀And s₀(k) point Not Wei the steering vector of echo signal and the complex envelope in the k moment, A_J=[a₁…a_P] and s_J(k)=[s₁(k)… s_P(k)]^TPoint Not Wei the array manifold of P interference signal and the complex envelope vector in the k moment, wherein a_i, i=1 ... P represent i-th interference believe Number steering vector, s_iK (), i=1 ... P represents i-th interference signal complex envelope in the k moment, and subscript T represents that transposition operates； If N (k) is the additive white Gaussian noise in the k moment；

1b) theoretical according to Array Signal Processing, the signal model of array received data is：

X (k)=a₀s₀(k)+A_Js_J(k)+N(k)

1c) sample covariance matrix of receiving data is：

Wherein subscript H represents conjugate transposition operation.

Step 2. obtains the initialization energy spectral density at angle of aspect θ according to the sample covariance matrix of receiving dataAnd initialize priori covariance matrix

2a) set the steering vector as angle of aspect θ for a (θ), calculate the initialization energy spectrum at angle of aspect θ using equation below Density

2b) equation below is utilized to initialize priori covariance matrix

Wherein angle of aspect

Step 3. online updating priori covariance matrix by the way of adaptive iteration.

3a) according to least square method, using the priori covariance matrix having obtained, angle of aspect is calculated using equation below Optimum power w (θ) of θ：

The energy of corresponding angles 3b) is updated as follows using the optimum power of angle of aspect and the covariance matrix of receiving data Spectrum density

3c) utilize the priori covariance matrix that equation below updates

3d) makeRepeat step 3a) to step 3c), until obtaining a stable priori covariance matrix R₀.

Step 4. shrinks weighting fusion treatment.

4a) it is calculated as follows the covariance matrix R after shrinking Weighted Fusion_E：

Wherein R₀For priori covariance matrix, α and β respectively receiving data sample covariance matrix and priori covariance square The weight coefficient of battle array；

4b) according to minimum mean-squared error criterion, weight coefficient α and β is calculated as follows respectively：

Wherein τ=beta/alpha,a₀ Steering vector for echo signal.

Step 5. calculates the optimum power of self adaptation air filter filtering, completes the air filter filtering of array data.

Equation below 5a) is utilized to calculate optimum power：

5b) output signal y (k) of k moment array antenna is：

Y (k)=w^H _optX(k)

Wherein subscript H represents conjugate transposition operation.

The effect of the present invention can be further illustrated by following simulation result.

1. emulate data：

Consider an even linear array being made up of 10 array elements, using same frequency narrow band signal as simulation object.Useful The direction of arrival of signal is 0 °, has 5 interference signals, and their direction of arrival [15 °, 50 °] of [- 50 °, -15 °] ∪ interval with 5 ° For being spaced uniformly random distribution；The signal to noise ratio of single array element is 10dB, and dry ratio of making an uproar is for 40dB；Array element is spaced apart signal frequency and corresponds to The half of wavelength.

2. emulation content and result

Emulation 1, if information source is independent source and information source direction of arrival does not change over time, is respectively adopted sample covariance matrix Inversion technique (being designated as SMI), contraction weighting fusion treatment method (being designated as S-SMI) lacking prior information, subspace projection side Method (being designated as SP), multi-Stage Wiener Filter method (being designated as MSWF) and the inventive method are to array output Signal to Interference plus Noise Ratio with array received The change of signal fast umber of beats is emulated, and simulation result is as shown in Figure 3.Wherein IAS-SMI is the inventive method.

When lacking prior information as seen from Figure 3, after shrinking weighting fusion treatment, the output letter of S-SMI method is dry to make an uproar Ratio increases, and has close convergence rate with multi-Stage Wiener Filter (MSWF) method；And the inventive method is due to priori Covariance matrix carries out online iteration self-adapting renewal, can obtain the performance close with subspace projection (SP) hence it is evident that improve The little output Signal to Interference plus Noise Ratio taking soon.But, subspace projection method and multi-Stage Wiener Filter method all rely on correctly son sky Between dimension, owe to estimate that the lower Signal to Interference plus Noise Ratio that exports declines substantially.The inventive method not it needs to be determined that subspace dimension, in small sample ring The suitability in border is higher.

Emulation 2, if information source is coherent and information source direction of arrival does not change over time, has 2 interference signals to be concerned with, respectively Contraction weighting fusion treatment method using sample covariance matrix inversion technique (being designated as SMI), shortage prior information (is designated as S- SMI), subspace projection method (being designated as SP), multi-Stage Wiener Filter method (being designated as MSWF) and the inventive method export to array Signal to Interference plus Noise Ratio is emulated with the change of array received signal fast umber of beats, and simulation result is as shown in Figure 4.Wherein IAS-SMI is this Inventive method.

When there is coherent as seen from Figure 4, the main feature space dimension reduction of array data, using the letter of data estimation Work song space cannot represent the true array manifold of interference, and the four kinds of control methods of other in the present invention were all lost efficacy；Side of the present invention The priori covariance matrix that method is adopted make use of adaptive matched filter to be reconstructed in itself, there is not main feature space Dimensionality reduction problem, remains to obtain larger output Signal to Interference plus Noise Ratio.

Emulation 3, is entered with the variation relation of iterationses to the iteration error of the reconstruct priori covariance matrix in the present invention Row Performance Analysis, simulation result is as shown in Figure 5.Wherein：Iteration error is defined as| | | | represents 2 models Number, simulation result in figure L is the fast umber of beats of sample.

As seen from Figure 5, after increasing iterationses, iteration error reduces substantially, and under the premise of identical iterationses, increases It is loaded this fast umber of beats and can reduce iteration error.This shows accurately be weighed by iterative operation through the inventive method Structure covariance matrix.

Fig. 3 to Fig. 5 further demonstrates that, the inventive method can significantly improve the covariance matrix essence under condition of small sample Degree, improves filtering performance, is simultaneously suitable for coherent signal source environment, and does not need to determine subspace dimension, be self adaptation air filter The practical application of filtering provides a kind of effective solution.

Claims (1)

1. a kind of self adaptation air filter filtering method based on iterative shrinkage Weighted Fusion, comprises the steps：

(1) signal model is set up by receiving data X (k) in array antenna k moment, and calculate the sampling covariance square of receiving data Battle array

(2) the initialization energy spectral density of angle of aspect θ is obtained using the sample covariance matrix of receiving dataAnd initialize Priori covariance matrix

(3) according to the priori covariance matrix having obtained, using least square method, obtain the optimum power w in angle of aspect space , and update the energy spectral density in angle of aspect space (θ)With priori covariance matrixRepeat step (3), online updating Priori covariance matrix, until obtaining a stable priori covariance matrix R₀；

(4) priori covariance matrix R₀Sample covariance matrix with receiving dataCarry out shrinking weighting fusion treatment, profit Calculate weight coefficient with minimum mean-squared error criterion, obtain the covariance matrix R after shrinking Weighted Fusion_E；

(5) calculate the optimum weight vector w of Adaptive beamformer_opt, process receiving data using the optimum weight vector obtaining, from And obtain the useful signal of height output Signal to Interference plus Noise Ratio；Wherein

Signal model described in step (1) and covariance matrix, are carried out as follows：

1a) set X (k) as k moment array received data, wherein k=1 ..., L, L are fast umber of beats of sampling；If a₀And s₀K () is respectively The steering vector of echo signal and the complex envelope in the k moment, A_J=[a₁… a_P] and s_J(k)=[s₁(k) … s_P(k)]^TPoint Not Wei the array manifold of P interference signal and the complex envelope vector in the k moment, wherein a_i, i=1 ... P represent i-th interference believe Number steering vector, s_iK (), i=1 ... P represents i-th interference signal complex envelope in the k moment, and subscript T represents that transposition operates； If N (k) is the additive white Gaussian noise in the k moment；

1b) theoretical according to Array Signal Processing, the signal model of receiving data is：

X (k)=a₀s₀(k)+A_Js_J(k)+N(k)；

1c) covariance matrix of receiving data is：

Wherein subscript H represents conjugate transposition operation；

The sample covariance matrix to priori covariance matrix and receiving data in described step (4) carries out shrinking Weighted Fusion Process, carry out as follows：

4a) it is calculated as follows the covariance matrix R after shrinking Weighted Fusion_E：

Wherein R₀For priori covariance matrix, the weight coefficient of α and β respectively sample covariance matrix and priori covariance matrix；

4b) according to minimum mean-squared error criterion, calculate weight coefficient α and β respectively using equation below：

Whereina₀For The steering vector of echo signal；

The optimum weight vector of self adaptation air filter filtering described in step (5) can be calculated as follows：

$w_{opt}=R_E^{-1}{a}_0,$

And then output signal y (k) of computing array antenna：

Y (k)=w^H _optX (k),

Wherein subscript H represents conjugate transposition operation；

It is characterized in that：

The sample covariance matrix by receiving data described in step (2)Obtain the initialization energy spectral density of angle of aspectAnd initialize priori covariance matrixCarry out as follows：

2a) set the steering vector as angle of aspect θ for a (θ), calculate the initialization energy spectral density at angle of aspect θ using equation below

$\hat{P}\left(\mathrm{\θ}\right)=a^H\left(\mathrm{\θ}\right){\hat{R}}_{X}a\left(\mathrm{\θ}\right);$

2b) initialize priori covariance matrixFor：

${\hat{R}}_0={\∫}_{-\mathrm{\π}/2}^{\mathrm{\π}/2}\hat{P}\left(\mathrm{\θ}\right)a\left(\mathrm{\θ}\right)a^H\left(\mathrm{\θ}\right)d\mathrm{\θ}$

Wherein angle of aspect

The described online updating priori covariance matrix by the way of adaptive iteration of step (3), is carried out as follows：

3a) according to least square method, and using the priori covariance matrix having obtained, angle of aspect θ is calculated using equation below Optimum power w (θ)：

$w\left(\mathrm{\θ}\right)=\frac{{\hat{R}}_{0}a\left(\mathrm{\θ}\right)}{a^H\left(\mathrm{\θ}\right){{\hat{R}}_0}^{-1}a\left(\mathrm{\θ}\right)};$

The energy of corresponding angles 3b) is updated as follows using the optimum power of angle of aspect and the sample covariance matrix of receiving data Spectrum density

${\hat{P}}^{\′}\left(\mathrm{\θ}\right)=w^H\left(\mathrm{\θ}\right){\hat{R}}_{X}w\left(\mathrm{\θ}\right);$

3c) equation below is utilized to calculate the priori covariance matrix updating

${{\hat{R}}_0}^{\′}={\∫}_{-\mathrm{\π}/2}^{\mathrm{\π}/2}{\hat{P}}^{\′}\left(\mathrm{\θ}\right)a\left(\mathrm{\θ}\right)a^H\left(\mathrm{\θ}\right)d\mathrm{\θ};$

3d) makeRepeat step 3a) to step 3c), until obtaining a stable priori covariance matrix R₀.