CN106161303A - Response error envelope card weighting least square spatial domain matrix filter design method - Google Patents

Abstract

The invention belongs to array signal process technique field, the data relating to sensor array process, and are related specifically to utilize the least square spatial domain matrix filter method for designing of response error envelope card weighting.It is characterized in that by the way of to least square spatial domain matrix filter weighting parameter iteration, it is thus achieved that constant passband response error and the response of constant stopband.And can be by arranging passband response error and the proportionality coefficient of stopband response, regulation passband and the response effect of stopband.

Description

Response error envelope card weighting least square spatial domain matrix filter design method

Technical field

The invention belongs to array signal process technique field, the data relating to sensor array process, and relate to especially And to utilizing the least square spatial domain matrix filter method for designing of extreme point envelope card weighting.

Background technology

This patent is by project of national nature science fund project " spatial domain matrix filtering technique and in Underwater acoustic signal processing Applied research " subsidize, bullets No.11374001.

Spatial domain matrix filtering technique is by the array data pretreatment received, it is achieved retains passband signal, presses down Make strongly disturbing purpose.This technology has in Array Signal Processing field, especially field of underwater acoustic signal processing It is widely applied.Spatial domain matrix filter can be used for the array data pretreatment of target Bearing Estimation, it is also possible to Array data pretreatment in Matched Field location.The core of spatial domain matrix filtering technique is wave filter design.? In the matrix filter method for designing of spatial domain, least square, zeros constrained and passband zero response error constrained procedure The solution of optimum spatial domain matrix filter can be directly given.And stopband response, passband response error are the most about Bundle, bilateral stopband global response retrain spatial domain matrix filter can directly give optimum spatial domain matrix filter, But wherein comprise 1 to 2 unknown numbers, need to solve nonlinear equation.Constant stopband response constraint spatial domain square Battle array wave filter, constant passband response error spatial domain matrix filter can obtain flat passband error or stopband rings Should, but which can not directly obtain optimal solution, needs by complicated Optimum Theory and Algorithm for Solving, Calculate complexity, be unfavorable for that real-time empty domain matrix wave filter designs.The mode how using simplification obtains constant resistance Real-time array data is processed most important by the wave filter of band response and passband response error.Utilize least square The mode of spatial domain matrix filter response weighting, can directly give the optimal solution of wave filter, add response simultaneously Weight coefficient iteration, it is possible to obtain constant stopband and respond or constant passband response error, but existing iteration side The method of weighting iteration performance that method uses is low, and convergence rate is slow.

The present invention uses the mode of response weighting to design spatial domain matrix filter, and this spatial domain matrix filter designs Method can be by the way of successive iteration, it is thus achieved that constant passband response error and the response filtering of constant stopband Effect.Weight coefficient uses passband response error and the envelop forms of stopband response, and design efficiency is high.\

Summary of the invention

The technical problem to be solved in the present invention is constant by alternative manner generation passband response error, and stopband rings Answer the spatial domain matrix filter that error is constant.

The technical scheme is that

Spatial domain matrix filter was done Element space data before target Bearing Estimation at array data and is processed.If pin Spatial domain matrix filter to frequencies omega design is H (ω), utilizes target Bearing Estimation and Matched Field location information source Incide the mathematical model of array, do data filtering and process.Array received far field plane wave, receiving array number According to for direction vector and information source product, and superposition environment noise n (t, ω):

X (t, ω)=A (τ, ω) s (t, ω)+n (t, ω)

Wherein, A (τ, ω) is time delay vector, and s (t, ω) is source signal, and n (t, ω) is environment noise, and x (t, ω) is array Receive data.

Utilize the spatial domain matrix filter that frequency is ωTo receiving array data filtering, filtered Output y (t, ω) is:

Y (t, ω)=H (ω) x (t, ω)=H (ω) A (τ, ω) s (t, ω)+H (ω) n (t, ω) (1)

Known array manifold matrix is A (ω)={ a (φ, θ, ω) | φ ∈ Φ, θ ∈ Θ }, Φ and Θ corresponds respectively to water here Gentle vertical orientations angle range.The effect that spatial domain matrix filter produces enhancer or inhibitor to plane wave signal is By direction vector being acted on realization, whenDuring close to 0, wave filter pair is described (φ_i,θ_i) direction frequency is that the plane wave signal of ω has stronger inhibitory action.Otherwise, whenEqual to 0, illustrate that wave filter is to (φ_i,θ_i) direction frequency be ω plane wave letter Number filtering after undistorted.For matrix norm square.The design of spatial domain matrix filter is to not by design Equidirectional (φ_i,θ_i) response value, it is achieved to (φ_i,θ_i) the undistorted response of bearing data or suppression.

For linear array sensor, then direction vector a (φ_i,θ_i, ω) only relevant with direction θ.Now, direction vector For a (θ_i, ω), in the case of given frequency band of detection ω, a (θ_i, ω) and a (θ can be abbreviated as_i).H (ω) is abbreviated as H。

Below for linear array, weighting type spatial domain matrix filter method for designing is described.

Assuming that spatial domain discretization number is M, the direction vector in each orientation is a (θ_m), m=1 ..., M, it is desirable to ring Should vector be b (θ_m).For making this matrix filter retain the signal of passband, filter the noise of stopband, then preferable Matrix filter should meet:

$\mathrm{Ha}\left(\mathrm{\θ}\right)=b\left(\mathrm{\θ}\right)=\left\{\begin{array}{cc}a\left(\mathrm{\θ}\right),& \mathrm{\θ}\∈{\mathrm{\Θ}}_P\\ 0_{N\×1},& \mathrm{\θ}\∈{\mathrm{\Θ}}_S\end{array}\right.---\left(2\right)$

Wherein Θ_P,Θ_SRepresent passband and the set of stopband space incident azimuth respectively.

Error between real response and the Expected Response of array signal is given by by spatial domain matrix filter.

$\left\{\begin{array}{c}E\left({\mathrm{\θ}}_1\right)={\left|\right|\mathrm{Ha}\left({\mathrm{\θ}}_1\right)-b\left({\mathrm{\θ}}_1\right)\left|\right|}_F^2\\ .\\ .\\ .\\ E\left({\mathrm{\θ}}_M\right)={\left|\right|\mathrm{Ha}\left({\mathrm{\θ}}_M\right)-b\left({\mathrm{\θ}}_M\right)\left|\right|}_F^2\end{array}\right.---\left(3\right)$

Utilizing the error of real response and Expected Response, structure weighting type optimization problem is as follows.

Optimization problem 1:

$\underset{H}{\min }J\left(H\right)=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}w\left({\mathrm{\θ}}_m\right){\left|\right|\mathrm{Ha}\left({\mathrm{\θ}}_m\right)-b\left({\mathrm{\θ}}_m\right)\left|\right|}_F^2---\left(4\right)$

Wherein, w (θ_m) it is the response weight coefficient of each direction vector.

From optimized theory, as w (θ_m) when taking smaller value,Contribution to J (H) Less, otherwise, then the impact on J (H) is bigger.Along with w (θ_m) increase of value, Value increase therewith, cause the increase of J (H).Now to obtain optimum spatial domain matrix filter, the most necessarily need Balance, big w (θ is obtained between all of response error_m), matrix filter will necessarily be obtained at θ_mPosition Less response error value.Therefore, it can to realize the optimal value to object function by regulating this coefficient Regulation, thus regulate the response effect of spatial domain matrix filter.

The optimal solution of optimization problem 1 is:

$\hat{H}={\mathrm{BRA}}^H{\left({\mathrm{ARA}}^H\right)}^{-1}---\left(5\right)$

In formula:

A=[a (θ₁),…,a(θ_M)]

B=[b (θ₁),…,b(θ_M)]

R=diag [w (θ₁),w(θ₂),…,w(θ_M)]_M×M

By the iteration to weighting coefficient matrix R, passband response error can be realized and stopband responds constant effect Really.

Assume to obtain kth electric-wave filter matrix H through k-1 iteration_k, then H can be passed through_kObtain filtering now Device Expected Response and the Error Absolute Value of real response | E_k(θ_m) |=| H_ka(θ_m)-b(θ_m) |, m=1 ..., M, to error Absolute value seeks all of local maximum, and is connected by local maximum straightway, utilizes phase on straightway The value answered responds orientation θ as current iteration_mWeight coefficient w_k(θ_m).Here, it is assumed that total Q local pole Big value, abscissa isCorresponding extreme value i.e. vertical coordinate is

It is pointed out that the end points orientation that orientation is estimated, owing to local maximum is not generally two herein End occurs, therefore, between the left end point of directional bearing and the 1st local maximum, and directional bearing Between right endpoint and last maximum, the weighted value of employing needs to set especially.Utilize the 1st local Maximum pointWith the 2nd local maximum positionThe reverse extending line of line, Obtain the value (θ of this straight line of left end point position₁,z₁), make (θ₁,max(|E_k(θ₁)|,z₁)) be left end point weighting initiate Point, and withIt is connected, it is thus achieved thatInterval weight coefficient.In like manner, 1st reciprocal is utilized Local modulus maximaWith second-to-last Local modulus maximaBetween line Extended line, it is thus achieved that right endpoint value (θ on this straight line_M,z_M), make (θ_M,max(z_M,|E_k(θ_M) |)) it is right-hand member Point weighting starting point, and withIt is connected, the value conduct on corresponding lineOn weighting Value.

The iteration of weighting coefficient matrix R, relates to weighing vector w (θ therein_m), from discussed above, The value that passband response error and stopband are responded by weighing vector with wave filter is relevant.

β is set_k(θ_m) it is the weighted product coefficient in kth time iterative process, and makeHere, α_k(θ_m) it is θ_mValue on corresponding response error envelope line segment. γ(θ_m) it is the response ratio of left and right stopband and passband response error, set in the following way:

$\mathrm{\γ}\left(\mathrm{\θ}\right)=\left\{\begin{array}{cc}a,& \mathrm{\θ}\∈{\mathrm{\Θ}}_P\\ b,& \mathrm{\θ}\∈{\mathrm{\Θ}}_{S1}\\ c,& \mathrm{\θ}\∈{\mathrm{\Θ}}_{S2}\end{array}\right.---\left(6\right)$

Wherein, Θ_S1And Θ_S2It it is the set of stopband space incident azimuth, left and right.A, b, c be default passband, left stopband, Right stopband response ratio.

By by response ratio coefficient gamma (θ_m) it is brought into weight coefficient w (θ_m), m=1 ..., in the iteration of M, algorithm is eventually After Zhi, then the response of left and right stopband and the difference of passband response errorWithIt is respectively as follows:

$E_{{\mathrm{PS}}_1}=10\lg \left(b\right)-10\lg \left(a\right)---\left(7\right)$

$E_{{\mathrm{PS}}_2}=10\lg \left(c\right)-10\lg \left(a\right)---\left(8\right)$

Above formula is the response difference be given in db form.When selecting a=b=c, then spatial domain matrix filter Passband response error is identical with left and right stopband response value.

Accompanying drawing explanation

Fig. 1 a represents passband response error weighting spatial domain matrix filter (a=b=c=1, iteration 1 time).

Fig. 1 b represents passband response error weighting spatial domain matrix filter (a=b=c=1, iteration 1 time).

Fig. 2 a represents the wave filter left stopband response envelope card weighting of the 1st iteration gained.

Fig. 2 b represents the wave filter right stopband response envelope card weighting of the 1st iteration gained.

Fig. 2 c represents the filter passband response error envelope card weighting of the 1st iteration gained.

Fig. 3 a passband response weighting spatial domain matrix filter (a=b=c=1, iteration 7 times).

Fig. 3 b passband response error weighting spatial domain matrix filter (a=b=c=1, iteration 7 times).

Fig. 4 a represents the wave filter left stopband response envelope card weighting of the 7th iteration gained.

Fig. 4 b represents the wave filter right stopband response envelope card weighting of the 7th iteration gained.

Fig. 4 c represents the filter passband response error envelope card weighting of the 7th iteration gained.

Fig. 5 a represents passband response error weighting spatial domain matrix filter (a=b/2=4c=1, iteration 7 times)

Fig. 5 b represents passband response error weighting spatial domain matrix filter (a=b/2=4c=1, iteration 7 times)

In figure, the array element number N=30 that designed wave filter is corresponding, array element is equidistant, and passband is [-15 °, 15 °], stopband is [-90 ° ,-20 °) ∪ (20 °, 90 °], and passband and stopband discrete sampling are spaced 0.1 °, for Battle array half-wavelength Frequency Design spatial domain matrix filter.

In the case of Fig. 1 a and Fig. 1 b gives a=b=c=1, use response error weighting, the young waiter in a wineshop or an inn obtained Take advantage of the design effect of spatial domain matrix filter, here weighting coefficient matrix R only iteration 1 time.Fig. 1 a represents filter Ripple device respondsFig. 1 b represents wave filter response errorIn figure Giving the design effect of least square matrix filter, weighted least-squares matrix filter is to pass through simultaneously Least square matrix filter is starting point, utilizes the envelope card weighting iteration of response error local maximum to obtain.

Fig. 2 a, Fig. 2 b and Fig. 2 c, give passband response error and the left and right resistance of least square matrix filter Band responds, and utilizes the line of the Local modulus maxima of passband response error and stopband response, structure weighting simultaneously Coefficient matrix R.

Fig. 3 a and Fig. 3 b is the further iteration result of Fig. 3 a and Fig. 3 b, altogether the matrix of gained after iteration 7 times Filter effect.

Fig. 4 a, Fig. 4 b and Fig. 4 c are each envelope card weighting line segments used in iteration the last time.

Fig. 5 a and Fig. 5 b gives the matrix filter effect of gained, a=b/2=4c=1 here after 7 iteration. From effect in figure, left stopband response ratio passband response error height 3dB, right stopband response ratio passband response is by mistake The few 6dB of difference.

Detailed description of the invention

It is embodied as example below in conjunction with what scheme and accompanying drawing described the present invention in detail.

Iterative algorithm based on response error envelope card weighting criterion is as follows:

Step 1: make k=0, will detect spatial domain discretization, calculate A_,B.Make w₀(θ_s)=1, calculates Excellent spatial domain matrix filterLeft stopband, passband, right stopband response ratio coefficient gamma (θ are set_m),

Step 2: calculate E_k(θ_m)=H_ka(θ_m)-b(θ_m), m=1 ..., M.Ask | E_k(θ_m) | Local modulus maxima, Obtain the abscissa of local maximumAnd corresponding vertical coordinateSuch as, In Fig. 2 a, Fig. 2 b and Fig. 2 c, being passband response error, the response of left and right stopband, line segment is correspondence Line between local maximum.

Step 3: utilizeWithThe extended line of point-to-point transmission line, calculates at abscissa θ₁Value z at place₁, (θ is set₁,max(|E_k(θ₁)|,z₁)) it is envelope card weighting starting point.

Step 4: utilizeWithThe extended line of point-to-point transmission line, calculates at horizontal seat Mark θ_MValue z at place_M, (θ is set_M,max(z_M,|E_k(θ_M) |)) it is envelope card weighting terminal.

Step 5: calculate (θ₁,max(|E_k(θ₁)|,z₁))、 (θ_M,max(z_M,|E_k(θ_M) |)) it is total to the line segment between Q+2 point, and take α_k(θ_m) it is θ_m? Value on corresponding line segment.

Step 6: calculate following various

${\mathrm{\β}}_k\left({\mathrm{\θ}}_m\right)={\mathrm{\α}}_k\left({\mathrm{\θ}}_m\right)/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k\left({\mathrm{\θ}}_m\right)$

w_k+1(θ_m)=β_k(θ_m)γ(θ_m)w_k(θ_m)

R_k+1=diag [w_k+1(θ₁),w_k+1(θ₂),…,w_k+1(θ_M)]

H_k+1=BR_k+1A^H(AR_k+1A^H)^-1

Wherein, β_k(θ_m) it is the Product-factor of kth time iteration, w_k+1(θ_m) it is the kth time weighting system used by iteration Number, R_k+1For the weighting coefficient matrix used by+1 iteration of kth, H_k+1Spatial domain for+1 iteration gained of kth Matrix filter.

Judge H_k+1Whether meet one of following end condition:

(a) k+1=K.Now, now iteration K time, algorithm terminates；

(b)After iteration, the spatial domain matrix filter reality to all orientation Response and Expected Response difference are less than constantAlgorithm terminates；

(c)After iteration, spatial domain matrix filter is to all The response error rate of change in orientation is both less than constant valueAlgorithm terminates.

Step 7: if stopping criterion for iteration meets, then H_k+1It is final spatial domain matrix filter.Otherwise, Make k=k+1, repeat step 2～6.

Claims (2)

1. a response error envelope card weighting least square spatial domain matrix filter design method, by optimum spatial domain square Battle array filter passband response error envelope structure weighting matrix, utilizes the mode of parameter iteration, it is thus achieved that constant Passband response error and stopband response；It is characterized in that following steps:

Step 1: left stopband, passband, right stopband response ratio coefficient gamma (θ are set_m), make k=1；

Step 2: calculate E_k(θ_m)=H_ka(θ_m)-b(θ_m), m=1 ..., M；Ask | E_k(θ_m) | Local modulus maxima, Obtain the abscissa of local maximumAnd corresponding vertical coordinate

Step 3: utilizeWithThe extended line of point-to-point transmission line, calculates at abscissa θ₁Value z at place₁, (θ is set₁,max(|E_k(θ₁)|,z₁)) it is envelope card weighting starting point；

Step 4: utilizeWithThe extended line of point-to-point transmission line, calculates at horizontal seat Mark θ_MValue z at place_M, arrangeFor envelope card weighting terminal；

Step 5: calculate (θ₁,max(|E_k(θ₁)|,z₁))、 Line segment between Q+2 point altogether, and take α_k(θ_m) it is θ_mValue on corresponding line segment；Order

Step 6: calculate following various

w_k+1(θ_m)=β_k(θ_m)γ(θ_m)w_k(θ_m)

R_k+1=diag [w_k+1(θ₁),w_k+1(θ₂),…,w_k+1(θ_M)]

H_k+1=BR_k+1A^H(AR_k+1A^H)^-1

Judge H_k+1Whether meet one of following end condition:

(a) k=K；Now, now iteration K time, algorithm terminates；

(b)After iteration, the spatial domain matrix filter reality to all orientation Response and Expected Response difference are less than constantAlgorithm terminates；

(c)After iteration, spatial domain matrix filter is to all The response error rate of change in orientation is both less than constant valueAlgorithm terminates；

Step 7: if stopping criterion for iteration meets, then H_k+1It is final spatial domain matrix filter；Otherwise, Make k=k+1, repeat step 2～6.

A kind of spatial domain the most according to claim 1 matrix filter method for designing, is further characterized in that by adjusting Joint passband response error, left and right stopband response ratio coefficient gamma (θ_m), it is achieved passband response error and left and right stopband The difference regulation of response；

By such as arranging:

$\mathrm{\γ}\left(\mathrm{\θ}\right)=\left\{\begin{array}{cc}a,& \mathrm{\θ}\∈{\mathrm{\Θ}}_P\\ b,& \mathrm{\θ}\∈{\mathrm{\Θ}}_{S1}\\ c,& \mathrm{\θ}\∈{\mathrm{\Θ}}_{S2}\end{array}\right.$

The difference that can obtain the response of left and right stopband and passband response error is:

$E_{{\mathrm{PS}}_1}=101g\left(b\right)-101g\left(a\right)$

$E_{{\mathrm{PS}}_2}=101g\left(c\right)-101g\left(a\right).$