CN108008348A - Underwater Wave arrival direction estimating method and device based on adjustable angle even linear array - Google Patents

Abstract

The invention discloses a kind of underwater Wave arrival direction estimating method and device based on adjustable angle even linear array, the even linear array that the present invention can be adjusted using two angles, the velocity of sound this variable has been eliminated by the relation between two array angles and direction of arrival angle, so that last operation result is unrelated with the velocity of sound, so as to improve estimated accuracy, simultaneously because two linear array angles are variable, by taking different value to take multiple measurements, error can be preferably eliminated.

Description

Underwater DOA Estimation Method and Device Based on Adjustable Angle Uniform Linear Array

technical field

The invention relates to the technical field of underwater target positioning, in particular to an underwater direction-of-arrival estimation method and device based on an adjustable angle uniform linear array.

Background technique

Array signal processing technology has been widely used in many fields, and one of the basic problems of array signal processing is the direction of arrival (DOA estimation) of space signals. DOA estimation, that is, spatial spectrum estimation, adopts a processing method of placing multiple sensors in a noisy environment to form an array to receive the target signal, and then process the received signal of the array, and finally estimate the target signal relative to the array. direction of incidence. The subspace decomposition algorithm is a high-resolution method developed in the 1970s. It can accurately estimate the parameters of the signal (frequency, orientation, etc.), and its performance is ideal, and its resolution and estimation accuracy are better than traditional The method is high, so it is widely used in the field of DOA estimation. The characteristic of the subspace decomposition algorithm is to decompose the received signal of the array into two mutually orthogonal subspaces, that is, the signal subspace and the noise subspace, through appropriate mathematical transformation, and then use the respective characteristics of the two types of subspaces to perform DOA estimate. Therefore, subspace decomposition algorithms can be divided into two types of subspace algorithms: signal subspace and noise subspace. Algorithm) as a representative. MUSIC is an extremum search method, and ESPRIT algorithm is a direct solution method, so ESPRIT algorithm does not need to search for full-space spectral peaks, and its calculation amount is much smaller than that of MUSIC algorithm. In addition, the ESPRIT algorithm has the advantages of practicality and high resolution, so it is widely used in DOA estimation.

However, the existing methods for DOA estimation using the ESPRIT algorithm have the problem of low accuracy. On the one hand, in the process of DOA estimation using the ESPRIT algorithm, the propagation speed of the signal in the medium needs to be regarded as a known parameter. In the underwater environment, the sound velocity is related to many environmental factors and is a constantly changing parameter. Therefore, using a fixed sound velocity parameter for underwater DOA estimation will produce large errors. On the other hand, the linear arrays used in the existing direction of arrival estimation all have a fixed angle. In the actual measurement process, only multiple measurements can be made for this fixed angle, which cannot effectively improve the estimation accuracy.

Contents of the invention

The main purpose of the present invention is to overcome the shortcomings of the above-mentioned ESPRIT algorithm, and provide a method for estimating the underwater direction of arrival based on an adjustable angle uniform line array, using two adjustable angle uniform line arrays as receiving arrays, During the algorithm process, the propagation speed of the signal in the medium is eliminated, and multiple sets of measurements with different angles are used to obtain higher measurement accuracy than the existing DOA method.

Another object of the present invention is to provide an underwater DOA estimation device based on a uniform linear array with an adjustable angle, which can be measured by setting a plurality of different linear array angle values.

The purpose of the present invention is achieved through the following technical solutions:

An underwater direction-of-arrival estimation method based on an adjustable angle uniform line array, comprising the following steps:

Step 1: Establish a uniform linear array model with adjustable angle;

Place two uniform linear arrays with an included angle of α _n in the water, one uniform linear array in the horizontal direction and one inclined uniform linear array. There are M array elements and the distance between the array elements is d; K narrow-band target sound sources are S ₁ , S ₂ ,..., S _K , and the center frequency is f; The included angle is β,β∈(0,π);

Step 2: Establish a signal receiving model of two uniform linear arrays;

When the angle between the line arrays is α _n , the direction angles of the K narrowband target sound sources corresponding to the horizontal line array are θ _nx1 , θ _nx2 ,...,θ _nxK , and the direction angles corresponding to the inclined line array are θ _ny1 ,θ _ny2 ,...,θ _nyK ; taking the first array element as a reference point, the signal received by the first array element at time t is:

Where s _i (t) represents the i-th source signal, n ₁ (t) represents the noise on the first array element;

The received signal satisfies the narrowband condition, that is, when the signal delay is much smaller than the reciprocal of the bandwidth, the delay effect is equivalent to causing a phase shift of the baseband signal, then the signal received by the mth array element at the same time is:

Among them, _λi represents the wavelength of the acoustic wave reflected by the i-th target source, and n _m (t) represents the noise on the m-th array element; if the received signals of each array element are arranged in the form of a column vector, the signal received by the entire horizontal line array It can be represented by the following vector formula:

X(t)=AS(t)+N(t) (1)

in, is the steering vector matrix of M×K, X(t)=[x ₁ (t),x ₂ (t),…,x _M (t)] ^T is the received signal matrix of M×1, S(t)= [s ₁ (t),s ₂ (t),…,s _K (t)] ^T is the source signal matrix of K×1, N(t)=[n ₁ (t),n ₂ (t),… ,n _M (t)] ^T is the noise matrix of M×1. In the same way, the signal receiving model of the inclined uniform line array can be obtained;

Step 3: Establish a uniform linear array subarray model, and derive the expressions of rotation operators Φ _x and Φ _y ;

Divide the M array elements in the horizontal linear array into two sub-arrays Z _hx and Z _hy whose translation vectors are d; the sub-array Z _hx consists of the first to M-1th array elements of the horizontal array, then:

x _h1 (t) = x ₁ (t), x _h2 (t) = x ₂ (t), ..., x _h(M-1) (t) = x _M-1 (t)

Among them, x _h1 (t), x _h2 (t), ..., x _h(M-1) (t) are the signals received by the first array element to the M-1th array element on the subarray Z _hx ;

The sub-array Z _hy is composed of the second to M array elements of the horizontal array, then:

y _h1 (t)=x ₂ (t), y _h2 (t)=x ₃ (t),...,y _h(M-1) (t)=x _M (t)

Among them, y _h1 (t), y _h2 (t), ..., y _h(M-1) (t) are the signals received by the first array element to the M-1th array element on the subarray Z _hy ;

Then the received signals of the mth array element in the two sub-arrays are respectively:

in n _hxm (t) and n _hym (t) are the additive noise of the mth array element on the sub-arrays Z _hx and Z _hy respectively, and the above formula is written in vector form:

X _h (t) = AS (t) + N _hx (t)

Y _h (t) = AΦ _x S (t) + N _hy (t)

The matrix Φ _x is a K×K diagonal matrix, which is a unitary matrix that connects the output of the sub-array Z _hx and Z _hy , also called a rotation operator, and its diagonal elements contain the wavefronts of K signals in The phase delay information between any pair of array elements is expressed as:

According to the above steps, similarly, the inclined uniform linear array can be divided into two sub-arrays Z _vx and Z _vy to obtain the received signals X _v (t) and Y _v (t), so that the rotation operator can be obtained as:

Step 4: Establish the relationship between rotation operators Φ _x , Φ _y and θ _nxi , θ _nyi ;

Step 5: Establish the relationship between the two direction angles when the acoustic wave signal is incident from different regions;

Step 6: pairing the diagonal elements on matrix Φ _x and matrix Φ _y ;

Step 7: Calculate the size of θ _nxi according to the pairing result.

Preferably, step four specifically includes:

The covariance matrix of X _h (t) can be expressed as:

R _hxx ＝E[X _h (t)X _h ^H (t)]＝AR _ss A ^H +σ ² I

Where R _ss =E{S(t)S ^H (t)}, which is the covariance matrix of the source part;

The cross-covariance matrix of X _h (t) and Y _h (t) is:

R _hxy ＝E{X _h (t)Y _h ^H (t)}＝AR _ss Φ _x ^H A ^H +σ ² Z

The eigenvalue decomposition of the matrix covariance matrix can obtain the minimum eigenvalue σ ² , and the matrix bundle {C _hxx ,C _hxy } can be obtained by using σ ² , where C _hxx ＝R _hxx -σ ² I＝AR _ss A ^H , C _hxy ＝R _hxy -σ ² Z＝AR _ss Φ _x ^H A ^H ; calculate the generalized eigenvalue decomposition of the matrix bundle {C _hxx ,C _hxy } to obtain non-zero eigenvalues λ _x1 , λ _x2 ,...,λ _xK , one of them One corresponds to the elements on the diagonal of the matrix Φ _x , but the corresponding relationship is uncertain, so it can be recorded by formula (2):

Where φ _xi is the diagonal element on the matrix Φ _x , and φ _xi ∈ {λ _x1 ,λ _x2 ,…,λ _xK }, i=1,2,…,K;

According to the above steps, the two covariance matrices R _vxx and R _vxy of the inclined uniform array can be obtained in the same way, and then the eigenvalue decomposition of the matrix bundle {C _vxx , C _vxy } is performed to obtain the eigenvalues λ _y1 , λ _y2 ,…, λ _yK , they also correspond to the diagonal elements on the matrix Φ _y one by one, but the corresponding relationship is also uncertain, which can be recorded by formula (3):

Where φ _yi is the diagonal element on the matrix Φ _y , and φ _yi ∈ {λ _y1 ,λ _y2 ,…,λ _yK }, i=1,2,…,K.

Preferably, step five specifically includes:

According to the angle α _n of the linear array and the angle β between the incident direction of the sound wave and the positive axis of the x-axis, the incident area of the acoustic wave signal is set to 4: when β∈(0,α _n ), the acoustic wave signal is incident in area 1; when When β∈(α _n ,π/2), the acoustic wave signal is incident on area 2; when β∈(π/2,π/2+α _n ), the acoustic wave signal is incident on area 3; when β∈(π/2 +α _n ,π), the sound wave signal is incident in area 4;

(1) When the sound wave is incident from area 1, θ _1i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _1j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. At this time, θ _1i + θ _1j =π-α _n ; Since the array signal on the x-axis is based on the array element in the most negative direction of the x-axis, and the sub-array Z _hx is also in the negative x-axis direction of the sub-array Z _hy , Therefore, when the sound wave is incident from area 1, the reference array element is the latest to receive the signal, and the array elements in the sub-array Z _hx also receive the signal later than the corresponding array elements in the sub-array Z _hy , so that the time delay can be obtained The parameter τ is less than 0, and because So at this time, θ _nxi ＝-θ _1i , and θ _nyi ＝-θ _1j in the same way; in summary, it can be concluded that:

θ _nyi = -θ _nxi +α _n -π (6)

(2) When the sound wave is incident from area 2, θ _2i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _2j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. At this time, θ _2j -θ _2i =α _n , according to the analysis method used in (1), there are θ _nxi ＝-θ _2i , θ _nyi =-θ _2j , in summary, we can get:

θ _nyi = θ _nxi -α _n (7)

(3) When the sound wave is incident from area 3, θ _3i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _3j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. At this time, θ _3i + θ _3j =α _n , according to the analysis method used in (1), there are θ _nxi ＝θ _3i , θ _nyi =-θ _3j , in summary, we can also get:

θ _nyi = θ _nxi -α _n

(4) When the sound wave is incident from area 4, θ _4i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _4j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. At this time, θ _4i - θ _4j ＝α _n , according to the analysis method used in (1), there are θ _nxi ＝θ _4i , θ _nyi ＝θ _4j , in summary, we can also get:

θ _nyi = θ _nxi -α _n

According to formula (6) and formula (7), it can be obtained:

sinθ _nyi ＝sin(θ _nxi -α _n ) (8)

Put formula (8) into formula (5), then:

Preferably, step six specifically includes:

According to formula (4) and formula (9), if the pairing is successful, the following formula holds:

Arrange arg(λ _x1 ), arg(λ _x2 ),…,arg(λ _xK ) according to their respective square sizes from large to small to obtain sequence H; arrange arg(λ _y1 ), arg(λ _y2 ),…, arg(λ _yK ) is arranged according to the order of their respective square sizes from small to large to obtain the sequence V; then:

Among them, h _i is the i-th element in the sequence H; v _i is the i-th element in the sequence V.

Preferably, in step seven,

Preferably, change the angle α _n between the two uniform linear arrays, n=1, 2,..., N, repeat steps 1 to 7; for different linear array angles α _n , use the formula (12) to find Get the corresponding DOA, and finally take the average of the N results to get the final result θ _xi , i=1,2,...,K.

An underwater direction-of-arrival estimation device based on an adjustable angle uniform linear array, including a data processing and control module, an angle control module, a transmitting module, a receiving module, an output module, and a power supply module; the power supply module and the data processing and control module , the angle control module, the transmitting module, the receiving module and the output module are connected, and it can supply power to these modules;

The data processing and control module is the core part of the whole device, and all other modules are directly connected to it; it can control the transmitting module to make the transmitting module emit the specified signal; it can control the angle control module to make the angle between the two uniform linear arrays rotate To the set value; it can also process the signal transmitted by the receiving module, calculate the direction of arrival angle, and then transmit the result to the transmitting module.

Preferably, the data processing and control module is composed of a pair of A/D, D/A converters and a processor.

Preferably, the angle control module includes a stepper motor and a drive circuit, used to control the angle between the two linear arrays; the stepper motor is an open-loop control motor that converts electrical pulse signals into angular displacement or linear displacement. When the circuit receives a pulse signal, it will drive the stepper motor to rotate a fixed angle in the set direction, and the desired angle value can be achieved by making the data processing and control module emit a certain number of pulse signals.

Preferably, the receiving module includes two ultrasonic receiving probe arrays, the angle between the two arrays is variable and the angle can be adjusted through the angle control module.

Specifically, the horizontal array L1 and the stepping motor are fixed together, the array L2 is installed on the stepping motor and ensure that the array L1 and the array L2 are on the same plane, and the array L2 can be rotated by the stepping motor, so as to achieve the angle between the two linear arrays purpose of regulation.

Specifically, there is a fixed bracket at the end of the array L1, and the fixed bracket is made of plastic; the stator of the stepping motor is connected to the bracket, and the rotor of the stepping motor is connected to the array L2.

Preferably, the transmitting module includes an impedance matching circuit and an ultrasonic transmitting probe.

Preferably, the output module includes a USB interface and a display, which can provide human-computer interaction, and output the data processed in the data processing and control module to an external device through the USB interface or display it on the display.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

1. Compared with the method of using the traditional ESPRIT algorithm to estimate the direction of arrival of underwater targets, the present invention is more practical and has higher estimation accuracy. The traditional ESPRIT algorithm usually assumes that the speed of sound is a constant, but in the actual complex underwater environment, the speed of sound is often changing, if it is calculated as a constant, it will lead to a large error. The present invention adopts two uniform linear arrays whose included angle can be adjusted, and eliminates the variable of sound velocity through the relationship between the included angle of the two arrays and the direction of arrival angle, so that the final calculation result has nothing to do with the sound velocity, thereby improving the estimation accuracy. At the same time, because the angle between the two linear arrays is variable, the error can be better eliminated by taking different values for multiple measurements.

2. The present invention improves the traditional ESPRIT algorithm while retaining the advantages of high resolution of the ESPRIT algorithm, and the calculation amount and complexity of the improved algorithm do not increase too much, which ensures the feasibility of the algorithm.

3. The device of the present invention is an improvement on the traditional measuring device, and uses a uniform line array with an adjustable included angle, which is highly feasible and easy to install. In addition, the continuous improvement of computing and processing capabilities of modern processors makes chips such as processors used in the present invention highly integrated and powerful in computing, thereby ensuring the feasibility of the present invention.

Description of drawings

Fig. 1 is a block diagram of the hardware structure of the embodiment device.

Figure 2 is a schematic diagram of the connection of the receiving module.

Figure 3 is a top view of the connection of the receiving module.

Figure 4 is a side view of the connection of the receiving module.

Fig. 5 is the adjustable angle uniform linear array model used in the embodiment.

Figure 6 is the received signal model of the horizontal uniform line array.

Figure 7 is a uniform linear array model with adjustable angle when the signal is incident from area 1.

Figure 8 is a uniform linear array model with adjustable angle when the signal is incident from area 2.

Figure 9 is a uniform linear array model with adjustable angle when the signal is incident from area 3.

Fig. 10 is a uniform linear array model with adjustable angle when the signal is incident from area 4.

Fig. 11 is a flowchart of the embodiment method.

Detailed ways

The present invention will be further described in detail below in conjunction with the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

Example 1

An underwater direction-of-arrival estimation method based on a uniform linear array with an adjustable angle. By processing the received signals of the two linear arrays, the factor of sound velocity can be eliminated in the direction-of-arrival estimation, thereby eliminating the uncertainty of underwater sound velocity influence on the target positioning accuracy. Secondly, because the included angle between the two uniform linear arrays is variable, the included angle can be changed for multiple measurements in actual measurement to better eliminate errors.

This method adopts two uniform linear arrays with adjustable angles. Both linear arrays have M array elements and the distance between array elements is d; K narrowband target sound sources are S ₁ , S ₂ ,…,S _K , the center frequency is f; the angle between the incident direction of the sound wave and the positive axis of the horizontal uniform line array is β,β∈(0,π); this method will measure N times of different line array angle values α _n ,n=1 ,2,...,N and α _n ∈(0,π/2), the specific steps are as follows:

Step 1: Establish a uniform linear array model with adjustable angle, as shown in Figure 5. Place two uniform linear arrays with an included angle of α _n in the water, one horizontal uniform linear array and one inclined uniform linear array, which are respectively set as x-axis and y-axis. According to the angle α _n of the linear array and the angle β between the incident direction of the sound wave and the positive axis of the x-axis, the incident area of the acoustic wave signal is set to 4: when β∈(0,α _n ), the acoustic wave signal is incident in area 1; when When β∈(α _n ,π/2), the acoustic wave signal is incident on area 2; when β∈(π/2,π/2+α _n ), the acoustic wave signal is incident on area 3; when β∈(π/2 +α _n ,π), the sound wave signal is incident in area 4;

Step 2: Establish the signal receiving model of two uniform linear arrays. When the angle between the line arrays is α _n , the direction angles of the K narrowband target sound sources corresponding to the horizontal line array are θ _nx1 , θ _nx2 ,...,θ _nxK , and the direction angles corresponding to the inclined line array are θ _ny1 ,θ _ny2 ,...,θ _nyK . The model scene of the horizontal uniform line array is shown in Figure 6. Taking the first array element as the reference point, the signal received by the first array element at time t is:

Among them, s _i (t) represents the i-th source signal, and n ₁ (t) represents the noise on the first array element.

The received signal meets the narrowband condition, that is, when the signal delay is much smaller than the reciprocal of the bandwidth, the delay effect is equivalent to causing a phase shift of the baseband signal. Then the signal received by the mth array element at the same time is:

Among them, λ _i represents the wavelength of the acoustic wave reflected by the i-th target source, and n _m (t) represents the noise on the m-th array element. Arrange the received signals of each array element into a column vector form, then the signal received by the entire horizontal line array can be expressed by the following vector formula:

X(t)=AS(t)+N(t) (1)

in, is the steering vector matrix of M×K, X(t)=[x ₁ (t),x ₂ (t),…,x _M (t)] ^T is the received signal matrix of M×1, S(t)= [s ₁ (t),s ₂ (t),…,s _K (t)] ^T is the source signal matrix of K×1, N(t)=[n ₁ (t),n ₂ (t),… ,n _M (t)] ^T is the noise matrix of M×1. In the same way, the signal receiving model of the tilted uniform line array can be obtained.

Step 3: Establish a uniform linear array subarray model, and derive the rotation operator expression. The M array elements in the horizontal line array are divided into two sub-arrays Z _hx and Z _hy with translation vectors d. The sub-array Z _hx consists of the first to M-1 array elements of the horizontal array, then:

x _h1 (t) = x ₁ (t), x _h2 (t) = x ₂ (t), ..., x _h(M-1) (t) = x _M-1 (t)

Among them, x _h1 (t), x _h2 (t), ..., x _h(M-1) (t) are the signals received by the first array element to the M-1th array element on the subarray Z _hx .

The sub-array Z _hy is composed of the second to M array elements of the horizontal array, then:

y _h1 (t)=x ₂ (t), y _h2 (t)=x ₃ (t),...,y _h(M-1) (t)=x _M (t)

Among them, y _h1 (t), y _h2 (t), ..., y _h(M-1) (t) are the signals received by the first array element to the M-1th array element on the subarray Z _hy .

Then the received signals of the mth array element in the two sub-arrays are respectively:

in n _hxm (t) and n _hym (t) are the additive noise of the mth array element on the sub-arrays Z _hx and Z _hy respectively. Write the above formula in vector form:

X _h (t) = AS (t) + N _hx (t)

Y _h (t) = AΦ _x S (t) + N _hy (t)

The matrix Φ _x is a K×K diagonal matrix, which is a unitary matrix that connects the output of the sub-array Z _hx and Z _hy , also called a rotation operator, and its diagonal elements contain the wavefronts of K signals in The phase delay information between any pair of array elements is expressed as:

According to the above steps, similarly, the inclined uniform linear array can be divided into two sub-arrays Z _vx and Z _vy to obtain the received signals X _v (t) and Y _v (t), so that the rotation operator can be obtained as:

Step 4: Establish the relationship between rotation operators Φ _x and Φ _y and θ _nxi and θ _nyi . The covariance matrix of X _h (t) can be expressed as:

R _hxx ＝E[X _h (t)X _h ^H (t)]＝AR _ss A ^H +σ ² I

Where R _ss =E{S(t) ^SH (t)} is the covariance matrix of the information source part.

The cross-covariance matrix of X _h (t) and Y _h (t) is:

R _hxy ＝E{X _h (t)Y _h ^H (t)}＝AR _ss Φ _x ^H A ^H +σ ² Z

The eigenvalue decomposition of the matrix covariance matrix can obtain the minimum eigenvalue σ ² , and the matrix bundle {C _hxx ,C _hxy } can be obtained by using σ ² , where C _hxx ＝R _hxx -σ ² I＝AR _ss A ^H , C _hxy =R _hxy -σ ² Z =AR _ss Φ _x ^H A ^H . Calculate the generalized eigenvalue decomposition of the matrix bundle {C _hxx ,C _hxy } to obtain non-zero eigenvalues λ _x1 , λ _x2 ,…,λ _xK , which correspond to the elements on the diagonal of the matrix Φ _x one by one, but the correspondence is not sure, so it can be remembered by formula (2):

Where φ _xi is the diagonal element on the matrix Φ _x , and φ _xi ∈ {λ _x1 ,λ _x2 ,…,λ _xK }, i=1,2,…,K.

According to the above steps, the two covariance matrices R _vxx and R _vxy of the inclined uniform array can be obtained in the same way, and then the eigenvalue decomposition of the matrix bundle {C _vxx , C _vxy } is performed to obtain the eigenvalues λ _y1 , λ _y2 ,…, λ _yK , they also correspond to the diagonal elements on the matrix Φ _y one by one, but the corresponding relationship is also uncertain, which can be recorded by formula (3):

Where φ _yi is the diagonal element on the matrix Φ _y , and φ _yi ∈ {λ _y1 ,λ _y2 ,…,λ _yK }, i=1,2,…,K.

Step 5: Establish the relationship between the two direction angles when the acoustic wave signal is incident from different regions.

(1) When the sound wave is incident from area 1, as shown in Figure 7, θ _1i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _1j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. There is θ _1i +θ _1j =π-α _n . Since the array signal on the x-axis is based on the array element in the most negative direction of the x-axis, and the sub-array Z _hx is also in the negative x-axis direction of the sub-array Z _hy . Therefore, when the sound wave is incident from area 1, the reference array element is the latest to receive the signal, and the array elements in the sub-array Z _hx also receive the signal later than the corresponding array elements in the sub-array Z _hy , so that the time delay can be obtained The parameter τ is less than 0, and because So at this time, θ _nxi =-θ _1i , and similarly, θ _nyi =-θ _1j . In summary, it can be concluded that:

θ _nyi = -θ _nxi +α _n -π (6)

(2) When the sound wave is incident from area 2, as shown in Figure 8, θ _2i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _2j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. There is θ _2j -θ _2i = α _n , according to the analysis method used in (1), at this time, θ _nxi = -θ _2i , θ _nyi = -θ _2j , in summary, it can be concluded that:

θ _nyi = θ _nxi -α _n (7)

(3) When the sound wave is incident from area 3, as shown in Figure 9, θ _3i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _3j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. There is θ _3i + θ _3j ＝ α _n , according to the analysis method used in (1), at this time θ _nxi ＝ θ _3i , θ _nyi ＝-θ _3j , it can be concluded that:

θ _nyi = θ _nxi -α _n

(4) When the sound wave is incident from the area 4, as shown in Figure 10, θ _4i is the angle between the incident direction of the sound wave and the normal line of the horizontal line array, and θ _4j is the angle between the incident direction of the sound wave and the normal line of the inclined line array. There is θ _4i -θ _4j = α _n , according to the analysis method used in (1), at this time there are θ _nxi = θ _4i , θ _nyi = θ _4j , in summary, it can also be concluded that

θ _nyi = θ _nxi -α _n

According to formula (6) and formula (7), it can be obtained:

sinθ _nyi ＝sin(θ _nxi -α _n ) (8)

Put formula (8) into formula (5), then:

Step 6: Pair the diagonal elements φ _xi and φ _yi on the matrix Φ _x and the matrix Φ _y . According to formula (4) and formula (9), if the pairing is successful, the following formula holds:

Arrange arg(λ _x1 ), arg(λ _x2 ),…,arg(λ _xK ) according to their respective square sizes from large to small to obtain sequence H; arrange arg(λ _y1 ), arg(λ _y2 ),…, Arrange arg(λ _yK ) according to their respective square sizes from small to large to obtain the sequence V. So there are:

Among them, h _i is the i-th element in the sequence H; v _i is the i-th element in the sequence V.

Step 7: Calculate the size of θ _nxi according to the pairing result.

According to formula (10), it can be drawn that:

Step 8: Change the angle α _n between the two uniform linear arrays, n=1, 2, . . . , N, and repeat steps 1 to 7. For different linear array angles α _n , the corresponding DOA is obtained from Formula 12, and finally the average of N results is obtained to obtain the final result θ _xi , i=1,2,...,K.

According to the above algorithm flow, the improved algorithm proposed in this embodiment can accurately estimate θ _xi without knowing the speed of sound, that is, it can estimate the value of the direction of arrival angle θ _xi when the sound speed is uncertain, and overcome the The shortcomings of the traditional ESPRIT algorithm are eliminated. At the same time, the error can be effectively eliminated by changing the angle between the two linear arrays for multiple estimations and finally taking the average value.

The flowchart of the above method can be represented by FIG. 11 .

Example 2

The underwater DOA estimation device based on the adjustable angle uniform linear array provided in this embodiment is shown in Figure 1, including a data processing and control module, an angle control module, a transmitting module, a receiving module, an output module and a power supply module.

The data processing and control module is composed of a pair of A/D, D/A converter and a processor, which is the core part of the whole device, and all other modules are directly connected with it. It can control the transmitting module, so that the transmitting module can emit a specified signal; it can control the angle control module, so that the angle between the two uniform linear arrays can be turned to a set value; it can also process the signal transmitted by the receiving module, through embodiment 1 The algorithm calculates the angle of arrival, and then transmits the result to the transmitting module.

The angle control module is used to control the angle between the two linear arrays, and consists of a stepper motor and a drive circuit. A stepper motor is an open-loop control motor that converts electrical pulse signals into angular displacement or linear displacement. When the drive circuit receives a pulse signal, it drives the stepper motor to rotate a fixed angle in the set direction, called the step distance horn. Therefore, the desired angle value can be achieved by making the data processing and control module transmit a certain number of pulse signals.

The receiving module consists of two ultrasonic receiving probe arrays. The angle between the two arrays is variable and the angle can be adjusted through the angle control module. As shown in Figure 2, the horizontal array L1 and the stepping motor are fixed together. The array L2 is installed on the stepping motor and ensures that the array L1 and the array L2 are on the same plane, and the array L2 can be rotated by the stepping motor, so as to achieve the purpose of adjusting the angle between the two linear arrays. Figure 3 and Figure 4 are the top view and side view of the device connection respectively. As shown in the figure, there is a fixed bracket at the end of the array L1. Because the receiving module will be placed in water, the fixed bracket is made of plastic to increase buoyancy. The stepper motor stator is connected to this bracket, and the stepper motor rotor is connected to the array L2. The two arrays can also receive the signal emitted from the target sound source, and then send it to the processor after A/D conversion.

The transmitting module is composed of an impedance matching circuit and an ultrasonic transmitting probe, which is connected to the processor through a D/A converter, and can transmit specified signals according to the instructions issued by the processor.

The output module is composed of a USB interface and a display, and is connected with the data processing and control module and the power supply module. It can provide human-computer interaction, and output the data processed in the data processing and control module to an external device through a USB interface or display it on a monitor.

The power supply module is composed of a power supply, and is connected with the data processing and control module, the angle control module, the transmitting module, the receiving module and the output module. It is able to power these modules.

The main working process of this device is as follows: In the actual measurement process, according to the signal parameters to be transmitted, the corresponding parameters are input through the data processing and control module, so that the processor generates corresponding digital signals, and then transmitted to the transmitter through D/A conversion. module, the ultrasonic transmitting probe can generate the signal we need and transmit it. The angle value between the two linear arrays can be set through the data processing and control module, the processor sends a specific pulse signal to the drive circuit of the angle control module, and then the drive circuit can drive the stepper motor to rotate to the required angle. After receiving the signal reflected from the target sound source, the receiving array in the receiving module converts it into a digital signal through A/D and sends it to the processor, and then the processor calculates the result according to the provided algorithm. Finally, the data processing and control module transmits the calculation result to the output module, and the output module transmits the result to an external device through a USB interface or displays it on a display. The power module supplies power to all other modules.

The device includes a data processing and control module, an angle control module, a transmitting module, a receiving module, an output module and a power supply module. The data processing and control module can be implemented with a DSP chip (such as the DSP chip of the TMS320VC5509A model of TI Company). This DSP chip can realize the functions of A/D conversion and D/A conversion, and can realize the rotation operator and Calculation of the final direction of arrival; the angle control module includes a stepper motor and a drive circuit, using a stepper motor of the type HSTM42-1.8-D-26-4-0.4 of Fuxing Company, and the step angle of this stepper motor is 1.8 degrees , the driving circuit adopts ULN2003 chip; the transmitting module uses an ultrasonic transmitting probe; the receiving module uses two uniform linear arrays with adjustable angles, each of which includes multiple ultrasonic receiving probes, and the number is the same, and the two linear arrays are as shown in Figure 2 Assembled as shown; the output module uses a USB port and an LCD display. FIG. 1 is a block diagram of the hardware structure of the device of the present invention.

The working steps are as follows:

Step 1: Set 5 different linear array angle values, that is, take N=5, which are 15°, 30°, 45°, 60°, and 75° respectively. Set the angle value of the line array in the data processing and control module, and turn the angle between the two line arrays to 15° through the angle control module. Place 4 target sound sources underwater, and the included angles with the horizontal array normal are 30°, 60°, -30°, -60° respectively. The parameters of the transmitting module are set through the data processing and control module so that the frequency of the transmitting signal is 100kHz and the pulse length is 5ms. Set the parameters of the receiving array, set the number M of the array elements of the two uniform linear arrays to 10, and set the distance d between the array elements to 5mm, then the first 9 array elements are one sub-array, and the last 9 array elements are another sub-array. The distance between two sub-arrays is d.

Step 2: Sampling the target sound source signal received by the ultrasonic receiving probe; the signals received by the uniform array in the horizontal direction are respectively x _x1 (t), x _x2 (t), ..., x _x8 (t) and y _x1 ( t), y _x2 (t), ..., y _x8 (t), the signals received by the uniform array in the inclined direction are x _y1 (t), x _y2 (t), ..., x _y8 (t) and y _y1 (t ), y _y2 (t),..., y _y8 (t). A total of 200 samples are received, and the received signal is passed to the data acquisition processing and control module for calculation and processing.

Step 3: The processing steps of the signal in the data acquisition processing and control module are as follows:

1) arrange the signals received by the uniform array in the horizontal direction into vector form X _h (t) and Y _h (t), calculate the covariance matrix R _hxx of X _h (t) =E[X _h (t )X _h ^H (t)], the cross-covariance matrix R _hxy between X _h (t) and Y _h (t) =E{X _h (t)Y _h ^H (t)}. Simultaneously, the signal received by the uniform array in the inclined direction is also processed in the same way, and R _vxx =E[X _v (t)X _v ^H (t)] and R _vxy =E{X _v (t)Y _v ^H ( t)}

2) Perform eigenvalue decomposition on the two covariance matrices R _hxx and R _hxy in the horizontal array to obtain the smallest eigenvalue σ ² , thus C _hxx =R _hxx -σ ² I=AR _ss A ^H and C _hxy = R _hxy −σ ² Z=AR _ss Φ ^H A ^H . Simultaneously doing the same for the two covariance matrices in the tilted array yields C _vxx and C _vxy .

3) Calculate the generalized eigenvalue decomposition of the matrix bundles {C _hxx , C _hxy } and {C _vxx , C _vxy } respectively to obtain λ _x1 ,λ _x2 ,…,λ _xK and λ _y1 ,λ _y2 ,…,λ _yK .

4) Arrange arg(λ _x1 ), arg(λ _x2 ),…,arg(λ _xK ) according to their respective square sizes from large to small to obtain the sequence H, and arrange arg(λ _y1 ), arg(λ _y2 ), ..., arg(λ _yK ) are arranged according to their respective square sizes from small to large to obtain the sequence V. Then assign the value of i-th element h _i in H to arg(φ _xi ), and assign the value of i-th element v _i in V to arg(φ _yi ).

5) According to the matching arg(φ _xi ) and arg(φ _yi ) and the angle between the two linear arrays, it is finally obtained:

Step 4: Store the calculated direction angle information and send it to the output module, so that it can be output to an external device through the USB interface or displayed on the LCD display.

Step 5: Change the included angle between the two linear arrays and set them to 30°, 45°, 60°, and 75° respectively. Take the average value based on the results calculated each time, and the direction angles estimated according to the algorithm are 30° , 60°, -30°, -60° are the same as the actual angles, indicating that the estimated results are correct and the method and device are feasible.

The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, Simplifications should be equivalent replacement methods, and all are included in the protection scope of the present invention.

Claims (10)

1. The underwater direction-of-arrival estimation method based on the adjustable included angle uniform linear array is characterized by comprising the following steps of:

the method comprises the following steps: establishing a linear array model with an adjustable included angle;

placing two pieces of water with an included angle of α_nThe two uniform linear arrays with adjustable included angles are provided with M array elements, and the distance between the array elements is d; k narrow-band target sound sources are S respectively₁,S₂,…,S_KThe included angle between the incident direction of the sound wave and the positive axis direction of the horizontal uniform linear array is β E (0, Pi);

step two: establishing signal receiving models of two uniform linear arrays;

when the included angle of the linear array is α_nIn time, the direction angles of the K narrow-band target sound sources corresponding to the horizontal linear arrays are respectively theta_nx1,θ_nx2,...,θ_nxKThe direction angles corresponding to the oblique linear arrays are respectively theta_ny1,θ_ny2,...,θ_nyK(ii) a Taking the first array element as a reference point, the signal received by the first array element at the time t is:

<mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>

wherein s is_i(t) denotes the ith source signal, n₁(t) represents noise on the first array element;

the received signal satisfies the narrow-band condition, that is, when the signal delay is much less than the reciprocal of the bandwidth, the delay action is equivalent to generating a phase shift to the baseband signal, and then the signal received by the mth array element at the same time is:

<mrow> <msub> <mi>x</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> </mfrac> <msub> <mi>dsin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>x</mi> <mi>i</mi> </mrow> </msub> </mrow> </msup> <mo>+</mo> <msub> <mi>n</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>M</mi> </mrow>

wherein λ_iRepresenting the wavelength of the sound wave reflected back from the ith target source, n_m(t) represents noise on the mth array element; arranging the received signals of each array element into a column vector form, the signals received by the whole horizontal linear array can be represented by the following vector equation:

X(t)＝AS(t)+N(t) (1)

wherein,a matrix of M × K steering vectors, X (t) ═ x₁(t),x₂(t),…,x_M(t)]^TFor a received signal matrix of M × 1, s (t) ═ s₁(t),s₂(t),…,s_K(t)]^TA matrix of K × 1 source signals, n (t) ═ n₁(t),n₂(t),…,n_M(t)]^TA noise matrix of mx 1; in the same way, a signal receiving model of the inclined uniform linear array can be obtained;

step three: establishing a uniform linear array subarray model, and deducing a rotation operator phi_xAnd phi_yAn expression;

dividing M array elements in the horizontal linear array into two subarrays Z with translation vector d_hxAnd Z_hy(ii) a Sub-array Z_hxThe array consists of the first to M-1 array elements of a horizontal array, and comprises the following components:

x_h1(t)＝x₁(t),x_h2(t)＝x₂(t),…,x_h(M-1)(t)＝x_M-1(t)

wherein x is_h1(t),x_h2(t),…,x_h(M-1)(t) are respectively subarrays Z_hxThe signals received by the first array element to the M-1 array element;

sub-array Z_hyThe second to Mth array elements of the horizontal array are composed of:

y_h1(t)＝x₂(t),y_h2(t)＝x₃(t),…,y_h(M-1)(t)＝x_M(t)

wherein, y_h1(t),y_h2(t),…,y_h(M-1)(t) are respectively subarrays Z_hyThe signals received by the first array element to the M-1 array element;

then the received signals of the m-th array element in the two sub-arrays are respectively:

<mrow> <msub> <mi>x</mi> <mrow> <mi>h</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mrow> <mi>h</mi> <mi>x</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>M</mi> </mrow>

<mrow> <msub> <mi>y</mi> <mrow> <mi>h</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>x</mi> <mi>i</mi> </mrow> </msub> </mrow> </msup> <msub> <mi>a</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mrow> <mi>h</mi> <mi>y</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>M</mi> </mrow>

whereinn_hxm(t) and n_hym(t) are each subarrays Z_hxAnd Z_hyAdditive noise of the upper m-th array element, the above formula is written as a vector:

X_h(t)＝AS(t)+N_hx(t)

Y_h(t)＝AΦ_xS(t)+N_hy(t)

wherein the matrix phi_xA diagonal matrix of K x K, which is a sub-matrix Z_hxAnd Z_hyThe diagonal elements of the unitary matrix, also called the rotation operator, contain phase delay information of wave fronts of K signals between any matrix element pair, and are expressed as:

<mrow> <msub> <mi>&amp;Phi;</mi> <mi>x</mi> </msub> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>{</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>x</mi> <mn>1</mn> </mrow> </msub> </mrow> </msup> <mo>,</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>x</mi> <mn>2</mn> </mrow> </msub> </mrow> </msup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mi>K</mi> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>x</mi> <mi>k</mi> </mrow> </msub> </mrow> </msup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

according to the steps, the inclined uniform linear array can be divided into two sub-arrays Z_vxAnd Z_vyObtaining a received signal X_v(t) and Y_v(t), thereby deriving the rotation operator as:

<mrow> <msub> <mi>&amp;Phi;</mi> <mi>y</mi> </msub> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>{</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>y</mi> <mn>1</mn> </mrow> </msub> </mrow> </msup> <mo>,</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>y</mi> <mn>2</mn> </mrow> </msub> </mrow> </msup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mi>K</mi> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>y</mi> <mi>k</mi> </mrow> </msub> </mrow> </msup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

step four: establishing a rotation operator phi_x、Φ_yAnd theta_nxi、θ_nyiThe relationship between;

step five: establishing a relation between two direction angles when the sound wave signals are incident from different areas;

step six: for matrix phi_xSum matrix Φ_yThe diagonal elements on the upper board are paired;

step seven: determining theta from the pairing result_nxiThe size of (2).

2. The underwater direction-of-arrival estimation method based on the adjustable included angle uniform linear array according to claim 1, characterized in that the fourth step specifically comprises:

X_hthe covariance matrix of (t) can be expressed as:

R_hxx＝E[X_h(t)X_h ^H(t)]＝AR_ssA^H+σ²I

wherein R is_ss＝E{S(t)S^H(t) }, which is a source part covariance matrix;

X_h(t) and Y_hThe cross-covariance matrix of (t) is:

R_hxy＝E{X_h(t)Y_h ^H(t)}＝AR_ssΦ_x ^HA^H+σ²Z

performing eigenvalue decomposition on the covariance matrix of the matrix to obtain the minimum eigenvalue sigma²Using σ²A matrix beam C can be obtained_hxx,C_hxyIn which C is_hxx＝R_hxx-σ²I＝AR_ssA^H，C_hxy＝R_hxy-σ²Z＝AR_ssΦ_x ^HA^H(ii) a Computing a matrix Beam { C_hxx,C_hxyDecomposing the generalized eigenvalue of the method to obtain a non-zero eigenvalue lambda_x1,λ_x2,…,λ_xKThey correspond to the matrix phi one by one_xThe elements on the diagonal line, but the correspondence is not determined, so can be written by equation (2):

<mrow> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>x</mi> <mi>i</mi> </mrow> </msub> </mrow> </msup> <mo>=</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

wherein phi_xiIs a matrix phi_xUpper diagonal element, and phi_xi∈{λ_x1,λ_x2,…,λ_xK},i＝1,2,…,K；

According to the steps, two covariance matrixes R of the inclined uniform array can be obtained_vxxAnd R_vxyThen to the matrix beam { C_vxx,C_vxyResolving the eigenvalue to obtain an eigenvalue lambda_y1,λ_y2,…,λ_yKThey are also in one-to-one correspondence with the matrix phi_yThe above diagonal elements, but the corresponding relationship is also uncertain, and can be written by formula (3):

<mrow> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>n</mi> <mi>y</mi> <mi>i</mi> </mrow> </msub> </mrow> </msup> <mo>=</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

wherein phi_yiIs a matrix phi_yUpper diagonal element, and phi_yi∈{λ_y1,λ_y2,…,λ_yK},i＝1,2,…,K。

3. The method for estimating the underwater direction of arrival of the uniform linear array based on the adjustable included angle as claimed in claim 2, wherein the fifth step specifically comprises:

according to linear array included angle α_nAnd the included angle β between the incident direction of the sound wave and the positive axis direction of the x axis sets the incident area of the sound wave signal to be 4 when β epsilon (0, α)_n) When the acoustic signal is in the area 1, β E (α)_nπ/2), the acoustic signal is incident for region 2, when β ∈ (π/2, π/2+ α)_n) When the acoustic wave signal is incident in the area 3, β epsilon (pi/2 + α)_nAnd pi), the acoustic signal is incident in the area 4;

(1) when an acoustic wave is incident from the region 1, θ_1iIs the angle theta between the incident direction of the sound wave and the normal of the horizontal linear array_1jThe angle between the incident direction of sound wave and the normal of the inclined linear array isθ_1i+θ_1j＝π-α_n(ii) a Because the array signal on the x-axis is referenced to the array element in the most negative direction of the x-axis, and the subarray Z_hxAlso in subarray Z_hySo that when an acoustic wave is incident from region 1, the reference array element is the one that received the signal the latest, sub-array Z_hxThe array element in (1) is also larger than the subarray Z_hyThe corresponding array element in the array receives the signal late, so that the time delay parameter tau is less than 0So there is theta at this time_nxi＝-θ_1iFor the same reason have theta_nyi＝-θ_1j(ii) a In conclusion, it can be obtained that:

θ_nyi＝-θ_nxi+α_n-π (6)

(2) when the acoustic wave is incident from the region 2, θ_2iIs the angle theta between the incident direction of the sound wave and the normal of the horizontal linear array_2jThe angle between the incident direction of the sound wave and the normal line of the inclined linear array is theta_2j-θ_2i＝α_nAccording to the analytical method used in (1), in which case there is theta_nxi＝-θ_2i，θ_nyi＝-θ_2jIn summary, the following can be obtained:

θ_nyi＝θ_nxi-α_n(7)

(3) when the acoustic wave is incident from the region 3, θ_3iIs the angle theta between the incident direction of the sound wave and the normal of the horizontal linear array_3jThe angle between the incident direction of the sound wave and the normal line of the inclined linear array is theta_3i+θ_3j＝α_nAccording to the analytical method used in (1), in which case there is theta_nxi＝θ_3i，θ_nyi＝-θ_3jIn conclusion, the following can be obtained:

θ_nyi＝θ_nxi-α_n

(4) when the acoustic wave is incident from the region 4, θ_4iIs the angle theta between the incident direction of the sound wave and the normal of the horizontal linear array_4jThe angle between the incident direction of the sound wave and the normal line of the inclined linear array is theta_4i-θ_4j＝α_nAccording to (1)) In the analytical method used in (1), in this case there is theta_nxi＝θ_4i，θ_nyi＝θ_4jIn conclusion, the following can be obtained:

θ_nyi＝θ_nxi-α_n

from equations (6) and (7), we can obtain:

sinθ_nyi＝sin(θ_nxi-α_n) (8)

substituting equation (8) into equation (5) then there is:

4. the underwater direction-of-arrival estimation method based on the adjustable included angle uniform linear array according to claim 3, characterized in that the sixth step specifically comprises:

as can be seen from the equations (4) and (9), if pairing is successful, the following equation holds:

will arg (lambda)_x1),arg(λ_x2),…,arg(λ_xK) Arranging the sequences from large to small according to respective square size sequences to obtain a sequence H; will arg (lambda)_y1),arg(λ_y2),…,arg(λ_yK) Arranging the sequences from small to large according to respective square size sequences to obtain a sequence V; thus, there are:

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>arg</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>arg</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>v</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>

wherein h is_iIs the ith element in the sequence H; v. of_iIs the ith element in the sequence V.

5. The underwater direction-of-arrival estimation method based on the adjustable included angle uniform linear array as claimed in claim 4, wherein in step seven,i＝1,2,...K。

6. the method as claimed in claim 5, wherein the angle α between two uniform linear arrays is changed_nN1, 2,.. multidot.n, repeating steps one to seven, and α for different linear array angles_nCalculating the corresponding direction of arrival angle by formula (12), and averaging the N results to obtain the final result theta_xi,i＝1,2,...,K。

7. The underwater direction-of-arrival estimation device based on the adjustable included angle uniform linear array based on the method of claim 1 is characterized by comprising a data processing and control module, an angle control module, a transmitting module, a receiving module, an output module and a power supply module; the power module is connected with the data processing and control module, the angle control module, the transmitting module, the receiving module and the output module and can supply power to the modules;

the data processing and control module is the core part of the whole device, and all other modules are directly connected with the data processing and control module; it can control the transmitting module to make the transmitting module transmit the appointed signal; the angle control module can be controlled to enable the included angle of the two uniform linear arrays to be converted to a set value; and the signal transmitted by the receiving module can be processed, the direction of arrival angle is calculated, and the result is transmitted to the transmitting module.

8. The apparatus of claim 7, wherein the angle control module comprises a stepping motor and a driving circuit for controlling an angle between the two linear arrays; the stepping motor is an open-loop control motor which converts an electric pulse signal into angular displacement or linear displacement, when the driving circuit receives a pulse signal, the driving circuit drives the stepping motor to rotate for a fixed angle according to a set direction, and a desired angle value can be achieved by enabling the data processing and control module to emit a certain number of pulse signals.

9. The device of claim 7, wherein the receiving module comprises two ultrasonic receiving probe arrays, the included angle between the two arrays is variable and can be adjusted through the angle control module; the horizontal array L1 and the stepping motor are fixed together, the array L2 is installed on the stepping motor and ensures that the array L1 and the array L2 are on the same plane, and the array L2 can be driven by the stepping motor to rotate, so that the purpose of adjusting the included angle of the two arrays is achieved.

10. The apparatus of claim 9, wherein a mounting bracket is provided at the end of the array L1, the mounting bracket being made of plastic; the stepper motor stator is attached to this bracket and the stepper motor rotor is attached to the array L2.