CN109581274B - Non-circular signal underwater DOA estimation method and device based on included angle-adjustable three-dimensional array - Google Patents
Non-circular signal underwater DOA estimation method and device based on included angle-adjustable three-dimensional array Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
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Abstract
The invention discloses a non-circular signal underwater DOA estimation method and device based on an included angle-adjustable three-dimensional array, which uses a two-dimensional included angle-adjustable uniform three-dimensional linear array as a receiving array, wherein the array can carry out flexible measurement, and the aim of improving estimation performance can be achieved by realizing that the included angle of the linear array in two dimensions is adjustable for a plurality of times. In order to overcome the problem of rapid signal attenuation in an underwater acoustic environment, a non-circular signal is applied to underwater DOA estimation, and an NC-ESPRIT algorithm based on the non-circular signal is adopted to improve estimation performance; in order to eliminate estimation deviation caused by sound velocity influence, a sound velocity independent two-dimensional DOA estimation expression is adopted; meanwhile, in order to realize successful pairing of three groups of parameters under the three-dimensional angle-adjustable uniform linear array, a three-parameter pairing method based on subspace projection angle pairing is adopted, and the underwater DOA estimation accuracy is improved. In summary, the method has high estimation accuracy and strong practicability.
Description
Technical Field
The invention relates to the technical field of target positioning, in particular to a non-circular signal underwater DOA estimation method and device based on an included angle-adjustable three-dimensional array.
Background
Spatial signal direction of arrival estimation (DOA estimation) has been widely used in many fields, and two-dimensional underwater DOA estimation refers to a method for estimating the direction of arrival of an underwater target in two dimensions by using an array signal processing technology by placing a sensor array on the water surface. The existing underwater DOA estimation method mainly comprises a MUSIC algorithm and an ESPRIT algorithm.
The underwater DOA estimation uses acoustic waves as a propagation carrier, resulting in attenuation of the signal due to acoustic scattering caused by various obstructions in the underwater acoustic channel and rugged seafloor as the acoustic signal propagates in the underwater environment. In addition to the rapid decay of the signal caused by the underwater acoustic environment, another problem faced by underwater DOA estimation is the sound velocity effect. Because of complex and unstable underwater environments such as rivers, oceans and the like, the speed of sound waves changes with position and time, the estimation accuracy of the underwater DOA algorithm is greatly affected, and when the actual sound speed deviates from the preset speed, the estimation accuracy is reduced.
In the DOA estimation algorithm based on the non-circular signal, the characteristic that the non-circular signal pseudo covariance matrix is not zero is equivalent to a virtual expansion array, and the estimation performance can be remarkably improved. Meanwhile, the addition of the non-circular signal virtual array elements also enables the algorithm to process the number of the information sources which is more than the number of the arrays. However, the existing two-dimensional direction-of-arrival estimation method based on non-circular signals mostly adopts a fixed right-angle orthogonal linear array structure. The conventional array structure is fixed and not easy to change, the requirement on structural stability is high, and the corresponding flexibility is reduced.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a non-circular signal underwater DOA estimation method and device based on an included angle-adjustable three-dimensional array. Meanwhile, as the two-dimensional included angle of the uniform linear array is variable, great flexibility is brought to the arrangement mode of the array, and the included angle can be changed to carry out multiple measurements in actual measurement, so that errors are better eliminated.
The first object of the present invention can be achieved by adopting the following technical scheme:
a method for estimating underwater two-dimensional direction of arrival based on an included angle adjustable three-dimensional linear array and non-circular signals in an unknown sound velocity environment comprises the following steps of 2 The estimation method comprises the following steps of:
s1, establishing an array signal receiving model of a three-dimensional angle-adjustable uniform linear array, wherein the three-dimensional angle-adjustable uniform linear array comprises an L-shaped array and a radial arm array with 2 degrees of freedom, 2 subarrays of the L-shaped array are respectively arranged as a linear array 1 and a linear array 2, the radial arm array with 2 degrees of freedom is arranged as a linear array 3, and the radial arm array with 2 degrees of freedom is arranged as a linear array 31 is arranged on an x axis of a coordinate system, a linear array 2 is arranged on a y axis of the coordinate system, a linear array 3 has a rotation characteristic of 2 degrees of freedom, an included angle between the linear array 3 and the linear array 1 is delta x, an included angle between the linear array 3 and the linear array 2 is delta y, the included angle delta x and the included angle delta y are adjustable, the linear array 1, the linear array 2 and the linear array 3 are all uniform linear arrays and all have M receiving array elements, and the average interval of the array elements is d; assuming that the total number of underwater targets incident on the array is K by taking the origin of the coordinate system as a reference point, the azimuth angle and the elevation angle of the kth target can be expressed as theta k And phi k ，θ k ∈[0,π]，At the same time, the included angles between the target and the x-axis and the y-axis of the coordinate system are alpha respectively k And beta k The target signal satisfies the narrowband condition, that is, when the delay of the target signal is far smaller than the inverse of the bandwidth, the delay action is equivalent to making the baseband signal generate a phase shift, the snapshot number is L, and the received data matrices of the linear array 1, the linear array 2 and the linear array 3 are respectively denoted as X, Y and Z:
X＝A x S+N x (1)
Y＝A y S+N y (2)
Z＝A z S+N z (3)
where S is a KXL-dimensional source signal matrix, N x ,N y And N y Then it is the noise matrix in M x L dimensions, A x 、A y And A z Then is formed by azimuth angle theta k And elevation angle phi k An M x K-dimensional vector matrix of representations;
s2, solving characteristic value parameters u corresponding to the linear arrays 1,2 and 3 by utilizing a non-circular signal one-dimensional DOA estimation algorithm based on NC-ESPRIT k 、v k And w k ,k＝1,2,…,K；
S3, characteristic value parameters u corresponding to the linear array 1, the linear array 2 and the linear array 3 in the three-dimensional array with the adjustable included angle k 、v k And w k Carrying out parameter pairing;
s4, solving a two-dimensional direction-of-arrival estimation solution of the target, namely solving an azimuth angle theta for the K-th=1, 2, … and K targets k And elevation angle phi k Is a function of the estimated value of (2);
s5, obtaining N under the condition of different array included angles 2 And performing windowing function processing on the group estimation values to obtain an optimal estimation result.
Further, in the step S1, there is s=Φs according to the non-circular characteristic of the signal R Wherein For the non-circular phase of the signal, equations (1), (2) and (3) are written as
X＝A x ΦS R +N x (4)
Y＝A y ΦS R +N y (5)
Z＝A z ΦS R +N z (6)
Wherein the steering vector matrix A x 、A y And A z Expressed as:
A x ＝[a x (θ 1 ,φ 1 ) a x (θ 2 ,φ 2 )…a x (θ K ,φ K )] (7)
A y ＝[a y (θ 1 ,φ 1 ) a y (θ 2 ,φ 2 )…a y (θ K ,φ K )] (8)
A z ＝[a z (θ 1 ,φ 1 ) a z (θ 2 ,φ 2 )…a z (θ K ,φ K )] (9)
for the kth target, there is
a x (θ k ,φ k )＝[a x，0 (θ k ,φ k )…a x，M-1 (θ k ,φ k )] T (10)
a y (θ k ,φ k )＝[a y，0 (θ k ,φ k )…a y，M-1 (θ k ,φ k )] T (11)
a z (θ k ,φ k )＝[a z，0 (θ k ,φ k )…a z，M-1 (θ k ,φ k )] T (12)
Let the projection of the linear array 3 on the xoy plane and the included angle of the x axis be theta z The included angle between the linear array 3 and the z-axis is phi z According to the relation of the included angles of the linear array 1, the linear array 2 and the linear array 3 and the coordinate axis, the method comprises the following steps:
since the steering vector is affected by the angle between the target-origin line and the linear array, it is obtained
Wherein lambda is k Is the wavelength of the sound wave, i.e. the spacing d between two adjacent array elements of the uniform linear array is less than half the wavelength of the sound wave signal, and the velocity v of the sound wave on the detection path is unknown, so v is taken as the minimum in its range to determine lambda k Is a value of (2).
Further, the step S2 is as follows:
reconstructing a received signal array for a linear array 1, first defining a row switching matrix J
By means of rowsThe switching matrix J reconstructs a receiving signal matrix, and the reconstructed receiving signal matrix W x Expressed as:
wherein the method comprises the steps ofAnd construct W x Covariance matrix R of (2) w ：
Wherein R is s Is the real part S of the source signal R Is used for the co-variance matrix of (a),is the variance of the noise component, I 2M For covariance matrix R, the unit matrix is 2Mx2M w Decomposing the characteristic value to obtain
Because of the signal subspace U s And B is connected with x The relation of (2) is: span { U s }＝span{B x -so that there is a full order matrix T such that U s T=b, defining a matrix T 1 ＝[0 (M-1)×1 I M-1 ]、T 2 ＝[I M-1 0 (M-1)×1 ]Line switching matrixWherein->A zero matrix of (M-1) x M dimension;
covariance matrix R w Estimate of (2)Obtained by sampling
Wherein L is the number of shots,
for a pair ofCharacteristic decomposition is carried out to obtain a characteristic vector matrix U s * Estimate of +.>Construction of matrix->And performing a second feature decomposition on the matrix to obtain a feature vector matrix delta x ，δ x Is a diagonal matrix:
obtaining u k ，k＝1,2,…,K；
The parameters v corresponding to the linear array 2 and the linear array 3 are obtained by the same method k And w k Wherein v is k The corresponding expression is written as:
since the linear array 3 is an array with one end fixed to the origin for free rotation, w is k The corresponding expression is written as:
further, the step S3 is as follows:
first, a matrix Q= [ X, Y, Z is constructed] T ＝A·S+N Q Wherein N is Q For the corresponding 3M x L dimensional noise matrix, the steering vector matrix A is represented by A x 、A y And A z The composition comprises:
A＝[A x ,A y ,A z ] T (26)
acquiring covariance matrix R of Q Q The method comprises the following steps:
R Q ＝Q·Q H (27)
for R Q Performing eigenvalue decomposition to obtain corresponding noise subspace U NQ Since the steering vector matrix has an orthogonal relationship with the noise subspace, namely: a is that H ·U NQ =0 sumThe construction cost function F is as follows:
construction of the guide vector a (θ) i ,φ i )＝[u,v,w] T Wherein u, v and w are vectors of K×1 dimension, and are three sets of eigenvalue parameters u k ,v k And w k Is arranged and combined together to form K 3 And (3) group guide vectors, wherein the combination corresponding to the K groups with the maximum value of the cost function is the combination of successful parameter pairing.
Further, the process of solving the two-dimensional direction of arrival estimation solution of the target in the step S4 is as follows:
for the kth target, find the azimuth θ k And elevation angle phi k Using the parameter u after pairing in step S3 k 、v k And w k Obtain azimuth angle theta k And elevation angle phi k Is estimated by (a):
further, the processing procedure of the N sets of estimated values obtained under the condition of different array angles in the step S5 is as follows:
adjusting the included angles delta x and delta y between the two uniform linear arrays, wherein delta x is N groups, delta y is N groups, and each time (delta x is obtained i ,Δy j ) I=0, 1,2, …, N-1, j=0, 1,2, …, N-1, let n·i+j estimate, the angle between two uniform linear arrays bei, j=0, 1,2, …, N-1 repeating steps S1 to S5 to obtain the n·i+j-th set of estimated values of the target direction of arrival estimate, since the angle (Δx) is calculated for different linear arrays i ,Δy j ) Obtaining the corresponding direction of arrival angle by the formula (29), and estimating the result p ij The method comprises the following steps:
for N 2 Windowing the results to obtain optimal estimation results, firstly, obtaining a two-dimensional angle interval of a target, and performing N 2 Averaging the group estimation results to obtain average estimation values of K targets
Average according to the kth targetJudging the two-dimensional angle interval of the target, if
Then the kth target is considered to be at (n) k ,m k ) A two-dimensional angle interval;
constructing a weighting gain matrix G ij ：
G ij ＝diag{g(i-Δ i1 ,j-Δ j1 ),g(i-Δ i2 ,j-Δ j2 ),…,g(i-Δ iK ,j-Δ iK )} (33)
Where g (i, j) is a two-dimensional window function, offset delta ik And delta jk In relation to the two-dimensional angular interval in which the kth object is located, there is the following relationship:
for N 2 The group estimation results are subjected to window function weighting to obtain optimal estimation values P of K targets:
further, the two-dimensional window function g (i, j) is a gaussian window, a hamming window, a rectangular window or a chebyshev window.
The second object of the invention can be achieved by adopting the following technical scheme:
an angle-adjustable three-dimensional array-based non-circular signal underwater DOA estimation device comprises a data processing and control module, and a transmitting module, a receiving module, an output module and a power module which are respectively connected with the data processing and control module, wherein the data processing and control module comprises an A/D converter, a D/A converter and a processor which are sequentially connected,
the transmitting module comprises a power amplifier, an impedance matching circuit and an ultrasonic transmitting probe which are sequentially connected, and is connected with the processor through the D/A converter, and transmits a specified non-circular signal according to an instruction sent by the processor;
the receiving module adopts a three-dimensional angle-adjustable uniform linear array, the three-dimensional angle-adjustable uniform linear array comprises an L-shaped array and a radial arm array with 2 degrees of freedom, wherein 2 subarrays of the L-shaped array are respectively arranged as a linear array 1 and a linear array 2, the radial arm array with 2 degrees of freedom is arranged as a linear array 3, the linear array 1 is arranged on an x-axis of a coordinate system, the linear array 2 is arranged on a y-axis of the coordinate system, the linear array 3 has the rotation characteristic with 2 degrees of freedom, the angle between the linear array 3 and the linear array 1 is delta x, the angle between the linear array 3 and the linear array 2 is delta y, the angle delta x and the angle delta y are adjustable, the linear array 1, the linear array 2 and the linear array 3 are uniform linear arrays and all have M receiving array elements, and the average distance between the array elements is d;
the output module comprises a USB interface and a display, and outputs the data processed in the data processing and control module to an external device or the display for display through the USB interface;
the power module is respectively connected with the data processing and control module, the transmitting module, the receiving module and the output module and supplies power.
Further, the linear arrays 3 are respectively installed on the stepper motor 1 and the stepper motor 2, and are driven to rotate by the stepper motor, the stepper motor is an open loop control motor for converting an electric pulse signal into angular displacement or linear displacement, when the stepper motor driving circuit receives a pulse signal, the stepper motor is driven to rotate by a fixed angle according to a set direction, which is called a step angle, and a data processing and control module transmits a certain number of pulse signals to achieve a desired angle value.
Further, the linear array 1, the linear array 2 and the linear array 3 are connected through a fixed support made of plastic materials.
Compared with the prior art, the invention has the following advantages and effects:
1. according to the invention, a three-dimensional uniform linear array with 2 dimension included angles adjustable is adopted as a receiving array, and then a NC-ESPRIT algorithm based on non-circular signals is utilized to estimate the two-dimensional underwater arrival direction. The invention makes full use of the non-circular characteristic of the signal to expand the aperture of the array, so that DOA estimation is more accurate. Furthermore, the addition of virtual array elements also enables the algorithm to estimate a greater number of sources.
2. Compared with the traditional method adopting a fixed L-shaped right-angle array, the invention adds a 2-degree-of-freedom radial arm array, realizes the variable two-dimensional included angle between three-dimensional linear arrays, can better eliminate errors by taking different values to carry out multiple measurements, improves the angle resolution, lateral precision and ambiguity resistance of an estimation result, and simultaneously ensures that the placement of an ultrasonic receiving probe has very strong flexibility.
3. Compared with the method for estimating the direction of arrival of the underwater target by using the traditional two-dimensional DOA algorithm, the method provided by the invention has the advantages of higher practicability and higher estimation accuracy. Conventional two-dimensional DOA algorithms generally assume the speed of sound to be a constant, whereas in actual complex underwater environments, the speed of sound tends to vary continuously, which can lead to large errors if calculated as a constant. The invention adopts the three-dimensional uniform linear array with adjustable included angle, eliminates the variable of sound velocity through the relation between the included angle of the array and the direction angle of arrival, and leads the final operation result to be irrelevant to the sound velocity, thereby improving the estimation precision.
4. The device is improved on the traditional measuring device, and the uniform linear array with adjustable included angles is used, so that the feasibility is high and the installation is simple. In addition, the computing processing capacity of modern processors is continuously improved, so that the integration level of the chips such as the processors used by the invention is high, and the computing capacity is high, thereby ensuring the feasibility of the invention.
Drawings
FIG. 1 is a block diagram of the hardware architecture of the device of the present invention;
FIG. 2 is a schematic diagram showing the connection of three arrays of receiving elements to a processor in the apparatus of the present invention;
FIG. 3 is a three-dimensional array element layout of a three-dimensional angle-adjustable linear array in the device of the invention;
FIG. 4 is a schematic diagram of the rotational connection of the sub-array 3 in the device of the present invention;
FIG. 5 is a schematic diagram of a three-dimensional angle-adjustable uniform linear array model used in the present invention;
FIG. 6 is a diagram x Receiving signal module of uniform axis linear arrayA shape;
FIG. 7 is a flow chart of a method for estimating underwater DOA of non-circular signals based on an included angle-adjustable three-dimensional array.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
In the embodiment, a three-dimensional uniform linear array is adopted, wherein 2 linear arrays can rotate to realize that the array included angle in 2 dimension directions is adjustable, a narrow-band target sound source is S, and the center frequency is f. The direction of incidence of the sound wave, i.e. azimuth and elevation, can be expressed as θ k And phi k (θ k ∈[0,π]，) The method comprises the steps of carrying out a first treatment on the surface of the The method of the embodiment is to measure the included angle value of the N different linear arrays.
As shown in fig. 7, the method for estimating underwater two-dimensional DOA in the unknown sound velocity environment based on the non-circular signal and the three-dimensional linear array with the adjustable two-dimensional included angle in the embodiment comprises the following steps:
s1, establishing an array signal receiving model of the three-dimensional uniform linear array with adjustable included angles. The three-dimensional uniform linear array shown in fig. 5 is placed, and can be regarded as being composed of an L-shaped array and a radial arm array with 2 degrees of freedom, wherein 2 sub-linear arrays of the L-shaped array are respectively arranged as a linear array 1 and a linear array 2, the radial arm array with 2 degrees of freedom is arranged as a linear array 3, the linear array 1 is arranged on the x-axis of a coordinate system, the linear array 2 is arranged on the y-axis of the coordinate system, the linear array 3 has the rotation characteristic of 2 degrees of freedom, and the included angle between the radial array 3 and the linear array 1 is deltax (the included angle is adjustable), and the included angle between the radial array 2 and the radial array is deltay (the included angle is adjustable). The 3 uniform linear arrays all have M receiving array elements, and the average spacing of the array elementsD is d. Assuming that the total number of underwater targets incident on the array is K by taking the origin of the coordinate system as a reference point, the azimuth angle and the elevation angle of the kth target can be expressed as theta k And phi k (θ k ∈[0,π]，) At the same time, the included angles of the target and the coordinate system are alpha respectively k And beta k . The target signal satisfies the narrowband condition that the delay effect is equivalent to a phase shift of the baseband signal when the signal delay is much smaller than the inverse of the bandwidth. The snapshot number is L, and the received data matrices of the three subarrays can be respectively expressed as X, Y and Z:
X＝A x S+N x (1)
Y＝A y S+N y (2)
Z＝A z S+N z (3)
where S is a KXL-dimensional source signal matrix, otherwise N x ,N y And N y Then it is the noise matrix in M x L dimensions, finally a x ,A y And A z Then is formed by azimuth angle theta k And elevation angle phi k An M x K dimensional vector matrix is represented. At the same time the signal meets the narrowband condition, i.e. when the signal delay is much smaller than the inverse of the bandwidth, the delay effect amounts to a phase shift of the baseband signal.
According to the non-circular nature of the signal, there is s=Φs R The method comprises the steps of carrying out a first treatment on the surface of the Wherein the method comprises the steps of Is the non-circular phase of the signal. Equations (1) (2) and (3) can be written as
X＝A x ΦS R +N x (4)
Y＝A y ΦS R +N y (5)
Z＝A z ΦS R +N z (6)
Wherein the steering vector matrix can be expressed as:
A x ＝[a x (θ 1 ,φ 1 ) a x (θ 2 ,φ 2 )…a x (θ K ,φ K )] (7)
A y ＝[a y (θ 1 ,φ 1 ) a y (θ 2 ,φ 2 )…a y (θ K ,φ K )] (8)
A z ＝[a z (θ 1 ,φ 1 ) a z (θ 2 ,φ 2 )…a z (θ K ,φ K )] (9)
for the kth target, there is
a x (θ k ,φ k )＝[a x，0 (θ k ,φ k )…a x，M-1 (θ k ,φ k )] T (10)
a y (θ k ,φ k )＝[a y，0 (θ k ,φ k )…a y，M-1 (θ k ,φ k )] T (11)
a z (θ k ,φ k )＝[a z，0 (θ k ,φ k )…a z，M-1 (θ k ,φ k )] T (12)
Let the projection of the linear array 3 on the xoy plane and the included angle of the x axis be theta z The included angle between the linear array 3 and the z-axis is phi z According to the relation between the included angles of the three sub-linear arrays and the coordinate axis, the following steps are obtained:
since the steering vector is affected by the angle between the target-origin line and the linear array, it is possible to obtain
Wherein lambda is k Is the wavelength of the sound wave, i.e. the spacing d between two adjacent array elements of the uniform linear array is less than half the wavelength of the sound wave signal, and the velocity v of the sound wave on the detection path is unknown, so v is taken as the minimum in its range to determine lambda k Is a value of (2).
S2, calculating characteristic value parameters u corresponding to the three sub-linear arrays by using a non-circular signal one-dimensional DOA estimation algorithm based on NC-ESPRIT k ,v k And w k K=1, 2, …, K; can be obtained by combining the existing one-dimensional DOA estimation algorithm based on non-circular signals, such as NC-ESPRIT algorithm. Taking the sub-linear array 1 as an example, the received signal array can be reconstructed:
a row switching matrix J is first defined.
Reconstructing a received signal matrix by using the row switching matrix J, and reconstructing the reconstructed received signal matrix W x Expressed as:
wherein the method comprises the steps ofAnd construct W x Covariance matrix R of (2) w ：
Wherein R is s Is the source letterNumber real part S R Is used for the co-variance matrix of (a),is the variance of the noise component, I 2M Is a unit matrix, for covariance matrix R w Decomposing the characteristic value to obtain
Because of the signal subspace U s And B is connected with x The relation of (2) is: span { U s }＝span{B x -so that there is a full order matrix T such that U s T=b. Definition matrix T 1 ＝[0 (M-1)×1 I M-1 ]，T 2 ＝[I M-1 0 (M-1)×1 ]Line switching matrixWherein->Is a zero matrix of (M-1) x M dimensions.
In actual case, covariance matrix R w Estimate of (2)Obtained by sampling
Wherein L is the number of shots,
for a pair ofCharacteristic decomposition is carried out to obtain a characteristic vector matrix U s * Estimate of +.>Construction of matrix->And performing a second feature decomposition on the matrix to obtain a feature vector matrix delta x (diagonal matrix):
obtaining u k K=1, 2, … K; parameters v corresponding to the linear arrays 2 and 3 can be obtained in the same way k And w k . Wherein v is k The corresponding expression is written as:
since the linear array 3 is an array with one end fixed to the origin for free rotation, w is k The corresponding expression is written as:
s3, three groups of characteristic value parameters (i.e. u) k ,v k And w k K=1, 2, …, K) performs parameter pairing; the method adopts 3-parameter pairing based on subspace projection angles, and is suitable for the array configuration proposed by the patent;
first, constructing Q= [ X, Y, Z by using received data matrix] T ＝A·S+N Q Wherein N is Q For the corresponding 3M x L dimensional noise matrix, the steering vector matrix A is represented by A x ，A y And A z The structure is as follows:
further, obtainTaking the covariance matrix R of Q Q The method comprises the following steps:
for R Q Performing eigenvalue decomposition to obtain corresponding noise subspace U NQ Since the steering vector matrix has an orthogonal relationship with the noise subspace: a is that H ·U NQ =0 sum
The cost function F can be constructed as follows:
construction of the guide vector a (θ) i ,φ i )＝[u,v,w] T Wherein u, v and w are vectors of K×1 dimension, and are three sets of eigenvalue parameters u k ,v k And w k Is arranged and combined together to form K 3 And (3) group guide vectors, wherein the combination corresponding to the K groups with the maximum value of the cost function is the combination of successful parameter pairing.
S4, solving a two-dimensional direction-of-arrival estimation solution of the target, namely solving an azimuth angle theta for the K-th=1, 2, … and K targets k And elevation angle phi k Is used for the estimation of the estimated value of (a). For the kth target, find the azimuth θ k And elevation angle phi k Is used for the estimation of the estimated value of (a). Parameter u completed by the last step of pairing k ,v k And w k K=1, 2, …, K, the azimuth θ can be obtained k And elevation angle phi k Is estimated by (a):
s5, obtaining N under the condition of different array included angles 2 And carrying out window function weighting processing on the group estimation values to obtain an optimal estimation result. Two uniform linear arrays are adjustedThe angles Δx and Δy between them, where Δx is taken as N groups and Δy is taken as N groups, each time (Δx is obtained i ,Δy j ),i＝0,1，2,…,N-1,j＝0,1，2,…,N-1。
Let the n.i+j times of estimation, the included angle between two uniform linear arrays isAnd (3) repeating the steps one to five to obtain an estimated value of the Nth group i+j of the target direction of arrival estimation, wherein i, j=0, 1,2, … and N-1. Due to the angle (Deltax for different linear arrays i ,Δy j ) Obtaining the corresponding direction of arrival angle by the formula (29), and estimating the result p ij The method comprises the following steps:
MATLAB simulation results show that when the target incidence direction is located between 2 sub-linear arrays of the two-dimensional linear array with the adjustable included angle, the smaller the included angle of the linear array is, the more accurate the DOA estimation result is. According to the conclusion, the patent is directed to N 2 The results are windowed to obtain the optimal estimation results. Firstly, a two-dimensional angle interval of a target is obtained, and the angle interval is equal to N 2 Averaging the group estimation results to obtain average estimation values of K targets/>
Average according to the kth targetJudging the two-dimensional angle interval of the target, if
Then the kth target is considered to be at (n) k ,m k ) A two-dimensional angle interval. Constructing a weighting gain matrix G ij ：
G ij ＝diag{g(i-Δ i1 ,j-Δ j1 ),g(i-Δ i2 ,j-Δ j2 ),…,g(i-Δ iK ,j-Δ iK )} (33)
Where g (i, j) is a two-dimensional window function (e.g., gaussian, hamming, rectangular, chebyshev, etc.), offset Δ ik And delta jk In relation to the two-dimensional angular interval in which the kth object is located, there is the following relationship:
for N 2 The group estimation results are subjected to window function weighting to obtain optimal estimation values P of K targets:
example two
The embodiment discloses a two-dimensional underwater direction of arrival estimation device of unknown sound velocity environment based on a three-dimensional uniform linear array with an adjustable two-dimensional included angle, wherein the estimation device comprises a data processing and control module, a transmitting module, a receiving module, an output module and a power supply module, as shown in fig. 1 and 2.
The data processing and controlling module consists of a pair of multipath A/D, D/A converters and a processor, and is the core part of the whole device, and all other modules are directly connected with the data processing and controlling module. The device can control the transmitting module to enable the transmitting module to transmit the appointed signal; the included angle adjustable linear array of the receiving module can be controlled, so that the linear array 1 and the linear array 2 are kept fixed, and the linear array 3 can freely rotate by taking the connecting point as the center and can be rotated to a set value; meanwhile, the method can process the signals transmitted by the receiving module, calculate the direction of arrival angle through the algorithm of the invention, and then transmit the result to the output module.
The receiving module comprises 3 ultrasonic probe arrays which are placed at uniform intervals, a stepping motor and a stepping motor driving circuit. The stepping motor is an open loop control motor which converts an electric pulse signal into angular displacement or linear displacement, and when the stepping motor driving circuit receives a pulse signal, the stepping motor is driven to rotate by a fixed angle according to a set direction, which is called a step angle. The desired angle value can be achieved by having the data processing and control module transmit a certain number of pulse signals. As shown in fig. 3, the linear array 1 is arranged on the x-axis of the coordinate system and kept fixed, and the linear array 2 is arranged on the y-axis of the coordinate system and kept fixed, and because the receiving module is placed in water, the fixing support is made of plastic materials so as to increase buoyancy. The linear arrays 3 are respectively installed on the stepper motor 1 and the stepper motor 2, and can be driven to rotate by the stepper motor, so that the aim of adjusting the included angle of 2 dimensions is achieved, fig. 4 is a connection rotation schematic diagram of the linear arrays 3 and the stepper motor, and the stepper motor 1 and the stepper motor 2 are connected with the linear arrays 3 through rotating rotors to control 2-degree-of-freedom rotation of the linear arrays 3 as shown in the drawing.
The transmitting module consists of an impedance matching circuit and an ultrasonic transmitting probe, is connected with the processor through the D/A converter, and can transmit specified signals according to instructions sent by the processor.
The output module consists of a USB interface and a display and is connected with the data processing and control module and the power supply module. The device can provide man-machine interaction, and output the data processed in the data processing and control module to an external device or display the data on a display through a USB interface.
The power module consists of a power supply and is connected with the data processing and control module, the transmitting module, the receiving module and the output module. It is able to power these modules.
The main working flow of the device is as follows: in the actual measurement process, according to the signal parameters required to be transmitted, the corresponding parameters are input through the data processing and control module, so that the processor generates corresponding digital signals, the digital signals are transmitted to the transmitting module after D/A conversion, and the ultrasonic transmitting probe can generate and transmit the required signals. The included angle value deltax between the linear array 1 and the linear array 3 and the included angle value deltay between the linear array 2 and the linear array 3 can be set through a data processing and control module, and the processor sends a specific pulse signal to the stepping motor driving circuit and then drives the stepping motor to rotate to a required angle. The receiving array in the receiving module receives the signal reflected from the target sound source, converts the signal into a digital signal through A/D, and sends the digital signal to the processor, and then the processor calculates the result according to the algorithm provided by the invention. And finally, the data processing and control module transmits the calculation result to the output module, and the output module transmits the result to external equipment through a USB interface or displays the result through a display. The power module supplies power to all other modules.
Example III
The embodiment discloses a two-dimensional underwater direction of arrival estimation device of unknown sound velocity environment based on a three-dimensional uniform linear array with an adjustable two-dimensional included angle, wherein the estimation device comprises a data processing and control module, a transmitting module, a receiving module, an output module and a power supply module, as shown in fig. 1 and 2.
The data processing and control module can be realized by a DSP chip (such as a DSP chip of TMS320VC5509A model of TI company), the DSP chip can realize the functions of A/D conversion and D/A conversion, and can realize the calculation of a rotation operator and a final direction of arrival of the three-dimensional uniform linear array;
the stepping motor in the receiving module adopts a 23HY6606-CP model motor of Toshiba company, the stepping angle of the stepping motor is 1.8 degrees, and the stepping motor driving circuit adopts a TC78S600FTG type chip of Toshiba company. In addition, the receiving module also uses 2 fixed uniform linear arrays and 1 freely rotating uniform linear arrays, wherein each array comprises a plurality of ultrasonic receiving probes, and the number of the ultrasonic receiving probes is the same, and 3 uniform arrays are assembled according to the figure 3; the transmitting module uses an ultrasonic transmitting probe; the output module uses a USB interface and an LCD display. Fig. 1 is a block diagram of a hardware structure of the device according to the present invention.
The main working steps of the invention are as follows:
step T1, the specific devices are connected according to FIG. 2, wherein each of the receiving modules is uniformThe number M of array elements in the linear array is always 8. The data processing and control module is used for sending instructions to control the ultrasonic transmitting probe to transmit ultrasonic signals s (t), the transmitted signals are BPSK signals with initial phases of 20 degrees and non-circular rate rho=1, and the frequency of the signals is f s =10 kHz, pulse length 5ms; the minimum sound velocity in the sea water is 1430m/s to 1550m/s, and the minimum half wavelength is 7.15cm. The average distance between two uniform linear arrays is set to be 5cm, namely the first array element and the last array element are separated by 35cm. The distance between any two adjacent linear arrays is required to be smaller than 7.15cm, and the array element spacing can be selected arbitrarily under the condition that the limiting condition is met, wherein the spacing between 3 uniform linear arrays is 4cm. The included angle deltax between the linear array 1 and the linear array 3 is set to be 18 degrees, 36 degrees, 54 degrees, 72 degrees, 90 degrees, 108 degrees, 126 degrees, 144 degrees, 162 degrees, 180 degrees, and the included angle deltay between the linear array 2 and the linear array 3 is also set to be 8 different linear array included angles which are 18 degrees, 36 degrees, 54 degrees, 72 degrees, 90 degrees, 108 degrees, 126 degrees, 144 degrees, 162 degrees, 180 degrees, namely all included angle combinations are n=64. Setting a linear array included angle value at a data processing and control module, and firstly converting an even linear array included angle delta x into 18 degrees, wherein an included angle delta y is also set to be converted into 18 degrees. A target sound source is placed under water, and the two-dimensional direction of arrival angle of the target sound source incident on the horizontal array is (60 degrees, 45 degrees).
Step T2, sampling a target sound source signal received by the ultrasonic receiving probe linear array; the signal received by the linear array 1 is x 1 (t),x 2 (t),…,x 8 (t) the signal received by the linear array 2 is y 1 (t),y 2 (t),…,y 8 (t) the signal received by the linear array 3 is z 1 (t),z 2 (t),…,z 8 (t). And the sampling is carried out for 200 times, and the received signals are transmitted to a data processing and control module for analysis processing.
The analyzing and processing steps of the signals in the processing module in the step T3 are specifically as follows:
1) According to the received signals, respectively obtaining 3 uniform linear arrays of received signal matrixes X, Y and Z, and then using a one-dimensional NC-ESPRIT algorithm based on non-circular signals to obtain a corresponding parameter u k ,v k And w k ,k＝1,2,…,K。
2) By using the determined parameter u k ,v k And w k K=1, 2, …, K, pairing of three sets of parameters was performed. And performing full combination traversal of the parameters, and traversing and finding out the parameter combination corresponding to the maximum value of the cost function F, namely finishing parameter pairing.
3) Solving the two-dimensional direction-of-arrival estimation solution of the target, i.e. for the kth target, solving the azimuth angle θ k And elevation angle phi k Is used for the estimation of the estimated value of (a). The parameters which are successfully paired are used for respectively solving K two-dimensional direction-of-arrival angles (azimuth angle theta and elevation angle phi) according to a formula (29).
And step T4, storing the calculated two-dimensional direction-of-arrival angle information, and transmitting the information to an output module, so that the information is output to an external device through a USB interface or displayed on an LCD display screen.
And step T5, according to the setting, using angles of 18 degrees, 36 degrees, 54 degrees, 72 degrees, 90 degrees, 108 degrees, 126 degrees, 144 degrees, 162 degrees and 180 degrees, and rotating the linear array 3 to change the included angle delta x and the included angle delta y. And divided into 64 measurements. And finally, carrying out two-dimensional Gaussian window function weighting processing according to a formula (35) according to the result obtained by each calculation, and estimating the two-dimensional direction of arrival angle (60.15 degrees, 44.89 degrees) according to the algorithm of the invention, so that the target estimation reaches the expected precision, and the estimation result is accurate.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (8)
1. An angle-adjustable three-dimensional array-based non-circular signal underwater DOA estimation method is characterized in that the estimation method is used for measuring N 2 The method comprises the following steps of:
s1, establishing an array signal receiving model of a three-dimensional angle-adjustable uniform linear array, wherein the three-dimensional angle-adjustable uniform linear arrayThe array comprises an L-shaped array and a radial arm array with 2 degrees of freedom, wherein 2 subarrays of the L-shaped array are respectively arranged as a linear array 1 and a linear array 2, the radial arm array with 2 degrees of freedom is arranged as a linear array 3, the linear array 1 is arranged on an x-axis of a coordinate system, the linear array 2 is arranged on a y-axis of the coordinate system, the linear array 3 has the rotation characteristic with 2 degrees of freedom, an included angle between the linear array 3 and the linear array 1 is delta x, an included angle between the linear array 3 and the linear array 2 is delta y, the included angle delta x and the included angle delta y are adjustable, the linear array 1, the linear array 2 and the linear array 3 are uniform linear arrays and are provided with M receiving array elements, and the average spacing between the array elements is d; taking the origin of a coordinate system as a reference point, assuming that the total number of underwater targets incident on the array is K, the azimuth angle and the elevation angle of the kth target are expressed as theta k And phi k ，θ k ∈[0,π]，At the same time, the included angles between the target and the x-axis and the y-axis of the coordinate system are alpha respectively k And beta k The target signal meets the narrow-band condition, namely when the target signal delay is far smaller than the bandwidth reciprocal, the delay action is equivalent to making the baseband signal generate a phase shift, the snapshot number is set as L, and the received data matrixes of the linear array 1, the linear array 2 and the linear array 3 are respectively denoted as X, Y and Z
X＝A x S+N x (1)
Y＝A y S+N y (2)
Z＝A z S+N z (3)
Where S is a KXL-dimensional source signal matrix, N x ，N y And N y Then it is the noise matrix in M x L dimensions, A x 、A y And A z Then is formed by azimuth angle theta k And elevation angle phi k An M x K-dimensional vector matrix of representations;
according to the non-circular nature of the signal, there is s=Φs R Wherein For the non-circular phase of the signal, equations (1), (2) and (3) are written as
X＝A x ΦS R +N x (4)
Y＝A y ΦS R +N y (5)
Z＝A z ΦS R +N z (6)
Wherein the steering vector matrix A x 、A y And A z Expressed as:
A x ＝[a x (θ 1 ,φ 1 ) a x (θ 2 ,φ 2 )…a x (θ K ,φ K )] (7)
A y ＝[a y (θ 1 ,φ 1 ) a y (θ 2 ,φ 2 )…a y (θ K ,φ K )] (8)
A z ＝[a z (θ 1 ,φ 1 ) a z (θ 2 ,φ 2 )…a z (θ K ,φ K )] (9)
for the kth target, there is
a x (θ k ,φ k )＝[a x，0 (θ k ,φ k )…a x，M-1 (θ k ,φ k )] T (10)
a y (θ k ,φ k )＝[a y，0 (θ k ,φ k )…a y，M-1 (θ k ,φ k )] T (11)
a z (θ k ,φ k )＝[a z，0 (θ k ,φ k )…a z，M-1 (θ k ,φ k )] T (12)
Let the projection of the linear array 3 on the xoy plane and the included angle of the x axis be theta z The included angle between the linear array 3 and the z-axis is phi z According to the relation between the included angles of the linear array 1, the linear array 2 and the linear array 3 and the coordinate axis,the method comprises the following steps:
since the steering vector is affected by the angle between the target-origin line and the linear array, it is obtained
Wherein lambda is k Is the wavelength of the sound wave, i.e. the spacing d between two adjacent array elements of the uniform linear array is less than half the wavelength of the sound wave signal, and the velocity v of the sound wave on the detection path is unknown, so v is taken as the minimum in its range to determine lambda k Is a value of (2);
s2, solving characteristic value parameters u corresponding to the linear arrays 1,2 and 3 by utilizing a non-circular signal one-dimensional DOA estimation algorithm based on NC-ESPRIT k 、v k And w k ，k＝1,2,…,K；
Reconstructing a received signal array for a linear array 1, first defining a row switching matrix J
Reconstructing a received signal matrix by using the row switching matrix J, and reconstructing the reconstructed received signal matrix W x Expressed as:
wherein the method comprises the steps ofAnd construct W x Covariance matrix R of (2) w ：
Wherein R is s Is the real part S of the source signal R Is used for the co-variance matrix of (a),is the variance of the noise component, I 2M For covariance matrix R, the unit matrix is 2Mx2M w Decomposing the characteristic value to obtain
Because of the signal subspace U s And B is connected with x The relation of (2) is: span { U s }＝span{B x -so that there is a full order matrix T such that U s T=b, defining a matrix T 1 ＝[0 (M-1)×1 I M-1 ]、T 2 ＝[I M-1 0 (M-1)×1 ]Line switching matrixWherein->A zero matrix of (M-1) x M dimension;
covariance matrix R w Estimate of (2)Obtained by sampling
Wherein L is the number of shots,
for a pair ofCharacteristic decomposition is carried out to obtain a characteristic vector matrix U s * Estimate of +.>Construction of matrix->And performing a second feature decomposition on the matrix to obtain a feature vector matrix delta x ，δ x Is a diagonal matrix:
obtaining u k ,k＝1,2,…K；
The parameters v corresponding to the linear array 2 and the linear array 3 are obtained by the same method k And w k Wherein v is k The corresponding expression is written as:
since the linear array 3 is an array with one end fixed to the origin for free rotation, w is k The corresponding expression is written as:
s3, characteristic value parameters u corresponding to the linear array 1, the linear array 2 and the linear array 3 in the three-dimensional array with the adjustable included angle k 、v k And w k Carrying out parameter pairing;
s4, solving a two-dimensional direction-of-arrival estimation solution of the target, namely solving an azimuth angle theta for the K-th=1, 2, … and K targets k And elevation angle phi k Is a function of the estimated value of (2);
s5, obtaining N under the condition of different array included angles 2 And performing windowing function processing on the group estimation values to obtain an optimal estimation result.
2. The method for estimating underwater DOA of non-circular signals based on an angle-adjustable three-dimensional array according to claim 1, wherein the step S3 comprises the following steps:
first, a matrix Q= [ X, Y, Z is constructed] T ＝A·S+N Q Wherein N is Q For the corresponding 3M x L dimensional noise matrix, the steering vector matrix A is represented by A x 、A y And A z The composition comprises:
A＝[A x ,A y ,A z ] T (26)
acquiring covariance matrix R of Q Q The method comprises the following steps:
R Q ＝Q·Q H (27)
for R Q Performing eigenvalue decomposition to obtain corresponding noise subspace U NQ Since the steering vector matrix has an orthogonal relationship with the noise subspace, namely: a is that H ·U NQ =0 sumThe construction cost function F is as follows:
construction of the guide vector a (θ) i ,φ i )＝[u,v,w] T Wherein u, v, w are K×1-dimensional vectors, respectively three sets of eigenvalue parameters u k ，v k And w k Is arranged and combined together to form K 3 And (3) group guide vectors, wherein the combination corresponding to the K groups with the maximum value of the cost function is the combination of successful parameter pairing.
3. The method for estimating underwater DOA of non-circular signals based on an angle-adjustable three-dimensional array according to claim 2, wherein the process of solving the two-dimensional direction of arrival estimation solution of the target in the step S4 is as follows:
for the kth target, find the azimuth θ k And elevation angle phi k Using the parameter u after pairing in step S3 k 、v k And w k Obtain azimuth angle theta k And elevation angle phi k Is estimated by (a):
4. the method for estimating underwater DOA of non-circular signals based on three-dimensional array with adjustable included angles according to claim 3, wherein the processing of the N sets of estimated values obtained under the condition of different included angles of the array in the step S5 is as follows:
adjusting the included angles delta x and delta y between the two uniform linear arrays, wherein delta x is N groups, delta y is N groups, and each time (delta x is obtained i ,Δy j ) I, j=0, 1,2, …, N-1, let n·i+j estimate, the angle between two uniform linear arrays beRepeating steps S1 to S5 to obtain the estimated value of the Nth group of i+j of the target direction of arrival estimation, wherein the estimated value is calculated according to the different linear array included angles (deltax i ,Δy j ) Obtaining the corresponding direction of arrival angle by the formula (29), and estimating the result p ij The method comprises the following steps:
for N 2 Windowing the results to obtain optimal estimation results, firstly, obtaining a two-dimensional angle interval of a target, and performing N 2 Averaging the group estimation results to obtain average estimation values of K targets
Average according to the kth targetJudging the two-dimensional angle interval of the target, if
Then the kth target is considered to be at (n) k ,m k ) A two-dimensional angle interval;
constructing a weighting gain matrix G ij ：
G ij ＝diag{g(i-Δ i1 ,j-Δ j1 ),g(i-Δ i2 ,j-Δ j2 ),…,g(i-Δ iK ,j-Δ iK )} (33)
Where g (i, j) is a two-dimensional window function, offset delta ik And delta jk In relation to the two-dimensional angular interval in which the kth object is located, there is the following relationship:
for N 2 The group estimation results are subjected to window function weighting to obtain optimal estimation values P of K targets:
5. the method for estimating underwater DOA of non-circular signals based on a three-dimensional array with adjustable included angles according to claim 4, wherein the two-dimensional window function g (i, j) is a Gaussian window, a Hamming window, a rectangular window or a Chebyshev window.
6. An estimation device based on the angle-adjustable three-dimensional array non-circular signal underwater DOA estimation method according to any one of claims 1 to 5, wherein the estimation device comprises a data processing and control module, and a transmitting module, a receiving module, an output module and a power module which are respectively connected with the data processing and control module, wherein the data processing and control module comprises an A/D converter, a D/A converter and a processor which are sequentially connected,
the transmitting module comprises a power amplifier, an impedance matching circuit and an ultrasonic transmitting probe which are sequentially connected, and is connected with the processor through the D/A converter, and transmits a specified non-circular signal according to an instruction sent by the processor;
the receiving module adopts a three-dimensional angle-adjustable uniform linear array, the three-dimensional angle-adjustable uniform linear array comprises an L-shaped array and a radial arm array with 2 degrees of freedom, wherein 2 subarrays of the L-shaped array are respectively arranged as a linear array 1 and a linear array 2, the radial arm array with 2 degrees of freedom is arranged as a linear array 3, the linear array 1 is arranged on an x-axis of a coordinate system, the linear array 2 is arranged on a y-axis of the coordinate system, the linear array 3 has the rotation characteristic with 2 degrees of freedom, the angle between the linear array 3 and the linear array 1 is delta x, the angle between the linear array 3 and the linear array 2 is delta y, the angle delta x and the angle delta y are adjustable, the linear array 1, the linear array 2 and the linear array 3 are uniform linear arrays and all have M receiving array elements, and the average distance between the array elements is d;
the output module comprises a USB interface and a display, and outputs the data processed in the data processing and control module to an external device or the display for display through the USB interface;
the power module is respectively connected with the data processing and control module, the transmitting module, the receiving module and the output module and supplies power.
7. The device for estimating underwater DOA based on non-circular signals of three-dimensional array with adjustable included angle according to claim 6, wherein the linear array 3 is installed on the stepper motor 1 and the stepper motor 2 respectively, the stepper motor is an open loop control motor which converts the electric pulse signal into angular displacement or linear displacement, when the stepper motor driving circuit receives a pulse signal, it drives the stepper motor to rotate a fixed angle according to the set direction, called as the step angle, and the data processing and control module transmits a certain number of pulse signals to reach the desired angle value.
8. The device for estimating the underwater DOA of the non-circular signal based on the three-dimensional array with the adjustable included angle according to claim 6, wherein the linear array 1, the linear array 2 and the linear array 3 are connected through a fixed support made of plastic materials.
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