Method for searching underwater object by using ultra-short baseline of L-shaped co-prime array

Abstract

According to the method for searching the underwater object by using the ultra-short baseline of the L-shaped co-prime array, a ship or an aircraft travels and is berthed in a water surface area near the underwater object or on the water surface area, a coordinate system is established by taking a certain point of the ship or the aircraft as a coordinate origin, a base station is arranged on the origin, N + M-2 array elements are respectively arranged on an X axis and a Y axis, N and M are both prime numbers, and M is a prime number; the included angle between the underwater object and the X axis is alpha, the included angle between the underwater object and the Y axis is beta, the included angle between the underwater object and the Z axis is psi, the position of the underwater object in a coordinate system is (X, Y, Z), and the method for searching the underwater object by using the ultra-short baseline of the L-shaped co-prime array comprises the following steps: transmitting and receiving acoustic signals; determining a distance; constructing a received signal model; determining an incident angle to obtain alpha, beta and psi; calculating the position of the underwater object: X = Rcos alpha; y is equal to Rcos beta; according to the invention, the large aperture of the sparse array and the advantages of small array size and convenient installation of the ultra-short baseline positioning system are fully utilized.

Description

Technical Field

[0001] The present invention relates to the field of underwater positioning, and particularly to a method for finding underwater objects using a super short baseline of an L-shaped co-prime array. Background Art

[0002] Super short baseline positioning is a technology applied to underwater acoustic positioning and is widely used in fields such as ocean exploration, resource exploration, underwater robot navigation, and military applications. Compared with traditional long baseline and short baseline positioning systems, the super short baseline system has the advantages of easy installation, low cost, and high accuracy. Array signal processing is an important branch of signal processing technology, which refers to processing the signals transmitted or received by the transceiver units of an array antenna to enhance useful signals, suppress noise and interference signals, or obtain parameter estimates from the received signals.

[0003] Traditional super short baseline array positioning is mainly based on time delay difference positioning. This type of method has the advantages of fast operation speed and easy hardware implementation, but there are also some disadvantages. In complex environments (such as underwater), the multipath effect is serious, resulting in signals arriving at the receiver through different paths, thereby affecting the accurate measurement of the time delay difference and reducing the positioning accuracy. Due to the very small time delay difference, the super short baseline array is sensitive to noise, and environmental noise and system noise will significantly affect the accuracy and stability of positioning.

[0004] The mainstream super short baseline array structures are mainly divided into two types: the four-element array and the eight-element array. They are both distributed in the same plane and are orthogonally distributed on the X-axis and Y-axis of the coordinate axis. Compared with the uniform array, the sparse array has a higher degree of freedom. In the case of the same number of array elements, as the array element spacing increases, the DOA estimation algorithm can obtain higher direction finding accuracy and resolution. Summary of the Invention

[0005] The object of the present invention of this application is to solve the inherent defects of time delay difference estimation, apply modern spectral estimation theory to super short baseline positioning, that is, replace the mainstream cross array with an L-shaped co-prime array, and provide a method for finding underwater objects using a super short baseline of an L-shaped co-prime array, which increases the array aperture and improves the DOA estimation accuracy.

[0006] To achieve the object of the present invention of this application, the following technical solutions are adopted in this application:

[0007] A method for finding underwater objects using an L-shaped co-prime array with ultra-short baseline. A ship or aircraft sails and anchors in the water area near or on the water surface of the underwater object. A transponder is installed on the underwater object. A coordinate system is established with a certain point on the ship or aircraft as the coordinate origin. The X-axis and Y-axis are the horizontal and vertical axes respectively, and the Z-axis is the vertical axis. A base station is arranged at the origin, and N + M - 2 array elements are arranged on the X-axis and Y-axis respectively. The array elements on the X-axis and Y-axis are evenly distributed on the X-axis and Y-axis. d is the spacing between the array elements on the X-axis and Y-axis, and S is the distance between the first array element on the X-axis and Y-axis and the origin. Both N and M are prime numbers. Suppose the angle between the underwater object and the X-axis is α, the angle with the Y-axis is β, and the angle with the Z-axis is ψ. The position of the underwater object in this coordinate system is (X, Y, Z). The underwater object is located in the underwater plane parallel to the plane formed by the X-axis and Y-axis. In the above underwater plane, there are an auxiliary X'-axis, Y'-axis and an auxiliary origin O'. The angle between the line connecting the underwater object and the auxiliary origin O' and the Y'-axis is θ, where:

[0008] (1). Transmitting and receiving acoustic signals

[0009] The base station transmits an acoustic signal with a specific frequency. After receiving the signal, the underwater object immediately sends a response signal. The base station records the time difference T between the transmitted and received response signals T,R ;

[0010] (2). Determining the distance

[0011] The distance between the base station and the underwater object is

[0012] where: c is the propagation speed of sound in water, c = 1449.2 + 4.6T - 0.055T 2 + 0.00029T 3 ----Formula (2), T is the temperature of water in degrees Celsius, and the unit of c is m / s; T T,R is the time difference recorded by the base station from transmission to reception;

[0013] (3). Constructing the received signal model

[0014] According to the geometric relationship, we get:

[0015] cosα = sinψcosθ ---- Formula (3)

[0016] cosβ = sinψsinθ ---- Formula (4)

[0017] (4). Determining the incident angle

[0018] By derivation, the relationship of the spectral density function of the array is obtained,

[0019]

[0020] is the true incident angle. When is orthogonal to the noise subspace U N the denominator approaches 0, that is: U N when the multiplication is 0, the spectral value P appears as a peak, where: U N is the noise subspace,

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] where: λ is the wavelength, and its value is 20 cm; d is the element spacing, and its value is 10 cm; j is a complex number; θ i is the trial value of θ; β i is the trial value of β; the value range of θ is within 0 - 90°, increasing with a step of 1°; the value range of β is within 0 - 90°, increasing with a step of 1°; through trial calculation, obtain when it is orthogonal to the noise subspace U N the θ and β; and according to the formula and the formula, deduce: cosα = (cosβ) / (tanθ) --- formula (11) to obtain α; sinψ = (cosα) / (cosθ) --- formula (12) to obtain ψ;

[0027] (V). Calculate the position of the underwater object

[0028] Through the above θ, β and ψ, obtain the position of the underwater object

[0029] X = Rcosα; Y = Rcosβ; Z = Rcosψ.

[0030] The method for finding an underwater object using the ultra - short baseline of an L - type coprime array in the present invention, where: N = 2, M = 3, S = 0.2 m, three elements are arranged in the X - axis direction, and their coordinates are respectively (0.2 m, 0 m), (0.3 m, 0 m) and (0.4 m, 0 m); three elements are arranged in the Y - axis direction, and their coordinates are respectively (0 m, 0.2 m), (0 m, 0.3 m) and (0 m, 0.4 m).

[0031] The method for finding underwater objects using the ultra-short baseline of an L-shaped co-prime array in the present invention, wherein: the two-dimensional coordinate system composed of the X-axis and the Y-axis is defined within a 1000m×1000m area, divided into 100×100 positions for positioning, the signal-to-noise ratio is set to 5dB, and the number of Monte Carlo simulations is 100 times.

[0032] The method for finding underwater objects using the ultra-short baseline of an L-shaped co-prime array in the present invention, wherein: the U N The noise subspace is obtained in the following manner:

[0033] Let the covariance matrix of the array received signal be R, which is a Hermitian self-adjoint positive definite matrix. Perform eigenvalue decomposition on R:

[0034]

[0035] Among them, U S Corresponds to the first K largest eigenvalues, namely: the signal subspace, U N Corresponds to the last M+N-1-K smallest eigenvalues, namely: the noise subspace, Σ S = diag(λ1,...,λ K ), Σ N =(λ K+1 ,...,λ M+M-1 ), U H Represents the conjugate transpose of U, and

[0036] Suppose there are K independent signal sources, namely: the number of signals, K < N+M-1, then:

[0037] The signal subspace corresponds to the first K largest eigenvalues and their eigenvectors:

[0038] U s =[u1,u2,...,u K

[0039] The noise subspace corresponds to the last M+N-1-K smaller eigenvalues and their eigenvectors. The explicit expression of the noise subspace is

[0040] U N =[u K+1 ,u K+2 ,...,u M+N-1

[0041] These eigenvectors correspond to the smallest M+N-1-K eigenvalues of the covariance matrix R.

[0042] The method for finding underwater objects using the ultra-short baseline of an L-shaped co-prime array in the present invention, wherein: the ship is an underwater robot, a submersible or a vessel.

[0043] ​​The present invention discloses a method for finding underwater objects using an L-shaped co-prime array as an ultra-short baseline. Ultra-short baseline positioning is an underwater positioning technology widely used in underwater robots, submersibles, etc. A base station is installed on a ship or platform, and a transponder is installed on the underwater object for preliminary calibration; the base station emits an acoustic wave signal at a specific frequency, and the signal is transmitted to the underwater object; after receiving the signal, the transponder immediately sends a response signal, which is received by the base station; the base station records the time difference between the emission and the reception of the response signal and calibrates it according to the sound speed in water; the distance between the base station and the target device is calculated using the time difference and the sound speed; the arrival angle of the signal is determined through two-dimensional signal direction-of-arrival estimation; the three-dimensional position of the target device is calculated through triangulation by combining the distance and angle information; the data is filtered and error-corrected to display the position of the underwater object; the base station continuously updates the position of the underwater object and dynamically adjusts parameters to maintain high-precision positioning. The present invention uses an L-shaped co-prime array as the receiving array for ultra-short baseline positioning, making full use of the advantages of the large aperture of the sparse array and the small size and convenient installation of the ultra-short baseline positioning system array.

[0044] The ultra-short baseline positioning of the present invention is an underwater positioning technology widely used in underwater robots, submersibles, etc. The system operates in a synchronous beacon mode, obtaining the slant range of the target through the one-way propagation time. The array elements are located on two mutually perpendicular baselines (i.e., on the x-axis and y-axis), and the angles between the acoustic rays emitted by the base station and the x-axis and y-axis are α k and β k . The array structure used is an L-shaped co-prime array composed of relatively prime numbers M = 2 and N = 3. The x-axis and y-axis start from the same array element at the origin and form an L-shaped array by two identical co-prime linear arrays on the x-axis and y-axis. The ultra-short baseline positioning system has been widely applied in the fields of ocean engineering, marine mineral resources, underwater archaeology, marine national defense, etc. due to its advantages such as small size, low cost, and strong flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flowchart of the present invention;

[0046] Figure 2 is an array structure diagram of the present invention;

[0047] Figure 3 is the signal waveform of the present invention;

[0048] Figure 4 is the root mean square error positioning effect diagram of the position error within one square kilometer of the present invention under a signal-to-noise ratio of 10 dB; Figure 4 (a) represents the three-dimensional view of the positioning error, Figure 4 (b) represents the contour map of the positioning error, Figure 4 (c) is Figure 4 a partial enlargement of (b);

[0049] Figure 5 This is the localization effect diagram of the root mean square error of angle estimation within one square kilometer under a 10 dB signal-to-noise ratio for the present invention; Figure 5 (a) represents the three-dimensional view of the positioning error, Figure 5 (b) represents the contour map of the positioning error, Figure 5 (c) is Figure 5 the partial enlargement of (b);

[0050] Figure 6 This is the localization effect diagram of the root mean square error of relative distance within one square kilometer under a 10 dB signal-to-noise ratio for the present invention; Figure 6 (a) represents the three-dimensional view of the positioning error, Figure 6 (b) represents the contour map of the positioning error, Figure 6 (c) is Figure 6 the partial enlargement of (b);

[0051] Figure 7 is the RMSE distribution diagram of the present invention, a four-element array, and an eight-element array. Figure 7(a) represents the contour map of the positioning error of the eight-element array, and Figure 7(b) is the partial enlargement of Figure 7(a); Figure 7(c) represents the contour map of the positioning error of the four-element array, and Figure 7(d) is the partial enlargement of Figure 7(c);

[0052] In Figure 2 , label 1 is the underwater object; label 2 is the ship or aircraft; label 3 is the array element; label 4 is the base station. Specific embodiments

[0053] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below in conjunction with specific embodiments.

[0054] As Figure 1 and Figure 2As shown in the figure, the method for finding underwater objects using the ultra-short baseline of the L-shaped co-prime array of the present invention is to make a ship or aircraft 2 travel and anchor in the water area near or on the water surface of the underwater object 1. The ship is an underwater robot, a submersible or a vessel. A transponder is installed on the underwater object 1. A coordinate system is established with a certain point on the ship or aircraft 2 as the coordinate origin. The X-axis and Y-axis are the horizontal axis and the vertical axis respectively, and the Z-axis is the vertical axis. The two-dimensional coordinates formed by the X-axis and Y-axis are limited within a 1000m×1000m area, which is divided into 100×100 positions for positioning. The signal-to-noise ratio is set to 5dB, and the number of Monte Carlo simulations is 100 times. A base station 4 is arranged at the origin, and N+M-2 array elements 3 are respectively arranged on the X-axis and Y-axis. The array elements 3 on the X-axis and Y-axis are evenly distributed on the X-axis and Y-axis. d is the distance between the array elements 3 on the X-axis and Y-axis, d = 0.1m, S is the distance between the first array element 3 on the X-axis and Y-axis and the origin, S = 0.2m, both N and M are prime numbers, N = 2; M = 3. Three array elements 3 are arranged in the X-axis direction, and their coordinates are (0.2m, 0m), (0.3m, 0m) and (0.4m, 0m) respectively; three array elements 3 are arranged in the Y-axis direction, and their coordinates are (0m, 0.2m), (0m, 0.3m) and (0m, 0.4m) respectively. Assume that the angle between the underwater object 1 and the X-axis is α, the angle with the Y-axis is β, and the angle with the Z-axis is ψ. The position of the underwater object 1 in this coordinate system is (X, Y, Z). The underwater object 1 is located in the underwater plane parallel to the plane formed by the X-axis and Y-axis. In the above underwater plane, there are an auxiliary X'-axis, Y'-axis and an auxiliary origin O'. The angle between the line connecting the underwater object 1 and the auxiliary origin O' and the Y'-axis is θ. This method includes the following steps:

[0055] (I). Transmitting and receiving acoustic signals

[0056] The base station 4 transmits an acoustic signal with a specific frequency. After receiving the signal, the underwater object 1 immediately sends a response signal. The base station 4 records the time difference T between the transmitted and received response signals T,R ;

[0057] (II). Determining the distance

[0058] The distance between the base station 4 and the underwater object 1 is

[0059] where: c is the propagation speed of sound in water, c = 1449.2 + 4.6T - 0.055T 2 + 0.00029T 3 ----Formula (2), T is the temperature of water, in degrees Celsius, and the unit of c is m / s; T T,R is the time difference recorded by the base station 4 from transmission to reception;

[0060] (3). Construct the received signal model

[0061] According to the geometric relationship, we get:

[0062] cosα = sinψcosθ ---- Equation (3)

[0063] cosβ = sinψsinθ ---- Equation (4)

[0064] (4). Determine the incident angle

[0065] By derivation, the relationship of the spectral density function of the array is obtained.

[0066]

[0067] is the true incident angle. When is orthogonal to the noise subspace U N , the denominator approaches 0, that is: When the multiplication is 0, the spectral value P appears as a peak, where: U N is the noise subspace.

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] Among them: λ is the wavelength, and its value is 20 cm; d is the element spacing, and its value is 10 cm; j is a complex number; θ i is the trial value of θ; β i is the trial value of β; the value range of θ is within 0 - 90°, increasing with a step of 1°; the value range of β is within 0 - 90°, increasing with a step of 1°; through trial calculation, we get when it is orthogonal to the noise subspace U N the θ and β; and according to the above Equation (3) and Equation (4), it is deduced that: cosα = (cosβ) / (tanθ) to obtain α; sinψ = (cosα) / (cosθ) to obtain ψ;

[0074] (5). Calculate the position of the underwater object 1

[0075] Through the above θ, β and ψ, the position of the underwater object 1 is obtained

[0076] X = Rcosα; Y = Rcosβ; Z = Rcosψ.

[0077] The derivation process is as follows:

[0078] The distance between the underwater object 1 and the origin is R, and the relationship between the coordinates X, Y and the depth h of the underwater object 1 is

[0079] R 2 = X 2 + Y 2 + h 2

[0080] Considering that the angles between the transponder and the x-axis and y-axis are α and β respectively, we get

[0081] X 2 = R 2 cos 2 α

[0082] Y 2 = R 2 cos 2 β

[0083] When using a transponder instead of a beacon, the distance can be obtained through the round-trip time T of the interrogation and response, that is T,R Obtained, that is

[0084]

[0085] Then, by solving cosα and cosβ, the x-coordinate and y-coordinate of the target can be obtained

[0086] α and β respectively represent the angles between the incident signal and the x-axis and y-axis. The geometric relationship between θ, ψ and α, β is

[0087] cosα = sinψcosθ

[0088] cosβ = sinψsinθ

[0089] (1). Received signal model

[0090] Suppose there are K far-field uncorrelated signals incident on the array, and the number of sensors on the X-axis is M + N - 2, then the received signal of the X-axis sensors is

[0091] X = A x S x + N x

[0092] where A x = [a x (Φ1), a x (Φ2), …, a x (Φ K )] is the array manifold in the X-axis direction

[0093] denotes the steering vector,

[0094] S x =[S x1 ,S x2 ,…,S xK is the source matrix, and S xk (1 ≤ k ≤ K) represents the signal vector received by the array,

[0095] N x is the Gaussian white noise matrix with zero mean received on the X-axis, (·) T denotes the matrix transpose.

[0096] Similarly, the number of sensors on the Y-axis is M + N − 2, and the received signal of the Y-axis sensors can be expressed as

[0097] Y = A y S + N y

[0098] where A y =[a y (Φ1), a y (Φ2), …, a y (Φ K )] is the array manifold in the Y-axis direction,

[0099] denotes the steering vector,

[0100] S y =[S y1 , S y2 , …, S yK is the source matrix, and S yk (1 ≤ k ≤ K) represents the signal vector received by the array,

[0101] N y is the noise matrix received on the Y-axis.

[0102] From the above analysis, the received signal S of the L-shaped array r is

[0103]

[0104] (2). Construct the corresponding covariance matrix according to the received signal

[0105] R = E[S r (t)S r H (t)]

[0106] In an actual situation, the covariance matrix R cannot be directly obtained. In this case, the sampled covariance matrix can be used.

[0107]

[0108] where P represents the number of snapshots, and R S = E[S(t)S H (t)] is the covariance matrix of the signal source; σ n is the noise power, and I is the identity matrix.

[0109] Performing eigenvalue decomposition on the covariance matrix gives:

[0110]

[0111] where U S corresponds to the first K largest eigenvalues (signal subspace), U N corresponds to the last M + N - 1 - K smallest eigenvalues (noise subspace), Σ S = diag(λ1,...,λ K ), Σ N =(λ K+1 ,...,λ M+M-1 ), U H represents the conjugate transpose of U, and

[0112]

[0113] According to the definition of the covariance matrix:

[0114]

[0115] At the same time, R can be expressed as:

[0116]

[0117] After expansion:

[0118]

[0119] From this, we can obtain:

[0120] AR S A H U N = 0

[0121] Since the received signal is a non-coherent signal, R S is a full-rank matrix and is non-singular, and A is column full-rank. Therefore, it can be written as:

[0122] A H U N = 0

[0123] This means that:

[0124]

[0125] that is, the array manifold A and the noise subspace U N are orthogonal.

[0126] Finally, from the orthogonality relationship between the noise subspace and the signal subspace, the spectral density function relationship of the array can be obtained:

[0127]

[0128] where θ i represents the elevation angle search space, i = 1, 2,..., K, represents the azimuth angle search space, j = 1, 2,..., K. When is the true incident angle, is orthogonal to U N and the denominator approaches 0, and the spectral value P appears as a peak. By searching for the spectral peak, the azimuth angle and elevation angle can be estimated.

[0129] At this time, the x coordinate and y coordinate of the target can be obtained

[0130] X = Rcosα

[0131] Y = Rcosβ

[0132] Through the relationship between the slant range R and X a and Y a the depth h can be solved

[0133]

[0134] The effects of the present invention will be further described below in conjunction with simulation examples.

[0135] The simulation scenario is set as follows: There are a total of 6 array elements 3, and their coordinates are (0.2 m, 0 m), (0.3 m, 0 m), (0.4 m, 0 m); (0 m, 0.2 m), (0 m, 0.3 m), (0 m, 0.4 m). The two-dimensional coordinate estimation is limited to a 1000 m × 1000 m area, divided into 100 × 100 positions for positioning, the signal-to-noise ratio is set to 5 dB, and the number of Monte Carlo simulations is 100 times.

[0136] In the simulation, in order to verify the performance of the ultra-short baseline positioning algorithm, the position coordinate estimation values of the nodes are estimated within the defined range, and the root mean square error (RMSE) of the position estimation, angle estimation, and relative distance error are used to evaluate the parameter estimation performance of the proposed algorithm.

[0137] The RMSE of position coordinate estimation is defined as

[0138]

[0139] where (x, y) is the actual two-dimensional position of the target in the positioning estimation, and the j-th result of the target position estimation is (x i , y i ), and the target position is estimated J times in total.

[0140] The RMSE estimation of angle estimation is defined as

[0141]

[0142] where γ is the actual two-dimensional position of the target in the positioning estimation, and the d-th result of the angle position estimation is γ i , and the target position is estimated D times in total.

[0143] The RMSE estimation of relative distance error estimation is defined as

[0144]

[0145] where (x, y) is the actual two-dimensional position of the target in the positioning estimation, and the l-th result of the target position estimation is (x i , y i ), and the target position is estimated L times in total.

[0146] Simulation 1: Figure 4 It is the distribution diagram of the RMSE estimation results of the position coordinate estimation of the method proposed by the invention at a signal-to-noise ratio of 10 dB. It can be seen from the figure that the algorithm can still effectively perform position estimation at a low signal-to-noise ratio.

[0147] Simulation 2: Figure 5 It is the distribution diagram of the RMSE estimation results of the angle estimation of the method proposed by the invention at a signal-to-noise ratio of 10 dB. It can be seen from the figure that the algorithm can still effectively perform angle estimation at a low signal-to-noise ratio.

[0148] Simulation 3: Figure 6 It is the distribution diagram of the RMSE estimation results of the relative distance error estimation of the method proposed by the invention at a signal-to-noise ratio of 10 dB. It can be seen from the figure that the algorithm can still effectively perform position estimation at a low signal-to-noise ratio.

[0149] Simulation 4: Figure 7 is the distribution diagram of the RMSE estimation results of the position coordinate estimation of the eight-element array and the four-element array at a signal-to-noise ratio of 10 dB. It can be seen from the figure that the RMSE of the proposed L-shaped array is smaller and the positioning accuracy is higher.

[0150] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, for those of ordinary skill in the art, it is still possible to modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions required to be protected by the present invention.

Claims

1. A method for finding underwater objects using an L-shaped co-prime array with ultra-short baseline. A ship or aircraft (2) sails and anchors in a water surface area near or on the water surface of an underwater object (1). A transponder is installed on the underwater object (1). A coordinate system is established with a certain point on the ship or aircraft (2) as the coordinate origin. The X-axis and Y-axis are the horizontal axis and vertical axis respectively, and the Z-axis is the vertical axis. A base station (4) is arranged at the origin, and N + M - 2 array elements (3) are arranged on the X-axis and Y-axis respectively. The array elements (3) on the X-axis and Y-axis are evenly distributed on the X-axis and Y-axis. d is the spacing between the array elements (3) on the X-axis and Y-axis, and S is the distance between the first array element (3) on the X-axis and Y-axis and the origin. Both N and M are prime numbers. Assume the angle between the underwater object (1) and the X-axis is α, the angle with the Y-axis is β, and the angle with the Z-axis is ψ. The position of the underwater object (1) in this coordinate system is (X, Y, Z). The underwater object (1) is located in an underwater plane parallel to the plane formed by the X-axis and Y-axis. In the above underwater plane, there are an auxiliary X'-axis, Y'-axis, and an auxiliary origin O'. The angle between the line connecting the underwater object (1) and the auxiliary origin O' and the Y'-axis is θ. It is characterized in that: (1). Transmit and receive acoustic signals The base station (4) emits an acoustic wave signal of a specific frequency. After receiving the signal, the underwater object (1) immediately sends a response signal, and the base station (4) records the time difference T between the emission of the signal and the reception of the response signal. T,R ; (2). Determine the distance The distance between the base station (4) and the underwater object (1) is where: c is the propagation speed of sound waves in water, c = 1449.2 + 4.6T - 0.055T 2 + 0.00029T 3 ----Formula (2), T is the temperature of water, in degrees Celsius, and the unit of c is m / s; T T,R is the time difference recorded by the base station (4) from transmission to reception; (3). Construct a received signal model According to the geometric relationship, we get: cosα = sinψcosθ ---- Formula (3) cosβ = sinψsinθ ---- Formula (4) (4). Determine the incident angle By derivation, the relationship of the spectral density function of the array is obtained. θ, is the true incident angle. When is orthogonal to the noise subspace U N , the denominator approaches 0, that is: U N multiplied is 0, the spectral value P appears as a peak, where: U N is the noise subspace, where: λ is the wavelength, with a value of 20 cm; d is the element spacing, with a value of 10 cm, j is a complex number; θ i is the trial value of θ; β i is the trial value of β; the value range of θ is within 0 - 90°, increasing in steps of 1°; the value range of β is within 0 - 90°, increasing in steps of 1°; through trial calculation, obtain when it is orthogonal to the noise subspace U N the θ and β; and according to the above formulas (3) and (4), deduce: cosα = (cosβ) / (tanθ) to obtain α; sinψ = (cosα) / (cosθ) to obtain ψ; (5). Calculate the position of the underwater object (1) Through the above α, β, and ψ, the position of the underwater object (1) is obtained. X = Rcosα; Y = Rcosβ; Z = Rcosψ.

2. The method for finding underwater objects using an L-shaped co-prime array with an ultra-short baseline as described in claim 1, characterized in that: N = 2, M = 3, S = 0.2m. Three array elements (3) are arranged in the X-axis direction, and their coordinates are (0.2m, 0m), (0.3m, 0m), and (0.4m, 0m) respectively; three array elements (3) are arranged in the Y-axis direction, and their coordinates are (0m, 0.2m), (0m, 0.3m), and (0m, 0.4m) respectively.

3. The method for finding underwater objects using an L-shaped co-prime array with an ultra-short baseline as claimed in claim 2, wherein: The two-dimensional coordinate formed by the X-axis and Y-axis is limited within a 1000m × 1000m area, divided into 100 × 100 positions for positioning. The signal-to-noise ratio is set to 5dB, and the number of Monte Carlo simulations is 100 times.

4. The method for finding underwater objects using the ultra-short baseline of the L-shaped co-prime array according to claim 3, characterized in that: The said U N The noise subspace is obtained in the following manner: Let the covariance matrix of the array received signal be R, which is a Hermitian self-adjoint positive definite matrix. Perform eigenvalue decomposition on R: Among them, U S corresponds to the first K largest eigenvalues, that is, the signal subspace, U N corresponds to the last M + N - 1 - K smallest eigenvalues, that is, the noise subspace, Σ S = diag(λ1,..., λ K ), Σ N =(λ K+1 ,..., λ M+M-1 ), U H denotes the conjugate transpose of U, and Suppose there are K independent signal sources, that is: the number of signals, K < N + M - 1, then: The signal subspace corresponds to the first K largest eigenvalues and their eigenvectors: U s = [u1, u2,..., u K ​ The noise subspace corresponds to the last M + N - 1 - K smaller eigenvalues and their eigenvectors. The explicit expression of the noise subspace is: U N = [u K+1 , u K+2 ,..., u M+N-1 ​ These eigenvectors correspond to the smallest M + N - 1 - K eigenvalues of the covariance matrix R.

5. The method for finding underwater objects using an L-shaped co-prime array with ultra-short baseline according to claim 4, characterized in that: The ship is an underwater robot, a submersible, or a vessel.

Images