Underwater moving target positioning method based on variable forgetting operator

Abstract

The invention discloses an underwater moving target positioning method based on a variable forgetting operator, and relates to the field of ocean engineering, in particular to the underwater moving target positioning method based on the variable forgetting operator. The objective of the invention is to solve the problem that the existing projection approximation subspace tracking algorithm cannot give consideration to both subspace estimation precision and convergence speed, and the problems that the ultra-short baseline positioning precision is low and the operating distance is short. The method specifically comprises the following steps: acquiring a response signal received by an ultra-short baseline array; establishing an objective function introducing a variable forgetting operator; based on an objective function, converting a solving problem of the signal subspace into an unconstrained minimization problem of the objective function, and solving the unconstrained minimization problem of the objective function through a recursive least square method to obtain a time-varying signal subspace; constructing a projection matrix, and performing subspace projection on the response signal received by the ultra-short baseline array based on the projection matrix to obtain a projected signal; and estimating the distance and orientation between the ship and the underwater target.

Description

Technical Field

[0001] The invention relates to the field of marine engineering, and in particular to an underwater moving target positioning method based on a variable forgetting operator. Background Art

[0002] With the rapid development of marine economy, the Ultra Short Baseline (USBL) positioning system plays an increasingly important role in marine engineering due to its advantages of small size, light weight, simple operation and flexible use. Various interferences such as platform directional interference and marine environmental noise in actual engineering will lead to low signal-to-noise ratio of received data, which restricts the further improvement of positioning accuracy of ultra short baseline system. In recent years, underwater interference suppression technology based on subspace method has been continuously developed, which generally requires estimation of signal subspace. However, in actual engineering, underwater targets to be located are usually moving, which causes the signal subspace to change over time. This requires the application of subspace tracking algorithms, among which the Projection Approximation Subspace Tracking (PAST) algorithm is currently the most robust and effective subspace tracking algorithm, but the fixed forgetting factor of the Projection Approximation Subspace algorithm cannot take into account both the subspace estimation accuracy and convergence speed. In addition, while the Projection Approximation Subspace algorithm is used to suppress platform directional interference and marine environmental noise, the amplitude and phase characteristics of the desired signal are affected. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the existing projection approximate subspace tracking algorithm cannot take into account both the subspace estimation accuracy and the convergence speed, as well as the problem of low ultra-short baseline positioning accuracy and short effective range, and propose an underwater moving target positioning method based on a variable forgetting operator.

[0004] A method for locating underwater moving targets based on a variable forgetting operator. The specific process is as follows:

[0005] Step 1: The ultra-short baseline array on the surface ship transmits an interrogation signal;

[0006] Step 2: After receiving the interrogation signal, the acoustic transponder on the underwater target replies with a response signal to the ultra-short baseline array;

[0007] Step 3: After receiving the reply signal, the ultra-short baseline array transmits it to the signal processing terminal; the signal processing terminal calculates the target position; the specific process is as follows:

[0008] Step 31: According to the subspace theory, the reply signal x(t) received by the ultra-short baseline array is obtained. The reply signal x(t) received by the ultra-short baseline array includes the desired signal, interference and noise.

[0009] Step 32: Based on the response signal x(t) received by the ultra-short baseline array, establish an objective function that introduces a variable forgetting operator;

[0010] Step 33: Based on the objective function with variable forgetting operator established in step 32, the signal subspace solution problem is transformed into an unconstrained minimization problem of the objective function, and the unconstrained minimization problem of the objective function is solved by recursive least squares method to obtain the time-varying signal subspace;

[0011] Step 34: construct a projection matrix based on the time-varying signal subspace obtained in step 33, and perform subspace projection on the response signal x(t) received by the ultra-short baseline array based on the projection matrix to obtain a projected signal;

[0012] Step 35: Estimate the distance between the ship and the underwater target based on the projected signal z(t) obtained in step 34;

[0013] The positions of the ship and the underwater target are estimated based on the projected signal z(t) obtained in steps three and four.

[0014] The beneficial effects of the present invention are:

[0015] The purpose of the present invention is to improve the positioning accuracy of an ultra-short baseline positioning system by effectively suppressing interference and noise in the ultra-short baseline positioning system.

[0016] The advantage of the present invention is that when the underwater target is moving, the subspace tracking algorithm based on the variable forgetting factor can accurately track the time-varying signal subspace, which is more suitable for real-time signal processing. Through the linear phase advantage of the subspace projection, the interference and noise in the ultra-short baseline system can be suppressed without affecting the amplitude and phase characteristics of the expected signal, thereby improving the positioning accuracy of the ultra-short baseline positioning system, extending the effective distance and reducing the calculation complexity.

[0017] The variable forgetting operator of the present invention can take into account both the subspace estimation accuracy and the convergence speed, thereby improving the positioning accuracy of the ultra-short baseline positioning system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flow chart of the algorithm of the present invention described in Example 1;

[0019] Figure 2 d is a diagram of the acoustic array structure of the ultra-short baseline positioning system in Example 2, where d is the distance;

[0020] Figure 3 1 is the output SINR gain curve in Example 2, (a) is the output SINR gain curve under SINR, and (b) is the output SINR gain curve under INR;

[0021] Figure 4 1 is the RMSE curve of delay estimation in Example 2, (a) is the RMSE curve output under SINR, and (b) is the RMSE curve output under INR. DETAILED DESCRIPTION

[0022] Specific implementation method 1: Combination Figure 1 This embodiment is described. The specific process of the underwater moving target positioning method based on a variable forgetting operator in this embodiment is as follows:

[0023] Step 1: The ultra-short baseline array on the surface ship transmits an interrogation signal;

[0024] Step 2: After receiving the interrogation signal, the acoustic transponder on the underwater target replies with a response signal to the ultra-short baseline array;

[0025] Step 3: After receiving the reply signal, the ultra-short baseline array transmits it to the signal processing terminal; the signal processing terminal calculates the target position; the specific process is as follows:

[0026] Step 31: According to the subspace theory, the reply signal x(t) received by the ultra-short baseline array is obtained (x(t)=λU(t)A(t)+V(t)B(t)+n(t)). The reply signal x(t) received by the ultra-short baseline array includes the desired signal, interference and noise.

[0027] Step 32: Based on the response signal x(t) received by the ultra-short baseline array, establish an objective function that introduces a variable forgetting operator;

[0028] Step 33: Based on the objective function of introducing a variable forgetting operator established in step 32, the signal subspace The problem of solving is transformed into the unconstrained minimization problem of the objective function. The unconstrained minimization problem of the objective function is solved by the recursive least squares method, and the time-varying signal subspace is obtained.<U(t)> ;

[0029] Step 34: Time-varying signal subspace obtained based on step 33<U(t)> Construct a projection matrix, and perform subspace projection on the reply signal x(t) received by the ultra-short baseline array based on the projection matrix (subspace projection suppresses interference and noise), and obtain the projected signal z(t);

[0030] Step 35: Estimate the distance between the ship and the underwater target based on the projected signal z(t) obtained in step 34;

[0031] The positions of the ship and the underwater target are estimated based on the projected signal z(t) obtained in steps three and four.

[0032] Specific implementation method 2: This implementation method is different from specific implementation method 1 in that, in step 31, according to the subspace theory, the response signal x(t) (x(t)=λU(t)A(t)+V(t)B(t)+n(t)) received by the ultra-short baseline array is obtained, and the response signal x(t) received by the ultra-short baseline array includes the desired signal, interference and noise; the specific process is:

[0033] Step 3: Assume that the ultra-short baseline array is a planar array consisting of N non-directional primitives, receiving L x sampling points;

[0034] t∈Ω x ={1,2,...,L x } is an N×1-dimensional column vector, Ω x represents the time series, t represents the time, L x Indicates the moment;

[0035] Step 3.12: Assume that the reply signal received by the ultra-short baseline array at time t is Contains expected signal interference and additive white Gaussian noise

[0036] x(t)=λs(t)+i(t)+n(t) (1)

[0037] in, Represents an N-dimensional complex field;

[0038] λ is the weighting coefficient of the desired signal;

[0039] When λ=1, the reply signal x(t) received by the ultra-short baseline array contains the desired signal, interference and additive white Gaussian noise.

[0040] When λ = 0, the reply signal x(t) received by the ultra-short baseline array contains only interference and additive white Gaussian noise;

[0041] Subspace theory shows that any high-dimensional vector in a linear space can be described by a finite number of features, which constitute a signal subspace.

[0042] Step 3: Assume that the expected signal s(t) is located in an independent subspace In the above example, the expected signal s(t) is represented as a column-full rank matrix Linear combinations of the columns of ;

[0043] Assume that the interference i(t) is located in an independent subspace <v>In the above example, the interference i(t) is represented as a column full rank matrix Linear combinations of the columns of ;

[0044] s(t)=UA(t) (2)

[0045] i(t)=VB(t) (3)

[0046] Among them, A(t) is the expected signal s(t) in the subspace The coordinates in m is the subspace The dimension of represents an m×1-dimensional complex field, and U represents a column-full rank matrix;

[0047] B(t) is the interference i(t) in the subspace <v>The coordinates in n is the subspace <v>The dimension of represents a complex field of n×1 dimensions, and V represents a column full rank matrix;

[0048] Step 314: Based on step 313, the response signal received by the ultra-short baseline array at time t is obtained; expressed as

[0049] x(t)=λUA(t)+VB(t)+n(t) (4)

[0050] Step 315: In actual situations, the target sound source usually moves, which causes the signal subspace to change over time. U and V are expressed as U=U(t) and V=V(t), respectively. The response signal received by the ultra-short baseline array at time t is further expressed as

[0051] x(t)=λU(t)A(t)+V(t)B(t)+n(t) (5)

[0052] Among them, U(t) represents U at time t, and V(t) represents V at time t.

[0053] The other steps and parameters are the same as those in the first or second embodiment.

[0054] Specific implementation method three: This implementation method is different from specific implementation method one or two in that, in step three-two, an objective function introducing a variable forgetting operator is established based on the response signal x(t) received by the ultra-short baseline array; the specific process is:

[0055] Step 321: According to the response signal x(t) received by the ultra-short baseline array obtained in step 31, construct the objective function J0(W(t)): the expression is:

[0056]

[0057] Among them, J0(W(t)) is the objective function; x(i) is the reply signal received by the ultra-short baseline array at time i;

[0058] W(t) represents a column-full rank matrix, represents the complex field of N×m dimensions; (·) H represents the conjugate transpose operation, || || 2 represents the square of the norm;

[0059] Objective function to estimate the time-varying signal subspace;

[0060] It can be proved that the signal subspace can be estimated when and only when W(t) = U(t)Q(t) and the objective function J0(W(t)) reaches a minimum value. , where U(t) contains C xx (t) is the first m principal eigenvectors of Q(t), Q(t) is a unitary matrix;

[0061] Step 3:22: J0(W(t)) contains the fourth-order statistics of W(t), which will greatly increase the amount of subsequent calculations. To simplify the calculation, W H (t)x(i) is approximately W H (i-1)x(i),W H (i-1)x(i) is represented as the intermediate variable y(i); the expression is:

[0062] y(i)=W H (i-1)x(i)≈W H (t)x(i) (7)

[0063] Wherein, W(i-1) represents a column full rank matrix, i = 1, 2, …, t;

[0064] The fourth-order statistics are converted into second-order statistics; however, this approximation will bring about approximation errors, and the farther away from the current moment, the greater the error. To address this problem, the forgetting factor β is introduced into the objective function for exponential weighting, giving smaller weights to data farther away from the current moment and larger weights to data closer to the current moment, thereby reducing the error caused by data farther away from the current moment.

[0065] Step 3: Rewrite the objective function J0(W(t)) into the objective function that introduces the forgetting operator, as follows

[0066]

[0067] Wherein, J1(W(t)) represents the objective function of introducing the forgetting operator; β represents the forgetting factor, 0<β<1;

[0068] Step 324. However, through research, it is known that a fixed forgetting factor cannot take into account both the convergence speed of the algorithm and the subspace estimation accuracy. The smaller the forgetting factor, the faster the convergence speed, but the lower the estimation accuracy; and vice versa. Therefore, when β takes a fixed value, only a compromise can be made between the two. At the beginning of the algorithm iteration, the estimated error e(t) = x(t)-W(t-1)y(t) is large, and the algorithm needs to converge quickly. At this time, the value of β should be small; as the iteration proceeds, the estimated error e(t) gradually becomes smaller, and the algorithm requires a higher convergence accuracy. At this time, the value of β should be larger. Therefore, the forgetting factor β should change in a negative correlation with the change of the estimated error e(t). Therefore, the present invention introduces an adaptive variable forgetting factor in the objective function, that is, the forgetting operator β is set to a negatively correlated function of the estimated error e(t), and a variable forgetting operator is obtained;

[0069] The forgetting operator β is set as a negative correlation function of the estimation error e(t) to obtain a variable forgetting operator β(e(t));

[0070] Step 325: Variable forgetting operator β(e(t)), obtain the objective function of introducing the variable forgetting operator; the objective function of introducing the variable forgetting operator is expressed as

[0071]

[0072] Among them, J(W(t)) is the objective function that introduces the variable forgetting operator.

[0073] The other steps and parameters are the same as those in the first or second embodiment.

[0074] Specific implementation method 4: This implementation method is different from the specific implementation methods 1 to 3 in that the variable forgetting operator β(e(t)) in steps 3, 2, and 4 is expressed as:

[0075]

[0076] e(t)=x(t)-W(t-1)y(t) (11)

[0077] Where ζ is the critical value, 0<ζ<1, to avoid algorithm divergence; x(t) is the response signal received by the ultra-short baseline array at time t; W(t-1) represents the column full rank matrix, y(t) represents the intermediate variable (y(t)=W H (t-1)x(t)≈W H (txt)).

[0078] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0079] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the objective function of introducing a variable forgetting operator established in step 33 is used to convert the signal subspace The problem of solving is transformed into the unconstrained minimization problem of the objective function. The unconstrained minimization problem of the objective function is solved by the recursive least squares method to obtain the time-varying signal subspace. The specific process is:

[0080] From the objective function introduced by the variable forgetting operator established in step 3.2, it can be found that the problem of solving the signal subspace can be equivalent to the unconstrained minimization problem of the objective function. When W(t) is obtained so that the objective function J(W(t)) achieves the global minimum value, the signal subspace can be estimated.<U(t)> , and the column vector of W(t) forms a signal subspace. In the present invention, the unconstrained minimization problem is solved by recursive least squares method. It can be known from the adaptive filtering theory that the optimal solution to the minimization problem is the Wiener filter;

[0081] Step 331: When the objective function of introducing the variable forgetting operator established in step 32 takes the global minimum value, the corresponding expression of W(t) is:

[0082]

[0083] Among them, C xy (t) represents the cross-correlation matrix at time t, C yy (t) represents the autocorrelation matrix at time t, Represents the autocorrelation matrix C at time t yy The inverse matrix of (t);

[0084] Cross-correlation matrix C xy (t) and the autocorrelation matrix C yy The recursion of (t) is as follows:

[0085]

[0086] Among them, y(t) represents the intermediate variable; C xy (t-1) represents the cross-correlation matrix at time t-1;

[0087] Step 332: P(t) can be further expressed as

[0088]

[0089] Where P(t) is the value of C at time t. yy The inverse matrix of C(t), P(t-1) is the inverse matrix of C(t) at time t-1. yy The inverse matrix of (t-1);

[0090] Step 333: Substituting g(t) into equation (15), we get P(t) = β(e(t)) -1 P(t-1)-β(e(t)) -1 g(t)y H (t)P(t-1);

[0091] Where g(t) is the gain vector;

[0092] Step 334: Further write g(t) as

[0093]

[0094] Step 335: Let h(t) = P(t-1)y(t), α(t) = β(e(t)) + y H (t)h(t), then

[0095] P(t)=β(e(t)) -1 [P(t-1)-h(t)h H (t) / α(t)] (17)

[0096] Among them, h(t) is the intermediate variable, α(t) is the intermediate variable;

[0097] Step 336: Substitute P(t) into In the above equation, g(t) = h(t) / α(t), we can get

[0098]

[0099] Where, e(t) is the estimation error of each iteration;

[0100] Step 337: Based on W(t)=U(t)Q(t), the estimated signal subspace is obtained<U(t)> ;

[0101] Among them, Q(t) is a unitary matrix.

[0102] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0103] Specific implementation method 6: This implementation method is different from any one of the specific implementation methods 1 to 5 in that the time-varying signal subspace obtained in step 34 is based on step 33.<U(t)> Construct a projection matrix, and perform subspace projection on the reply signal x(t) received by the ultra-short baseline array based on the projection matrix (subspace projection suppresses interference and noise) to obtain the projected signal z(t); the specific process is as follows:

[0104] Step 341: The subspace projection is an orthogonal projection. After obtaining the time-varying signal subspace 〈U(t)〉, an orthogonal projection matrix is ​​constructed;

[0105] Step 342: Perform subspace projection on the response signal x(t) received by the ultra-short baseline array based on the orthogonal projection matrix to obtain the projected signal z(t).

[0106] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0107] Specific implementation method 7: This implementation method is different from specific implementation methods 1 to 6 in that the orthogonal projection matrix expression in step 341 is:

[0108] P U(t) =U(t)(U(t) H U(t) -1 U(t) H (19)

[0109] Among them, P U(t) is the orthographic projection matrix.

[0110] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0111] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the expression of the projected signal z(t) in step three four two is:

[0112] z(t)=P U(t) x(t)=s(t)+Δ i (t)+Δ n (t) (20)

[0113] Among them, z(t) is the projected signal; Δ i (t) is the residual component of the interference after projection, Δ n (t) is the residual component of the noise after projection.

[0114] From this formula, we can find that after orthogonal projection, the desired signal will be completely retained, while the undesired interference and noise will be greatly suppressed.

[0115] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0116] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that, in step 35, the distance between the ship and the underwater target is estimated based on the projected signal z(t) obtained in step 34; the specific process is:

[0117] The distance is obtained by estimating the mean of the propagation time of the sound wave from the target to each element in the receiving array and multiplying it by the propagation speed of the sound wave in water;

[0118] The formula for obtaining the distance is:

[0119]

[0120] Among them, R is the distance between the ship and the underwater target, c is the propagation speed of sound waves in water, It is the time taken for the sound wave to be transmitted and received by the array.

[0121] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0122] Specific implementation method ten: This implementation method is different from the first to ninth specific implementation methods in that the positions of the ship and the underwater target are estimated based on the projected signal z(t) obtained in step three-four in step three-five; the specific process is as follows:

[0123] 1) Estimate the time difference between the sound wave propagating from the target to any two elements in the receiving array that are not on the same straight line based on the projected signal z(t);

[0124] 2) Obtain the position of the ship and the underwater target based on the time difference. The expression is:

[0125]

[0126] in,

[0127] θ x It represents the angle between the incident azimuth of the acoustic wave received by the ultra-short baseline array and the x-axis of the northeast celestial coordinate axis;

[0128] θ y It represents the angle between the incident azimuth of the acoustic wave received by the ultra-short baseline array and the y-axis of the northeast celestial coordinate axis;

[0129] θ z It represents the angle between the incident azimuth of the acoustic wave received by the ultra-short baseline array and the z-axis of the northeast celestial coordinate axis;

[0130] c represents the speed of sound waves in water;

[0131] τ e,f It represents the time difference between the e-th and f-th primitives in the receiving array that are not on the same straight line, estimated based on the projected signal z(t);

[0132] It indicates that the sound wave estimated based on the projected signal z(t) propagates from the target to the receiving array which is not on the same straight line. The time difference between the ξth and ξth primitives;

[0133] d x Indicates the distance between the e-th and f-th primitives in the receiving matrix that are not on the same straight line;

[0134] d y Indicates that the first The distance between the ξth and ξth primitives;

[0135] The origin of the northeast celestial coordinate system is the center of the ultra-short baseline array on the ship, the east is the x-axis direction, the north is the y-axis direction, and the sky is the z-axis direction.

[0136] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0137] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0138] Example 1

[0139] Combine the following Figure 1 The present invention is further described. The method and system for locating an underwater moving target based on a variable forgetting operator described in this embodiment include the following steps:

[0140] Step 1: According to the subspace theory, a receiving data model is established under the subspace framework, and the received data includes the desired signal, interference and noise;

[0141] Step 2: Based on the received data model and subspace optimization theory obtained in step 1, establish an objective function that introduces a variable forgetting operator;

[0142] Step 3: According to the objective function obtained in step 2, the signal subspace solution problem is transformed into an unconstrained minimization problem of the objective function, and the minimization problem is solved by recursive least squares method to recursively obtain the time-varying signal subspace to be estimated;

[0143] Step 4: Based on the signal subspace obtained in step 3, a projection matrix is ​​constructed and subspace projection is performed on the receiving system to suppress interference and noise.

[0144] Step 5: Estimate the distance between the system and the underwater moving target and the target direction based on the received data after noise reduction in step 4.

[0145] Example 2: A simulation comparison analysis is performed on the performance of the underwater moving target positioning method based on the variable forgetting operator proposed in the present invention and the traditional subspace algorithm - eigendecomposition method and the classic subspace tracking algorithm - PAST algorithm.

[0146] in,

[0147] The simulation uses an ultra-short baseline quaternary cross array, the structure is as follows Figure 2 As shown. The received signal x(t) includes the desired signal s(t), interference i(t) and noise n(t), that is

[0148] x(t)=s(t)+i(t)+n(t)

[0149] The system sampling rate is 100kHz. To facilitate the simulation of the time-varying subspace, the expected signal is a single-frequency sinusoidal signal with f0=15kHz, the interference is a random interference signal with a fixed incident angle, and the noise is additive Gaussian white noise. The simulation results are obtained through 500 Monte Carlo simulations. Assuming that within a sampling period, the signal incident azimuth angle remains unchanged, and the incident elevation angle changes linearly from θ1 to θ2, with a range of Δθ=|θ1-θ2|. The simulation simulates the time-varying subspace by changing Δθ, and sets Δθ=1°.

[0150] The simulation evaluates the interference suppression performance and target positioning performance of the proposed method by outputting SINR gain and delay estimation RMSE, such as Figure 3-4 As shown, it can be seen that the performance of the method proposed in the present invention is significantly better than the eigendecomposition method and the PAST algorithm.

[0151] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention. < / v> < / v> < / v>

Claims

1. A method for locating underwater moving targets based on a variable forgetting operator, characterized in that: The specific process of the method is: Step 1: The ultra-short baseline array on the surface ship transmits an interrogation signal; Step 2: After receiving the interrogation signal, the acoustic transponder on the underwater target replies with a response signal to the ultra-short baseline array; Step 3: After receiving the reply signal, the ultra-short baseline array transmits it to the signal processing terminal; the signal processing terminal calculates the target position; the specific process is as follows: Step 31: According to the subspace theory, the reply signal x(t) received by the ultra-short baseline array is obtained. The reply signal x(t) received by the ultra-short baseline array includes the desired signal, interference and noise. Step 32: Based on the response signal x(t) received by the ultra-short baseline array, establish an objective function that introduces a variable forgetting operator; Step 33: Based on the objective function with variable forgetting operator established in step 32, the signal subspace solution problem is transformed into an unconstrained minimization problem of the objective function, and the unconstrained minimization problem of the objective function is solved by recursive least squares method to obtain the time-varying signal subspace; Step 34: construct a projection matrix based on the time-varying signal subspace obtained in step 33, and perform subspace projection on the response signal x(t) received by the ultra-short baseline array based on the projection matrix to obtain a projected signal; Step 35: Estimate the distance between the ship and the underwater target based on the projected signal z(t) obtained in step 34; The positions of the ship and the underwater target are estimated based on the projected signal z(t) obtained in steps three and four.

2. The underwater moving target positioning method based on a variable forgetting operator according to claim 1, characterized in that: In the step 31, according to the subspace theory, the response signal x(t) received by the ultra-short baseline array is obtained, and the response signal x(t) received by the ultra-short baseline array includes the desired signal, interference and noise; the specific process is: Step 3: Assume that the ultra-short baseline array is a planar array consisting of N non-directional primitives, receiving L x sampling points; t∈Ω x ={1,2,...,L x } is an N×1-dimensional column vector, Ω x represents the time series, t represents the time, L x Indicates the moment; Step 3.12: Assume that the reply signal received by the ultra-short baseline array at time t is Contains expected signal interference and additive white Gaussian noise x(t)=λs(t)+i(t)+n(t) (1) in, Represents an N-dimensional complex field; λ is the weighting coefficient of the desired signal; When λ=1, the reply signal x(t) received by the ultra-short baseline array contains the desired signal, interference and additive white Gaussian noise. When λ = 0, the reply signal x(t) received by the ultra-short baseline array contains only interference and additive white Gaussian noise; Step 3: Assume that the expected signal s(t) is located in an independent subspace In the above example, the expected signal s(t) is represented as a column-full rank matrix Linear combinations of the columns of ; Assume that the interference i(t) is located in an independent subspace <v>In the above example, the interference i(t) is represented as a column full rank matrix Linear combinations of the columns of ;< / v> s(t)=UA(t) (2) i(t)=VB(t) (3) Among them, A(t) is the expected signal s(t) in the subspace The coordinates in m is the subspace The dimension of represents an m×1-dimensional complex field, and U represents a column-full rank matrix; B(t) is the interference i(t) in the subspace <v>The coordinates in n is the subspace <v>The dimension of represents a complex field of n×1 dimensions, and V represents a column full rank matrix;< / v> < / v> Step 314: Based on step 313, the response signal received by the ultra-short baseline array at time t is obtained; expressed as x(t)=λUA(t)+VB(t)+n(t) (4) Step 315: Express U and V as U=U(t) and V=V(t) respectively, and further express the reply signal received by the ultra-short baseline array at time t as x(t)=λU(t)A(t)+V(t)B(t)+n(t) (5) Among them, U(t) represents U at time t, and V(t) represents V at time t.

3. The underwater moving target positioning method based on a variable forgetting operator according to claim 2 is characterized in that: In the step 32, based on the response signal x(t) received by the ultra-short baseline array, an objective function introducing a variable forgetting operator is established; the specific process is: Step 321: According to the response signal x(t) received by the ultra-short baseline array obtained in step 31, construct the objective function J0(W(t)): the expression is: Among them, J0(W(t)) is the objective function; x(i) is the reply signal received by the ultra-short baseline array at time i; W(t) represents a column-full rank matrix, represents the complex field of N×m dimensions; (·) H represents the conjugate transpose operation, || || 2 represents the square of the norm; Step 322: W H (t)x(i) is approximately W H (i-1)x(i),W H (i-1)x(i) is represented as the intermediate variable y(i); the expression is: y(i)=W H (i-1)x(i)≈W H (t)x(i) (7) Wherein, W(i-1) represents a column full rank matrix, i = 1, 2, …, t; Step 3: Rewrite the objective function J0(W(t)) into the objective function that introduces the forgetting operator, as follows Wherein, J1(W(t)) represents the objective function of introducing the forgetting operator; β represents the forgetting factor, 0<β<1; Step 324: Set the forgetting operator β to a negative correlation function of the estimation error e(t) to obtain a variable forgetting operator β(e(t)); Step 325: Variable forgetting operator β(e(t)), obtain the objective function of introducing the variable forgetting operator; the objective function of introducing the variable forgetting operator is expressed as Among them, J(W(t)) is the objective function that introduces the variable forgetting operator.

4. The underwater moving target positioning method based on a variable forgetting operator according to claim 3 is characterized in that: The expression of the variable forgetting operator β(e(t)) in step 324 is: e(t)=x(t)-W(t-1)y(t) (11) Among them, ζ is the critical value, 0<ζ<1; x(t) is the response signal received by the ultra-short baseline array at time t; W(t-1) represents the column full rank matrix, and y(t) represents the intermediate variable.

5. The underwater moving target positioning method based on a variable forgetting operator according to claim 4 is characterized in that: In the step 33, based on the objective function of introducing a variable forgetting operator established in step 32, the problem of solving the signal subspace is converted into an unconstrained minimization problem of the objective function, and the unconstrained minimization problem of the objective function is solved by the recursive least squares method to obtain the time-varying signal subspace; the specific process is: Step 331: When the objective function of introducing the variable forgetting operator established in step 32 takes the global minimum value, the corresponding expression of W(t) is: Among them, C xy (t) represents the cross-correlation matrix at time t, C yy (t) represents the autocorrelation matrix at time t, Represents the autocorrelation matrix C at time t yy The inverse matrix of (t); Cross-correlation matrix C xy (t) and the autocorrelation matrix C yy The recursion of (t) is as follows: Among them, y(t) represents the intermediate variable; C xy (t-1) represents the cross-correlation matrix at time t-1; Step 332: P(t) can be further expressed as Where P(t) is the value of C at time t. yy The inverse matrix of C(t), P(t-1) is the inverse matrix of C(t) at time t-1. yy The inverse matrix of (t-1); Step 333: Substituting g(t) into equation (15), we get P(t) = β(e(t)) -1 P(t-1)-β(e(t)) -1 g(t)y H (t)P(t-1); Where g(t) is the gain vector; Step 334: Further write g(t) as Step 335: Let h(t) = P(t-1)y(t), α(t) = β(e(t)) + y H (t)h(t), then P(t)=β(e(t)) -1 [P(t-1)-h(t)h H (t) / α(t)] (17) Among them, h(t) is the intermediate variable, α(t) is the intermediate variable; Step 336: Substitute P(t) into In the above equation, g(t) = h(t) / α(t), we can get Where, e(t) is the estimation error of each iteration; Step 337: Based on W(t)=U(t)Q(t), the estimated signal subspace is obtained<U(t)> ; Among them, Q(t) is a unitary matrix.

6. The underwater moving target positioning method based on a variable forgetting operator according to claim 5 is characterized in that: In the step 34, a projection matrix is ​​constructed based on the time-varying signal subspace obtained in the step 33, and a subspace projection is performed on the response signal x(t) received by the ultra-short baseline array based on the projection matrix to obtain a projected signal; The specific process is: Step 341. Construct an orthogonal projection matrix; Step 342: Perform subspace projection on the response signal x(t) received by the ultra-short baseline array based on the orthogonal projection matrix to obtain the projected signal z(t).

7. The underwater moving target positioning method based on a variable forgetting operator according to claim 6 is characterized in that: The orthogonal projection matrix expression in step 341 is: P U(t) =U(t)(U(t) H U(t)) -1 U(t) H (19) Among them, P U(t) is the orthographic projection matrix.

8. The underwater moving target positioning method based on a variable forgetting operator according to claim 7 is characterized in that: The expression of the projected signal z(t) in step 342 is: z(t)=P U(t) x(t)=s(t)+Δ i (t)+Δ n (t) (20) Among them, z(t) is the projected signal; Δ i (t) is the residual component of the interference after projection, Δ n (t) is the residual component of the noise after projection.

9. The underwater moving target positioning method based on a variable forgetting operator according to claim 8, characterized in that: In step 35, the distance between the ship and the underwater target is estimated based on the projected signal z(t) obtained in step 34; the specific process is: The formula for obtaining the distance is: Among them, R is the distance between the ship and the underwater target, c is the propagation speed of sound waves in water, It is the time taken for the sound wave to be transmitted and received by the array.

10. The underwater moving target positioning method based on a variable forgetting operator according to claim 9, characterized in that: In step 35, the positions of the ship and the underwater target are estimated based on the projected signal z(t) obtained in step 34; the specific process is: 1) Estimate the time difference between the sound wave propagating from the target to any two elements in the receiving array that are not on the same straight line based on the projected signal z(t); 2) Obtain the position of the ship and the underwater target based on the time difference. The expression is: in, θ x It represents the angle between the incident azimuth of the acoustic wave received by the ultra-short baseline array and the x-axis of the northeast celestial coordinate axis; θ y It represents the angle between the incident azimuth of the acoustic wave received by the ultra-short baseline array and the y-axis of the northeast celestial coordinate axis; θ z It represents the angle between the incident azimuth of the acoustic wave received by the ultra-short baseline array and the z-axis of the northeast celestial coordinate axis; c represents the speed of sound waves in water; τ e,f It represents the time difference between the e-th and f-th primitives in the receiving array that are not on the same straight line, estimated based on the projected signal z(t); It indicates that the sound wave estimated based on the projected signal z(t) propagates from the target to the receiving array which is not on the same straight line. The time difference between the ξth and ξth primitives; d x Indicates the distance between the e-th and f-th primitives in the receiving matrix that are not on the same straight line; d y Indicates that the first The distance between the ξth and ξth primitives; The origin of the northeast celestial coordinate system is the center of the ultra-short baseline array on the ship, the east is the x-axis direction, the north is the y-axis direction, and the sky is the z-axis direction.

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