Ultra-short baseline positioning method based on matching constraint subspace tracking

Abstract

The invention discloses an ultra-short baseline positioning method based on matching constraint subspace tracking, and relates to the field of ultra-short baseline positioning, in particular to the ultra-short baseline positioning method based on matching constraint subspace tracking. The invention aims to solve the problems that an existing ultra-short baseline receiving array is generally provided with four receiving elements, and the array gain is relatively small; a part of positioning signals are suppressed while the radiation noise of a water surface ship is suppressed; the invention provides an ultra-short baseline positioning method based on matching constraint subspace tracking in order to solve the problems of poor positioning precision, short operating distance and high calculation complexity of an ultra-short baseline positioning system caused by matching constraint subspace tracking in the prior art. The method comprises the following steps: S1, transmitting an inquiry signal by an ultra-short baseline array mounted on a water surface ship; s2, after an acoustic transponder installed on the underwater target receives the inquiry signal, replying a response signal to the ultra-short baseline array; and S3, after receiving the response signal, the ultra-short baseline array transmits the response signal to a signal processing terminal, and the signal processing terminal calculates a target position.

Description

Technical Field

[0001] The invention relates to the field of ultra-short baseline positioning, and in particular to an ultra-short baseline positioning method based on matching constraint subspace tracking. Background Art

[0002] Ultra-short baseline positioning technology is an indispensable technology in the development and utilization of marine resources. During the ultra-short baseline positioning process, the receiving array is installed on the surface ship to receive the response signal emitted by the underwater transponder and locate the underwater target based on the received signal. In actual work, the ultra-short baseline receiving array will receive the radiation noise of the surface ship while receiving the positioning signal, which seriously affects the positioning accuracy and range of the ultra-short baseline.

[0003] The existing ultra-short baseline receiving array usually has 4 receiving elements, and the array gain is small. While suppressing the radiation noise of surface ships, it also suppresses part of the positioning signal; the calculation complexity is high. Summary of the invention

[0004] The purpose of the present invention is to solve the problems that the existing ultra-short baseline receiving array usually consists of 4 receiving elements with small array gain; while suppressing the radiation noise of surface ships, it also suppresses part of the positioning signal; resulting in poor positioning accuracy, short operating range and high computational complexity of the ultra-short baseline positioning system, and propose an ultra-short baseline positioning method based on matching constrained subspace tracking.

[0005] An ultra-short baseline positioning method based on matching constraint subspace tracking. The specific process is as follows:

[0006] S1. The ultra-short baseline array installed on the surface ship transmits an interrogation signal;

[0007] S2, after receiving the interrogation signal, the acoustic transponder installed on the underwater target replies with a response signal to the ultra-short baseline array;

[0008] S3. After receiving the response signal, the ultra-short baseline array transmits it to the signal processing terminal, which calculates the target position.

[0009] The beneficial effects of the present invention are:

[0010] The present invention discloses an ultra-short baseline positioning method based on matching constraint subspace tracking. An ultra-short baseline array installed on a surface ship transmits an inquiry signal. After receiving the inquiry signal, an acoustic transponder installed on an underwater target replies a reply signal to the ultra-short baseline array. After receiving the reply signal, the ultra-short baseline array transmits the reply signal to a signal processing terminal, which calculates the target position. The process is as follows: the ultra-short baseline array receives the reply signal, estimates the mean of the time-varying subspace based on all received reply signals, constructs an orthogonal projection operator based on the estimated mean of the time-varying subspace, and uses the orthogonal projection operator to calculate the received signal. The signal is linearly projected to realize the feasible domain constraint, and the received signal after the feasible domain constraint is obtained; the subspace tracking problem of the received signal after the feasible domain constraint and the reply signal received by the ultra-short baseline array at time t is converted into an unconstrained minimization problem, and the unconstrained minimization problem at time t is solved to obtain the subspace of the received signal; a projection operator is constructed according to the obtained subspace of the received signal, and the projection operator performs spatial projection on the reply signal received by the ultra-short baseline array to suppress undesired noise, and obtains the reply signal after noise reduction; the distance between the ship and the underwater target and the azimuth of the ship and the underwater target are estimated according to the reply signal after noise reduction. The present invention can be used to quickly and accurately estimate the time-varying signal subspace, effectively suppress noise, and then realize accurate positioning of underwater targets, improve the positioning accuracy of the ultra-short baseline system, increase the effective distance, and have low computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of the present invention;

[0012] Figure 2 This is the array structure diagram for ultra-short baseline array reception;

[0013] Figure 3 is the eigenvalue graph of the received data;

[0014] Figure 4 This is the target positioning result map. DETAILED DESCRIPTION

[0015] Specific implementation method 1: Combination Figure 1 The present embodiment is described. The specific process of the ultra-short baseline positioning method based on matching constraint subspace tracking is as follows:

[0016] S1. The ultra-short baseline array installed on the surface ship transmits an interrogation signal;

[0017] S2, after receiving the interrogation signal, the acoustic transponder installed on the underwater target replies with a response signal to the ultra-short baseline array;

[0018] S3: After receiving the reply signal, the ultra-short baseline array transmits it to the signal processing terminal, which calculates the target position. Figure 2 .

[0019] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the ultra-short baseline array in S3 receives the response signal and transmits it to the signal processing terminal, which calculates the target position; the specific process is:

[0020] S31, the ultra-short baseline array receives a reply signal, and estimates a mean of a time-varying subspace based on all received reply signals;

[0021] S32, constructing an orthogonal projection operator according to the mean of the time-varying subspace estimated in S31, and using the orthogonal projection operator to perform linear projection on the received signal to implement feasible domain constraints, thereby obtaining a received signal after the feasible domain constraints;

[0022] S33, based on the received signal constrained by the feasible domain, convert the subspace tracking problem of the reply signal received by the ultra-short baseline array at time t into an unconstrained minimization problem, solve the unconstrained minimization problem at time t, and obtain the subspace of the received signal;

[0023] S34, constructing a projection operator according to the subspace of the received signal obtained in S33, wherein the projection operator performs spatial projection on the reply signal received by the ultra-short baseline array to suppress undesired noise, and obtains a noise-reduced reply signal;

[0024] S35. Estimate the distance between the ship and the underwater target and the direction of the ship and the underwater target according to the noise-reduced response signal.

[0025] The present invention has the advantage of being able to accurately separate the radiation noise of a surface ship from the positioning signal, thereby reducing the influence of noise on the ultra-short baseline positioning performance, and ultimately improving the positioning accuracy and range of the system.

[0026] Specific implementation method three: This implementation method is different from specific implementation method one or two in that the ultra short baseline array in S31 is a planar array, and the planar array consists of 1 transmitting element and no less than 15 receiving elements;

[0027] The receiving array element is an isotropic and non-directional piezoelectric ceramic transducer (acoustic transponder).

[0028] The other steps and parameters are the same as those in the first or second embodiment.

[0029] Specific implementation method 4: This implementation method is different from any one of specific implementation methods 1 to 3 in that, in S31, the ultra-short baseline array receives a response signal, and estimates the mean of the time-varying subspace based on all received response signals;

[0030] The specific process is:

[0031] S311. Assume that the response signal received by the ultra-short baseline array is x(t), and x(t) is expressed as:

[0032]

[0033] Among them, s(t) is the positioning signal, is the radiation noise of the ship, n(t) is Gaussian white noise;

[0034] S312, estimating the mean of the time-varying subspace based on all received response signals; the specific process is:

[0035] The received reply signal is estimated by using the eigenvalue decomposition method to obtain the mean of the time-varying subspace;

[0036] The mean of the time-varying subspace represents the mean of the subspace over a certain period of time.

[0037] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0038] Specific implementation method 5: This implementation method is different from any one of specific implementation methods 1 to 4 in that the received response signal is estimated by using the eigenvalue decomposition method to obtain the mean of the time-varying subspace;

[0039] The specific process is:

[0040] 1) The received signal from time 1 to time t is expressed as follows:

[0041] X(t)=[x(1),x(2),…,x(t)] (2)

[0042] Wherein, X(t) is the reply signal sequence received by the ultra-short baseline array from time 1 to time t, x(1) is the reply signal received by the ultra-short baseline array at time 1, x(2) is the reply signal received by the ultra-short baseline array at time 2, and x(t) is the reply signal received by the ultra-short baseline array at time t;

[0043] 2) Perform eigenvalue decomposition on the reply signal sequence X(t) received by the ultra-short baseline array from time 1 to time t to obtain:

[0044] X(t)=[UVU T ] (3)

[0045] Where U represents the eigenvector matrix of X(t), and each column of U is called an eigenvector;

[0046] V represents the eigenvalue matrix of X(t), and each value on the diagonal of V represents an eigenvalue;

[0047] The superscript T indicates the conjugate transpose operation;

[0048] 3) The first k columns of U are the mean H(t) of the time-varying subspace at time t;

[0049] The k is the dimension of the response signal x(t) received by the ultra-short baseline array at time t.

[0050] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0051] Specific implementation method six: This implementation method is different from any one of specific implementation methods one to five in that, in S32, an orthogonal projection operator is constructed according to the mean of the time-varying subspace estimated in S31, and the orthogonal projection operator is used to perform linear projection on the received signal to implement the feasible domain constraint, thereby obtaining the received signal after the feasible domain constraint;

[0052] The specific process is:

[0053] The orthogonal projection operator is constructed according to the mean of the time-varying subspace estimated by S31. The orthogonal projection operator is expressed as follows:

[0054] P=H(t)(H T (t)H(t)) -1 H T (t) (4)

[0055] Where, P is the orthogonal projection operator;

[0056] The orthogonal projection operator P is used to linearly project the reply signal x(t) received by the ultra-short baseline array at time t to realize the feasible domain constraint, and the received signal y(t) after the feasible domain constraint is obtained; it is expressed as:

[0057] y(t)=H(t)(H T (t)H(t)) -1 H T (t)x(t) (5).

[0058] The purpose of narrowing the estimation range and thus reducing the calculation complexity of the present invention is achieved.

[0059] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0060] Specific implementation method 7: This implementation method is different from any one of specific implementation methods 1 to 6 in that, in S33, based on the received signal after the feasible domain constraint, the subspace tracking problem of the reply signal received by the ultra-short baseline array at time t is converted into an unconstrained minimization problem, and the unconstrained minimization problem at time t is solved to obtain the subspace of the received signal;

[0061] The specific process is:

[0062] S331. The unconstrained minimization problem is shown in formula (6):

[0063] J1(F(t))=E{||y(t)-F(t)(F T (t)F(t)) -1 F T (t)x(t)|| 2} (6)

[0064] Where, E{} represents the averaging operation, F(t) represents the subspace of the received signal at time t to be calculated; J1(F(t)) represents the objective function; |||| 2 represents the square of the norm;

[0065] S332. In order to reduce the computational complexity of formula (6), the present invention sets an orthogonal basis W(t) of the subspace F(t) of the received signal at time t;

[0066] W(t)W T (t) = F(t)(F T (t)F(t)) -1 F T (t) (7)

[0067] Substitute the orthogonal product W(t) expression into the objective function J1(F(t)) of formula (6), and then rewrite the objective function J1(F(t)) into a summation form to obtain a new objective function J2(W(t));

[0068] The expression of the new objective function J2(W(t)) is:

[0069]

[0070] Among them, y(i) represents the received signal after the feasible domain constraint at time i; x(i) represents the reply signal received by the ultra-short baseline array at time i;

[0071] S333, W T (t)x(i) is approximately W T (i-1)x(i),W T (i-1)x(i) is represented as the intermediate variable Z(i); the expression is:

[0072] Z(i)=W T (i-1)x(i)≈W T (t)x(i) (9)

[0073] Wherein, W(i-1) represents the orthogonal basis of the subspace F(t) of the received signal at time i-1, i=1,2,…,t;

[0074] S334. Substitute Z(i) into formula (7) to obtain the objective function J3(W(t)); the expression is:

[0075]

[0076] S335. In order to reduce the error of the above approximate operation, the present invention adds an error forgetting factor δ, which is a function that decays exponentially. Therefore, the above formula is further expressed as:

[0077]

[0078] Among them, δ represents the error forgetting factor, which is an exponentially decaying function;

[0079] S336. Use the recursive least squares method to solve the objective function J3(W(t)) of formula (11), and W(t) that minimizes the objective function J3(W(t)) is the subspace of the received signal.

[0080] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0081] Specific implementation eight: This implementation is different from any one of specific implementations one to seven in that, in S34, a projection operator is constructed according to the subspace of the received signal obtained in S33, and the projection operator performs spatial projection on the reply signal received by the ultra-short baseline array to suppress undesired noise, thereby obtaining a noise-reduced reply signal; the specific process is as follows:

[0082] The spatial projection is an oblique projection, and the expression of the oblique projection is:

[0083] G(t)=Ex(t) (12)

[0084] Among them, E is the projection operator, G(t) is the response signal after noise reduction;

[0085] Through formula (12), it is found that after oblique projection, the desired signal will be completely retained, while the undesired signal will be greatly suppressed.

[0086] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0087] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that the distance between the ship and the underwater target is estimated according to the noise-reduced response signal in S35; the specific process is as follows:

[0088] 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;

[0089] The formula for obtaining the distance is:

[0090]

[0091] 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.

[0092] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0093] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the positions of the ship and the underwater target are estimated according to the noise-reduced response signal in S35; the specific process is as follows:

[0094] 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 noise-reduced response signal G(t);

[0095] 2) Obtain the position of the ship and the underwater target based on the time difference. The expression is:

[0096]

[0097] in,

[0098] 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;

[0099] 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;

[0100] c represents the speed of sound waves in water;

[0101] 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 noise-reduced response signal G(t);

[0102] It indicates that the sound wave estimated based on the noise-reduced response signal G(t) propagates from the target to the first point in the receiving array that is not on the same straight line. The time difference between the ξth and ξth primitives;

[0103] 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;

[0104] d y Indicates that the first The distance between the ξth and ξth primitives;

[0105] 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.

[0106] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0107] 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.

[0108] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention is further described below in conjunction with the drawings and specific embodiments, but is not intended to be a limitation of the present invention.

[0109] Embodiment 1: The purpose of the present invention is to improve the positioning accuracy and range of an ultra-short baseline positioning system. The advantage of the present invention is that it can accurately separate the radiation noise of a surface ship from the positioning signal, thereby reducing the impact of noise on the ultra-short baseline positioning performance, and ultimately improving the positioning accuracy and range of the system.

[0110] Assume that the receiving array of the ultra-short baseline positioning system comprises 30 receiving array elements and 1 transmitting array element. The specific structure is as follows: Figure 1 As shown, the transmitting element is located at the center of the array and the receiving elements are located around it.

[0111] Specific implementation method 1: This implementation method is an ultra-short baseline positioning method based on matching constraint subspace tracking. The specific process is as follows:

[0112] S1. The ultra-short baseline array installed on the surface ship transmits an interrogation signal;

[0113] S2, after receiving the interrogation signal, the acoustic transponder installed on the underwater target replies with a response signal to the ultra-short baseline array;

[0114] S3. After receiving the response signal, the ultra-short baseline array transmits it to the signal processing terminal, which calculates the target position.

[0115] S3, after receiving the response signal, the ultra-short baseline array transmits it to the signal processing terminal, and the signal processing terminal calculates the target position; the specific process is:

[0116] S31, the ultra-short baseline array receives a reply signal, and estimates a mean of a time-varying subspace based on all received reply signals;

[0117] S32, constructing an orthogonal projection operator according to the mean of the time-varying subspace estimated in S31, and using the orthogonal projection operator to perform linear projection on the received signal to implement feasible domain constraints, thereby obtaining a received signal after the feasible domain constraints;

[0118] S33, based on the received signal constrained by the feasible domain, convert the subspace tracking problem of the reply signal received by the ultra-short baseline array at time t into an unconstrained minimization problem, solve the unconstrained minimization problem at time t, and obtain the subspace of the received signal;

[0119] S34, constructing a projection operator according to the subspace of the received signal obtained in S33, wherein the projection operator performs spatial projection on the reply signal received by the ultra-short baseline array to suppress undesired noise, and obtains a noise-reduced reply signal;

[0120] S35. Estimate the distance between the ship and the underwater target and the direction of the ship and the underwater target according to the noise-reduced response signal.

[0121] The present invention has the advantage of being able to accurately separate the radiation noise of a surface ship from the positioning signal, thereby reducing the influence of noise on the ultra-short baseline positioning performance, and ultimately improving the positioning accuracy and range of the system.

[0122] The ultra-short baseline array in S31 is a planar array, which is composed of 1 transmitting element and no less than 15 receiving elements;

[0123] The receiving array element is an isotropic and non-directional piezoelectric ceramic transducer (acoustic transponder).

[0124] In S31, the ultra-short baseline array receives a reply signal, and estimates a mean of the time-varying subspace based on all received reply signals;

[0125] The specific process is:

[0126] S311. Assume that the response signal received by the ultra-short baseline array is x(t), and x(t) is expressed as:

[0127]

[0128] The positioning signal s(t) is a linear frequency modulation signal with a bandwidth of 8kHz-16kHz, and the surface ship radiation noise is a CW signal with a frequency of 12kHz,

[0129] S312, estimating the mean of the time-varying subspace based on all received response signals; the specific process is:

[0130] The received reply signal is estimated by using the eigenvalue decomposition method to obtain the mean of the time-varying subspace;

[0131] The mean of the time-varying subspace represents the mean of the subspace over a certain period of time.

[0132] The received response signal is estimated by using the eigenvalue decomposition method to obtain the mean of the time-varying subspace;

[0133] The specific process is:

[0134] 1) The received signal from time 1 to time t is expressed as follows:

[0135] X(t)=[x(1),x(2),…,x(t)] (2)

[0136] Wherein, X(t) is the reply signal sequence received by the ultra-short baseline array from time 1 to time t, x(1) is the reply signal received by the ultra-short baseline array at time 1, x(2) is the reply signal received by the ultra-short baseline array at time 2, and x(t) is the reply signal received by the ultra-short baseline array at time t;

[0137] 2) Perform eigenvalue decomposition on the reply signal sequence X(t) received by the ultra-short baseline array from time 1 to time t to obtain:

[0138] X(t)=[UVU T ] (3)

[0139] Where U represents the eigenvector matrix of X(t), and each column of U is called an eigenvector;

[0140] V represents the eigenvalue matrix of X(t), and each value on the diagonal of V represents an eigenvalue;

[0141] The superscript T indicates the conjugate transpose operation;

[0142] 3) The first k columns of U are the mean H(t) of the time-varying subspace at time t;

[0143] The k is the dimension of the response signal x(t) received by the ultra-short baseline array at time t.

[0144] Figure 3 σ 2 Represents the variance of Gaussian white noise, which is used as the threshold for selecting eigenvalues, and r represents the subspace dimension.

[0145] In the S32, an orthogonal projection operator is constructed according to the mean of the time-varying subspace estimated in S31, and the received signal is linearly projected by the orthogonal projection operator to realize the feasible domain constraint, so as to obtain the received signal after the feasible domain constraint;

[0146] The specific process is:

[0147] The orthogonal projection operator is constructed according to the mean of the time-varying subspace estimated by S31. The orthogonal projection operator is expressed as follows:

[0148] P=H(t)(H T (t)H(t)) -1 H T (t) (4)

[0149] Where, P is the orthogonal projection operator;

[0150] The orthogonal projection operator P is used to linearly project the reply signal x(t) received by the ultra-short baseline array at time t to realize the feasible domain constraint, and the received signal y(t) after the feasible domain constraint is obtained; it is expressed as:

[0151] y(t)=H(t)(H T (t)H(t)) -1 H T (t)x(t) (5).

[0152] The purpose of narrowing the estimation range and thus reducing the calculation complexity of the present invention is achieved.

[0153] In the S33, based on the received signal constrained by the feasible domain, the subspace tracking problem of the reply signal received by the ultra-short baseline array at time t is converted into an unconstrained minimization problem, and the unconstrained minimization problem at time t is solved to obtain the subspace of the received signal; the specific process is:

[0154] S331. The unconstrained minimization problem is shown in formula (6):

[0155] J1(F(t))=E{||y(t)-F(t)(F T (t)F(t)) -1 F T (t)x(t)|| 2} (6)

[0156] Where, E{} represents the averaging operation, F(t) represents the subspace of the received signal at time t to be calculated; J1(F(t)) represents the objective function; |||| 2 represents the square of the norm;

[0157] S332. In order to reduce the computational complexity of formula (6), the present invention sets an orthogonal basis W(t) of the subspace F(t) of the received signal at time t;

[0158] W(t)W T (t) = F(t)(F T (t)F(t)) -1 F T(t) (7)

[0159] Substitute the orthogonal product W(t) expression into the objective function J1(F(t)) of formula (6), and then rewrite the objective function J1(F(t)) into a summation form to obtain a new objective function J2(W(t));

[0160] The expression of the new objective function J2(W(t)) is:

[0161]

[0162] Among them, y(i) represents the received signal after the feasible domain constraint at time i; x(i) represents the reply signal received by the ultra-short baseline array at time i;

[0163] S333, W T (t)x(i) is approximately W T (i-1)x(i),W T (i-1)x(i) is represented as the intermediate variable Z(i); the expression is:

[0164] Z(i)=W T (i-1)x(i)≈W T (t)x(i) (9)

[0165] Wherein, W(i-1) represents the orthogonal basis of the subspace F(t) of the received signal at time i-1, i=1,2,…,t;

[0166] S334. Substitute Z(i) into formula (7) to obtain the objective function J3(W(t)); the expression is:

[0167]

[0168] S335. In order to reduce the error of the above approximate operation, the present invention adds an error forgetting factor δ, which is a function that decays exponentially. Therefore, the above formula is further expressed as:

[0169]

[0170] Among them, δ represents the error forgetting factor, which is an exponentially decaying function;

[0171] S336. Use the recursive least squares method to solve the objective function J3(W(t)) of formula (11), and W(t) that minimizes the objective function J3(W(t)) is the subspace of the received signal.

[0172] In S34, a projection operator is constructed according to the subspace of the received signal obtained in S33, and the projection operator performs spatial projection on the reply signal received by the ultra-short baseline array to suppress undesired noise, thereby obtaining a noise-reduced reply signal. The specific process is as follows:

[0173] The spatial projection is an oblique projection, and the expression of the oblique projection is:

[0174] G(t)=Ex(t) (12)

[0175] Among them, E is the projection operator, G(t) is the response signal after noise reduction;

[0176] Through formula (12), it is found that after oblique projection, the desired signal will be completely retained, while the undesired signal will be greatly suppressed.

[0177] The S35, estimating the distance between the ship and the underwater target according to the noise-reduced response signal; the specific process is:

[0178] 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;

[0179] The formula for obtaining the distance is:

[0180]

[0181] 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.

[0182] The S35, estimating the position of the ship and the underwater target according to the noise-reduced response signal; the specific process is:

[0183] 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 noise-reduced response signal G(t);

[0184] 2) Obtain the position of the ship and the underwater target based on the time difference. The expression is:

[0185]

[0186] in,

[0187] 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;

[0188] 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;

[0189] c represents the speed of sound waves in water;

[0190] 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 noise-reduced response signal G(t);

[0191] It indicates that the sound wave estimated based on the noise-reduced response signal G(t) propagates from the target to the first point in the receiving array that is not on the same straight line. The time difference between the ξth and ξth primitives;

[0192] 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;

[0193] d y Indicates that the first The distance between the ξth and ξth primitives.

[0194] like Figure 4 It can be seen that the positioning accuracy of the method proposed in the present invention is significantly better than that before processing and the traditional method.

[0195] 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.

[0196] 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.

Claims

1. An ultra-short baseline positioning method based on matching constrained subspace tracking, characterized in that: The specific process of the method is: S1. The ultra-short baseline array installed on the surface ship transmits an interrogation signal; S2, after receiving the interrogation signal, the acoustic transponder installed on the underwater target replies with a response signal to the ultra-short baseline array; S3. After receiving the response signal, the ultra-short baseline array transmits it to the signal processing terminal, which calculates the target position.

2. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 1, characterized in that: After receiving the response signal, the ultra-short baseline array in S3 transmits it to the signal processing terminal, and the signal processing terminal calculates the target position; the specific process is: S31, the ultra-short baseline array receives a reply signal, and estimates a mean of a time-varying subspace based on all received reply signals; S32, constructing an orthogonal projection operator according to the mean of the time-varying subspace estimated in S31, and using the orthogonal projection operator to perform linear projection on the received signal to implement feasible domain constraints, thereby obtaining a received signal after the feasible domain constraints; S33, based on the received signal constrained by the feasible domain, convert the subspace tracking problem of the reply signal received by the ultra-short baseline array at time t into an unconstrained minimization problem, solve the unconstrained minimization problem at time t, and obtain the subspace of the received signal; S34, constructing a projection operator according to the subspace of the received signal obtained in S33, wherein the projection operator performs spatial projection on the reply signal received by the ultra-short baseline array to suppress undesired noise, and obtains a noise-reduced reply signal; S35. Estimate the distance between the ship and the underwater target and the direction of the ship and the underwater target according to the noise-reduced response signal.

3. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 2, characterized in that: The ultra-short baseline array in S31 is a planar array, which is composed of 1 transmitting element and no less than 15 receiving elements; The receiving array element is an isotropic and non-directional piezoelectric ceramic transducer.

4. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 3 is characterized in that: In S31, the ultra-short baseline array receives a reply signal, and estimates the mean of the time-varying subspace based on all received reply signals; the specific process is: S311. Assume that the response signal received by the ultra-short baseline array is x(t), and x(t) is expressed as: Among them, s(t) is the positioning signal, is the radiation noise of the ship, n(t) is Gaussian white noise; S312, estimating the mean of the time-varying subspace based on all received response signals; the specific process is: The received reply signal is estimated using the eigenvalue decomposition method to obtain the mean of the time-varying subspace.

5. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 4, characterized in that: The eigenvalue decomposition method is used to estimate the received response signal to obtain the mean of the time-varying subspace; the specific process is: 1) The received signal from time 1 to time t is expressed as follows: X(t)=[x(1),x(2),…,x(t)] (2) Wherein, X(t) is the reply signal sequence received by the ultra-short baseline array from time 1 to time t, x(1) is the reply signal received by the ultra-short baseline array at time 1, x(2) is the reply signal received by the ultra-short baseline array at time 2, and x(t) is the reply signal received by the ultra-short baseline array at time t; 2) Perform eigenvalue decomposition on the reply signal sequence X(t) received by the ultra-short baseline array from time 1 to time t to obtain: X(t)=[U V U T ] (3) Where U represents the eigenvector matrix of X(t), and each column of U is called an eigenvector; V represents the eigenvalue matrix of X(t), and each value on the diagonal of V represents an eigenvalue; The superscript T indicates the conjugate transpose operation; 3) The first k columns of U are the mean H(t) of the time-varying subspace at time t; The k is the dimension of the response signal x(t) received by the ultra-short baseline array at time t.

6. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 5, characterized in that: In the S32, an orthogonal projection operator is constructed according to the mean of the time-varying subspace estimated in S31, and the orthogonal projection operator is used to perform linear projection on the received signal to implement the feasible domain constraint, so as to obtain the received signal after the feasible domain constraint; the specific process is: The orthogonal projection operator is constructed according to the mean of the time-varying subspace estimated by S31. The orthogonal projection operator is expressed as follows: P=H(t)(H T (t)H(t)) -1 H T (t) (4) Where, P is the orthogonal projection operator; The orthogonal projection operator P is used to linearly project the reply signal x(t) received by the ultra-short baseline array at time t to realize the feasible domain constraint, and the received signal y(t) after the feasible domain constraint is obtained; it is expressed as: y(t)=H(t)(H T (t)H(t)) -1 H T (t)x(t) (5)。 7. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 6, characterized in that: In the S33, based on the received signal constrained by the feasible domain, the subspace tracking problem of the reply signal received by the ultra-short baseline array at time t is converted into an unconstrained minimization problem, and the unconstrained minimization problem at time t is solved to obtain the subspace of the received signal; the specific process is: S331. The unconstrained minimization problem is shown in formula (6): J1(F(t))=E{||y(t)-F(t)(F T (t)F(t)) -1 F T (t)x(t)|| 2 } (6) Where, E{} represents the averaging operation, F(t) represents the subspace of the received signal at time t to be determined; J1(F(t)) represents the objective function; || || 2 represents the square of the norm; S332, setting an orthogonal basis W(t) of the subspace F(t) of the received signal at time t; W(t)W T (t)=F(t)(F T (t)F(t)) -1 F T (t) (7) Substitute the orthogonal product W(t) expression into the objective function J1(F(t)) of formula (6), and then rewrite the objective function J1(F(t)) into a summation form to obtain a new objective function J2(W(t)); The expression of the new objective function J2(W(t)) is: Among them, y(i) represents the received signal after the feasible domain constraint at time i; x(i) represents the reply signal received by the ultra-short baseline array at time i; S333, W T (t)x(i) is approximately W T (i-1)x(i),W T (i-1)x(i) is represented as the intermediate variable Z(i); the expression is: Z(i)=W T (i-1)x(i)≈W T (t)x(i) (9) Wherein, W(i-1) represents the orthogonal basis of the subspace F(t) of the received signal at time i-1, i=1,2,…,t; S334. Substitute Z(i) into formula (7) to obtain the objective function J3(W(t)); the expression is: S335. The above formula is further expressed as: Among them, δ represents the error forgetting factor; S336. Use the recursive least squares method to solve the objective function J3(W(t)) of formula (11), and W(t) that minimizes the objective function J3(W(t)) is the subspace of the received signal.

8. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 7, characterized in that: In S34, a projection operator is constructed according to the subspace of the received signal obtained in S33, and the projection operator performs spatial projection on the reply signal received by the ultra-short baseline array to suppress undesired noise, thereby obtaining a noise-reduced reply signal. The specific process is as follows: The spatial projection is an oblique projection, and the expression of the oblique projection is: G(t)=Ex(t) (12) Among them, E is the projection operator, and G(t) is the response signal after noise reduction.

9. The ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 8, characterized in that: In S35, the distance between the ship and the underwater target is estimated according to the noise-reduced response signal; 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 ultra-short baseline positioning method based on matching constrained subspace tracking according to claim 9, characterized in that: In the step S35, the positions of the ship and the underwater target are estimated according to the noise-reduced response signal; 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 noise-reduced response signal G(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; 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 noise-reduced response signal G(t); It indicates that the sound wave estimated based on the noise-reduced response signal G(t) propagates from the target to the first point in the receiving array that 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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