An intelligent positioning method and system for an underwater vehicle with enhanced sparse underwater acoustic ranging

Abstract

The present invention discloses an intelligent positioning method and system for an underwater vehicle with enhanced sparse underwater acoustic ranging, wherein the positioning method includes: obtaining the global reconstruction matrix of the underwater acoustic network; obtaining the mapping matrix \(w_{u}\) of the time of arrival of the underwater acoustic signal and the mapping matrix \(w_{v}\) of the position of the underwater acoustic network, as well as the eigenvalues of the matrix \((w_{u}, w_{v})\); obtaining the measured value of the position of the underwater acoustic transponder and the measured value of the distance from the underwater acoustic transponder to the underwater acoustic base station; using an improved genetic algorithm to optimize the position of the underwater acoustic transponder to obtain an estimated value of the position of the underwater acoustic transponder, and further obtaining the position coordinate value of the underwater vehicle. This method solves the problem that the positioning accuracy of the vehicle is greatly affected by measurement uncertainty under sparse underwater acoustic signals in existing underwater acoustic positioning.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater vehicle positioning and tracking, and particularly relates to intelligent positioning of underwater vehicles by using enhanced sparse underwater acoustic ranging. Background Art

[0002] As an important carrier for exploring and developing marine resources, underwater vehicles integrate functions such as power propulsion, multi-sensor fusion, navigation communication, and computer control, and can play an important role in fields such as marine resource exploration, environmental monitoring, underwater facility detection, and disaster rescue. Underwater vehicles move freely in the underwater three-dimensional space, and positioning technology can help underwater vehicles move to the destination along a predetermined route. Due to the skin effect, an electromagnetic propagation characteristic, electromagnetic waves have a serious attenuation phenomenon in water, and the radio positioning commonly used on the ground or in space cannot be used for the positioning of underwater vehicles; since satellite wireless signals have a serious attenuation in water, they can be used for positioning targets above the water surface but cannot perform real-time positioning of underwater targets. Currently, the commonly used underwater vehicle positioning technologies can be divided into three categories according to the sensor type and working mode: inertial navigation positioning, geophysical positioning, and underwater acoustic positioning. Passive and autonomous inertial navigation uses accelerometers and gyroscopes to measure the target acceleration and angular acceleration, and calculates the position of the vehicle by integrating twice with respect to time. However, it is prone to cumulative errors during long-term operation and requires external reference information for correction; geophysical positioning includes methods such as terrain matching, geomagnetic matching, and gravity matching, which require pre-measuring the topographic maps, geomagnetic fields, and gravity reference maps at different planar positions in water. However, its positioning accuracy is limited by prior information such as topographic maps, geomagnetic values, and gravity fields; the attenuation effect of sound waves in seawater is small, and the propagation distance can reach up to thousands of meters at most. However, underwater acoustic signals have strong spatio-temporal variation characteristics and are prone to large positioning errors in some areas.

[0003] Underwater acoustic signals can propagate over longer distances compared to electromagnetic signals. Therefore, acoustic positioning has become an important means for the positioning and tracking of underwater vehicles. The acoustic positioning of underwater vehicles mainly includes an array, a transponder, and a ground station. Among them, the array is a set of arrays capable of converting acoustic and electrical signals, and the positions of its elements have been accurately determined; the transponder equipped with a transducer can respond to signals of a specific frequency band and form; the ground station consists of components such as a network switch, a data storage device, a data processing system, and a human-computer interaction platform. According to the baseline length, underwater acoustic positioning can be divided into long baseline, short baseline, and ultra-short baseline. The long baseline positioning system consists of transponders distributed on the seabed, with a working frequency usually around 10 kHz, an operating range of several kilometers, and a positioning accuracy of several meters. The baseline length of the short baseline positioning system is generally between several meters and dozens of meters, and the elements are distributed on the bottom or side of the ship. This system is suitable for the navigation system of underwater vehicles near the mother ship, and its positioning accuracy is generally 1% to 3% of the distance. The array of the ultra-short baseline positioning system can be integrated into a compact overall unit, with a baseline length of decimeter level or less than or equal to half the wavelength. It can be conveniently placed in a favorable position where both the ambient noise and structural noise are weak. The system is simple to install and easy to use, but its main disadvantage is that the navigation accuracy is lower than that of the long baseline and short baseline positioning systems. Underwater acoustic positioning belongs to methods based on distance information. The principle is to calculate the position of the vehicle by solving the signal propagation time or phase from the underwater acoustic array to each moving transponder.

[0004] Limited by the physical properties of the seawater medium and the influence of ocean environmental conditions, underwater positioning technology faces problems such as few available information sources, many underwater interferences, and difficulty in improving the accuracy of sensors. Although acoustic positioning of underwater vehicles has become a major means, there are uncertain factors such as the maneuvering operation of underwater targets and unknown complex environments. At the same time, various interferences such as ocean environmental noise, ocean biological noise, and ships, especially when the underwater acoustic base stations are coplanar or the underwater acoustic ranging is abnormal, seriously reduce the positioning performance of underwater vehicles. Summary of the Invention

[0005] Objective of the Invention: Aiming at the problems existing in the prior art, the present invention provides an intelligent positioning method for underwater vehicles with enhanced sparse underwater acoustic ranging, which solves the problem that the positioning accuracy of vehicles under sparse underwater acoustic signals in existing underwater acoustic positioning is greatly affected by measurement uncertainties.

[0006] Technical Solution: On the one hand, the present invention discloses an intelligent positioning method for underwater vehicles with enhanced sparse underwater acoustic ranging, including the steps of:

[0007] Step 1: Collect the arrival times of underwater acoustic signals obtained by each underwater acoustic base station at multiple different positions of underwater acoustic transponders. The underwater acoustic transponders are installed on the fuselage of the underwater vehicle, and the positions of the underwater acoustic base stations are fixed. The position coordinates of the i-th underwater acoustic base station are a i; a i The corresponding h-th sample is the time of arrival of the underwater acoustic signal, is the coordinate of the underwater acoustic transponder, h = 1, 2, …, Num, where Num is the total number of samples corresponding to the i-th underwater acoustic base station; i = 1, 2, ..., n, and n is the number of underwater acoustic base stations; the samples obtained by the n underwater acoustic base stations form a sample set (u, v), where u is the matrix composed of the time of arrival of the underwater acoustic signals, and v is the matrix composed of the coordinates of the underwater acoustic transponders;

[0008] According to the time of arrival of the underwater acoustic signal of the K nearest neighbors to calculate the first local reconstruction weight matrix of the i-th underwater acoustic base station

[0009]

[0010] where the i-th element of is 0, ||·||1 represents the 1-norm calculation;

[0011] According to the coordinates of the underwater acoustic transponder of the K nearest neighbors to calculate the second local reconstruction weight matrix of the i-th underwater acoustic base station

[0012]

[0013] where the i-th element of is 0,

[0014] Construct the first global reconstruction matrix S u , S u the element in the i-th row and j-th column of is: where ne(i k ) represents the local neighbor set of the paired sample set ;

[0015] The signal domain global reconstruction weight matrix considering the underwater acoustic network topology is

[0016] Construct the second global reconstruction matrix S v , S v the element in the i-th row and j-th column of is:

[0017] The position domain global reconstruction weight matrix considering the underwater acoustic network topology is

[0018] Step 2: Based on the sparse underwater acoustic signal characteristics, the global nonlinear analysis problem is decomposed into a local linear problem. The structural characteristics of the original underwater acoustic signal are approximated and maintained through the inverse combination of local linear methods. The optimization problem can be expressed as:

[0019]

[0020] Where: the symbol ⊙ represents the Hadamard operator; D uv is a symmetric matrix whose diagonal elements are equal to the matrix S u ⊙S v The sum of the elements in the i-th row of ;

[0021] Solve the optimization problem and get the mapping matrix w of u u and the mapping matrix w of v v , and the matrix (w u ,w v )’s eigenvalues;

[0022] Step 3: When positioning the underwater vehicle, obtain the arrival time of the signal from each underwater acoustic base station and construct the matrix u t , obtain the measured values of each underwater acoustic transponder position and form the matrix v t ;

[0023] By using the basis vectors (w u ,w v ) The signal arrival time u t and position v t Mapped to and Each underwater acoustic base station can obtain g signal arrival times within its communication range, and the signal arrival times obtained by n underwater acoustic base stations form a matrix The distance d between the acoustic signal received by the underwater acoustic transponder to be located and the acoustic signal set in the training phase after linear transformation j Expressed as:

[0024]

[0025] Where: k is the kth eigenvalue; represents the kth component of the underwater acoustic signal after linear transformation at the jth sampling point in the training stage; represents the kth component of the underwater acoustic signal received by the underwater acoustic transponder to be located after linear transformation; p is the number of underwater acoustic transponders;

[0026] Step 4: Establish a distributed solution model including the coordinate error of the underwater acoustic base station and the underwater acoustic ranging error. Use the distributed solution output as the search initial value, and improve the fitness function, adaptive crossover probability, and mutation probability of the genetic algorithm for positioning to optimize the position of the underwater acoustic transponder. The specific steps are as follows:

[0027] S4.1. The distance difference between the distance from the i-th underwater acoustic base station a i to the j-th underwater acoustic transponder m j and the distance from the base station a1 to m j can be expressed as where: ||·|| represents the two-norm; since there is an error in the underwater acoustic ranging between the underwater acoustic base station and the underwater acoustic transponder the actual distance difference is expressed as where Δd follows a Gaussian distribution; at the same time, the pre-calibrated underwater acoustic base station has an initial coordinate error Δa = [Δa1, Δa2,..., Δa g T , and the actual coordinate is expressed as where Δa i = [Δx i , Δy i , Δz i T , and Δa follows a Gaussian distribution;

[0028] Establish an underwater transponder position estimation equation:

[0029]

[0030] where is the position estimation value of the j-th underwater acoustic transponder, and θ L+1 is the minimum eigenvalue of the augmented matrix ;

[0031]

[0032] is the geometric distance measurement value between the underwater acoustic base station a i and the underwater acoustic transponder m j ;

[0033] S4.2. Initialize the population with the position estimation[[ID=?]] , and its individual is expressed as It should be noted that there seems to be an unclear tag in the original text at line 68 where it says " " which might be an error or an incomplete reference. I've translated it as best as possible with the available information.E is the overall scale of the population; Gussian(·) is a Gaussian random number; the difference between the distance of an individual from the underwater acoustic base station and the underwater acoustic ranging value is used as the fitness function f(x e (t)):

[0034]

[0035] S4.3 Binary code the individual x e (t), and convert it into binary genes; according to the selection probability Determine excellent individuals. If a random number between 0 and 1 is less than the selection probability p e , then the individual x e (t) is an excellent individual Gx e (t);

[0036] S4.4 Perform gene crossover operations on the determined excellent individuals with an adaptive crossover probability, and the adaptive crossover probability is:

[0037]

[0038] where: p max and p min are the maximum and minimum crossover probabilities, taking values of 0.9 and 0.6 respectively; t max is the maximum number of iterations; f max and f avg are the maximum fitness value and the average fitness value respectively; w is the adaptive weight; if a random number between 0 and 1 is less than the crossover probability p(t), then perform gene crossover operations on this excellent individual;

[0039] S4.5 As the iterative search progresses, it is necessary to improve the population diversity. Arrange the population fitness values in descending order and perform mutation operations on their genes. The mutation probability is where p' max and p' min are the maximum and minimum mutation probabilities. If a random number between 0 and 1 is less than the mutation probability p v , then flip the genes of this individual; if t < t max then continue the iterative search; otherwise, output the optimal individual value as the position of the underwater transponder

[0040] Furthermore, in step 2, the Lagrange multiplier method and the elimination method are used to solve the optimization problem, and the mapping matrix w u of the signal arrival time u and the mapping matrix w v of the position are obtained; and the eigenvalues of the matrix (w u , w v ).

[0041] Furthermore, the geometric distance in step 3 is the Euclidean distance.

[0042] Furthermore, the maximum mutation probability p' in step S4.5 max takes a value of 0.2, and the minimum mutation probability p' min takes a value of 0.02.

[0043] On the other hand, the present invention also discloses an intelligent positioning system for an underwater vehicle with enhanced sparse underwater acoustic ranging, including:

[0044] A global reconstruction matrix construction module (1) for obtaining the global reconstruction matrix of the underwater acoustic network. The specific steps are as follows:

[0045] Collect the arrival times of underwater acoustic signals obtained by each underwater acoustic base station at multiple underwater acoustic transponders located at different positions. The underwater acoustic transponders are installed on the fuselage of the underwater vehicle, and the positions of the underwater acoustic base stations are fixed. The position coordinates of the i-th underwater acoustic base station are a i ; a i The corresponding h-th sample is is the arrival time of the underwater acoustic signal, is the coordinate of the underwater acoustic transponder, h = 1, 2,..., Num, where Num is the total number of samples corresponding to the i-th underwater acoustic base station; i = 1, 2,..., n, and n is the number of underwater acoustic base stations; the samples obtained by the n underwater acoustic base stations form a sample set (u, v), where u is the matrix composed of the arrival times of underwater acoustic signals, and v is the matrix composed of the coordinates of underwater acoustic transponders;

[0046] According to the arrival time of the underwater acoustic signal of the K nearest neighbors to calculate the first local reconstruction weight matrix

[0047]

[0048] where the i-th element of is 0, ||||1 represents the calculation of the 1-norm;

[0049] According to the coordinates of the underwater acoustic transponder of the K nearest neighbors to calculate the second local reconstruction weight matrix

[0050]

[0051] where the i-th element of is 0,

[0052] Construct the first global reconstruction matrix S u , where the element in the i-th row and j-th column of S u is as follows: That is: where ne(i k ) represents the local neighbor set of the paired sample set ;

[0053] The global reconstruction weight matrix in the signal domain considering the underwater acoustic network topology is

[0054] Construct the second global reconstruction matrix S v , where the element in the i-th row and j-th column of S v is as follows: That is:

[0055] The global reconstruction weight matrix in the position domain considering the underwater acoustic network topology is

[0056] The mapping matrix calculation module (2) is used to obtain the mapping matrix w of u and the mapping matrix w of v in the underwater acoustic network u , as well as the eigenvalues of the matrix (w v , w u , w v ); the specific steps are as follows:

[0057] Based on the characteristics of sparse underwater acoustic signals, the global non-linear analysis problem is decomposed into local linear problems, and the original structure characteristics of the underwater acoustic signals are approximated and maintained through the inverse combination of local linearity. Then the optimization problem can be expressed as:

[0058]

[0059] where: the symbol ⊙ represents the Hadamard operator; D uv is a symmetric matrix, and its diagonal elements are equal to the sum of the elements in the i-th row of the matrix s u ⊙ s v ;

[0060] Solve the optimization problem to obtain the mapping matrix w of u u and the mapping matrix w of v v , as well as the eigenvalues of the matrix (w u , w v );

[0061] The position and distance measurement value acquisition module (3) is used to obtain measurement values. The specific steps are as follows:

[0062] When positioning an underwater vehicle, obtain the signal arrival times of each underwater acoustic base station and form a matrix u t, obtain the measurement values of the positions of each underwater acoustic transponder and form a matrix v t ;

[0063] Through the basis vectors (w u , w v ), map the time of arrival of the signal u t and the position v t to and Each underwater acoustic base station can obtain g times of arrival of signals within its communication range. Then, the times of arrival of signals obtained by n underwater acoustic base stations form a matrix The distance d between the underwater acoustic signal received by the underwater acoustic transponder to be located and the set of underwater acoustic signals after linear transformation in the training phase j is expressed as:

[0064]

[0065] where: λ k is the k-th eigenvalue; represents the k-th component after linear transformation of the underwater acoustic signal at the j-th sampling point in the training phase; represents the k-th component after linear transformation of the underwater acoustic signal received by the underwater acoustic transponder to be located; p is the number of underwater acoustic transponders;

[0066] The position optimization module (4) is used to optimize the position measurement values to obtain the optimized estimated value of the position of the underwater acoustic transponder. The specific steps are as follows:

[0067] S4.1. The difference between the distance from the i-th underwater acoustic base station a i to the j-th underwater acoustic transponder m j and the distance from the base station a1 to m j can be expressed as where: ||·|| represents the second norm; Since there is an error in the underwater acoustic ranging between the underwater acoustic base station and the underwater acoustic transponder The actual distance difference is expressed as where Δd conforms to a Gaussian distribution; At the same time, the pre-calibrated underwater acoustic base station has an initial coordinate error Δa = [Δa1, Δa2,..., Δa g T , and the actual coordinates are expressed as where Δa i = [Δx i , Δy i , Δz i T , and Δa conforms to a Gaussian distribution;

[0068] Establish an underwater transponder position estimation equation: ​​

[0069]

[0070] where is the estimated position value of the j-th underwater acoustic transponder, and θ L+1 is the augmented matrix is the minimum eigenvalue of;

[0071]

[0072] is the underwater acoustic base station a i to the underwater acoustic transponder m j is the measured value of the geometric distance between;

[0073] S4.2. Initialize the population with the position estimate The individuals are represented as E is the overall scale of the population; Gussian(·) is a Gaussian random number; the difference between the distance of the individual from the underwater acoustic base station and the underwater acoustic ranging value is used as the fitness function f(x e (t)):

[0074]

[0075] S4.3. Binary code the individual x e (t) and convert it into binary genes; determine the excellent individuals according to the selection probability If a random number between 0 and 1 is less than the selection probability p e , then the individual x e (t) is the excellent individual Gx e (t);

[0076] S4.4. Perform gene crossover operations on the determined excellent individuals with an adaptive crossover probability, and the adaptive crossover probability is:

[0077]

[0078] where: p max and p min are the maximum and minimum crossover probabilities, taking values of 0.9 and 0.6 respectively; t max is the maximum number of iterations; f max and f avg are the maximum fitness value and the average fitness value respectively; w is the adaptive weight; if a random number between 0 and 1 is less than the crossover probability p(t), then perform gene crossover operations on this excellent individual;

[0079] S4.5. As the iterative search progresses, it is necessary to improve the population diversity. The population is sorted in descending order according to the fitness value, and its genes are mutated. The mutation probability is where p' max and p' min are the maximum and minimum mutation probabilities. If a random number between 0 and 1 is less than the mutation probability p v , then the genes of this individual are flipped; if t < t max , then continue the iterative search; otherwise, output the optimal individual value as the position of the underwater transponder

[0080] Beneficial effects: The intelligent positioning method and system for underwater vehicles with enhanced sparse underwater acoustic ranging disclosed by the present invention have the following advantages:

[0081] (1) Introduce the underwater acoustic network topology into underwater acoustic ranging. By fusing local non-linear related underwater acoustic signals, the performance of underwater acoustic ranging is enhanced, and a mapping between the underwater acoustic signal domain and the vehicle position domain for underwater vehicle positioning is established, weakening the influence of uncertain noise on the positioning performance of underwater vehicles;

[0082] (2) Unmodeled underwater acoustic measurement errors are likely to introduce ill-conditioned matrices into distributed solutions. By introducing underwater acoustic base station calibration errors and underwater acoustic ranging errors into the underwater acoustic distributed positioning solution model, relatively large positioning errors are likely to be brought to the positioning solution of underwater vehicles in some underwater areas;

[0083] (3) Considering the problems of slow search speed and low positioning accuracy in the whole positioning space by the classical genetic algorithm through randomly generated populations, use the position obtained by distributed solution as the search initial value, and design corresponding fitness functions, adaptive crossover probabilities, and mutation probabilities according to the underwater vehicle positioning problem to improve the search efficiency and avoid being trapped in local optima as much as possible. Brief description of the drawings

[0084] Figure 1 is a flowchart of the intelligent positioning method for underwater vehicles with enhanced sparse underwater acoustic ranging disclosed by the present invention;

[0085] Figure 2 is a schematic diagram of the composition of the intelligent positioning system for underwater vehicles with enhanced sparse underwater acoustic ranging disclosed by the present invention. Detailed implementation manners

[0086] The present invention will be further clarified below in conjunction with the drawings and specific implementation manners.

[0087] The present invention discloses an intelligent positioning method for underwater vehicles with enhanced sparse underwater acoustic ranging. As Figure 1 shown, it includes the steps:

[0088] Step 1: At multiple different positions of the underwater acoustic transponders, collect the arrival times of the underwater acoustic signals obtained by each underwater acoustic base station. The underwater acoustic transponders are installed on the fuselage of the underwater vehicle, and the positions of the underwater acoustic base stations are fixed. The position coordinates of the i-th underwater acoustic base station are a i ; a i The corresponding h-th sample is is the arrival time of the underwater acoustic signal, is the coordinate of the underwater acoustic transponder, h = 1, 2, …, Num, and Num is the total number of samples corresponding to the i-th underwater acoustic base station; i = 1, 2, ..., n, and n is the number of underwater acoustic base stations; the samples obtained by the n underwater acoustic base stations form a sample set (u, v), where u is the matrix composed of the arrival times of the underwater acoustic signals, and v is the matrix composed of the coordinates of the underwater acoustic transponders;

[0089] According to the arrival time of the underwater acoustic signal of the K nearest neighbors to calculate the first local reconstruction weight matrix

[0090]

[0091] where the i-th element of is 0, ||·||1 represents the 1-norm calculation;

[0092] According to the coordinates of the underwater acoustic transponder of the K nearest neighbors to calculate the second local reconstruction weight matrix

[0093]

[0094] where the i-th element of is 0,

[0095] Construct the first global reconstruction matrix S u , S u the element in the i-th row and j-th column of is: where ne(i k ) represents the local neighbor set of the paired sample set ;

[0096] The signal domain global reconstruction weight matrix considering the underwater acoustic network topology structure is

[0097] Construct the second global reconstruction matrix S v , S v the element in the i-th row and j-th column of is as follows:

[0098] The position domain global reconstruction weight matrix considering the underwater acoustic network topology structure is

[0099] Step 2: Based on the sparse underwater acoustic signal characteristics, decompose the global non-linear analysis problem into local linear problems, and approximate and maintain the original structure characteristics of the underwater acoustic signal through the inverse combination of local linearity. Then the optimization problem can be expressed as:

[0100]

[0101] where: the symbol ⊙ represents the Hadamard operator; D uv is a symmetric matrix, and its diagonal elements are equal to the sum of the elements in the i-th row of the matrix S u ⊙S v ;

[0102] Solve the optimization problem to obtain the mapping matrix w of u u and the mapping matrix w of v v , and the eigenvalues of the matrix (w u , w v );

[0103] In this embodiment, the Lagrange multiplier method and the elimination method are used to solve the optimization problem to obtain the mapping matrix w of u u and the mapping matrix w of v v ; and the eigenvalues of the matrix (w u , w v );

[0104] Step 3: When positioning the underwater vehicle, obtain the signal arrival times of each underwater acoustic base station and form a matrix u t , obtain the measured values of the positions of each underwater acoustic transponder and form a matrix v t ;

[0105] Map the signal arrival time u u , w v ) and the position v t and position v t to and Each underwater acoustic base station can obtain g signal arrival times within its communication range. Then the signal arrival times obtained by n underwater acoustic base stations form a matrix The distance d between the underwater acoustic signal received by the underwater acoustic transponder to be positioned and the underwater acoustic signal set after linear transformation in the training phase j is expressed as:

[0106]

[0107] where: λ k is the k-th eigenvalue; represents the k-th component after the linear transformation of the underwater acoustic signal at the j-th sampling point in the training stage; represents the k-th component after the linear transformation of the underwater acoustic signal received by the underwater acoustic transponder to be located; p is the number of underwater acoustic transponders;

[0108] Step 4: Establish a distributed solution model including the coordinate error of the underwater acoustic base station and the underwater acoustic ranging error, use the distributed solution output as the search initial value, and improve the fitness function, adaptive crossover probability, and mutation probability of the genetic algorithm for positioning to optimize the position of the underwater acoustic transponder; specifically including the following steps:

[0109] S4.1. The distance difference between the i-th underwater acoustic base station a i and the j-th underwater acoustic transponder m j and the distance between the base station a1 and m j can be expressed as where: ||·|| represents the two-norm; since there is an error in the underwater acoustic ranging between the underwater acoustic base station and the underwater acoustic transponder the actual distance difference is expressed as where Δd conforms to Gaussian distribution; at the same time, the pre-calibrated underwater acoustic base station has an initial coordinate error Δa = [Δa1, Δa2,..., Δa g T , and the actual coordinate is expressed as where Δa i = [Δx i , Δy i , Δz i T , and Δa conforms to Gaussian distribution;

[0110] Considering the coordinate error Δa of the underwater acoustic base station and the ranging error Δd of the underwater acoustic, g arrival times can establish g - 1 equations to establish an underwater transponder position estimation equation:

[0111]

[0112] where is the position estimated value of the j-th underwater acoustic transponder, and θ L+1 is the minimum eigenvalue of the augmented matrix ;

[0113]

[0114] ​​For the underwater acoustic base station a i to the underwater acoustic transponder m j the measured value of the geometric distance between them;

[0115] S4.2. Since the estimated value of the position of the underwater acoustic transponder is sensitive to the ranging error, the calibration error of the underwater acoustic base station, and the uncertain error caused by the ill-conditioned matrix in the solution process, the present invention uses an improved genetic algorithm to fuse and optimize the positioning result, specifically as follows:

[0116] Initialize the population with the position estimate where the individuals are represented as E is the total size of the population; Gussian(·) is a Gaussian random number; the difference between the distance of the individual from the underwater acoustic base station and the underwater acoustic ranging value is used as the fitness function f(x e (t)):

[0117]

[0118] S4.3 Binary code the individual x e (t) and convert it into binary genes; determine the excellent individuals according to the selection probability if a random number between 0 and 1 is less than the selection probability p e , then the individual x e (t) is the excellent individual Gx e (t);

[0119] S4.4. In order to balance the genetic genes and the search speed performance, the present invention performs gene crossover operations on the determined excellent individuals with an adaptive crossover probability, and the adaptive crossover probability is:

[0120]

[0121] where: p max and p min are the maximum and minimum crossover probabilities, taking values of 0.9 and 0.6 respectively; t max is the maximum number of iterations; f max and f avg are the maximum fitness value and the average fitness value respectively; w is the adaptive weight; if a random number between 0 and 1 is less than the crossover probability p(t), then perform gene crossover operations on this excellent individual;

[0122] S4.5. As the iterative search progresses, it is necessary to improve the population diversity. Arrange the population in descending order of fitness value and perform mutation operations on its genes, and the mutation probability is where p' max and p' minare the maximum and minimum mutation probabilities; in this embodiment, the maximum mutation probability p' max is set to 0.2, and the minimum mutation probability p' min is set to 0.02; if a random number between 0 and 1 is less than the mutation probability p v , then the genes of this individual are flipped; if t < t max , then continue the iterative search; otherwise, output the optimal individual value as the position of the underwater transponder and then obtain the position coordinates of the underwater vehicle.

[0123] Since the sparse underwater acoustic signal measurement noise can affect the accuracy of underwater acoustic ranging and the positioning of underwater vehicles, the present invention performs fusion enhancement on the local underwater acoustic signals to improve the underwater acoustic ranging performance. On this basis, considering the coordinate error of the underwater acoustic base station and the underwater acoustic ranging error, an underwater acoustic distributed solution model is established and its output is used as the initial value of the population of the improved genetic algorithm. At the same time, based on the actual positioning optimization problem of underwater vehicles in the underwater acoustic network, the fitness function, adaptive crossover probability, and population mutation are improved, integrating the advantages of distributed positioning and intelligent search algorithms, and improving the positioning performance of underwater vehicles in the entire area.

[0124] The present invention also discloses a system for implementing the intelligent positioning method of an underwater vehicle for sparse underwater acoustic ranging enhancement, as Figure 2 shown, including:

[0125] A global reconstruction matrix construction module 1, which is used to obtain the global reconstruction matrix of the underwater acoustic network. The specific steps are as follows:

[0126] Collect the arrival times of underwater acoustic signals obtained by each underwater acoustic base station at multiple underwater acoustic transponders located at different positions. The underwater acoustic transponders are installed on the fuselage of the underwater vehicle, and the positions of the underwater acoustic base stations are fixed. The position coordinates of the i-th underwater acoustic base station are a i ; a i The corresponding h-th sample is is the arrival time of the underwater acoustic signal, is the coordinate of the underwater acoustic transponder, h = 1, 2,..., Num, and Num is the total number of samples corresponding to the i-th underwater acoustic base station; i = 1, 2,..., n, and n is the number of underwater acoustic base stations;

[0127] According to the K-nearest neighbor of the arrival time of the underwater acoustic signal to calculate the first local reconstruction weight matrix of the i-th underwater acoustic base station

[0128]

[0129] where the i-th element of is 0, ||·||1 represents the calculation of the 1-norm;

[0130] According to the coordinates of the underwater acoustic transponder of the K nearest neighbors to calculate the weight matrix of the second local reconstruction of the i-th underwater acoustic base station

[0131]

[0132] where the i-th element of is 0,

[0133] Construct the first global reconstruction matrix S u , S u the element in the i-th row and j-th column of is: where ne(i k ) represents the local neighbor set of the paired sample set ;

[0134] The global reconstruction weight matrix considering the underwater acoustic network topology in the signal domain is

[0135] Construct the second global reconstruction matrix S u , S u the element in the i-th row and j-th column of is:

[0136] The global reconstruction weight matrix considering the underwater acoustic network topology in the position domain is

[0137] The mapping matrix calculation module 2 is used to obtain the mapping matrix w of u and the mapping matrix w of v of the underwater acoustic network u and the eigenvalues of the matrix (w v , w u , w v ); The specific steps are:

[0138] Based on the characteristics of sparse underwater acoustic signals, the global non-linear analysis problem is decomposed into local linear problems, and the original structure characteristics of the underwater acoustic signals are approximated and maintained through the inverse combination of local linearity. Then the optimization problem can be expressed as:

[0139]

[0140] where: the symbol ⊙ represents the Hadamard operator; D uv is a symmetric matrix, and its diagonal elements are equal to the sum of the elements in the i-th row of the matrix S u ⊙ S v ;

[0141] Solve the optimization problem to obtain the mapping matrix w of u u and the mapping matrix w of v v , and the eigenvalues of the matrix (w u , w v );

[0142] The position and distance measurement value acquisition module 3 is used to acquire measurement values. The specific steps are as follows:

[0143] When positioning an underwater vehicle, obtain the signal arrival times of each underwater acoustic base station and form a matrix u t , obtain the measurement values of the positions of each underwater acoustic transponder and form a matrix v t ;

[0144] Through the basis vectors (w u , w v ), map the signal arrival time u t and the position v t to and If each underwater acoustic base station can obtain g signal arrival times within its communication range, the signal arrival times obtained by n underwater acoustic base stations form a matrix The distance d between the underwater acoustic signal received by the underwater acoustic transponder to be positioned and the linearly transformed underwater acoustic signal set in the training stage j is expressed as:

[0145]

[0146] where: λ k is the k-th eigenvalue; represents the k-th component after linear transformation of the underwater acoustic signal at the j-th sampling point in the training stage; represents the k-th component after linear transformation of the underwater acoustic signal received by the underwater acoustic transponder to be positioned; p is the number of underwater acoustic transponders;

[0147] The position optimization module 4 is used to optimize the position measurement values to obtain the optimized position estimation value of the underwater acoustic transponder. The specific steps are as follows:

[0148] S4.1. The difference between the distance from the i-th underwater acoustic base station a i to the j-th underwater acoustic transponder m j and the distance from the base station a1 to m j can be expressed as where: ||·|| represents the two-norm; due to the error in underwater acoustic ranging between the underwater acoustic base station and the underwater acoustic transponder The actual distance difference is expressed as where Δd conforms to Gaussian distribution; meanwhile, the pre-calibrated underwater acoustic base station has an initial coordinate error Δa = [Δa1, Δa2,..., Δa g T , and the actual coordinate is expressed as where Δa i = [Δx i , Δy i , Δz i T , and Δa conforms to Gaussian distribution;

[0149] Establish an underwater transponder position estimation equation:

[0150]

[0151] where is the position estimation value of the j-th underwater acoustic transponder, and θ L+1 is the minimum eigenvalue of the augmented matrix ;

[0152]

[0153] is the geometric distance measurement value from the underwater acoustic base station a i to the underwater acoustic transponder m j ;

[0154] S4.2. Initialize the population with the position estimation , and its individuals are expressed as E is the total size of the population; Gussian(·) is a Gaussian random number; the difference between the distance of the individual from the underwater acoustic base station and the underwater acoustic ranging value is used as the fitness function f(x e (t)):

[0155] <{

[0156] S4.3 Binary-encode the individual x e (t) and convert it into binary genes; determine the excellent individuals according to the selection probability . If a random number between 0 and 1 is less than the selection probability p e , then the individual x e (t) is an excellent individual Gx e (t);

[0157] S4.4. Perform a gene crossover operation on the determined excellent individuals with an adaptive crossover probability, and the adaptive crossover probability is: ​​

[0158]

[0159] where: p max and p min are the maximum and minimum crossover probabilities, taking values of 0.9 and 0.6 respectively; t max is the maximum number of iterations; f max and f avg are the maximum fitness value and the average fitness value respectively; w is the adaptive weight; if a random number between 0 and 1 is less than the crossover probability p(t), then gene crossover operation is performed on this excellent individual;

[0160] S4.5. As the iterative search progresses, it is necessary to improve the population diversity. Arrange the population in descending order of fitness value and perform mutation operation on its genes. The mutation probability is where p' max and p' min are the maximum and minimum mutation probabilities. If a random number between 0 and 1 is less than the mutation probability p v , then flip the genes of this individual; if t < t max then continue the iterative search; otherwise, output the optimal individual value as the position of the underwater transponder

Claims

1. An intelligent positioning method for an underwater vehicle with enhanced sparse underwater acoustic ranging, characterized in that, Including the steps: Step 1: Collect the arrival times of the underwater acoustic signals obtained by each underwater acoustic base station at multiple underwater acoustic transponders located at different positions. The underwater acoustic transponders are installed on the fuselage of the underwater vehicle, and the positions of the underwater acoustic base stations are fixed. The position coordinates of the i-th underwater acoustic base station are a i ; a i The corresponding h-th sample is is the arrival time of the underwater acoustic signal, is the coordinate of the underwater acoustic transponder, h = 1, 2, …, Num, where Num is the total number of samples corresponding to the i-th underwater acoustic base station; i = 1, 2, …, n, where n is the number of underwater acoustic base stations; the samples obtained by the n underwater acoustic base stations form a sample set (u, v), where u is the matrix composed of the arrival times of the underwater acoustic signals, and v is the matrix composed of the coordinates of the underwater acoustic transponders; According to the arrival time of the underwater acoustic signal K nearest neighbors to calculate the first local reconstruction weight matrix of the i-th underwater acoustic base station wherein the i-th element of ||||1 indicates 1-norm calculation; According to the coordinates of the underwater acoustic transponder K nearest neighbors to calculate the weight matrix of the second local reconstruction of the i-th underwater acoustic base station wherein the i-th element of Construct the first global reconstruction matrix S u , where the element in the u i-th row and j-th column of S is given by where ne(i k ) represents the local nearest neighbor set of the paired sample set ; The signal domain global reconstruction weight matrix considering the underwater acoustic network topology is Construct the second global reconstruction matrix S v , S v The element in the i-th row and j-th column of is: The position-domain global reconstruction weight matrix considering the underwater acoustic network topology is Step 2: Based on the characteristics of sparse underwater acoustic signals, decompose the global non-linear analysis problem into local linear problems, and approximate and maintain the structural characteristics of the original underwater acoustic signals through the inverse combination of local linearity. Then the optimization problem is expressed as: where: the symbol ⊙ represents the Hadamard operator; D uv is a symmetric matrix, and its diagonal elements are equal to the sum of the elements of the u i-th row of the matrix S v ⊙ S Solve the optimization problem to obtain the mapping matrix w of u u and the mapping matrix w of v v , as well as the eigenvalues of the matrix (w u , w v ); Step 3: When positioning the underwater vehicle, obtain the signal arrival times of each underwater acoustic base station and form a matrix u t , obtain the measured values of the positions of each underwater acoustic transponder and form a matrix v t ; By basis vectors (w u , w v ), the time of arrival of the signal u t and the position v t are mapped to and Each underwater acoustic base station can obtain g times of arrival of signals within its communication range. Then, the times of arrival of signals obtained by n underwater acoustic base stations form a matrix The distance d between the underwater acoustic signal received by the underwater acoustic transponder to be located and the underwater acoustic signal set after linear transformation in the training phase j is expressed as: where: λ k is the k-th eigenvalue; represents the k-th component after linear transformation of the underwater acoustic signal at the j-th sampling point in the training stage; represents the k-th component after linear transformation of the underwater acoustic signal received by the underwater acoustic transponder to be located; p is the number of underwater acoustic transponders; Step 4: Establish a distributed solution model including the coordinate error of the underwater acoustic base station and the underwater acoustic ranging error. Use the distributed solution output as the search initial value, and improve the fitness function, adaptive crossover probability, and mutation probability of the genetic algorithm for positioning to optimize the position of the underwater acoustic transponder. Specifically, it includes the following steps: S4.

1. The distance difference between the \(i\)-th underwater acoustic base station \(a\) i and the \(j\)-th underwater acoustic transponder \(m\) j is denoted as the distance difference between base station \(a1\) and \(m\) j where: \(\|\cdot\|\) represents the two-norm; since there is an error in the underwater acoustic ranging between the underwater acoustic base station and the underwater acoustic transponder the actual distance difference is denoted as where \(\Delta d\) follows a Gaussian distribution; meanwhile, the pre-calibrated underwater acoustic base station has an initial coordinate error \(\Delta a = [\Delta a_1,\Delta a_2,\cdots,\Delta a\) g T and the actual coordinates are denoted as where \(\Delta a\) i = [\Delta x\) i ,\Delta y\) i ,\Delta z\) i T and \(\Delta a\) follows a Gaussian distribution;​​​ Establish an underwater transponder position estimation equation: wherein is the position estimation value of the j-th underwater acoustic transponder, and θ L+1 is the augmented matrix is the minimum eigenvalue; is the geometric distance measurement value between the underwater acoustic base station a i and the underwater acoustic transponder m j ; S4.

2. Location Estimation Initialize the population, and its individuals are represented as e = 1, 2, …, E, where E is the total size of the population; Gussian(·) is a Gaussian random number; the difference between the distance from the individual to the underwater acoustic base station and the underwater acoustic ranging value is used as the fitness function f(x e (t)): S4.3 Binary code individual x e (t) and convert it into a binary gene; According to the selection probability determine the excellent individuals. If the random number between 0 and 1 is less than the selection probability p e , then individual x e (t) is the excellent individual Gx e (t); S4.4: Perform gene crossover operations on the determined excellent individuals with the adaptive crossover probability, and the adaptive crossover probability is: where: p max and p min are the maximum and minimum crossover probabilities, taking values of 0.9 and 0.6 respectively; t max is the maximum number of iterations; f max and f avg are the maximum fitness value and the average fitness value respectively; w is the adaptive weight; if a random number between 0 and 1 is less than the crossover probability p(t), then genetic crossover operation is performed on this excellent individual; S4.

5. As the iterative search progresses, it is necessary to increase the population diversity. The population is sorted in descending order of fitness values and gene mutation operations are performed on them. The mutation probability is where p' max and p' min are the maximum and minimum mutation probabilities. If a random number between 0 and 1 is less than the mutation probability p v , then the gene of this individual is flipped; if t < t max , continue the iterative search; otherwise, output the optimal individual value as the position of the underwater transponder 2. The underwater vehicle intelligent positioning method according to claim 1, characterized in that In step 2, the Lagrange multiplier method and the elimination method are used to solve the optimization problem, and the mapping matrix w of u is obtained. u and the mapping matrix w of v v ; and the eigenvalues of the matrix (w u , w v ).

3. The underwater vehicle intelligent positioning method according to claim 1, wherein The geometric distance in Step 4 is the Euclidean distance.

4. The intelligent positioning method for an underwater vehicle according to claim 1, characterized in that, The maximum mutation probability p' in the step S4.5 max takes the value of 0.2, and the minimum mutation probability p' min takes the value of 0.

02.

5. An intelligent positioning system for an underwater vehicle with enhanced sparse underwater acoustic ranging, characterized in that, Including: Global reconstruction matrix construction module (1), used to obtain the global reconstruction matrix of the underwater acoustic network. The specific steps are: Collect the arrival times of the underwater acoustic signals obtained by each underwater acoustic base station at multiple underwater acoustic transponders located at different positions. The underwater acoustic transponders are installed on the fuselage of the underwater vehicle, and the positions of the underwater acoustic base stations are fixed. The position coordinates of the i-th underwater acoustic base station are a i ; a i The corresponding h-th sample is is the arrival time of the underwater acoustic signal, is the coordinate of the underwater acoustic transponder, h = 1, 2, …, Num, where Num is the total number of samples corresponding to the i-th underwater acoustic base station; i = 1, 2, …, n, where n is the number of underwater acoustic base stations; the samples obtained by the n underwater acoustic base stations form a sample set (u, v), where u is the matrix composed of the arrival times of the underwater acoustic signals, and v is the matrix composed of the coordinates of the underwater acoustic transponders; According to the arrival time of the underwater acoustic signal of the K nearest neighbors to calculate the first local reconstruction weight matrix of the i-th underwater acoustic base station wherein the i-th element of ||||1 indicates the calculation of the 1-norm; According to the coordinates of the underwater acoustic transponder K nearest neighbors to calculate the weight matrix of the second local reconstruction of the i-th underwater acoustic base station wherein the i-th element of Construct the first global reconstruction matrix S u , the element in the i-th row and j-th column of S u is as follows: where ne(i ) represents the local nearest neighbor set of the paired sample set k ; ​ The signal domain global reconstruction weight matrix considering the underwater acoustic network topology is Construct the second global reconstruction matrix S v , the v element in the i-th row and j-th column of S is: The position-domain global reconstruction weight matrix considering the underwater acoustic network topology is The mapping matrix calculation module (2) is used to obtain the mapping matrix w of the signal arrival time u of the underwater acoustic network u and the mapping matrix w of the position v v , and the eigenvalues of the matrix (w u , w v ); The specific steps are: Based on the characteristics of sparse underwater acoustic signals, decompose the global non-linear analysis problem into local linear problems, and approximate and maintain the structural characteristics of the original underwater acoustic signals through the inverse combination of local linearity. Then the optimization problem is expressed as: where: the symbol ⊙ represents the Hadamard operator; D uv is a symmetric matrix, the diagonal elements of which are equal to the sum of the elements of the i-th row of the matrix S u ⊙S v ; Solve the optimization problem to obtain the mapping matrix w of u u and the mapping matrix w of v v , as well as the eigenvalues of the matrix (w u , w v ); Position and distance measurement value acquisition module (3), used to acquire measurement values. The specific steps are: When positioning an underwater vehicle, obtain the signal arrival times of each underwater acoustic base station and form a matrix u t , obtain the measured values of the positions of each underwater acoustic transponder and form a matrix v t ; Through the basis vectors (w u , w v ), the time of arrival of the signal u t and the position v t are mapped to and Each underwater acoustic base station can obtain g times of arrival of signals within its communication range. Then, the times of arrival of signals obtained by n underwater acoustic base stations form a matrix The distance d between the underwater acoustic signal received by the underwater acoustic transponder to be located and the set of underwater acoustic signals after linear transformation in the training phase j is expressed as: Where: λ k is the k-th eigenvalue; represents the k-th component after the linear transformation of the underwater acoustic signal at the j-th sampling point in the training stage; represents the k-th component after the linear transformation of the underwater acoustic signal received by the underwater acoustic transponder to be located; p is the number of underwater acoustic responses; Position optimization module (4), used to optimize the position measurement value to obtain the optimized position estimation value of the underwater acoustic transponder. The specific steps are: S4.

1. The distance difference between the $i$-th underwater acoustic base station $a$ i and the $j$-th underwater acoustic transponder $m$ j is denoted as the distance difference between base station $a_1$ and $m$ j where: $\|\cdot\|$ represents the Euclidean norm; due to the error in underwater acoustic ranging between the underwater acoustic base station and the underwater acoustic transponder the actual distance difference is denoted as where $\Delta d$ follows a Gaussian distribution; meanwhile, the pre-calibrated underwater acoustic base station has an initial coordinate error $\Delta a = [\Delta a_1, \Delta a_2, \ldots, \Delta a$ g T and the actual coordinates are denoted as where $\Delta a$ i $= [\Delta x$ i , $\Delta y$ i , $\Delta z$ i T and $\Delta a$ follows a Gaussian distribution;​​​ Establish an underwater transponder position estimation equation: where is the estimated position value of the j-th underwater acoustic transponder, and θ L+1 is the augmented matrix is the minimum eigenvalue; For the underwater acoustic base station a i To the geometric distance measurement value between the underwater acoustic transponder m j And; S4.

2. Position estimation Initialize the population, where the individuals are represented as e = 1, 2, …, E, where E is the total size of the population; Gussian(·) is a Gaussian random number; the difference between the distance of the individual from the underwater acoustic base station and the underwater acoustic ranging value is used as the fitness function f(x e (t)): S4.3 Binary code individual x e (t), convert it into a binary gene; According to the selection probability Determine the excellent individuals. If the random number between 0 and 1 is less than the selection probability p e , then individual x e (t) is the excellent individual Gx e (t); S4.4: Perform gene crossover operations on the determined excellent individuals with the adaptive crossover probability, and the adaptive crossover probability is: where: p max and p min are the maximum and minimum crossover probabilities, taking values of 0.9 and 0.6 respectively; t max is the maximum number of iterations; f max and f avg are the maximum fitness value and the average fitness value respectively; w is the adaptive weight; if a random number between 0 and 1 is less than the crossover probability p(t), then genetic crossover operation is performed on this excellent individual; S4.

5. As the iterative search progresses, it is necessary to improve the population diversity. The population is sorted in descending order according to the fitness value, and mutation operations are performed on its genes. The mutation probability is where p' max and p' min are the maximum and minimum mutation probabilities. If a random number between 0 and 1 is less than the mutation probability p v , then the genes of this individual are flipped; if t < t max , then continue the iterative search; otherwise, output the optimal individual value as the position of the underwater transponder 6. The underwater vehicle intelligent positioning system according to claim 5, wherein In the mapping matrix calculation module (2), the Lagrange multiplier method and the elimination method are used to solve the optimization problem, and the mapping matrix w of u is obtained. u and the mapping matrix w of v v ; and the eigenvalues of the matrix (w u , w v ).

7. The underwater vehicle intelligent positioning system according to claim 5, wherein, The geometric distance in the position optimization module (4) is the Euclidean distance.

8. The underwater vehicle intelligent positioning system according to claim 5, characterized in that, The maximum mutation probability p' in the position optimization module (4) max takes the value of 0.2, and the minimum mutation probability p' min takes the value of 0.02.

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