A Long Baseline Positioning Method Based on Chan and Parallel Swarm Intelligence Algorithm

Abstract

The present invention discloses a long baseline positioning method based on the Chan and parallel swarm intelligence algorithms. The method includes: obtaining a population search interval by using the Chan algorithm according to the time delay and the sound source position; performing chaotic initialization within the population search interval based on a chaotic sequence to generate an initial population; screening the optimal opposite solutions of population individuals based on a greedy rule and an orthogonal opposition learning strategy to improve the algorithm convergence speed; mutating the optimal and sub-optimal individuals of the population based on a Gaussian-Cauchy mixed mutation factor to balance the global search ability of the algorithm and the ability to jump out of local optimal solutions; using a parallel strategy and a screening mechanism to select the optimal solution and output the optimal individual as the positioning result. The present invention improves on the original African vulture algorithm, enhances the global search ability of the algorithm, avoids falling into local optimal solutions, improves the algorithm convergence speed, improves the positioning performance of the algorithm in a low signal-to-noise ratio environment, and has strong engineering application capabilities.

Description

Technical Field

[0001] The present invention belongs to a long baseline positioning method in the field of underwater acoustics, and specifically relates to a long baseline positioning method based on the Chan algorithm and a parallel swarm intelligence algorithm. Background Art

[0002] With the development of society and the progress of science, people have paid more and more attention to the ocean. The ocean contains rich resources, so countries have competed to formulate marine science development plans, give priority to the development of marine science and technology, and increase the intensity of ocean development. Underwater positioning and navigation technology is the basic premise for all marine development activities and the development of marine high-tech. Since the propagation attenuation of electromagnetic waves in the ocean is very large and the propagation distance is very limited. Therefore, electromagnetic waves cannot be used for communication in the ocean as on land. Sound waves are currently the only known form of energy that can propagate long distances in the ocean, and their propagation loss in water is much smaller than that of electromagnetic waves. Therefore, underwater acoustics has developed with the development and utilization of the ocean and has been widely used.

[0003] There are many classification criteria for underwater acoustic positioning systems. According to the different element spacings, they can be divided into Long Baseline (LBL) positioning systems, Short Baseline (SBL) positioning systems, and Ultra Short Baseline (USBL) positioning systems. Compared with SBL and USBL, LBL has a wider positioning range and higher positioning accuracy. Traditional long baseline positioning algorithms can be mainly divided into two categories. One is the analytical method. Such algorithms usually linearize the non-linear model and then use the least squares method for solution. They have the characteristics of simple solution and easy implementation, but the positioning accuracy is not high under low signal-to-noise ratio conditions. The second category is the iterative method. For example, using the Taylor series expansion to perform a first-order Taylor series expansion on the long baseline positioning model to achieve linearization, and then using methods such as the Gauss-Newton method for iterative solution. This type of method has problems such as being sensitive to the selection of the initial point and not necessarily converging. In recent years, more and more researchers have tried to use swarm intelligence optimization algorithms to solve underwater acoustic positioning problems. Algorithms such as genetic algorithms and particle swarm algorithms have been used to solve underwater acoustic positioning problems. However, the convergence speed of these intelligent algorithms is slow, the global search ability is not strong, and the ability to jump out of local optimal solutions is weak. In the past two decades, intelligent optimization algorithms have developed vigorously, and a series of excellent intelligent optimization algorithms have emerged. The African vulture optimization algorithm was proposed in 2021. After testing with the CEC2014 benchmark function, its solution accuracy and convergence speed for unimodal and multimodal multi-modal problems are better than other algorithms. However, there are still areas that need improvement: during the early exploration process, a certain development mechanism was introduced to accelerate the convergence speed, but this affected the global search ability of individuals in the solution space; in the later stage of the search, all population individuals consider the optimal or sub-optimal individuals, which affects the ability of the algorithm to jump out of local optimal solutions.

[0004] In summary, the application of the African vulture algorithm in long baseline positioning is less, and there are still some deficiencies in the global search and the ability to jump out of local optimal solutions; in a low signal-to-noise ratio or large-scale positioning environment, it will inevitably affect the positioning accuracy. Summary of the Invention

[0005] To solve the problems existing in the background technology, the present invention provides a long baseline positioning method based on the Chan algorithm and the parallel swarm intelligence algorithm. First, based on the effective sound speed theory, the sound speed of the sound ray is corrected, and the effective sound speed is used to characterize the overall average sound speed of the sound ray on the propagation path; the Chan algorithm is used to obtain the initial value of the target position and the population search interval; in the initial stage of the intelligent algorithm, chaos theory is used for initialization, and the chaotic initial population is iteratively generated according to the initial value of the target position to enhance the traversability of the search; during the search process, for the optimal individual, a Gaussian-Cauchy hybrid mutation factor is introduced to improve its global search ability in the early stage of the search and its ability to jump out of the local optimal solution in the later stage of the search; for the individual after position update, an orthogonal opposition learning strategy based on the greedy rule is introduced to optimize the convergence speed of the algorithm; a parallel structure is used, and multiple sub-optimization systems simultaneously solve the problem to reduce the influence of random errors.

[0006] The specific technical solution of the present invention is as follows:

[0007] 1) Based on the time delay information, find the corresponding effective sound speed in the effective sound speed table;

[0008] 2) According to the current effective sound speed and the corresponding effective time delay, use the Chan algorithm to obtain the initial position of the target, and then use the parallel swarm intelligence optimization algorithm to optimize and update the initial position of the target to obtain the optimal position of the target, so as to achieve the optimal positioning of the target.

[0009] The specific content of S1 is as follows:

[0010] According to the time delay measured in the experiment, find the position t in the effective time delay table t e in, and find the effective sound speed c in the effective sound speed table c eij e in, and find the effective sound speed c eij .

[0011] The specific content of 2) is as follows:

[0012] First, set multiple sub-optimization systems, and then multiple sub-optimization systems respectively search for the optimal individual of the population according to the initial position of the target, and respectively obtain the optimal individuals corresponding to the multiple sub-optimization systems. Then, select the final optimal individual according to the fitness of the optimal individuals in the multiple sub-optimization systems, and use the position of the final optimal individual as the optimal position of the target to achieve the optimal positioning of the target.

[0013] For the search for the optimal individual of the population according to the initial population in each of the sub-optimization systems, and respectively obtaining the optimal individuals corresponding to the multiple sub-optimization systems, the specific content is as follows:

[0014] S1: In the population search interval, based on the initial position of the target and the chaos function, perform chaos initialization to generate the initial population;

[0015] S2: Calculate the fitness of all individuals in the current population, and select the optimal individual and the sub-optimal individual according to the fitness.

[0016] S3: Set the probability of the population entering the exploitation stage and the optimal / sub-optimal selection probability, select the moving direction of ordinary individuals based on the roulette wheel strategy, and calculate the hunger value of ordinary individuals after moving.

[0017] S4: Mutate the current optimal individual and the sub-optimal individual using a Gaussian-Cauchy hybrid mutation factor to obtain the corresponding mutated individuals, compare the current optimal individual, the sub-optimal individual and their respective mutated individuals based on the greedy strategy, and select the two best individuals as the new optimal individual and the sub-optimal individual.

[0018] S5: Select different position update strategies according to the individual hunger value to update the positions of all individuals in the current population, and obtain the offspring population of the current population.

[0019] S6: Optimize the current offspring population using the orthogonal opposition learning method and the greedy strategy to obtain a new offspring population as the new population, calculate the fitness of all individuals in the current population, and select the optimal individual and the sub-optimal individual according to the fitness.

[0020] S7: According to the current population and its optimal individual and sub-optimal individual, repeat S3 - S5 until the fitness of the optimal individual in the current population is less than the set fitness threshold or the number of iterations reaches the maximum number of iterations, and obtain the optimal individual of the current sub-optimization system.

[0021] Specifically, S1 is as follows:

[0022] First, after normalizing the initial position (x, y, z) of the target according to the population search interval, obtain the chaotic initial value u1, and the formula is as follows:

[0023]

[0024]

[0025]

[0026] where x, y, and z are the values of the initial position of the target in the x, y, and z dimensions respectively, x max , y max , z max are the upper limits of the search intervals of the population in the x, y, and z dimensions respectively, x min , y min , z min are the lower limits of the search intervals of the population in the x, y, and z dimensions respectively, u 1x , u 1y , u1z They are the values of the initial chaotic value u1 in the x, y, and z dimensions respectively;

[0027] Next, according to the initial chaotic value u1, a chaotic sequence U in the range of [0, 1] is generated using the Tent chaotic function c = [u2, u3, …, u N ;

[0028] Finally, after multiplying the chaotic sequence U c = [u2, u3, …, u N by the population search interval, the initial population X is obtained.

[0029] The fitness of the individual is calculated using the fitness function, and the calculation formula is as follows:

[0030] f = (ΔS - CS + S1) T (ΔS - CS + S1)

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] Among them, f represents fitness, ΔS represents the arrival time delay difference between the signals emitted by each sound source and the signal emitted by the first sound source, C represents the diagonal matrix composed of the reciprocals of the sound speeds corresponding to the propagation paths of each segment of the sound signal, S represents the distance from each sound source to the target, S1 represents the propagation time delay of the sound signal from the first sound source to the target, T1 represents the propagation time delay of the sound signal from the first sound source to the target, T i represents the propagation time delay of the sound signal from the i-th sound source to the target, diag() represents matrix diagonalization, c i represents the effective sound speed of the sound signal emitted by the i-th sound source to the target, x, y, and z respectively represent the values of the target in the x, y, and z dimensions, x i , y i and z i respectively represent the values of the i-th sound source in the x, y, and z dimensions, and N represents the number of sound sources.

[0037] Specifically, S3 is as follows:

[0038] S31: Set the selection probability p1 of the optimal individual and the selection probability p2 of the sub-optimal individual, and obtain the current selection probability value according to the roulette wheel strategy The formula is as follows:

[0039]

[0040] Among them, rand is the first random number between [0, 1];

[0041] When the ordinary individuals in the current population move towards the optimal individual, and when the ordinary individuals in the current population move towards the sub-optimal individual;

[0042] S32: Set the probability γ of an individual in the population entering the exploration stage, and calculate the hunger value of the ordinary individual after movement according to the probability γ of an individual in the population entering the exploration stage. The calculation formula is:

[0043]

[0044] Among them, F i t represents the hunger value of the ordinary individual after movement, η is the second random number between [-1, 1], h is the third random number between [-2, 2], t is the current iteration number, and T is the maximum iteration number.

[0045] In step S4, use the Gaussian-Cauchy hybrid mutation factor to mutate the current optimal individual and sub-optimal individual to obtain the corresponding mutated individuals. The specific formula is as follows:

[0046]

[0047]

[0048]

[0049] Among them, represents the optimal individual or sub-optimal individual in the current population, Cauthy(0, 1) represents the perturbation that satisfies the Cauchy distribution, represents the individual after Cauchy mutation; Gaussian(0, 1) represents the perturbation that satisfies the Gaussian distribution, represents the individual after Gaussian mutation, represents the individual generated using the Gaussian-Cauchy hybrid mutation factor.

[0050] Step S5 is specifically as follows:

[0051] First, calculate the hunger degree values of all individuals in the current population. When the absolute value of the hunger degree value of each individual is greater than or equal to 1, the current individual enters the exploration stage and then updates its own position; when the absolute value of the hunger degree value of each individual is less than 1, the current individual enters the exploitation stage and then updates its own position, thereby obtaining all individuals after updating their positions and using them as the offspring population of the current population.

[0052] In S6, the orthogonal opposition learning method is used to find the orthogonal opposition solution set corresponding to all individuals after updating their positions. For the i-th individual Satisfying Respectively represent the values of the i-th individual On the x, y, and z dimensions. The orthogonal opposition solution set of the i-th individual Is expressed as:

[0053]

[0054] Next, calculate the fitness of all individuals after updating their positions and all opposing individuals in their orthogonal opposition solution sets. Compare the fitness of each individual and all opposing individuals in their orthogonal opposition solution sets, and select the position corresponding to the individual with the minimum fitness as the new position of the current individual, thereby obtaining a new offspring population and using it as the new population.

[0055] The beneficial effects of the present invention are as follows:

[0056] 1) The present invention embeds the chaos theory to initialize the position. The traditional method of randomly generating initial values will cause uneven distribution of the positions of population individuals, which will lead to a decrease in search accuracy. Using the chaos theory to initialize the population can make the individual positions randomly distributed in the entire solution space, with randomness and ergodicity, and can improve the global convergence.

[0057] 2) The present invention uses the Gaussian-Cauchy hybrid mutation operator to mutate the optimal and sub-optimal individuals of the population. It balances the global search ability in the early stage and the local exploitation ability in the later stage of the algorithm.

[0058] 3) The present invention uses the orthogonal opposition learning method to find the orthogonal opposition solution. By solving the opposing individuals of the population individuals, it enhances the ability of the algorithm to jump out of the local optimal solution; at the same time, combining the opposition learning with the orthogonal experiment method makes up for the shortcoming of the dimension degradation of the traditional opposition learning, improves the search range of the opposition learning, and can effectively prevent the opposing solution from falling into the local optimal.

[0059] 4) The present invention adopts a parallel structure, and parallelly solves the problem by establishing multiple sub-optimization systems, reducing the influence of random errors and effectively improving the accuracy of the positioning result. Description of the Drawings

[0060] Figure 1 It is the flowchart of the method of the present invention.

[0061] Figure 2 It is the schematic diagram of the sound velocity profile used in the embodiment of the present invention.

[0062] Figure 3 It is the comparison chart of the convergence curves of the algorithm proposed in the present invention, the traditional Chan algorithm, the long baseline positioning algorithm based on the particle swarm algorithm, and the long baseline positioning algorithm based on the original African vulture algorithm.

[0063] Figure 4 It is the comparison chart of the positioning accuracies of the algorithm proposed in the present invention, the traditional Chan algorithm, the long baseline positioning algorithm based on the particle swarm algorithm, and the long baseline positioning algorithm based on the original African vulture algorithm. Detailed implementation manners

[0064] The present invention will be further described below by taking a long baseline positioning experiment as an example.

[0065] In this embodiment, the test environment is as follows:

[0066] The sound velocity profile is as Figure 2 shown. Assume that the number of sound sources N = 4, and the coordinates are (x1, y1, z1) = (0, 485, 1), (x2, y2, z2) = (-485, 0, 2), (x3, y3, z3) = (485, 0, 3), (x4, y4, z4) = (0, -485, 4). Assume that the true position of the target is (x s , y s , z s ) = (20, 20, 50), the population number is 30, the maximum number of iterations is 150, the timing error is set to satisfy a normal distribution with a mean of 0 and a standard deviation of , the velocity measurement error satisfies a normal distribution with a mean of 0 and a standard deviation of m / s, the sound source position error satisfies a normal distribution with a mean of 0 and a standard deviation of , and the number of parallel sub-optimization systems Q = 10.

[0067] The flowchart of the embodiment is as Figure 1 shown, and the specific steps are as follows:

[0068] 1) Based on the time delay information, search for the corresponding effective sound velocity in the effective sound velocity table;

[0069] S1 is specifically:

[0070] According to the time delay measured in the test at the position t e in the effective time delay table t eij , search for the effective sound velocity c e in the effective sound velocity table ceij , instead of the overall average sound speed of the acoustic ray in the propagation path.

[0071] Effective time delay table t e and effective sound speed table c e The formulas are as follows:

[0072]

[0073] There is a corresponding effective time delay table t e :

[0074]

[0075] Among them, c eij = c e (z SD , z RDi , r j ), c eij is the effective sound speed between the sound source at depth z SD and the receiver at horizontal distance r j and depth z RDi . c e () represents the effective sound speed table, t eij = t e (z SD , z RDi , r j ), t eij is the propagation time delay of the effective acoustic signal at the target location, t e () represents the effective time delay table.

[0076] 2) According to the current effective sound speed and the corresponding effective time delay, use the Chan algorithm to obtain the initial position of the target, and then use the parallel swarm intelligence optimization algorithm to optimize and update the initial position of the target to obtain the optimal position of the target, realizing the optimal positioning of the target.

[0077] 2) Specifically:

[0078] First, set multiple sub-optimization systems. Then, each of the multiple sub-optimization systems searches for the optimal individual in the population according to the initial position of the target, and respectively obtains the optimal individuals corresponding to the multiple sub-optimization systems. The searches for the optimal individuals in the populations of the multiple sub-optimization systems are parallel computations. Then, select the final optimal individual according to the fitness of the optimal individuals in the multiple sub-optimization systems, and use the position of the final optimal individual as the optimal position of the target to realize the optimal positioning of the target.

[0079] For the search for the optimal individual in the population according to the initial population in each sub-optimization system, and respectively obtaining the optimal individuals corresponding to the multiple sub-optimization systems, specifically:

[0080] S1: Within the population search range, perform chaotic initialization based on the initial position of the target and the chaotic function to generate the initial population;

[0081] From the sound source coordinates (x i , y i , z i ) and the target coordinates (x, y, z), the distance R from the i-th sound source to the target can be expressed as i Expressed as

[0082]

[0083] The difference between the distance from the first sound source to the target and the distance from the i-th sound source to the target Expressed as

[0084]

[0085] Let R i,1 = R i - R1, x i,1 = x i - x1, y i,1 = y i - y1, z i,1 = z i - z1, then the above formula can be expressed as

[0086]

[0087] Let

[0088]

[0089]

[0090]

[0091] Then the above formula can be expressed in matrix-vector form as:

[0092] h = Gm

[0093] Among them, K1 represents the square of the distance from the first sound source to the origin of coordinates, K i represents the square of the distance from the i-th sound source to the origin of coordinates, R i,1 represents the difference between the distance from the i-th sound source to the target and the distance from the first sound source to the target, x i,1 represents the difference in the x-axis coordinates between the i-th sound source and the first sound source, y i,1 represents the difference in the y-axis coordinates between the i-th sound source and the first sound source, z i,1 represents the difference in the z-axis coordinates between the i-th sound source and the first sound source, h represents the coefficient matrix, G represents the difference matrix, and m represents the parameter vector.

[0094] The solution of the parameter vector is as follows:

[0095] m = (G T Φ -1 G)G T Φ -1 h

[0096] where Φ is the covariance matrix of the measurement error, satisfying Φ = diag(δ2, δ3, …, δ N ), diag() is the matrix diagonalization function, and δ N is the variance of the ranging error of the distance from the Nth sound source to the target.

[0097] Specifically, S1 is as follows:

[0098] First, after normalizing the initial position (x, y, z) of the target according to the population search interval, the chaotic initial value u1 is obtained. The formula is as follows:

[0099]

[0100]

[0101]

[0102] where x, y, and z are the values of the initial position of the target in the x, y, and z dimensions respectively, x max , y max , z max are the upper limits of the search intervals of the population in the x, y, and z dimensions respectively, x min , y min , z min are the lower limits of the search intervals of the population in the x, y, and z dimensions respectively, and u 1x , u 1y , u 1z are the values of the chaotic initial value u1 in the x, y, and z dimensions respectively;

[0103] Then, according to the chaotic initial value u1 and the chaotic control parameter μ, where μ ∈ (0, 1). In this embodiment, μ = 0.4, the Tent chaotic function is used to generate a chaotic sequence U c , satisfying U c = [u1, u2, …, u N ;

[0104] Finally, after multiplying the chaotic sequence U c by the population search interval, that is, X = U c × (ub - lb) + lb, the initial population X is obtained, where the upper and lower limits of the population search interval are ub and lb respectively, and ub = [xmax , y max , z max and lb = [x min , y min , z min . In this embodiment, the population search range is ub = [x + 30, y + 30, z + 30], and lb = [x - 30, y - 30, z - 30].

[0105] The fitness of an individual is obtained by using the fitness function, and the calculation formula is as follows:

[0106] f = (ΔS - CS + S1) T (ΔS - CS + S1)

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] Among them, f represents the fitness, ΔS represents the arrival time delay difference between the signals emitted by each sound source and the signal emitted by the first sound source, C represents the diagonal matrix composed of the reciprocals of the sound velocities corresponding to the propagation paths of each segment of the sound signal, S represents the distance from each sound source to the target, S1 represents the propagation time delay of the sound signal from the first sound source to the target, T1 represents the propagation time delay of the sound signal from the first sound source to the target, T i represents the propagation time delay of the sound signal from the i-th sound source to the target, diag() represents matrix diagonalization, c i represents the effective sound velocity of the sound signal emitted by the i-th sound source to the target, x, y, and z respectively represent the values of the target in the x, y, and z dimensions, x i , y i and z i respectively represent the values of the i-th sound source in the x, y, and z dimensions, and N represents the number of sound sources.

[0113] S2: Calculate the fitness of all individuals in the current population, and select the optimal individual and the sub-optimal individual according to the fitness. Specifically, in the implementation, the individuals with the minimum and the second minimum fitness are respectively used as the optimal individual and the sub-optimal individual;

[0114] S3: Set the probability of the population entering the exploitation stage and the optimal / sub-optimal selection probability, select the moving direction of ordinary individuals based on the roulette wheel strategy, and calculate the hunger degree value of the ordinary individuals after moving;

[0115] S3 is specifically:

[0116] S31: Set the selection probability p1 of the optimal individual and the selection probability p2 of the sub-optimal individual, and obtain the current selection probability value according to the roulette wheel strategy The formula is as follows:

[0117]

[0118] where rand is the first random number between [0, 1];

[0119] When the ordinary individuals in the current population move towards the optimal individual. When the ordinary individuals in the current population move towards the sub-optimal individual;

[0120] S32: Set the probability γ of an individual in the population entering the exploitation stage, and calculate the hunger degree value of the ordinary individual after movement according to the probability γ of an individual in the population entering the exploitation stage. The calculation formula is:

[0121]

[0122] where represents the hunger degree value of the ordinary individual after movement, η is the second random number between [-1, 1], h is the third random number between [-2, 2], t is the current iteration number, and T is the maximum iteration number. In this embodiment, γ = 2.5, p1 = 0.6, p2 = 0.4.

[0123] S4: Use the Gaussian-Cauchy hybrid mutation factor to mutate the current optimal individual and sub-optimal individual to obtain the corresponding mutated individuals, compare the current optimal individual, sub-optimal individual and their respective mutated individuals based on the greedy strategy, and select the two best individuals among them as the new optimal individual and sub-optimal individual;

[0124] In S4, use the Gaussian-Cauchy hybrid mutation factor to mutate the current optimal individual and sub-optimal individual to obtain the corresponding mutated individuals. The specific formula is as follows:

[0125]

[0126]

[0127]

[0128] where represents the optimal individual or sub-optimal individual in the current population, Cauthy(0, 1) represents the perturbation satisfying the Cauchy distribution, represents the individual after Cauchy mutation; Gaussian(0, 1) represents the perturbation satisfying the Gaussian distribution, Represents an individual after Gaussian mutation, Represents an individual generated using a Gaussian-Cauchy hybrid mutation factor.

[0129] S5: Select different position update strategies according to the individual hunger degree value, and update the positions of all individuals in the current population to obtain the offspring population of the current population;

[0130] S5 is specifically as follows:

[0131] First, calculate the hunger degree values of all individuals in the current population. When the absolute value of the hunger degree value of each individual is greater than or equal to 1, the current individual enters the exploration stage and then updates its own position; when the absolute value of the hunger degree value of each individual is less than 1, the current individual enters the exploitation stage and then updates its own position, and then obtain all individuals after updating their positions and use them as the offspring population of the current population. Among them, when the absolute value of the hunger degree value of each individual is less than 1, the current individual enters the exploitation stage and then updates its own position, specifically as follows:

[0132] If the absolute value |F i t | of the hunger degree value of each individual is between 0.5 and 1, the current individual enters the first exploitation stage, and the strategy selection in the first exploitation stage is also determined by the first determination parameter p4, specifically expressed as:

[0133]

[0134]

[0135]

[0136]

[0137] Among them, r5, r p4 are the fourth and fifth random numbers between [0, 1], is the distance from the current individual to the optimal individual or the sub-optimal individual, represents the position of the i-th individual in the population at the (t + 1)-th iteration, represents the distance between the i-th individual in the population and the selected excellent individual, represents the excellent individual that the i-th individual in the population selects to approach at the t-th iteration, C is a random number uniformly distributed between [0, 2], and represent the spiral flight behavior of the individual, and are random numbers uniformly distributed between [0, 1].

[0138] If the absolute value |F i t | of the hunger level value of each individual is less than 0.5, the current individual enters the second stage of development. The strategy selection in the second stage of development is determined by the second determination parameter p5. First, a sixth random number r between [0, 1] is generated p5 , when r p5 < p5, the individual performs an aggregation behavior. When r p5 ≥ p5, the individual performs an attack behavior;

[0139] In this embodiment, p3 = 0.6, p4 = 0.4, p5 = 0.6.

[0140] S6: Use the orthogonal opposition learning method and the greedy strategy to optimize the current offspring population, obtain a new offspring population as the new population, calculate the fitness of all individuals in the current population, and select the optimal individual and the sub-optimal individual according to the fitness;

[0141] In S6, use the orthogonal opposition learning method to find the orthogonal opposition solution set corresponding to all individuals after updating their positions. For the i-th individual satisfies respectively represent the values of the i-th individual in the x, y, and z dimensions. Establish an orthogonal table, and the formula is:

[0142]

[0143] Then, based on the orthogonal table, generate the orthogonal opposition solution set of the i-th individual , and the formula is expressed as:

[0144]

[0145] Next, calculate the fitness of all individuals after updating their positions and all opposing individuals in their orthogonal opposition solution sets, compare the fitness of each individual and all opposing individuals in their orthogonal opposition solution sets, and select the position corresponding to the individual with the minimum fitness as the new position of the current individual, so as to obtain a new offspring population as the new population.

[0146] S7: According to the current population and its optimal individual and sub-optimal individual, repeat S3 - S5 until the fitness of the optimal individual in the current population is less than the set fitness threshold or the number of iterations reaches the maximum number of iterations, and obtain the optimal individual of the current sub-optimization system.

[0147] The comparison of the positioning accuracies between the methods is shown in Table 1 and Figure 4As shown, Chan, PSO, AVOA, and Chan-PIAVOA are respectively the long-baseline positioning algorithms based on the Chan algorithm, the long-baseline positioning algorithm based on the particle swarm optimization algorithm, the long-baseline algorithm based on the original African vulture algorithm, and the long-baseline positioning algorithm based on the Chan algorithm and the parallel swarm intelligence algorithm. It can be seen that the positioning accuracy of the improved method has been significantly improved.

[0148] Table 1 is a performance comparison table of the improved method and the basic long-baseline positioning method

[0149] Positioning performance Chan PSO AVOA Chan-PIAVOA RMSE(m) 5.556 4.862 1.49 0.4183

[0150] The comparison of the convergence performance among various methods is as Figure 3 shown. It can be seen that compared with the long-baseline positioning algorithm based on the original African vulture algorithm and the long-baseline positioning algorithm based on the particle swarm algorithm, the improved algorithm has a stronger ability to jump out of the local optimal solution and a faster convergence speed.

[0151] The basic principles and main features of the present invention have been elaborated in detail above in conjunction with the accompanying drawings. This method is based on the Chan and parallel swarm intelligence algorithms and improves the positioning performance of traditional TDOA positioning. The specific measures include the effective sound speed method to simplify the sound speed, chaotic initialization of the population, orthogonal opposition learning, Gaussian-Cauchy hybrid mutation, and parallel structure. The above improvements enhance the traversability of the search, improve the global search ability of the algorithm, mutate through excellent individuals to avoid falling into local solutions, and use a parallel structure to reduce the influence of random errors. For complex seabed environments, the present invention can better improve the positioning accuracy. The present invention has good engineering practical value.

[0152] The present invention is not limited to the above embodiments. For those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also considered within the protection scope of the present invention. The content not described in detail in this specification belongs to the prior art well-known to those skilled in the art.

Claims

1. A long baseline positioning method based on Chan and parallel swarm intelligence optimization algorithm, characterized in that Including the following steps: 1) Based on the time delay information, look up the corresponding effective sound speed in the effective sound speed table; 2) According to the current effective sound speed and the corresponding effective time delay, use the Chan algorithm to obtain the initial position of the target, and then use the parallel swarm intelligence optimization algorithm to optimize and update the initial position of the target to obtain the optimal position of the target, realizing the optimal positioning of the target; There are multiple sub-optimization systems set in the parallel swarm intelligence optimization algorithm; each sub-optimization system searches for the optimal individual of the population according to the initial position of the target to obtain the optimal individual corresponding to the current sub-optimization system, specifically including the following steps: S1: In the population search interval, based on the initial position of the target and the chaotic function, perform chaotic initialization to generate the initial population; S2: Calculate the fitness of all individuals in the current population, and select the optimal individual and the sub-optimal individual according to the fitness; S3: Set the probability of the population entering the exploitation stage and the optimal / sub-optimal selection probability, select the moving direction of the ordinary individual based on the roulette wheel strategy, and calculate the hunger degree value of the ordinary individual after moving; S4: Use the Gaussian-Cauchy hybrid mutation factor to mutate the current optimal individual and the sub-optimal individual to obtain the corresponding mutated individuals, and compare the current optimal individual, the sub-optimal individual and their respective mutated individuals based on the greedy strategy, and select the two optimal individuals among them and use them as the new optimal individual and the sub-optimal individual.

2. The long baseline positioning method based on the Chan and parallel swarm intelligence optimization algorithm according to claim 1, characterized in that, The specific content of 1) is: According to the time delay measured in the test, at the position t in the effective time delay table t e , look up the effective sound speed c in the effective sound speed table c eij . e eij .​ 3. A long baseline positioning method based on the Chan and parallel swarm intelligence optimization algorithm according to claim 1, characterized in that, In 2), according to the fitness of the optimal individuals in multiple sub-optimization systems, select the final optimal individual, and use the position of the final optimal individual as the optimal position of the target to realize the optimal positioning of the target.

4. A long baseline positioning method based on the Chan and parallel swarm intelligence optimization algorithm according to claim 1, characterized in that Each sub-optimization system searches for the optimal individual of the population according to the initial position of the target to obtain the optimal individual corresponding to the current sub-optimization system, and further includes the following steps: S5: Select different position update strategies according to the individual hunger degree value to update the positions of all individuals in the current population to obtain the offspring population of the current population; S6: Use the orthogonal opposition learning method and the greedy strategy to optimize the current offspring population to obtain a new offspring population and use it as the new population, calculate the fitness of all individuals in the current population, and select the optimal individual and the sub-optimal individual according to the fitness; S7: According to the current population and its optimal individual and sub-optimal individual, repeat S3 - S5 until the fitness of the optimal individual in the current population is less than the set fitness threshold or the number of iterations reaches the maximum iteration value, and obtain the optimal individual of the current sub-optimization system.

5. A long baseline positioning method based on the Chan and parallel swarm intelligence optimization algorithm according to claim 1, characterized in that The specific content of S1 is: First, after normalizing the initial position (x, y, z) of the target according to the population search interval, obtain the chaotic initial value u1, and the formula is as follows: where x, y, and z are the values of the initial position of the target in the x, y, and z dimensions, respectively, x max , y max , z max are the upper limits of the search intervals of the population in the x, y, and z dimensions, respectively, x min , y min , z min are the lower limits of the search intervals of the population in the x, y, and z dimensions, respectively, u 1x , u 1y , u 1z are the values of the initial chaotic value u1 in the x, y, and z dimensions; Next, according to the initial chaotic value u1, use the Tent chaotic function to generate a chaotic sequence U in the range of [0, 1] c = [u2, u3, …, u N ; Finally, multiply the chaotic sequence U c = [u2, u3, …, u N by the population search interval to obtain the initial population X.

6. A long baseline positioning method based on Chan and parallel swarm intelligence optimization algorithm according to claim 1, characterized in that The fitness of the individual is calculated using the fitness function, and the calculation formula is as follows: f = (ΔS - CS + S1) T (ΔS - CS + S1) Among them, f represents fitness, ΔS represents the arrival time delay difference between the signals emitted by each sound source and the signal emitted by the first sound source, C represents the diagonal matrix composed of the reciprocals of the sound speeds corresponding to the propagation paths of each segment of the sound signal, S represents the distance from each sound source to the target, S1 represents the propagation time delay of the sound signal from the first sound source to the target, T1 represents the propagation time delay of the sound signal from the first sound source to the target, and T i represents the propagation time delay of the sound signal from the i-th sound source to the target, diag() represents matrix diagonalization, and c i represents the effective sound speed of the sound signal emitted by the i-th sound source to the target. x, y, and z respectively represent the values of the target in the x, y, and z dimensions, and x i , y i and z i respectively represent the values of the i-th sound source in the x, y, and z dimensions, and N represents the number of sound sources.

7. A long baseline positioning method based on Chan and parallel swarm intelligence optimization algorithm according to claim 1, characterized in that, The specific content of S3 is: S31: Set the selection probability p1 of the optimal individual and the selection probability p2 of the sub-optimal individual, and obtain the current selection probability value according to the roulette wheel strategy The formula is as follows: Among them, rand is the first random number between [0, 1]; When the ordinary individuals in the current population move towards the optimal individual. When the ordinary individuals in the current population move towards the sub-optimal individual; S32: Set the probability γ of the individuals in the population entering the exploitation stage, and calculate the hunger degree value of the ordinary individual after moving according to the probability γ of the individuals in the population entering the exploitation stage. The calculation formula is: Among them, F i t represents the hunger value after the movement of an ordinary individual, η is the second random number between [-1, 1], h is the third random number between [-2, 2], t is the current iteration number, and T is the maximum iteration number.

8. A long baseline positioning method based on the Chan and parallel swarm intelligence optimization algorithm according to claim 1, characterized in that In S4, the Gaussian-Cauchy hybrid mutation factor is used to mutate the current optimal individual and the sub-optimal individual to obtain the corresponding mutated individuals. The specific formula is as follows: Among them, represents the optimal or sub-optimal individual in the current population, and Cauthy(0,1) represents the perturbation that satisfies the Cauchy distribution. represents the individual after Cauchy mutation; Gaussian(0,1) represents the perturbation that satisfies the Gaussian distribution. represents the individual after Gaussian mutation. represents the individual generated using the Gaussian-Cauchy mixed mutation factor.

9. A long baseline positioning method based on the Chan and parallel swarm intelligence optimization algorithm according to claim 4, characterized in that, S5 is specifically as follows: First, calculate the hunger degree values of all individuals in the current population. When the absolute value of the hunger degree value of each individual is greater than or equal to 1, the current individual enters the exploration stage and then updates its own position; when the absolute value of the hunger degree value of each individual is less than 1, the current individual enters the exploitation stage and then updates its own position, thereby obtaining all individuals after updating their positions and using them as the offspring population of the current population.

10. A long baseline positioning method based on the Chan and parallel swarm intelligence optimization algorithm according to claim 4, characterized in that In S6, the orthogonal opposition solution set corresponding to all individuals after updating their positions is obtained by using the orthogonal opposition learning method. For the i-th individual Satisfy Respectively represent the i-th individual Values in the x, y, and z dimensions. The i-th individual The orthogonal opposition solution set of is expressed as: Next, calculate the fitness of all individuals after updating their positions and all opposing individuals in their orthogonal opposition solution sets, compare the fitness of each individual and all opposing individuals in their orthogonal opposition solution sets, and select the position corresponding to the individual with the minimum fitness as the new position of the current individual, thereby obtaining a new offspring population and using it as the new population.

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