An Optimization Method for the Deployment of Underwater Acoustic Positioning Systems Based on Combined Conical Configuration

Abstract

This invention provides a method for optimizing the deployment of underwater acoustic positioning systems based on combined conical configurations. The method includes: expanding the single conical configuration in the underwater acoustic positioning system into multiple combined conical configurations based on the target and the number of stations; solving and optimizing the Global Directional Adjustment (GDOP) of each combined conical configuration from both the target trajectory and the target motion area to obtain the globally optimal GDOP of the target trajectory and the corresponding half-cone angle of the combined conical configuration, as well as the globally optimal GDOP of the target motion area and the corresponding half-cone angle of the combined conical configuration; and determining the deployment arrangement of the underwater acoustic positioning system based on the optimal combined conical configuration of the target trajectory and the optimal combined conical configuration of the target motion area. This optimization method improves the positioning accuracy of underwater targets.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic positioning systems, and more specifically to a method for optimizing the deployment of underwater acoustic positioning systems based on a combined conical configuration. Background Technology

[0002] With the deepening of marine development activities, the demand for target positioning in the sea area has expanded from above the water surface to the entire ocean space, both above and below the water. High-precision measurement and positioning of underwater targets has become a crucial aspect that urgently needs to be addressed in experimental missions. Due to the rapid attenuation of electromagnetic waves in water, satellite navigation and positioning systems cannot be directly used for the navigation and positioning of underwater targets. The excellent propagation characteristics of sound waves in seawater have led to the widespread application of underwater acoustic measurement systems.

[0003] The accuracy of underwater target acoustic positioning depends on many factors, including the measurement accuracy of the stations, the underwater positioning data processing algorithm, and the geometrical precision factor (GDOP) of the underwater positioning system. In underwater positioning systems, the need for all stations to be deployed on the same plane leads to coplanar constraints, preventing the GDOP from reaching its theoretical minimum value. The complex underwater environment also introduces uncertainties into the underwater target motion model, making configuration optimization for single-point GDOP insufficient to meet the requirements of high-precision positioning.

[0004] In recent years, metaheuristic algorithms have been widely used in station deployment optimization problems. However, due to the randomness of metaheuristic search, most algorithms still suffer from unstable calculation results, easy getting trapped in local optima, and low convergence efficiency when applied to the station deployment optimization problem of long-baseline positioning systems.

[0005] In summary, the existing technologies have the following problems: the mutual constraint of the stations prevents GDOP from reaching its theoretical minimum value; the configuration optimization of single-point GDOP cannot meet the requirements of high-precision positioning; when most metaheuristic algorithms are applied to the station deployment optimization problem of long-baseline positioning systems, the results are unstable, easily get trapped in local optima, and have low convergence efficiency. Summary of the Invention

[0006] To address the issues of GDOP failing to find the optimal solution and exhibiting low positioning accuracy and convergence efficiency, this invention provides a site optimization method for an underwater acoustic positioning system based on a combined conical configuration:

[0007] Based on the target and the number of stations, the single conical configuration in the underwater acoustic positioning system is expanded into multiple combinations of conical configurations. The target trajectory GDOP for each of these conical configurations is obtained as a function of the angles of the combined conical configurations. The target trajectory GDOP for each combined conical configuration is optimized to obtain the locally optimal GDOP. The globally optimal GDOP is obtained from the locally optimal GDOP. The optimal combined conical configuration for the target trajectory is obtained from the half-cone angle of the combined conical configuration corresponding to the globally optimal GDOP. Finally, the target motion region is combined into a circular... The target motion region (GDOP) of each of the combined conical configurations is obtained as a function of the angle of the conical configuration. The GDOP of each combined conical configuration is optimized to obtain the locally optimal GDOP of the target motion region for each combined conical configuration. The globally optimal GDOP of the target motion region is obtained from the locally optimal GDOP of the target motion region for each combined conical configuration. The optimal combined conical configuration of the target motion region is obtained from the half-cone angle of the combined conical configuration corresponding to the globally optimal GDOP of the target motion region. The deployment arrangement of the underwater acoustic positioning system is determined according to the optimal combined conical configuration of the target trajectory and the optimal combined conical configuration of the target region.

[0008] In underwater acoustic positioning systems, the technique of extending the traditional single-cone configuration into a combined-cone configuration solves the problem of GDOP not reaching its theoretical minimum due to the coplanar constraint of station placement, and the issue of infinite vertex GDOP in the single-cone configuration with the target as the vertex. Therefore, in the optimization of the combined-cone configuration, the global GDOP of the target trajectory and the global GDOP of the target motion area are used as the optimization objective function. A particle swarm optimization algorithm with adaptive step size and survival competition mechanism is used to optimize the objective function. The optimization result yields the final optimized station placement method. Compared with traditional typical station placement methods, this improves the problem of station placement optimization easily getting trapped in local optima and slow convergence speed, and solves the problem of optimal station placement for the target area. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart of a method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration, according to an embodiment of the present invention.

[0011] Figure 2 This is a schematic diagram of a long baseline positioning system in one embodiment of the present invention;

[0012] Figure 3 This is a schematic diagram of a single cone configuration and its semi-cone angle in one embodiment of the present invention;

[0013] Figure 4 This is a schematic diagram of a non-conical pattern station layout in one embodiment of the present invention;

[0014] Figure 5 This is a schematic diagram of a combined conical configuration in one embodiment of the present invention;

[0015] Figure 6 This is a rotational schematic diagram of a combined conical configuration in one embodiment of the present invention;

[0016] Figure 7 This is a flowchart of a site configuration optimization based on an adaptive particle swarm algorithm in one embodiment of the present invention;

[0017] Figure 8 This is a schematic diagram of the distribution of measuring stations and the target trajectory in one embodiment of the present invention;

[0018] Figure 9a This is a diagram of the first decompositional iterative result using different inertia factors APSO and the global GDOP of the target trajectory as the optimization criterion in one embodiment of the present invention.

[0019] Figure 9b This is a diagram showing the second decomposition-based iterative result using different inertia factors APSO and the global GDOP of the target trajectory as the optimization criterion in one embodiment of the present invention.

[0020] Figure 9c A schematic diagram of the optimal combination of conical configurations with different inertia factors APSO and global GDOP of the target trajectory as the optimization criterion is shown in one embodiment of the present invention.

[0021] Figure 10 This is a comparison chart of the results of three optimization methods, GD, PSO and APSO, using the global GDOP of the target trajectory as the optimization criterion in one embodiment of the present invention.

[0022] Figure 11a This is an embodiment of the present invention that uses the global GDOP of the target motion region as the optimization criterion, and the first decomposition iterative result diagram;

[0023] Figure 11b This is an embodiment of the present invention that uses the global GDOP of the target motion region as the optimization criterion, and the second decomposition iterative result diagram;

[0024] Figure 11cThis is a schematic diagram of the optimal combination of conical configurations based on the global GDOP of the target motion region as an optimization criterion in one embodiment of the present invention;

[0025] Figure 12a This is a diagram showing the first decomposition-based iterative result in an actual lake test according to an embodiment of the present invention;

[0026] Figure 12b This is a diagram showing the second decomposition-based iterative result in an actual lake test according to an embodiment of the present invention;

[0027] Figure 12c This is a schematic diagram of a conventional rectangular configuration according to an embodiment of the present invention;

[0028] Figure 12d This is a schematic diagram of the optimal combination of conical configuration under the first decomposition formula of an embodiment of the present invention.

[0029] The attached figures are labeled as follows: Target trajectory 11; Station 12; Straight-line distance 13; Actual sound ray 14; Calibration vessel 15; GNSS satellite 16; Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] The technical solutions of the present invention will be described in detail below with reference to specific application examples. For technical details not described in the implementation process, please refer to the relevant descriptions above.

[0032] This invention is a method for optimizing the deployment of underwater acoustic positioning systems based on a combined conical configuration, such as... Figure 1 As shown, the optimization method includes:

[0033] Based on the target to be measured and the number of stations, the single cone configuration in the underwater acoustic positioning system is expanded into a combination of multiple cone configurations;

[0034] like Figure 2 As shown, the underwater acoustic positioning system mainly consists of a seabed station 12, an acoustic beacon installed on the target, and a calibration vessel 15. Taking underwater mobile target measurement as an example, three or more stations are deployed on the seabed to form a seabed positioning baseline array with a certain geometric shape. The positions of the stations are pre-calibrated by the calibration vessel, while the GNSS satellite 16 in the figure is used to accurately locate the calibration vessel 15. The figure shows the changes in the target trajectory 11, straight-line distance 13, and actual sound ray 14.

[0035] The observation equation for an underwater long-baseline acoustic positioning system is: R i =d i +Δ+ε i ,i=1,...,n, where n≥3 is the number of stations, Δ is the distance error caused by clock error, and d i Let the underwater target X = (x, y, z)' and the i-th station X be... i =(x i ,y i ,z i The distance ε' is 0. i Distance error caused by other error factors.

[0036] A certain configuration G with n stations n The geometric precision factor for single-point positioning is defined as follows: Where J represents configuration G n The observation matrix is ​​defined as Where e i =[xx i yy i ,zz i ] / d i Let i = 1, ..., n be the distance from underwater target X to station X. i The direction cosine.

[0037] Let the cosine matrix J of the defense line e =[e'1,...,e' n ]',k n =[1,...,1]'. Because

[0038]

[0039] Where M = (IJ) e (J' e J e ) -1 J' e ).therefore

[0040] GDOP 2 =tr(J' e J e ) -1 +{tr[(J' e J e ) -1 J' e k n k' n J e (J' e J e ) -1 ]+1}(k'n Mk n ) -1

[0041] Due to GDOP 2 =tr(J' e J e ) -1 +{tr[(J' e J e ) -1 J' e k n k' n J e (J' e J e ) -1 ]+1}(k' n Mk n ) -1 In the middle, (J' e J e ) -1 J' e k n k' n J e (J' e J e ) -1 Since it is a non-negative definite matrix, we have GDOP. 2 ≥tr(J' e J e ) -1 +(k' n Mk n ) -1 , if and only if k' n J e When = 0, GDOP 2 ≥tr(J' e J e ) -1 +(k' n Mk n ) -1 The equality sign in the equation holds true. Additionally, there is... Where λ i (i = 1, 2, 3) is matrix J e eigenvalues, The equality holds if and only if λ1 = λ2 = λ3. Because Therefore, when hour, Take the minimum value In a certain G n Under this configuration, a minimum value for GDOP exists, and its value is... The necessary and sufficient condition is:

[0042]

[0043] The theoretical minimum value of the geometrical accuracy factor (GDOP) for a single-point positioning 3D station configuration can be obtained. However, due to the coplanar constraint of the underwater positioning system's station configuration, all stations must be placed on the same plane, and the theoretical minimum value of the geometrical accuracy factor cannot be reached. The reasons are as follows:

[0044] Due to environmental limitations, underwater positioning system stations can only be deployed on seabed-based platforms, meaning all stations are located on the same plane. For configuration G... n Assume its observation matrix is ​​J = [J e k n If ], then there are two cases: conical mode and non-conical mode.

[0045] a. The station configuration is a conical pattern, and the first condition of equation (1) holds, i.e.

[0046] By J e Based on the definition and the orthogonality of trigonometric functions, it can be seen that the configuration G can be obtained by factoring n integers. n It can be decomposed into T single conical configurations, i.e. like Figure 3 As shown, in each single conical configuration C qi In the middle, q i The stations are evenly distributed on a circle. Assume configuration C. qi The cone angle of the cone formed by the station and the target point is α(C). qi ), then α(C qi )=2θ i , called θ i For configuration C qi The semi-cone angle. Then Where q i ≥3 and satisfy Since all the stations are located on the same plane, 0 < θ i <π / 2, i=1,...,T, therefore for configuration G n have Then the second condition in equation (1) is not satisfied, GDOP(G n It cannot reach the minimum value.

[0047] b. If the station configuration is a non-conical pattern, then like Figure 4 As shown, assume that the angle between the line connecting each station and the target point to be determined and the straight line passing through the target point and perpendicular to the station layout plane is γ. j If j = 1, ..., n, then 0 < γ j <π / 2, j=1,...,n, then for configuration G nhave Therefore, neither of the two conditions in equation (1) is satisfied, GDOP(G n It cannot reach the theoretical minimum value.

[0048] When using a single conical configuration for station deployment, the underwater positioning system needs to be uniformly distributed around the circumference. Assuming that the n stations of the single conical configuration are uniformly distributed on the same circle, the observation matrix is ​​J. c =[J ec ,k n Then, according to the definition of the observation matrix and the orthogonality of trigonometric functions, we have:

[0049]

[0050] Where θ c For the semi-cone angle of the single conical configuration, substitute equation (2) into the following formula:

[0051] GDOP 2 =tr(J' e J e ) -1 +{tr[(J' e J e ) -1 J' e k n k' n J e (J' e J e ) -1 ]+1}(k' n Mk n ) -1

[0052] GDOP can be obtained 2 (C n Since the value of )→+∞, under the coplanar constraint, the single cone configuration is not suitable for the deployment configuration of underwater positioning systems. Therefore, as follows... Figure 5 As shown, two single cone configurations are superimposed and extended into a combined cone configuration.

[0053] Given the number of stations n, n can be decomposed into multiple single conical configurations. These single conical configurations can be superimposed to form a combined conical configuration. There are multiple ways to decompose the number of stations n, and each decomposition method forms a combined conical configuration. For example, for the number of stations 8, 8 can be decomposed into 3 and 5 or 8 into 4 and 4, which forms two combined conical configurations: a combined conical configuration composed of single conical configurations formed by 3 stations and single conical configurations formed by 5 stations, and a combined conical configuration composed of two single conical configurations formed by 4 stations.

[0054] After extending the single cone configuration to a combined cone configuration, the configuration optimization for a single-point GDOP can no longer meet the requirements for high-precision positioning. Underwater positioning performance is usually measured by the position estimation accuracy of the target trajectory globally or the entire target motion area. Therefore, the optimization problem of the combined cone configuration GDOP should also be aimed at the target trajectory globally or the entire target motion area.

[0055] The target trajectory GDOP for each of the combined conical configurations is obtained as a function of the angles of the target trajectory combined conical configuration;

[0056] The target trajectory GDOP of the combined conical configuration is a function of the angle of the combined conical configuration of the target trajectory. GDOP can be obtained from the half-cone angle in the combined conical configuration of the target trajectory. Conversely, when the value of the target trajectory GDOP is known, the half-cone angle of the corresponding combined conical configuration of the target trajectory can be found.

[0057] The target trajectory GDOP for each of the combined conical configurations is optimized to obtain the locally optimal GDOP for each combined conical configuration. The global GDOP of the target trajectory is obtained from the locally optimal GDOP of the target trajectory for each combined conical configuration. The optimal combined conical configuration of the target trajectory is obtained from the half-cone angle of the combined conical configuration corresponding to the globally optimal GDOP of the target trajectory. For an underwater acoustic positioning system with a given number of stations n, there are multiple ways to decompose the number of stations n. Each decomposition method forms a combined conical configuration. For example, for a number of stations 9, 9 can be decomposed into 3 and 6, or 9 can be decomposed into 4 and 5, or 9 can be decomposed into 3, 3, and 3, thus forming three kinds of combined conical configurations: a combined conical configuration composed of a single conical configuration formed by 3 stations and a single conical configuration formed by 6 stations, a combined conical configuration composed of a single conical configuration formed by 4 stations and a single conical configuration formed by 5 stations, and a combined conical configuration composed of three single conical configurations formed by 3 stations. After obtaining the GDOP of the target trajectory, the optimal GDOP is not yet obtained. It needs to be optimized to obtain the globally optimal GDOP. During optimization, the GDOP of the target trajectory is optimized for each combination of conical configurations. This yields the optimal GDOP for each combination of conical configurations, known as the locally optimal GDOP. Optimizing the GDOP for each combination of conical configurations results in multiple locally optimal GDOPs. Among these, the locally optimal GDOP with the smallest value is the globally optimal GDOP. The GDOP of the target trajectory is a semi-cone angle function of the combination of conical configurations within the target trajectory.

[0058] The target motion region GDOP for each of the combined conical configurations is obtained as a function of the angles of the target motion region combined conical configuration;

[0059] The target motion region GDOP of the combined conical configuration is a function of the angle of the combined conical configuration of the target motion region. GDOP can be obtained from the half-cone angle in the combined conical configuration of the target motion region. Conversely, when the value of GDOP of the target motion region is known, the half-cone angle of the corresponding combined conical configuration of the target motion region can be found.

[0060] The target motion region GDOP of each combined conical configuration is optimized to obtain the locally optimal GDOP of the target motion region for each combined conical configuration; the globally optimal GDOP of the target motion region is obtained from the locally optimal GDOP of the target motion region for each combined conical configuration; the optimal combined conical configuration of the target motion region is obtained from the half-cone angle of the combined conical configuration corresponding to the globally optimal GDOP of the target motion region.

[0061] The deployment arrangement of the underwater acoustic positioning system is determined based on the optimal combination conical configuration of the target trajectory and the optimal combination conical configuration of the target area.

[0062] Furthermore, the combined conical configuration is composed of at least two single conical configurations; the method for expanding the single conical configuration in the underwater acoustic positioning system into a combination of multiple combined conical configurations includes: forming at least two single conical configurations according to the number of stations; and adding each single conical configuration together to obtain the combined conical configuration.

[0063] Given the number of stations n, let the set of combined conical configurations be:

[0064]

[0065] Where T is the number of single conical configurations, C qi Single conical configuration, q i If the number of stations for the single conical configuration is given, then the combined conical configuration has ① superposition and rotatability, i.e., the set Δ n The elements in GDOP possess superposition invariance and rotation invariance; ② GDOP rotation invariance. The reason is as follows: For any natural numbers n and m, if we denote G... n +G m For configuration G n and G m If the combined positioning configuration of G, then n ∈Δ n G m ∈Δ m From the definition and representation of a composite cone, it can be seen that if Furthermore, the semi-cone angles of each individual cone are different. Single conical configuration C qi The rotated single-cone configuration obtained by rotating the line passing through the target point and perpendicular to the station layout plane by any angle is represented as follows: The combined conical configuration after rotation is: Configuration G n After each cone is rotated, the stations remain evenly distributed on each circumference, and the sum of their numbers is n. The combined conical configuration is superimposed and rotatable.

[0066] Assuming a combined conical configuration G n The observation matrix is ​​J = [J e ,k n The semi-cone angle of each single conical configuration is θ. i Since the stations are evenly distributed on the circle in each single-cone configuration, therefore...

[0067]

[0068] Then, by the orthogonality of trigonometric functions, we know...

[0069]

[0070] Rotated combined conical configuration The observation matrix is like Figure 6 As shown, assume that the angle of rotation of each single conical configuration about its axis is ω. i ∈(0,2π), i=1,...,T, then

[0071]

[0072] Then, by the orthogonality of trigonometric functions, we know...

[0073]

[0074] By GDOP 2 =tr(J' e J e ) -1 +{tr[(J' e J e ) -1 J' e k n k' n J e (J' e J e ) -1 ]+1}(k' n Mk n ) -1

[0075] It can be known that GDOP(G n ) = GDOP(G n R), that is, the combined conical configuration has GDOP rotational invariance.

[0076] Based on the superposition, rotatability, and GDOP rotation invariance of the combined conical configuration, it can be seen that, with a constant number of underwater stations, the single conical configuration in the underwater acoustic positioning system also possesses the superposition, rotatability, and GDOP rotation invariance of the combined conical configuration. Therefore, by superimposing the single conical configurations to form a combined conical configuration, and optimizing the combined conical configuration, the problem of the theoretical minimum GDOP not being achievable due to the coplanar constraint of the station layout configuration in the underwater acoustic positioning system can be solved. The GDOP of the combined conical configuration is related to the number of single conical configurations T and the number of stations q in each single conical configuration. i and the semi-cone angle θ i related.

[0077] Furthermore, the optimization of the target trajectory GDOP for each of the combined conical configurations to obtain the locally optimal target trajectory GDOP for each of the combined conical configurations, and the optimization of the target motion region GDOP for each of the combined conical configurations to obtain the locally optimal target motion region GDOP for each of the combined conical configurations, both employ an adaptive particle swarm optimization algorithm. The adaptive particle swarm optimization algorithm incorporates an adaptive step size for particle movement and survival and competition mechanisms into the particle swarm optimization algorithm.

[0078] The Particle Swarm Optimization (PSO) algorithm initializes a swarm of random particles and iteratively searches for the optimal solution through cooperation and competition among the particles. The PSO uses the optimization function as the fitness function. In each iteration, a particle updates its velocity and position by tracking two optimal values: the first is the optimal solution found by the particle itself, called the individual extremum, and the second is the optimal solution found by the entire swarm, called the global extremum. The formulas for updating the particle's velocity and position are:

[0079]

[0080] Among them, Z i (t)=(Z i1 (t),...,Z iD (t)), V i (t)=(V i1 (t),...,V iD (t) and (d) represent the position and velocity at time t of the i-th (i = 1, ..., M) particle in the D-dimensional target search space, respectively. D represents the total number of dimensions, d represents the d-th dimension, ω is a non-negative inertia factor, and each particle in the population is a possible solution to the optimization problem. P i and P gLet C1 and C2 represent the individual extreme value of the i-th particle at the current time and the global extreme value of the particle swarm, respectively. The individual extreme value and the global extreme value depend on the fitness function of the optimization problem. C1 and C2 are the individual learning factor and social learning factor of each particle, respectively, and r1 and r2 are random parameters uniformly distributed in the interval [0,1]. However, when applied to underwater station deployment optimization problems, the particle swarm algorithm is prone to getting trapped in local optima and has low convergence efficiency. To solve this problem, an adaptive step size is added to the update formula of the particle swarm algorithm. As the environment of the particle changes, it is given a certain survival ability. In this way, the particle has the strongest vitality near the global extreme value, thus having the longest lifespan. Particles located in local extreme values ​​will be reborn as they die, such as by randomly generating the next position of the particle, thus expanding the search. This not only saves storage space, but also improves the optimization ability and efficiency.

[0081] Furthermore, the adaptive step size for each particle's movement is obtained through each particle's current position, current velocity, current individual extremum, and current local extremum; wherein the current individual extremum refers to the optimal solution found for a particle within the target trajectory, and the local extremum refers to the optimal solution found in the entire particle swarm for a given combination of conical configurations.

[0082] The adaptive update formula for the velocity and position of each particle is:

[0083]

[0084] E c For Z i (t) The fitness value, E, is determined by the fitness function. i For P i The corresponding fitness value, E g For P g The corresponding fitness value. The velocity V at the next moment. id (t+1) is defined as the adaptive step size for the current movement. As shown in equation (4), the size of the adaptive step size depends on the current position, the particle's velocity at the current moment, the particle's individual extreme value at the current moment, and the particle's global extreme value at the current moment. Real-time adjustment of the adaptive step size helps to accelerate the convergence speed of the algorithm.

[0085] Furthermore, each of the aforementioned single-cone configurations consists of a target point and at least three measuring stations. The measuring stations on each single-cone configuration are located on the same horizontal plane and are evenly distributed around the circumference of the circular base of the single-cone configuration. Typically, the measuring stations of an underwater acoustic positioning system are arranged on the seabed. If there are fewer than three measuring stations, a single-cone configuration cannot be formed, and it is impossible to extend a single-cone configuration into a combined cone configuration. The necessary and sufficient condition for the GDOP of the cone configuration to reach its minimum value is... To satisfy the conditions in this formula, the underwater acoustic positioning system stations need to be evenly distributed on the circumference of the circular base of the single conical configuration. Furthermore, the target trajectory GDOP for each of the combined conical configurations is obtained as a function of the angles of the target trajectory combined with the conical configuration, using the following formula:

[0086]

[0087] Where Ω represents the target trajectory, GDOP Ω GDOP represents the global GDOP of the target trajectory, where n is the number of stations, and Gn is the combined conical configuration with n stations. n ) represents a single-point localization GDOP, w(X (k) (x) represents the position X (k) The weights of GDOP are given by k, where k is the sampling point, and satisfying the following conditions: Configuration G with n stations n Then the global GDOP of the target trajectory Ω is represented as:

[0088] GDOP Ω (G n )=∫ X∈Ω w(X)·GDOP(G n )dX

[0089] And ∫ X∈Ω w(X)dX=1,

[0090] GDOP Ω (G n )=∫ X∈Ω w(X)·GDOP(G n Discretize dX.

[0091] Therefore, we get:

[0092]

[0093] This yields the global GDOP value of the target trajectory, but this GDOP is not the globally optimal GDOP of the target trajectory. It needs to be optimized to obtain the globally optimal GDOP of the target trajectory.

[0094] Furthermore, the target motion region GDOP for each of the combined conical configurations is obtained as a function of the angles of the target motion region combination conical configuration using the following formula:

[0095]

[0096] Where V represents the target motion region, GDOP V This represents the global GDOP of the target motion region.

[0097] The global GDOP of the target motion region V is the weighted average of the GDOP at each location in space, i.e.:

[0098] GDOP V (G n )=∫∫∫ X∈V w(X)·GDOP(G n )dX

[0099] Discretize it to obtain:

[0100]

[0101] The GDOP value of the target motion region is obtained through the above formula. However, this GDOP is not the globally optimal GDOP of the target motion region. It needs to be optimized to obtain the globally optimal GDOP of the target motion region.

[0102] For a given number of stations n, the combined conical configuration G can be... n It can be decomposed into several simple conical configurations, and the decomposition method can be expressed as Θ=(T,q1,...q T ), where T is the number of single conical configurations, q i For each single conical configuration, with i = 1,...,T, the number of stations can be expressed as follows:

[0103]

[0104] Single-point positioning combined conical configuration G n The GDOP can be expressed as a decomposition Θ and the semi-cone angle θ of each single conical configuration. i A function of i = 1, ..., T can be decomposed in several ways, and can be represented as follows: Decomposition method Decomposition method …Decomposition method Under a fixed decomposition method, only the half-cone angle of each single cone configuration needs to be optimized. The optimization problem of the single-point positioning combined cone configuration GDOP can be expressed as:

[0105]

[0106] Where OS represents the optimal value of GDOP in the single-point positioning combined conical configuration. However, in the underwater target positioning problem, configuration optimization for single-point GDOP can no longer meet the requirements of high-precision positioning. The underwater target positioning performance is usually measured by the position estimation accuracy of the target trajectory globally or the entire target motion area. Therefore, the optimization problem of combined conical configuration GDOP also targets the GDOP of the target trajectory or the GDOP of the entire target motion area.

[0107] Furthermore, the target trajectory GDOP for each of the combined conical configurations is optimized to obtain the locally optimal GDOP for each of the combined conical configurations;

[0108] The objective function to be optimized is:

[0109]

[0110] Where Θ represents the decomposition method, f(Θ, θ1, ..., θ) T ) represents Θ and θ i The function composed of θ i Let represent the half-cone angle of each single cone configuration, and i = 1, ..., T; continuously search for the optimal solution to the optimization problem. According to the principle that the solution that makes the objective function smaller is better, substitute the solution into the objective function. By iteratively finding the optimal half-cone angle of the combined cone in the current combined cone configuration, the solution that makes the target trajectory GDOP reach a local minimum is the local optimal solution.

[0111] The optimization steps are as follows:

[0112] S301. For each of the combined conical configurations in the target trajectory, initialize the parameters of the adaptive particle swarm optimization algorithm, and randomly obtain the initial position of each particle in the target trajectory; the parameters of the adaptive particle swarm optimization algorithm include: scaling factor and consumption factor; the position of the i-th particle at time t is represented as:

[0113] Z i (t)=(θ i1 (t),...,θ iT (t)), i = 1, ..., M

[0114] Where M represents the particle swarm size, θ iT (t) represents the half-cone angle of the T-th single-cone configuration of the i-th particle at time t;

[0115] S302. Based on the target trajectory GDOP, obtain the target trajectory fitness value of each particle in the target trajectory at the current time, and initialize the individual extreme value and the local extreme value of each particle in the target trajectory.

[0116] In solving for the GDOP of the target trajectory for each of the aforementioned conical configurations, the formula has been used.

[0117]

[0118] Calculate the target trajectory GDOP, and based on GDOP... Ω (G n The fitness function of the target trajectory for the combined conical configuration is expressed as:

[0119]

[0120] The target trajectory fitness value of each particle at the current moment can be obtained by using the target trajectory fitness function formula of the combined conical configuration.

[0121] S303. Calculate the survival index of each particle in the target trajectory;

[0122] S304. If the survival index is greater than or equal to 1, then execute S305; if the survival index is less than 1, then execute S301.

[0123] S305. For each particle in the target trajectory, compare the current fitness value of the target trajectory with the individual extreme value of the target trajectory at the previous moment. If the current fitness value of the target trajectory is greater than the individual extreme value of the target trajectory at the previous moment, then use the current fitness value of the target trajectory as the individual extreme value of the target trajectory.

[0124] S306. Find the largest individual extreme value of the target trajectory among all individual extreme values ​​of all particles in the target trajectory at the current moment. The local extreme value of the target trajectory at the current moment is obtained from the largest individual extreme value of the target trajectory at the current moment. The local extreme value of the target trajectory at the current moment refers to the optimal solution found in the particle population of each combination of conical configurations in the target trajectory at the current moment. After obtaining the local extreme values ​​of the target trajectory at all moments, the final local extreme value of the target trajectory for a combination of conical configurations can be determined. After obtaining the final local extreme values ​​of the target trajectory for all combination of conical configurations in the target trajectory, the optimal solution, i.e., the global extreme value, can be obtained among all combination of conical configurations of the target trajectory.

[0125] S307. Calculate the velocity of the particle at the next moment by using the individual extreme value of the target trajectory of each particle, the local extreme value of the target trajectory at the current moment, the fitness value of the target trajectory at the current moment, and the position of each particle at the current moment.

[0126] S308. Using the velocity of each particle at the next moment as the adaptive step size, update the current position of each particle id by adding the result of the adaptive step size to the current position of each particle.

[0127] The formula for updating the velocity and position of the particle in the target trajectory at the next moment is expressed as:

[0128]

[0129] S309: Repeat S303-S308 until the number of repetitions reaches the preset maximum number of iterations, or the local fitness value of the target trajectory is greater than the preset threshold;

[0130] Whether to repeat the optimization steps is determined by the number of iterations or the fitness value. The iteration ends when the preset number of repetitions is reached, or a preset threshold is set, for example, a preset threshold of 1 / 3. When the local fitness value of the target trajectory is greater than 1 / 3, the iteration ends.

[0131] S310. Summarize the local extrema of the target trajectory at each time step, find the largest local extrema of the target trajectory as the final local extrema of the target trajectory, and obtain the local optimal GDOP of the target trajectory from the final local extrema of the target trajectory.

[0132] According to the formula:

[0133]

[0134] The local optimum of the target trajectory GDOP can be obtained from the local optimum of the fitness value of the combined conical configuration at the end of the iteration.

[0135] Furthermore, the target motion region GDOP for each of the combined conical configurations is optimized to obtain the locally optimal GDOP for each combined conical configuration. The optimization objective function is expressed as:

[0136]

[0137] The optimization steps are as follows:

[0138] S501. For each combined conical configuration in the target motion region, initialize the parameters of the adaptive particle swarm optimization algorithm and randomly obtain the initial positions of particles in the target motion region; the parameters of the adaptive particle swarm optimization algorithm include: scaling factor and consumption factor; the position of the i-th particle at time t is represented as: Z i (t)=(θ i1 (t),...,θ iT (t)), i=1,...,M, where M represents the particle swarm size, θ iT (t) represents the half-cone angle of the T-th single-cone configuration of the i-th particle at time t;

[0139] S502. Based on the target motion region GDOP, obtain the target motion region fitness value of each particle in the target motion region at the current time, and initialize the individual extreme value and the local extreme value of each particle in the target motion region.

[0140] In solving for the target motion region GDOP for each of the aforementioned conical configurations, the formula has been used.

[0141]

[0142] Calculate the target motion region GDOP, and based on the GDOPv (G n The fitness function of the target motion region for the combined conical configuration is expressed as:

[0143] The fitness value of the target motion region for each particle at the current moment can be obtained from the fitness function formula of the target motion region of the combined conical configuration.

[0144] S503. Calculate the survival index of each particle in the target motion region;

[0145] S504. If the survival index is greater than or equal to 1, then execute S505; if the survival index is less than 1, then execute S501.

[0146] S505. For each particle in the target motion region, compare the current fitness value of the target motion region of each particle with the individual extreme value of the target motion region at the previous moment. If the current fitness value of the target motion region is greater than the individual extreme value of the target motion region at the previous moment, then use the current fitness value of the target motion region as the individual extreme value of the target motion region.

[0147] S506. Find the largest individual extreme value of the target motion region among all the individual extreme values ​​of all particles in the target motion region at the current moment, and obtain the local extreme value of the target motion region at the current moment from the largest individual extreme value of the target motion region at the current moment.

[0148] The local extremum of the target motion region at the current moment refers to the optimal solution found in the particle population for each combined conical configuration in the target motion region at the current moment. After obtaining the local extremum of the target motion region at each moment, the final local extremum of the target motion region for a combined conical configuration can be determined. After obtaining the final local extremum of the target motion region for all combined conical configurations in the target motion region, the optimal solution among all combined conical configurations in the target motion region can be determined, which is the global extremum of the target motion region.

[0149] S507. Calculate the velocity of each particle at the next moment by using the individual extreme value of the target motion region of each particle, the local extreme value of the target motion region at the current moment, the fitness value of the target motion region at the current moment, and the position of each particle at the current moment.

[0150] S508. Using the velocity of each particle at the next moment as the adaptive step size, update the current position of each particle by adding the result of the adaptive step size to the current position of each particle.

[0151] The formula for updating the velocity and position of particles in the target's moving region at the next moment is expressed as:

[0152]

[0153] S509: Repeat S503-S508 until the number of repetitions reaches the preset maximum number of iterations, or the local fitness value of the target motion region is greater than the preset threshold; determine whether to repeat the optimization steps based on the number of repetitions or the fitness value. When the preset number of repetitions is reached, the iteration ends, or a preset threshold is set, for example, the preset threshold is 1 / 3. When the local fitness value of the target motion region is greater than 1 / 3, the iteration ends.

[0154] S510. Summarize the local extrema of the target motion region at each time step, find the largest local extrema of the target motion region as the final local extrema of the target motion region, and obtain the locally optimal GDOP of the target motion region from the final local extrema of the target motion region. According to the formula:

[0155]

[0156] The local optimum GDOP of the target trajectory can be obtained from the local extremum of the fitness value of the target motion region of the combined conical configuration at the end of the iteration.

[0157] Furthermore, the calculation of the survival index and generation period of each particle includes: calculating the survival index of each particle, expressed by the formula:

[0158] Where h is the survival index; E is the fitness value of the particle's current position; H is the particle's lifespan; λ is the consumption factor, i.e., the energy consumed per unit time; move indicates continuing to iterate and update the particle's velocity and position, and init indicates initializing the particle's position and velocity; based on the survival index value, it is determined whether to initialize the particle's position and velocity or update the particle's position and velocity according to the position and velocity formula. When the survival index h is greater than or equal to 1, move continues iterating. When the survival index h is less than 1, init initializes the particle's position and velocity, such as randomly generating the particle's position. When the energy at the particle's position is sufficient to sustain its life, the particle will continue to optimize and search for the optimal value, i.e., continue iterating. Otherwise, when the energy is lower than what is needed to sustain its life, it is near a non-global extreme point, and searching for the optimal value usually yields no results. Therefore, the particle is forced to initialize, such as by randomly generating the particle's position, causing it to jump out of this region. This is equivalent to increasing the number of optimization particles using the same storage space, thereby improving the efficiency of the algorithm. The lifespan of each particle is calculated using the formula:

[0159]

[0160] Where E maxε is the maximum fitness value among all current particle positions; ε is the scaling factor.

[0161] The concept of a lifespan is introduced, where particles are endowed with a certain survival ability as their environment changes. This allows particles to have the strongest vitality and the longest lifespan near the global extremum. Particles located at individual extrema will be reborn upon death, such as by randomly generating their next position, thus expanding the search scope. This not only saves storage space but also improves optimization capability and efficiency. As the optimization progresses, the lifespan of particles will be extended by the strongest competitors, allowing particles not near the global extremum to have the opportunity to conduct a wider search.

[0162] The effectiveness of this invention is further illustrated and verified using experimental data. First, the global GDOP of the target trajectory is used as the optimization function, and the optimization function is: The Adaptive Particle Swarm Optimization (APSO) algorithm is denoted as APSO. In... Figure 8 The two decomposition formulas for the eight stations shown and Below, optimization is performed using gradient descent (GD) and the traditional particle swarm optimization (PSO) algorithm, respectively. Figure 8 In the diagram, the diamond-shaped frame represents the measuring station, and the curve represents the target's trajectory. The structures of the three methods are compared below. Figure 10 As shown. Figure 9a , Figure 9b , Figure 9c As shown, Figure 9a and Figure 9b The horizontal axis of the coordinate system represents the number of iterations, and the vertical axis represents the global GDOP. As can be seen from the three graphs, the global optimality of APSO gradually increases with increasing ω, reaching global optimality when ω = 1.2. This is because a larger ω results in less randomness in the particle step size and a stronger global search capability. Figure 9a and Figure 9b We can conclude that the iterative results of the first decomposition method are superior to those of the second decomposition method, i.e., the configuration decomposition method. Superior Regardless of the value of ω, this may be because the first decomposition method can observe more effective information. Figure 9c The optimal conical configuration obtained by APSO optimization has semi-cone angles of θ1 = 37.31° and θ2 = 64.51°, where... Figure 9c The single cone configuration formed by the dashed lines represents the decomposition formula. The single conical configuration represented by the decomposition formula is achieved in The diamond-shaped frame represents the measuring station, and the curve represents the target's trajectory.

[0163] like Figure 10 As shown, Figure 10 The horizontal axis represents the number of iterations, and the vertical axis represents the global minimum GDOP. GD gets stuck in local optima during iteration. Compared to GD, APSO has higher convergence efficiency and better global optimality. Adding adaptive step size and a survival-of-the-fittest mechanism to PSO significantly improves the algorithm's efficiency, reducing the number of convergence iterations from 35 to 5. The globally minimum GDOP optimized by APSO is not significantly different from that optimized by PSO, indicating that APSO's advantage over PSO mainly lies in improving the algorithm's convergence efficiency. Assuming the standard deviation of the station location error δ after seabed station calibration is 0.1m, the standard deviation of the random ranging error σ is 0.05m, and the ranging system error is in the form of a first-order polynomial, specifically a + bt = 0.05 + 0.1t, the optimal configurations obtained by the GD, PSO, and APSO methods are then used to evaluate and compare the target trajectory positioning accuracy using the EMBET ballistic estimation method. Table 1 shows the decomposition methods, half-cone angles, global GDOP, and accuracy comparisons for the three configurations. The accuracy is the average of 100 simulations. σ in the table... x σ y σ z The solution accuracy in the x, y, and z directions, respectively, σ R The overall solution accuracy is shown in Table 1. As can be seen from Table 1, the global GDOP of the trajectory obtained from the optimal configurations optimized by PSO and APSO is not significantly different. Therefore, under the same error parameter settings, the optimal configuration obtained by APSO slightly improves the position solution accuracy of the target trajectory. Compared with GD, the optimal configuration of APSO significantly reduces GDOP. Ω This improves the accuracy of target trajectory position calculation. It demonstrates that in the optimization problem of the minimum global GDOP configuration for underwater targets with coplanar constraints, the single cone configuration needs to be expanded into a nested cone configuration. Using an adaptive particle swarm optimization algorithm can significantly improve the optimization efficiency of the optimal configuration, find the globally optimal combination of cone configurations, reduce the global GDOP of the trajectory, and improve target positioning accuracy.

[0164]

[0165] Table 1 Comparison of Three Optimal Configurations and Their Positioning Accuracy

[0166] Using the global GDOP of the target motion region as the optimization criterion, the optimization function is... The GDOP weights are set to be equal at all locations in the space. With the same number of stations, an adaptive particle swarm optimization algorithm is used to optimize the semi-cone angle of the combined conical configuration. The algorithm incorporates an adaptive step size and a survival competition mechanism, and the parameters are set accordingly. GDOP during optimization V The changing trend and the obtained optimal configuration are as follows Figure 11a , Figure 11b , Figure 11c As shown.

[0167] like Figure 11a As shown, the horizontal axis in the coordinate system represents the number of iterations, and the vertical axis represents the global GDOP. Figure 11a As can be seen, in the first decomposition method, the algorithm converges to the global optimum when ω = 1.2, with the optimal global GDOP being 5.6356. This conclusion is consistent with the conclusion obtained when the trajectory global GDOP is used as the optimization criterion. Global optimal configuration decomposition method The semi-cone angles are θ1 = 47.60° and θ2 = 46.40°. Statistical analysis of the GDOP distribution at each location in the target space shows that when using a single cone configuration, the proportion of GDOP values ​​less than 40° in the target motion region is 12.58%, while the corresponding proportion is 67.75% when using the optimal combined cone configuration. Different maximum GDOP values ​​were set, and the proportion of sampling points in the target space with GDOP values ​​less than each maximum value was statistically analyzed. The results are shown in Table 2. When the maximum values ​​are the same, the proportion of points with the optimal combined cone configuration is lower than that with the single cone configuration. Therefore, it can be concluded that using the optimal combined cone configuration significantly improves the GDOP distribution within the target motion region.

[0168]

[0169] Table 2 Comparison of GDOP Distribution in Target Areas

[0170] To further verify the underwater optimal global GDOP combined conical configuration optimization method based on adaptive particle swarm optimization (APSO), it was applied to a long-baseline lake test for underwater maneuvering target trajectory fusion calculation. Experimental analysis was conducted using data from the Songhua Lake long-baseline stations and target trajectory data. The equipment used in the experiment included long-baseline seabed stations and acoustic beacons. The station positions were calibrated using a survey vessel, and the acoustic beacons were installed on the target simulation cylinder. First, the APSO algorithm was used to optimize the station configuration to obtain the optimal combined conical configuration. Then, the EMBET method based on polynomial constraints was used to estimate and evaluate the accuracy of the simulation cylinder trajectory. In a long-baseline system with n=8 stations and a seabed platform range of 1km*2km, the traditional station configuration is a combined rectangular configuration, represented as follows: in and This represents two rectangular configurations with a total of 4 stations. The simulated tube trajectory is similar to that of a traditional configuration. Figure 12c As shown.

[0171] To reduce the global ground-to-ground (GDOP) trajectory of traditional long-baseline system configurations and improve trajectory estimation accuracy, an adaptive particle swarm optimization algorithm is used to find the optimal deployment configuration within the seabed-based platform. The algorithm incorporates both adaptive step size and survival competition mechanisms, and parameter settings are optimized accordingly. GDOP during optimization Ω The trend of change is as follows Figure 12a and Figure 12b As shown in the figure, the horizontal axis of the coordinate system represents the number of iterations, and the vertical axis represents the global GDOP. In the first decomposition method, the algorithm converges to the global optimum when ω = 1.2. The optimal combined conical configuration is as follows: Figure 12d As shown.

[0172] The trajectory of the cylinder was calculated using the EMBET ballistic estimation method, employing both a traditional combined rectangular configuration and an optimal combined conical configuration. Table 3 compares the accuracy of the two configurations. The table shows that the optimal combined conical configuration reduces GDOP by [percentage missing] compared to the traditional rectangular configuration. Ω The accuracy of trajectory estimation was improved by nearly 3.5 times.

[0173]

[0174] Table 3 Comparison between the traditional configuration and the optimal configuration

[0175] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process may be rearranged without departing from the scope of this disclosure. The appended method claims provide elements of various steps in an exemplary order and are not intended to limit the scope to the specific order or hierarchy described.

[0176] The disclosed embodiments have been described above to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit and scope of this disclosure. Therefore, this disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed in this application.

[0177] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the deployment of underwater acoustic positioning systems based on a combined conical configuration, characterized in that, include: Based on the target to be measured and the number of stations, the single cone configuration in the underwater acoustic positioning system is expanded into a combination of multiple cone configurations; The target trajectory GDOP for each of the combined conical configurations is obtained as a function of the angles of the target trajectory combined conical configuration; The target trajectory GDOP for each of the aforementioned combined conical configurations is optimized to obtain the locally optimal GDOP for each of the aforementioned combined conical configurations; the globally optimal GDOP for the target trajectory is obtained from the locally optimal GDOP for each of the aforementioned combined conical configurations; and the optimal combined conical configuration for the target trajectory is obtained from the half-cone angle of the combined conical configuration corresponding to the globally optimal GDOP for the target trajectory. The target motion region GDOP for each of the combined conical configurations is obtained as a function of the angles of the target motion region combined conical configuration; The target motion region GDOP of each of the aforementioned combined conical configurations is optimized to obtain the locally optimal GDOP of the target motion region for each of the aforementioned combined conical configurations; the globally optimal GDOP of the target motion region is obtained from the locally optimal GDOP of the target motion region for each of the aforementioned combined conical configurations; the optimal combined conical configuration of the target motion region is obtained from the half-cone angle of the combined conical configuration corresponding to the globally optimal GDOP of the target motion region. The deployment arrangement of the underwater acoustic positioning system is determined based on the optimal combination conical configuration of the target trajectory and the optimal combination conical configuration of the target motion area; Specifically, the optimization of the target trajectory GDOP for each of the combined conical configurations to obtain the locally optimal target trajectory GDOP for each of the combined conical configurations, and the optimization of the target motion region GDOP for each of the combined conical configurations to obtain the locally optimal target motion region GDOP for each of the combined conical configurations, both employ an adaptive particle swarm optimization algorithm. The adaptive particle swarm optimization algorithm incorporates an adaptive step size for particle movement and survival and competition mechanisms into the particle swarm optimization algorithm. The formula for calculating the survival index of each particle is expressed as: ； Where h is the survival index; when the survival index h is greater than or equal to 1, the iteration continues; when the survival index h is less than 1, the position and velocity of the particle are initialized; E is the fitness value of the particle's current position; H is the particle's lifespan; λ is the consumption factor, that is, the energy consumed per unit time. The lifespan of each particle is calculated using the following formula: ； in ε is the maximum fitness value among all current particle positions; ε is the scaling factor.

2. The method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration as described in claim 1, characterized in that, The combined conical configuration is composed of at least two single conical configurations; the method for expanding the single conical configuration in the underwater acoustic positioning system into a combination of multiple combined conical configurations includes: forming at least two single conical configurations according to the number of stations; and adding each single conical configuration together to obtain the combined conical configuration.

3. The method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration as described in claim 1, characterized in that, The adaptive step size for each particle's movement is obtained by taking the particle's current position, current velocity, current individual extremum, and current local extremum; wherein the current individual extremum refers to the optimal solution found for a particle within the target trajectory, and the local extremum refers to the optimal solution found for a given combination of conical configurations in the entire particle swarm.

4. The method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration as described in claim 1, characterized in that, Each of the single conical configurations consists of a target point and at least three measuring stations, with the measuring stations on each single conical configuration located on the same horizontal plane and evenly distributed on the circumference of the circular base of the single conical configuration.

5. The method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration as described in claim 1, characterized in that, The target trajectory GDOP for each of the combined conical configurations is obtained as a function of the angles of the target trajectory combination conical configuration, using the following formula: ； Where Ω represents the target trajectory, GDOP Ω GDOP represents the global GDOP of the target trajectory, where n is the number of stations, Gn is the combined conical configuration with n stations, and GDOP(Gn) represents the GDOP for single-point localization. For position The weights of GDOP are given, where k is the sampling point, and satisfy the following conditions: .

6. The method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration as described in claim 5, characterized in that... The target motion region GDOP for each of the combined conical configurations is obtained as a function of the angles of the target motion region combination conical configuration, using the following formula: ； Where V represents the target motion region, GDOP V This represents the global GDOP of the target motion region.

7. The method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration as described in claim 1, characterized in that, The target trajectory GDOP for each of the aforementioned combined conical configurations is optimized to obtain the locally optimal GDOP for each of the aforementioned combined conical configurations. The optimization steps are as follows: S301. For each of the combined conical configurations in the target trajectory, initialize the parameters of the adaptive particle swarm algorithm and randomly obtain the initial position of each particle in the target trajectory; the parameters of the adaptive particle swarm algorithm include: scaling factor and consumption factor; S302. Based on the target trajectory GDOP, obtain the target trajectory fitness value of each particle in the target trajectory at the current time, and initialize the individual extreme value and the local extreme value of each particle in the target trajectory. S303. Calculate the survival index of each particle in the target trajectory; S304. If the survival index is greater than or equal to 1, then execute S305; if the survival index is less than 1, then execute S301. S305. For each particle in the target trajectory, compare the current fitness value of the target trajectory with the individual extreme value of the target trajectory at the previous moment. If the current fitness value of the target trajectory is greater than the individual extreme value of the target trajectory at the previous moment, then use the current fitness value of the target trajectory as the individual extreme value of the target trajectory. S306. Find the largest individual extreme value of the target trajectory among all the individual extreme values ​​of all particles in the target trajectory at the current moment, and obtain the local extreme value of the target trajectory at the current moment from the largest individual extreme value of the target trajectory at the current moment; S307. Calculate the velocity of each particle at the next moment by using the individual extreme value of the target trajectory of each particle, the local extreme value of the target trajectory at the current moment, the fitness value of the target trajectory at the current moment, and the position of each particle at the current moment. S308. Using the velocity of each particle at the next moment as an adaptive step size, update the current position of each particle by adding the adaptive step size to the current position of each particle. S309: Repeat S303-S308 until the number of repetitions reaches the preset maximum number of iterations, or the local fitness value of the target trajectory is greater than the preset threshold; S310. Summarize the local extrema of the target trajectory at each time step, find the largest local extrema of the target trajectory as the final local extrema of the target trajectory, and obtain the local optimal GDOP of the target trajectory from the final local extrema of the target trajectory.

8. The method for optimizing the deployment of an underwater acoustic positioning system based on a combined conical configuration as described in claim 1, characterized in that, The target motion region GDOP for each of the aforementioned combined conical configurations is optimized to obtain the locally optimal GDOP for each of the aforementioned combined conical configurations. The optimization steps are as follows: S501. For each of the combined conical configurations in the target motion region, initialize the parameters of the adaptive particle swarm algorithm and randomly obtain the initial positions of the particles in the target motion region; the parameters of the adaptive particle swarm algorithm include: scaling factor and consumption factor; S502. Based on the target motion region GDOP, obtain the target motion region fitness value of each particle in the target motion region at the current time, and initialize the individual extreme value of each particle in the target motion region and the local extreme value of the particles in the target motion region. S503. Calculate the survival index of each particle in the target motion region; S504. If the survival index is greater than or equal to 1, then execute S505; if the survival index is less than 1, then execute S501. S505. For each particle in the target motion region, compare the current fitness value of the target motion region of each particle with the individual extreme value of the target motion region at the previous moment. If the current fitness value of the target motion region is greater than the individual extreme value of the target motion region at the previous moment, then use the current fitness value of the target motion region as the individual extreme value of the target motion region. S506. Find the largest individual extreme value of the target motion region among all the individual extreme values ​​of all particles in the target motion region at the current moment, and obtain the local extreme value of the target motion region at the current moment from the largest individual extreme value of the target motion region at the current moment. S507. Calculate the velocity of each particle at the next moment by using the individual extreme value of the target motion region of each particle, the local extreme value of the target motion region at the current moment, the fitness value of the target motion region at the current moment, and the position of each particle at the current moment. S508. Using the velocity of each particle at the next moment as an adaptive step size, update the current position of each particle by adding the adaptive step size to the current position of each particle. S509: Repeat S503-S508 until the number of repetitions reaches the preset maximum number of iterations, or the local fitness value of the target motion region is greater than the preset threshold. S510. Summarize the local extrema of the target motion region at each time step, find the largest local extrema of the target motion region as the final local extrema of the target motion region, and obtain the local optimal GDOP of the target motion region from the final local extrema of the target motion region.

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