Marine sensor network positioning optimization deployment method driven by quantum optimization framework

Abstract

The invention relates to an ocean sensor network positioning optimization deployment method driven by a quantum optimization framework, and the method comprises the following steps: obtaining related data of an ocean sensor network, considering the influence of an underwater acoustic signal in an ocean non-uniform environment, introducing a Snell law and a ray tracing theorem, and constructing a TOA-based constant-gradient acoustic signal ranging model; constructing an OSNs optimal deployment strategy function based on an A-optimal criterion according to the TOA-based constant gradient sound signal ranging model, and reconstructing the OSNs optimal deployment strategy function by considering unknown influence of target prior information; and solving the reconstructed OSNs optimal deployment strategy function based on the A-optimal criterion by adopting an improved sparrow search algorithm driven by quantum calculation to obtain the optimal deployment position of the anchor node in the ocean sensor network under the condition that the target is unknown in prior. Compared with the prior art, the method has the advantages of optimizing the deployment positions of the anchor nodes and the like.

Description

Technical Field

[0001] This invention relates to the field of marine wireless sensor network positioning technology, and in particular to a quantum optimization framework-driven method for optimal deployment of marine sensor network positioning. Background Technology

[0002] Marine sensor networks (OSNs) have broad application value in fields such as marine resource development and utilization, environmental monitoring, and deep-sea mining. Among them, positioning technology can provide key location information for data collection and is the basis for research on other theoretical issues of OSNs.

[0003] Existing research has shown that better deployment strategies can effectively improve positioning accuracy based on Time of Arrival (TOA). However, unlike terrestrial environments, the non-uniformity of the marine environment leads to a layered effect in the propagation of underwater acoustic signals, resulting in a curved propagation path. Furthermore, the dynamic nature of ocean altitude makes constructing an optimal deployment function for OSNs that minimizes positioning error challenging. Secondly, existing deployment strategies often rely on prior information about the target for overall deployment and the construction of corresponding optimization criteria. However, prior information about the target is uncertain in unknown marine environments, rendering existing prior assumptions based on target prior information inapplicable in real-world scenarios. Finally, existing technologies heavily rely on rigorous mathematical assumptions, such as fixed angles or distances, for ease of solution. However, these assumptions significantly limit their applicability in uncertain marine environments. Summary of the Invention

[0004] The purpose of this invention is to provide a quantum optimization framework-driven method for optimizing the positioning and deployment of marine sensor networks under conditions of unknown prior knowledge.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A quantum optimization framework-driven method for optimal deployment of marine sensor network localization includes the following steps:

[0007] To acquire relevant data from the marine sensor network, considering the influence of underwater acoustic signals in the non-uniform marine environment, Snell's law and ray tracing theorem are introduced to construct an equal gradient acoustic signal ranging model based on TOA.

[0008] Based on the TOA-based isogradient acoustic signal ranging model, an optimal deployment strategy function for OSNs based on the A-optimal criterion is constructed and reconstructed considering the influence of unknown prior target information.

[0009] The reconstructed optimal deployment strategy function of OSNs based on the A-optimality criterion is solved using an improved sparrow search algorithm driven by quantum computing to obtain the optimal deployment location of anchor nodes in the marine sensor network under the condition that the prior knowledge of the target is unknown.

[0010] Furthermore, the construction process of the TOA-based isogradient acoustic signal ranging model includes:

[0011] Given an ocean sensor network with N anchor nodes and one target node, acquire the TOA (Time of Arrival) observation information received by each anchor node at each time step, i.e.:

[0012] D i (x)=||xa i ||+ε i (1)

[0013] In the formula, D i (x) represents the distance between the i-th anchor node and the target node obtained through the TOA (Transmission of Affinity), where x = [x1, x2, x3]. T For the target node position, a i =[a i1 ,a i2 ,a i3 ] T Let be the position of the i-th anchor node, T denote the transpose, ||·|| be the second norm, and ε be the second norm. i This indicates that for the TOA noise of the i-th anchor node, the noise variance at each time step is assumed to be equal, and follows a mean of zero and a variance of . The Gaussian distribution of can be expressed as

[0014] Due to the non-uniformity of underwater cutoff, the underwater acoustic signal propagates along a curved path. By introducing Snell's law and the ray tracing theorem, an isogradient model is constructed, expressed as:

[0015] V(z)=μz+v (2)

[0016] In the formula, V(z) represents the isogradient model at a depth of z, z represents the depth information, μ represents the gradient of the sound velocity profile, and v represents the propagation speed of the sound wave at the water surface.

[0017] Therefore, underwater acoustic signals propagate according to the following rules:

[0018]

[0019] In the formula, This represents the angle of the underwater acoustic signal at a corresponding point on the ray. and V(x3) and V(a) represent the angles on the ray when the corresponding anchor node and target node are transmitting and receiving signals, respectively.i3 ) represent depths of x3 and a respectively. i3 When the gradient is constant, the corresponding isogradient model has λ as a constant.

[0020] Taking the integral form at a point along the propagation path of the curve, we have:

[0021]

[0022] In the formula, d represents the partial derivative sign, and ρ represents the lateral distance between the two points, i.e. The arc length represents the propagation of the curve, and τ is the propagation time of the underwater acoustic signal;

[0023] By rearranging the terms of formula (4) and... Taking the derivative, we get:

[0024]

[0025] Substituting equation (5) into equation (4), we obtain the compensation form for curve propagation corresponding to each anchor node, which is expressed as:

[0026]

[0027] In the formula, This represents the length between the i-th anchor node and the target node;

[0028] Based on equation (6), equation (1) is further transformed and used as the TOA-based isogradient acoustic signal ranging model for each anchor node, as follows:

[0029]

[0030] In the formula, D i (x) represents the distance between the i-th anchor node and the target node obtained through TOA, which is the TOA-based isogradient acoustic signal ranging model of the i-th anchor node.

[0031] Furthermore, the construction steps of the OSNs optimal deployment strategy function based on the A-optimal criterion include:

[0032] For N anchor nodes in an ocean sensor network, the TOA-based isogradient acoustic signal ranging model for all anchor nodes is represented as D(x)=[D1(x),…,D N (x)] T Its likelihood function is expressed as:

[0033]

[0034] In the formula, D1(x), D N(x) represents the TOA-based isogradient acoustic signal ranging models corresponding to the 1st and Nth anchor nodes, respectively, and κ represents the distances obtained between the 1st and Nth anchor nodes and the target node via TOA, respectively. N [det(Σ)], det(·) represents the corresponding determinant. diag(·) is a diagonal matrix function. For all anchor nodes gather, Let T represent the length between the i-th anchor node and the target node, and T represent the transpose.

[0035] Introducing the Claumme lower bound theory, we establish a Claumme lower bound expression as follows:

[0036]

[0037] in:

[0038]

[0039] In the formula, CRLB is the Clummerlow-based lower bound expression, and x = [x1, x2, x3]. T The target node location;

[0040] Based on the Crommellow lower bound expression, partial derivatives are taken with respect to the coordinates of the target node, resulting in:

[0041]

[0042] In the formula, μ represents the gradient of the sound velocity profile, and v represents the propagation speed of the sound wave on the water surface. and These represent the angles of the corresponding anchor node and target node on the ray when transmitting and receiving signals, respectively, and ρ represents the lateral distance between the two points. a i =[a i1 ,a i2 ,a i3 ] T This represents the position of the i-th anchor node;

[0043] For equation (5) Performing integration and division operations, and substituting into equation (3), we obtain:

[0044]

[0045] Further differentiating x3 and ρ, we obtain:

[0046]

[0047] Define G1, G2, G3, and G4 respectively, as follows:

[0048]

[0049] Then the partial derivatives in equation (12) are expressed as:

[0050]

[0051] Combining equations (10) to (14) above, we obtain the optimal deployment strategy function for OSNs based on the A-optimal criterion under the condition of equal gradient sound speed at known target location.

[0052] Furthermore, the expression for the OSNs optimal deployment strategy function based on the A-optimality criterion is as follows:

[0053]

[0054] In the formula, This is the optimal deployment strategy function for OSNs based on the A-optimality criterion.

[0055] a i =[a i1 ,a i2 ,a i3 ] T Let represent the position of the i-th anchor node, T denotes transpose, Trace represents the corresponding trace function, and CRLB is a Clummerlow-based lower bound expression.

[0056] Furthermore, the step of reconstructing the target based on the influence of unknown prior information includes:

[0057] Considering the influence of unknown prior information about the target, the monitored 3D sea area is gridded, with each grid vertex serving as a candidate target location. The minimization approach is then introduced to reconstruct the OSNs optimal deployment strategy function based on the A-optimality criterion, resulting in the reconstructed OSNs optimal deployment strategy function based on the A-optimality criterion, expressed as:

[0058]

[0059] In the formula, This is the reconstructed OSNs optimal deployment strategy function based on the A-optimality criterion. a i =[a i1 ,a i2 ,a i3 ] TLet represent the position of the i-th anchor node, T denotes transpose, Trace represents the corresponding trace function, CRLB is the expression based on the Crommellow lower bound, m is the candidate target position, and M is the total number of candidate target positions in the monitored sea area.

[0060] Furthermore, the solution process includes the following:

[0061] 1) An initial population is generated based on a quantum Bloch sphere-based initial population generation method, where individuals in the population correspond to anchor node positions;

[0062] 2) An adaptive producer-scavenger ratio adjustment strategy is adopted to adjust the allocation ratio coefficient between producers and scavengers, and the fitness function and optimal population of each individual are calculated.

[0063] 3) Update the weights and positions of producers and scavengers, and further update the number of producers and scavengers;

[0064] 4) Determine if the maximum iteration value has been exceeded. If yes, end the iteration process and output the optimal anchor node position. If no, return to step 3) to perform iterative solution until the maximum iteration value is reached.

[0065] Furthermore, the step of generating the initial population includes:

[0066] If we assume the Bloch sphere is a three-dimensional unit sphere, then the state of a qubit is represented as:

[0067] |Φ>=[cosΦsinθ,sinΦsinθ,cosθ] T ,

[0068] In the formula, |Φ> represents the state of the qubit at the corresponding point on the sphere, Φ is the corresponding azimuth angle, θ is the elevation angle from the point to the sphere, and T represents the transpose;

[0069] The position of the i-th anchor node in the q-th group is encoded as a qubit in Bloch spherical coordinates, represented as:

[0070]

[0071] In the formula, [a i,X ,a i,Y ,a i,Z ] represents the i-th qubit, a i =[a i1 ,a i2 ,a i3 ] T Let X, Y, and Z be the position of the i-th anchor node, corresponding to the X, Y, and Z coordinate systems of the 3D sphere, respectively. The position of the i-th anchor node corresponds to the i-th individual. Φ i1 ,Φ i2 ,Φi3 These are the corresponding azimuth angles, θ i1 ,θ i2 ,θ i3 These are the angles of elevation from the corresponding points to the sphere;

[0072] Let the Bloch coordinates of the i-th qubit and the h-th qubit be... Then the corresponding solution space is obtained, where Represented as:

[0073]

[0074] In the formula, UB h To correspond to the upper bound, LB h Indicates the corresponding lower bound, X ih Y ih Z ih These are the solutions for the h-th qubit of the i-th anchor node in the X, Y, and Z coordinates, respectively.

[0075] From X ih Y ih Z ih The solution with the highest fitness is selected as the encoding of the initial population.

[0076] Furthermore, the expression for calculating the distribution ratio coefficient between the producers and scavengers is as follows:

[0077]

[0078] In the formula, r represents the proportional coefficient controlling the distribution ratio between producers and scavengers, exp is an exponential function, t represents the index of the specific iteration number, and Iter max The maximum number of iterations is given by k, which represents the introduced perturbation bias factor used to adjust the nonlinear decreasing trend of r.

[0079] Furthermore, after being controlled by the aforementioned allocation ratio coefficient, producer Q pr The quantity is represented by Q. pr =rQ, Scavenger Q sc The quantity is represented by Q sc = (1-r)Q, where Q is the total population size.

[0080] Furthermore, the update expressions for the producer's weight and position are as follows:

[0081]

[0082] In the formula, w(t) represents the weight of the t-th iteration, w max and w min These represent the corresponding maximum and minimum weights, respectively.max The maximum number of iterations, and Let represent the j-th dimension values ​​of the i-th anchor node in the q-th sparrow population at iterations t+1 and t, respectively. Γ is an N×3 coefficient matrix whose elements are randomly selected from the interval (0,1]. R2 is the safety threshold for the current alarm level, with a value range of [0,1]. ST represents the predefined safety threshold, with a value of [0.5,1]. It is a normally distributed random variable. It is an N×3 matrix where all elements are equal to 1. When R2 < ST, it indicates a low-risk environment, allowing producers to conduct extensive exploration phases. When R2 ≥ ST, it indicates the presence of a potential threat, thus triggering an escape response, and producers migrate to a safe area.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] (1) Compared with existing technologies, this invention can more accurately characterize the curve propagation path based on TOA in a non-uniform, uniform gradient marine environment. Simultaneously, by utilizing a gridded approach, each vertex is used as a possible target location, eliminating the influence of target location uncertainty. Combined with minimizing the Clummerlow lower bound, the optimization function is reconstructed. Furthermore, in the solution process, a metaheuristic algorithm is employed, breaking free from the strict mathematical assumptions of existing technologies. A quantum computing-driven initial population generation method is used, combined with a multi-strategy improved SSA, to solve the optimization function, thereby obtaining the optimal deployment strategy for OSNs positioning anchor points under conditions of unknown target priors. This provides a feasible solution to the OSNs positioning optimization deployment problem under the influence of stratification effects in uncertain environments.

[0085] (2) In view of the fact that the initial sparrow population in the traditional sparrow search algorithm is usually generated randomly, which may lead to uneven distribution in the search space, and some individuals may be far from the global optimum, which may result in slow convergence speed and poor particle quality, this invention introduces Bloch sphere in quantum computing to generate a diverse and high-quality population, which also improves the global exploration capability of the algorithm.

[0086] (3) In the improved sparrow search algorithm, the present invention adopts an adaptive producer-scavenger ratio adjustment strategy to control the allocation ratio between producers and scavengers, so that in the initial iteration, a larger proportion of the population is designated as producers to promote a broad global search; as the algorithm progresses, the number of producers gradually decreases while the number of scavengers gradually increases, thereby realizing the transition from global exploration to fine-grained local search. This dynamic adjustment mechanism improves the overall convergence accuracy of the algorithm.

[0087] (4) In the process of improving the sparrow search algorithm, this invention introduces a perturbation based on inertia weight to update the producer's weight and position. This allows for a larger inertia weight in the initial iteration stage, which is beneficial for the producer to conduct extensive global exploration, while a smaller inertia weight in the later iteration stage enhances its local utilization ability. This adaptive adjustment allows individuals with higher fitness to perturb within the neighborhood of their original position, thereby improving the algorithm's global search efficiency, promoting information exchange among the population, and ultimately helping to accelerate convergence and improve the accuracy of the solution. Attached Figure Description

[0088] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0089] Figure 2 This is a schematic diagram of the gridding operation of the monitoring area according to the present invention.

[0090] Figure 3 This is a flowchart illustrating the solution process of the improved sparrow search algorithm based on quantum computing in this invention.

[0091] Figure 4 This is the probability density function when the number of anchor nodes in this invention is 4;

[0092] Figure 5 This is the probability density function when the number of anchor nodes in this invention is 8. Detailed Implementation

[0093] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0094] This embodiment provides a quantum optimization framework-driven method for optimal deployment of marine sensor network positioning, such as... Figure 1 As shown, the method includes the following steps:

[0095] S1. Considering the influence of acoustic signals in the non-uniform marine environment, Snell's law and ray tracing theorem are introduced to construct an equal gradient acoustic signal ranging model based on TOA, and an optimization function is constructed by combining the A-optimization criterion.

[0096] 1. Establishment of a TOA-based isogradient acoustic signal ranging model:

[0097] Assume there are N anchor nodes and one target node in OSNs, and the position of the i-th anchor node is denoted as a. i =[a i1 ,a i2 ,a i3 ] TThe target node position is represented as x = [x1, x2, x3] T Where T represents the transpose. Assume all nodes are equipped with depth pressure sensors, capable of calculating their own depth based on pressure information. Simultaneously, they receive corresponding TOA (Time of Arrival) observation information at each time step, i.e.:

[0098] D i (x)=||xa i ||+ε i (1)

[0099] In the formula, D i (x) represents the distance between the i-th anchor node and the target node obtained through TOA; ||·|| is the second norm; ε i This represents the TOA noise for the i-th anchor node, assuming the noise variance is equal at each time step and follows a mean of zero with a variance of . The Gaussian distribution of can be expressed as

[0100] Due to the non-homogeneity of the underwater medium, a stratification effect occurs, causing the underwater acoustic signal to propagate in a curved pattern. If a model based on straight-line propagation in free space is directly used, it can easily lead to significant errors in the distance measurement between the target node and the anchor node. Therefore, the ray tracing theorem and Snell's law are introduced, and an isogradient model is used to describe the expression, namely:

[0101] V(z)=μz+v, (2)

[0102] In the formula, μ represents the gradient of the sound velocity profile; v represents the propagation speed of the sound wave at the water surface; z represents the depth information; and V(z) represents the isogradient model function at a depth of z. According to Snell's law and the ray tracing theorem, underwater acoustic signals propagate underwater following the following rules:

[0103]

[0104] In the formula, λ is a constant; This represents the angle of the underwater acoustic signal at a corresponding point on the ray; and These represent the angles of the corresponding anchor node and target node on the ray when transmitting and receiving signals, as shown in the attached figure. Figure 2 As shown; V(x3) and V(a) i3 ) represent depths of x3 and a respectively. i3 When the gradient is constant, the corresponding isogradient model function is taken as the integral at a point in the curve propagation path, then:

[0105]

[0106] In the formula, d represents the partial derivative sign; τ represents the arc length of the curve propagation; τ is the propagation time of the underwater acoustic signal; ρ represents the lateral distance between the two points, i.e. By rearranging the terms of formula (4) and... After differentiation, we get:

[0107]

[0108] Substituting equation (5) into equation (4), we obtain the compensation form for curve propagation, namely:

[0109]

[0110] In the formula, This represents the length between the i-th anchor node and the target node.

[0111] Equation (1) can be further transformed into the TOA-based isogradient acoustic signal ranging model for the i-th anchor node, expressed as:

[0112]

[0113] 2. Construction of the OSNs optimal deployment strategy function based on the A-optimality criterion:

[0114] For N anchor nodes, the corresponding TOA observation information is represented as D(x)=[D1(x),…,D N (x)] T Since the observation noise follows a Gaussian distribution, the corresponding likelihood function can be further expressed as:

[0115]

[0116] In the formula, κ=-0.5log[(2π) N [det(Σ)], det(·) represents the corresponding determinant; diag(·) is a diagonal matrix function.

[0117] Introducing the Claummello lower bound theory, we establish an expression based on the Claummello lower bound, namely:

[0118]

[0119] In the formula,

[0120] Taking the partial derivatives with respect to the coordinates of the target node, we can obtain:

[0121]

[0122] By analyzing formula (5) By performing integration and division operations and substituting into (3), we can obtain:

[0123]

[0124] Then, by differentiating x3 and ρ, we can further obtain:

[0125]

[0126] Define G1, G2, G3, and G4 respectively, that is:

[0127]

[0128] Then the partial derivatives in formula (12) can be expressed as:

[0129]

[0130] By combining equations (10) to (14) above, we can obtain the optimal deployment strategy function (also known as the optimization function) for OSNs based on the A-optimal criterion under the condition of constant gradient sound speed at a known target location, namely:

[0131]

[0132] In the formula, This represents the corresponding optimization function; Trace represents the corresponding trace function; CRLB is the obtained expression based on the Clummerlow lower bound.

[0133] S2. Considering the influence of unknown prior information of the target, the three-dimensional monitoring sea area is gridded, and its vertices are used as possible positions of the target. The idea of ​​minimization and maximization is introduced to reconstruct the optimization function.

[0134] Optimization function reconstruction under conditions of target position uncertainty:

[0135] Typically, the lower bound expression based on Clummerroy's method is derived from the inverse of the Fisher information matrix, and this optimal deployment strategy function expression can only be obtained if and only if the target location is known. However, in real-world scenarios, obtaining the precise location of the target is often impractical, especially in the absence of prior information. To eliminate the uncertainty of the target's prior information, the monitored 3D region is meshed, with each mesh intersection considered as a candidate target location, as shown in the attached diagram. Figure 2 As shown. Therefore, the optimal deployment strategy function for OSNs based on the A-optimality criterion can be rewritten as:

[0136]

[0137] In the formula, m represents the potential location of the target; M represents the total number of potential locations in the region. This gridding operation further eliminates the uncertainty of the target location. The original trace that minimizes the CRLB is transformed into the trace that minimizes the CRLB corresponding to the largest potential location in the uncertain region.

[0138] S3. Introducing the Sparrow Search Algorithm (SSA) and combining it with quantum computing ideas, a quantum-driven SSA initial population generation method is proposed by mapping the quantum superposition state of the initial population through Bloch spheres, thereby improving the characteristics of the initial population being low-quality and small in quantity.

[0139] Existing technologies for solving equation (16) usually involve strict mathematical assumptions. However, these assumptions can only be valid under specific environments and conditions. In order to obtain a universal solution method for equation (16), an improved sparrow search algorithm driven by quantum computing is proposed.

[0140] Initial population generation method based on quantum Bloch sphere:

[0141] In sparrow search algorithms, the initial sparrow population is typically generated randomly, which can lead to uneven distribution within the search space. Consequently, some individuals may stray far from the global optimum, resulting in slow convergence and poor particle quality. To address this, Bloch spheres from quantum computing are introduced to generate a diverse and high-quality population.

[0142] In quantum mechanics, the smallest unit of information is the qubit. Introducing the Bloch sphere, any qubit state can be mapped to a corresponding point on the Bloch sphere. Assuming the Bloch sphere is a three-dimensional unit sphere, the qubit state can be represented in spherical coordinates:

[0143] |Φ>=[cosΦsinθ,sinΦsinθ,cosθ] T (17)

[0144] In the formula, |Φ> represents the quantum bit state of the corresponding point on the sphere; Φ is the corresponding azimuth angle; and θ is the elevation angle from the point to the sphere.

[0145] Then the position of the i-th anchor node (individual) in the q-th group can be encoded as the Bloch sphere coordinates of the qubit, that is:

[0146]

[0147] In the formula, X, Y, and Z correspond to the X, Y, and Z coordinate systems of a three-dimensional sphere, respectively.

[0148] A single qubit is represented by three Bloch coordinates, each of which can be interpreted as an independent candidate solution. Since each coordinate lies in the range [-1, 1], a transformation is required to map these values ​​to the target solution space. Let the Bloch coordinates of the i-th qubit and the h-th qubit be... The corresponding solution space is:

[0149]

[0150] In the formula, UB h For the corresponding upper bound; LB h Indicates the corresponding lower bound; X ih Y ih Z ih These are the solutions for the h-th qubit of the i-th anchor node in the X, Y, and Z coordinates, respectively. This generates three feasible solutions, from which the solution with the highest fitness is selected to represent the encoding of the initial population. This strategy improves the quality of the initial population distribution within the search space, thereby enhancing the algorithm's global exploration capability.

[0151] S4. Based on the population obtained in S3, an improved SSA is proposed using adaptive dynamic adjustment and population hierarchical stratification mechanism. The optimization function of S2 is solved, and then the optimal deployment of OSNs positioning anchor nodes is obtained under the condition that the target is unknown in the prior knowledge.

[0152] Multi-strategy improved Sparrow Search (SSA) algorithm:

[0153] (1) In the original SSA algorithm, the ratio of producers to scavengers remains constant throughout the optimization process. This fixed producer-scavenger ratio leads to inefficiency in the optimization process: in the early stages, the limited number of producers restricts the algorithm's ability to conduct comprehensive global exploration; while in the later stages, too many producers become redundant, requiring a larger proportion of scavengers to promote effective local development. Therefore, the first step in this invention's multi-strategy improvement of SSA is to employ an adaptive producer-scavenger ratio adjustment strategy, namely:

[0154]

[0155] In the formula, r represents the proportional coefficient controlling the allocation ratio between producers and scavengers; k represents the introduced disturbance bias factor, used to adjust the nonlinear decreasing trend of r; t represents the index of the specific iteration number; exp is an exponential function; Iter max This represents the maximum number of iterations. Therefore, producer Q... pr And Scavenger Q sc The quantities can be represented as Q. pr =rQ and Q sc= (1-r)Q, where Q is the total population size. In the initial iterations, a larger proportion of the population is designated as producers to facilitate a broad global search. As the algorithm progresses, the number of producers gradually decreases while the number of scavengers gradually increases, thus transitioning from global exploration to fine-grained local search. This dynamic adjustment mechanism improves the overall convergence accuracy of the algorithm.

[0156] (2) In the original SSA algorithm, the producer's movement towards the global optimum at the beginning of each iteration typically exhibits a "jump" step pattern. While this behavior can improve convergence speed, the rapid aggregation of individuals may reduce population diversity and increase the risk of premature convergence to local optima by ignoring search blind spots and limiting the search range. Furthermore, the dependence on the producer's current position remains constant throughout the algorithm during the update process. Therefore, the second step of this invention's multi-strategy improvement to SSA is to introduce a perturbation based on inertia weights to update the producer's position, namely:

[0157]

[0158] In the formula, w(t) represents the weight of the t-th iteration; w max and w min These represent the corresponding maximum and minimum weights, respectively. Since dynamic weights are involved in the iteration, the producer's position is updated at iteration t+1 as follows:

[0159]

[0160] In the formula, and Let represent the j-th dimension value of the i-th anchor node in the q-th sparrow population at the (t+1)-th and t-th iterations, respectively; Γ is an N×3 coefficient matrix whose elements are randomly selected from the interval (0,1]; R2 is the safety threshold of the current alarm level, with a value range of [0,1]; ST represents the predefined safety threshold, with a value of [0.5,1]. It is a normally distributed random variable; Let R² be an N×3 matrix with all elements equal to 1. When R² < ST, it indicates a low-risk environment, allowing producers to conduct extensive exploration. Conversely, when R² ≥ ST, it indicates a potential threat, triggering an escape response where producers migrate to a safer area. In the initial stages of iteration, a larger inertia weight favors extensive global exploration; while in the later stages, decreasing the inertia weight enhances local exploitation. This adaptive adjustment allows individuals with higher fitness to perturb within the neighborhood of their original location, thereby improving the algorithm's global search efficiency, promoting information exchange among the population, and ultimately contributing to faster convergence and improved solution accuracy.

[0161] Based on the above improvements, and combined with Figure 3 As shown, the solution process of this quantum computing-driven improved sparrow search algorithm roughly includes the following:

[0162] 1) An initial population is generated based on a quantum Bloch sphere-based initial population generation method, where individuals in the population correspond to anchor node positions;

[0163] 2) An adaptive producer-scavenger ratio adjustment strategy is adopted to adjust the allocation ratio coefficient between producers and scavengers, and the fitness function and optimal population of each individual are calculated.

[0164] 3) Update the weights and positions of producers and scavengers, and further update the number of producers and scavengers;

[0165] 4) Determine if the maximum iteration value has been exceeded. If yes, end the iteration process and output the optimal anchor node position. If no, return to step 3) to perform iterative solution until the maximum iteration value is reached.

[0166] Simulation Experiment

[0167] To further verify the effectiveness of the method of this invention, simulation was performed on the MATLAB R2022b platform. The simulation area was 200m × 200m × 200m, and other relevant parameters were configured as follows: μ = 0.1s -1 , v=1500m / s, ST=0.8, x=[50,50,50] T M = 20, radius of the uncertain region is 5m, Q = 30 Iter max =200, Monte Carlo simulation count is 100. The deployment strategies under the same elevation angle (35.26° and 48.4°) and random deployment strategies, based on rigorous mathematical assumptions, are compared with existing technologies. The root mean square error is used as the evaluation standard for positioning error.

[0168]

[0169] In the formula, MC represents the total number of Monte Carlo simulations; mc represents the index of the current simulation. x represents the estimated position; x represents the actual position.

[0170] The relevant experimental results are attached. Figure 4 Appendix Figure 5 As shown, the attached Figure 4 The graph shows the probability density function when the number of anchor nodes N=4. Figure 5The graph shows the probability density function when the number of anchor nodes N=8. The experimental results show that when the number of anchor nodes is small, the overall positioning effects at elevation angles of 35.26° and 48.4° are quite similar. The positioning error of the 35.26° elevation angle deployment strategy is relatively small. The confidence probability reached 95%, while the positioning error at a deployment strategy with an elevation angle of 48.4° to achieve the same probability was... In comparison, the positioning error of random deployment strategies is relatively large compared to other methods, while the positioning error of the method proposed in this invention is [missing information - likely a specific value]. This method outperforms existing optimal deployment strategies. The positioning effectiveness of the deployment strategy proposed in this invention was also verified when the number of anchor segments N=8, as shown in the attached figure. Figure 5 As shown. Due to the consideration of layered sound propagation, the performance of the 48.4°-based deployment scheme improves with the increase in the number of anchor nodes, and its positioning error... The probability reached 95%, which is better than the deployment scheme based on 35.26° (the positioning error is [missing information] when achieving the same probability). In comparison, the positioning error of the method proposed in this invention when achieving this probability condition is... This is better than the deployment scheme based on 48.4°. Therefore, it can be seen that the deployment technology of the present invention achieves a certain improvement in positioning accuracy compared to existing technologies.

[0171] In summary, the method of this invention first considers the influence of acoustic signals in the non-uniform marine environment, introduces Snell's law and ray tracing theorem, constructs a TOA-based isogradient acoustic signal ranging model, and combines the A-optimization criterion (minimizing the Cromerlow lower bound) to construct an optimization function to solve the problem of ranging difficulty under the stratification effect. Second, considering the influence of unknown prior information of the target, the three-dimensional monitoring sea area is gridded, and its vertices are used as the possible positions of the target. The minimization idea is introduced to reconstruct the optimization function to solve the problem of uncertain prior information of the target. Finally, the SSA algorithm is introduced, combined with the idea of ​​quantum computing. By mapping the quantum superposition state of the initial population through Bloch sphere, a quantum-driven SSA initial population generation method is proposed to improve the characteristics of low quality and small quantity of the initial population. Based on this, an improved SSA is proposed using adaptive dynamic adjustment and population hierarchical mechanism to solve the reconstructed optimization function, solving the limitation that the solution process strictly depends on mathematical assumptions, and thus obtaining the optimal deployment strategy of OSNs positioning anchor points under the condition of unknown prior information of the target.

[0172] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0173] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0174] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0175] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0177] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0178] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A quantum optimization framework-driven method for optimal deployment of marine sensor network positioning, characterized in that, Includes the following steps: To acquire relevant data from the marine sensor network, considering the influence of underwater acoustic signals in the non-uniform marine environment, Snell's law and ray tracing theorem are introduced to construct an equal gradient acoustic signal ranging model based on TOA. Based on the TOA-based isogradient acoustic signal ranging model, an optimal deployment strategy function for OSNs based on the A-optimal criterion is constructed and reconstructed considering the influence of unknown prior target information. The reconstructed optimal deployment strategy function of OSNs based on the A-optimal criterion is solved using an improved sparrow search algorithm driven by quantum computing to obtain the optimal deployment location of anchor nodes in the marine sensor network under the condition that the prior knowledge of the target is unknown.

2. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 1, characterized in that, The construction process of the TOA-based isogradient acoustic signal ranging model includes: Given an ocean sensor network with N anchor nodes and one target node, acquire the TOA (Time of Arrival) observation information received by each anchor node at each time step, i.e.: D i (x)=||x-a i ||+ε i (1) In the formula, D i (x) represents the distance between the i-th anchor node and the target node obtained through the TOA (Transmission of Affinity), where x = [x1, x2, x3]. T For the target node position, a i =[a i1 ,a i2 ,a i3 ] T Let be the position of the i-th anchor node, T denote the transpose, ||·|| be the second norm, and ε be the second norm. i This indicates that for the TOA noise of the i-th anchor node, the noise variance at each time step is assumed to be equal, and follows a mean of zero and a variance of . The Gaussian distribution of can be expressed as Due to the non-uniformity of underwater cutoff, the underwater acoustic signal propagates along a curved path. By introducing Snell's law and the ray tracing theorem, an isogradient model is constructed, expressed as: V(z)=μz+v (2) In the formula, V(z) represents the isogradient model at a depth of z, z represents the depth information, μ represents the gradient of the sound velocity profile, and v represents the propagation speed of the sound wave at the water surface. Therefore, underwater acoustic signals propagate according to the following rules: In the formula, This represents the angle of the underwater acoustic signal at a corresponding point on the ray. and V(x3) and V(a) represent the angles on the ray when the corresponding anchor node and target node are transmitting and receiving signals, respectively. i3 ) represent depths of x3 and a respectively. i3 When the gradient is constant, the corresponding isogradient model has λ as a constant. Taking the integral form at a point along the propagation path of the curve, we have: In the formula, d represents the partial derivative sign, and ρ represents the lateral distance between the two points, i.e. The arc length represents the propagation of the curve, and τ is the propagation time of the underwater acoustic signal; By rearranging the terms of formula (4) and... Taking the derivative, we get: Substituting equation (5) into equation (4), we obtain the compensation form for curve propagation corresponding to each anchor node, which is expressed as: In the formula, This represents the length between the i-th anchor node and the target node; Based on equation (6), equation (1) is further transformed and used as the TOA-based isogradient acoustic signal ranging model for each anchor node, as follows: In the formula, D i (x) represents the distance between the i-th anchor node and the target node obtained through TOA, which is the TOA-based isogradient acoustic signal ranging model of the i-th anchor node.

3. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 2, characterized in that, The steps for constructing the OSNs optimal deployment strategy function based on the A-optimality criterion include: For N anchor nodes in an ocean sensor network, the TOA-based isogradient acoustic signal ranging model for all anchor nodes is represented as D(x)=[D1(x),…,D N (x)] T Its likelihood function is expressed as: In the formula, D1(x), D N (x) represents the TOA-based isogradient acoustic signal ranging models corresponding to the 1st and Nth anchor nodes, respectively, and κ represents the distances obtained between the 1st and Nth anchor nodes and the target node via TOA, respectively. N [det(Σ)], det(·) represents the corresponding determinant. diag(·) is a diagonal matrix function. For all anchor nodes gather, Let T represent the length between the i-th anchor node and the target node, and T represent the transpose. Introducing the Claumme lower bound theory, we establish a Claumme lower bound expression as follows: in: In the formula, CRLB is the Clummerlow-based lower bound expression, and x = [x1, x2, x3]. T The target node location; Based on the Crommellow lower bound expression, partial derivatives are taken with respect to the coordinates of the target node, resulting in: In the formula, μ represents the gradient of the sound velocity profile, and v represents the propagation speed of the sound wave on the water surface. and These represent the angles of the corresponding anchor node and target node on the ray when transmitting and receiving signals, respectively, and ρ represents the lateral distance between the two points. a i =[a i1 ,a i2 ,a i3 ] T This represents the position of the i-th anchor node; For equation (5) Performing integration and division operations, and substituting into equation (3), we obtain: Further differentiating x3 and ρ, we obtain: Define G1, G2, G3, and G4 respectively, as follows: Then the partial derivatives in equation (12) are expressed as: Combining equations (10) to (14) above, we obtain the optimal deployment strategy function for OSNs based on the A-optimal criterion under the condition of equal gradient sound speed at known target location.

4. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 1, characterized in that, The expression for the OSNs optimal deployment strategy function based on the A-optimality criterion is as follows: In the formula, This is the optimal deployment strategy function for OSNs based on the A-optimality criterion. a i =[a i1 ,a i2 ,a i3 ] T Let represent the position of the i-th anchor node, T denotes transpose, Trace represents the corresponding trace function, and CRLB is a Clummerlow-based lower bound expression.

5. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 1, characterized in that, The steps for reconstructing the target based on the influence of unknown prior information include: Considering the influence of unknown prior information about the target, the monitored 3D sea area is gridded, with each grid vertex serving as a candidate target location. The minimization approach is then introduced to reconstruct the OSNs optimal deployment strategy function based on the A-optimality criterion, resulting in the reconstructed OSNs optimal deployment strategy function based on the A-optimality criterion, expressed as: In the formula, This is the reconstructed OSNs optimal deployment strategy function based on the A-optimality criterion. a i =[a i1 ,a i2 ,a i3 ] T Let represent the position of the i-th anchor node, T denotes transpose, Trace represents the corresponding trace function, CRLB is the expression based on the Crommellow lower bound, m is the candidate target position, and M is the total number of candidate target positions in the monitored sea area.

6. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 1, characterized in that, The solution process includes the following: 1) An initial population is generated based on a quantum Bloch sphere-based initial population generation method, where individuals in the population correspond to anchor node positions; 2) An adaptive producer-scavenger ratio adjustment strategy is adopted to adjust the allocation ratio coefficient between producers and scavengers, and the fitness function and optimal population of each individual are calculated. 3) Update the weights and positions of producers and scavengers, and further update the number of producers and scavengers; 4) Determine if the maximum iteration value has been exceeded. If yes, end the iteration process and output the optimal anchor node position. If no, return to step 3) to perform iterative solution until the maximum iteration value is reached.

7. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 6, characterized in that, The steps for generating the initial population include: If we assume the Bloch sphere is a three-dimensional unit sphere, then the state of a qubit is represented as: |Φ>=[cosΦsinθ,sinΦsinθ,cosθ] T , In the formula, |Φ> represents the state of the qubit at the corresponding point on the sphere, Φ is the corresponding azimuth angle, θ is the elevation angle from the point to the sphere, and T represents the transpose; The position of the i-th anchor node in the q-th group is encoded as a qubit in Bloch spherical coordinates, represented as: In the formula, [a i,X ,a i,Y ,a i,Z ] represents the i-th qubit, a i =[a i1 ,a i2 ,a i3 ] T Let X, Y, and Z be the position of the i-th anchor node, corresponding to the X, Y, and Z coordinate systems of the 3D sphere, respectively. The position of the i-th anchor node corresponds to the i-th individual. Φ i1 ,Φ i2 ,Φ i3 These are the corresponding azimuth angles, θ i1 ,θ i2 ,θ i3 These are the angles of elevation from the corresponding points to the sphere; Let the Bloch coordinates of the i-th qubit and the h-th qubit be... Then the corresponding solution space is obtained, where Represented as: In the formula, UB h To correspond to the upper bound, LB h Indicates the corresponding lower bound, X ih Y ih Z ih These are the solutions for the h-th qubit of the i-th anchor node in the X, Y, and Z coordinates, respectively. From X ih Y ih Z ih The solution with the highest fitness is selected as the encoding of the initial population.

8. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 6, characterized in that, The formula for calculating the distribution ratio coefficient between producers and scavengers is as follows: In the formula, r represents the proportional coefficient controlling the distribution ratio between producers and scavengers, exp is an exponential function, t represents the index of the specific iteration number, and Iter max The maximum number of iterations is given by k, which represents the introduced perturbation bias factor used to adjust the nonlinear decreasing trend of r.

9. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 8, characterized in that, After being controlled by the aforementioned allocation ratio coefficient, producer Q pr The quantity is represented by Q. pr =rQ, Scavenger Q sc The quantity is represented by Q sc = (1-r)Q, where Q is the total population size.

10. The quantum optimization framework-driven method for optimal deployment of marine sensor network positioning according to claim 6, characterized in that, The update expressions for the producer's weight and position are as follows: In the formula, w(t) represents the weight of the t-th iteration, w max and w min These represent the corresponding maximum and minimum weights, respectively. max The maximum number of iterations, and Let represent the j-th dimension values ​​of the i-th anchor node in the q-th sparrow population at iterations t+1 and t, respectively. Γ is an N×3 coefficient matrix whose elements are randomly selected from the interval (0,1]. R2 is the safety threshold for the current alarm level, with a value range of [0,1]. ST represents the predefined safety threshold, with a value of [0.5,1]. It is a normally distributed random variable. It is an N×3 matrix where all elements are equal to 1. When R2 < ST, it indicates a low-risk environment, allowing producers to conduct extensive exploration phases. When R2 ≥ ST, it indicates the presence of a potential threat, thus triggering an escape response, and producers migrate to a safe area.

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