A method for positioning a node of a wireless sensor network for monitoring a marine ecological environment

Abstract

The present application relates to a kind of ocean ecological environment monitoring wireless sensor network node positioning method, consider the path loss and absorption effect of node real-time movement and underwater communication, the position of node and path loss factor are estimated jointly;Convert original non-convex problem into non-negative constraint least square framework, find the optimal solution of marine node position based on two-stage of interior point method and block coordinate updating method;First stage is according to interior point method using penalty function to restate the problem, approximate solution is obtained;Second stage, the original problem is converted into generalized trust region subproblem, the approximate solution obtained by interior point method is used as the initial estimate of second stage, and the accurate estimation value of marine node position and path loss factor is obtained by combining a block coordinate updating method for iterative solution.The present application solves the problem that positioning error is relatively large due to node real-time movement, unknown path loss factor and absorption effect of underwater signal propagation in the process of underwater acoustic signal propagation, and realizes high-precision and high-robust positioning of marine target node.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of positioning of nodes in marine wireless sensor networks, and in particular to a high-precision and high-robustness positioning method for nodes in marine ecological environment monitoring wireless sensor networks. BACKGROUND

[0002] In recent years, with the continuous deterioration of the marine environment and the increasing scarcity of marine resources, great challenges have been brought to the monitoring and management of the marine environment, and effective monitoring and management of the marine environment have become particularly important. Marine environmental monitoring wireless sensor networks (MEM-WSNs) have a wide application prospect in the field of marine science and resource management as a new marine monitoring technology. However, the monitoring data collected with accurate node coordinates is essential for the monitoring of the marine environment, and the lack of positioning data will make the collected monitoring data meaningless. Therefore, obtaining accurate marine node position information is the basis and guarantee for the realization of marine environment monitoring. MEM-WSNs include anchor nodes deployed on the sea surface and unknown nodes deployed underwater. Among them, the anchor nodes have known position information or can obtain position information through the self-provided GPS / Beidou positioning module; however, the position information of the underwater unknown nodes needs to be indirectly obtained, i.e. through water acoustic communication with the anchor nodes to exchange data information such as received signal strength indication (RSSI) to calculate the own position coordinates.

[0003] The MEM-WSNs nodes mainly rely on the underwater acoustic channel for communication, which has unique technical characteristics and difficulties. First, the attenuation of the underwater acoustic channel increases exponentially with the frequency of the sound wave, resulting in narrow bandwidth, low communication rate and short transmission distance of the underwater acoustic communication. Second, in the marine environment, not only is there attenuation loss of signal transmission, but also there is absorption loss, which will greatly affect the positioning accuracy. In addition, the force mode of the nodes is relatively complex, and the inherent dynamic characteristics of the ocean, such as vortex, internal wave and thermocline, result in great uncertainty of the motion mode of the nodes, i.e. the topology of the network has high dynamicity, thus making it more difficult to achieve accurate positioning of the MEM-WSNs nodes.

[0004] Chinese patent application CN113242512A discloses a method for correcting ranging between ordinary nodes and anchor nodes by using sound ray compensation, introducing the crossover idea in genetic algorithm, embedding into particle swarm optimization algorithm to obtain the optimal position of particles and particle groups; Chinese patent application CN115038165A discloses a target position estimation method for constructing a ranging model of received signal strength based on Snell's law and ray tracing theorem according to the stratified propagation effect of acoustic signals underwater; patent application CN104302001A discloses a scheme in which each node updates its own movement mode according to the movement of the water flow to predict the future position of the node.

[0005] For MEM-WSNs node positioning, the existing positioning methods have at least one of the following deficiencies: 1) assuming that the path loss factor is known. In MEM-WSNs applications, the path loss factor is unknown and changes in real time with the dynamic changes of the marine environment; 2) not considering the scenario in which all nodes are moving in real time; 3) not considering the attenuation loss and absorption effect of signal transmission in underwater environment. Therefore, a new node positioning method is needed to achieve high-precision and high-robust positioning of marine ecological environment monitoring wireless sensor network nodes. SUMMARY

[0006] The purpose of the present application is to solve the problem of low positioning accuracy caused by the high dynamicity of underwater environment and the absorption effect of acoustic communication underwater, and to provide a high-precision and high-robust positioning method for marine monitoring wireless sensor network nodes.

[0007] The purpose of the present application can be achieved by the following technical solutions:

[0008] A marine ecological environment monitoring wireless sensor network node positioning method, the method steps comprising:

[0009] Constructing a received signal strength model according to signal propagation loss and underwater acoustic propagation absorption effect;

[0010] Establishing a joint estimation optimization function of path loss factor and target position;

[0011] Using a penalty function to re-express the optimization function, and using an interior point method to find an approximate solution of the marine node position coordinates;

[0012] Converting the original positioning problem into a generalized trust region subproblem, taking the approximate solution found by the interior point method as the initial estimate value of the generalized trust region subproblem, and combining the block coordinate update method to find the optimal solution.

[0013] Further, the received signal strength model is constructed as follows:

[0014] According to the wireless signal loss propagation model, the signal strength of the information received by node i from the node sent by the node is represented as:

[0015]

[0016] wherein, represents the power of the target node received by the i-th anchor node at time t; represents the transmit power of the target node at time t; L(l0) represents the loss value when the reference distance is l0; β represents the path loss factor; ||·|| represents the second norm; n i represents the signal attenuation noise of the i-th anchor node; α f represents the absorption coefficient; is the position of the i-th anchor node at time t; x t is the position of the target node at time t.

[0017] Further, the joint estimation of the path loss factor and the target position is as follows:

[0018]

[0019] wherein, x t is the position of the target node at time t; β is the path loss factor; represents the power of the target node received by the i-th anchor node at time t; represents the transmit power of the target node at time t; L(l0) represents the loss value when the reference distance is l0; is the position of the i-th anchor node at time t; α f represents the absorption coefficient.

[0020] Further, the joint estimation function of the path loss factor and the target position is optimized as an ANLS problem as follows:

[0021]

[0022] wherein, ψ=[||x t || 2 , (x t ) T , θ] T ; is the position of the i-th anchor node at time t; x t is the position of the target node at time t, β is the path loss factor; is the estimation parameter

[0023] Further, the optimization function is re-expressed by using the penalty function, and the steps of finding the approximate solution by using the interior point method include:

[0024] According to the interior point method, the problem is re-described by introducing a penalty function:

[0025]

[0026] where θ>0 is a penalty factor, which is gradually reduced to zero as the iteration proceeds, and the feasible region is D={ψ i >0, i=1, 2, …, k};

[0027] The KKT is solved by using Newton iteration method to find the optimal solution of the problem.

[0028] Further, the specific steps of using Newton iteration method to solve KKT to find the optimal solution of the problem include:

[0029] Let z k =(ψ k ) -1 , Z=diag(z1, z2, …, z k ), then the KKT condition is expressed as:

[0030] ψ T (A T Aψ-A T B)-z=0,

[0031] γZE-θE=0

[0032] The KKT condition is written in matrix form:

[0033]

[0034] According to , a linear system is constructed:

[0035]

[0036] where and are the Newton iteration directions;

[0037] An initial point satisfying the system is found, and linear search is performed along and respectively to find new iteration values; when the tolerances of all conditions are met, the final solution ψ * is obtained.

[0038] Further, the original positioning problem is converted into a generalized trust region subproblem, which is as follows:

[0039]

[0040] s.t.(ψ) T Dψ+2fT ψ = 0

[0041] wherein, and 0 denote the identity and zero matrices;

[0042] Introducing a regularization function

[0043]

[0044] s.t.(ψ) T Dψ + 2f t ψ = 0

[0045]

[0046] Further, the original positioning problem is transformed into two sub-problems

[0047]

[0048]

[0049] wherein, j denotes the number of iterations;

[0050] The first sub-problem is a non-convex function, which is solved by using a block coordinate update equation based on a Lipschitz constant;

[0051] The second sub-problem is a strictly convex function, which is solved according to the following formula in each iteration process:

[0052]

[0053] Further, the specific steps of solving the first sub-problem by using a block coordinate update equation based on a Lipschitz constant include:

[0054]

[0055] s.t.(ψ) T Dψ + 2f t ψ = 0

[0056] wherein, is a given extrapolation coefficient,

[0057] Introducing a multiplier When the KKT condition is satisfied, there is a global minimum

[0058]

[0059] (ψ) T Dψ + 2f t ψ = 0,

[0060]

[0061] The optimal solution is obtained by the following formula

[0062]

[0063] Wherein, Obtained by the following formula:

[0064]

[0065]

[0066] After the variable ψ is obtained, the accurate position coordinates x of the marine node are calculated t And the estimated value of the path loss factor Wherein The first column of the last row of ψ.

[0067] Further, in order to further optimize the estimated value of the path loss factor, according to the solved position information, the average value of the path loss factor is calculated:

[0068]

[0069] Wherein, The estimated value of the distance between the estimated position of the unknown node and the anchor node.

[0070] Compared with the prior art, the present application has the following beneficial effects:

[0071] The positioning method proposed in the present application is suitable for highly dynamic marine environment, and can jointly estimate the node position and the path loss factor. The real-time movement of all nodes is considered, as well as the path loss and absorption effect of underwater communication. This conforms to the real situation when using wireless sensor network to perform marine environment monitoring; and the positioning method based on interior point method and block coordinate update is proposed to jointly estimate the marine node position and the path loss factor, so as to realize high-precision and high-robust positioning of the marine target node. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 It is a model diagram of a marine environment monitoring wireless sensor network system;

[0073] Figure 2 It is a flow chart of a marine ecological environment monitoring wireless sensor network node positioning method of the present application;

[0074] Figure 3 It is a schematic diagram of the motion restriction area of the anchor node;

[0075] Figure 4A comparison chart of position and path loss factor estimation error corresponding to different anchor node quantity scenarios;

[0076] Figure 5 A comparison chart of position and path loss factor estimation error corresponding to different deployment range scenarios;

[0077] Figure 6 A comparison chart of position and path loss factor estimation error corresponding to different absorption coefficient scenarios. DETAILED DESCRIPTION

[0078] The application will be described in detail below with reference to the drawings and specific embodiments. The embodiments are implemented on the premise of the technical scheme of the application, and give detailed implementation modes and specific operation processes, but the protection scope of the application is not limited to the following embodiments.

[0079] Embodiment 1

[0080] The application provides a high-precision and high-robustness positioning method for nodes of a marine monitoring wireless sensor network, to solve the problem of low positioning accuracy caused by high dynamicity of an underwater environment and absorption effect of acoustic communication under water. The method is suitable for accurate positioning of nodes in a three-dimensional underwater space under the condition of unknown path loss factor, and effectively improves the positioning accuracy of nodes of a MEM-WSNs.

[0081] The application is suitable for positioning needs of underwater nodes in a marine ecological environment, and a scene is as shown in Figure 1 .

[0082] As shown in Figure 2 , on the basis of comprehensively considering the complexity and particularity of an underwater target node of marine ecological environment monitoring, and in view of the characteristics of positioning of nodes of an underwater wireless sensor network, the application discloses a node positioning method for a wireless sensor network of marine ecological environment monitoring, and introduces an estimation parameter to jointly estimate a node position and an environmental path loss factor. The method includes two stages. First, an original non-convex problem is converted into a non-negative constraint least square framework, and a two-stage method based on an interior point method (IPM) and a block coordinate update (BCU) is proposed to find an optimal solution of a marine node position. In the first stage, a penalty function is used according to the interior point method to restate the problem, and an approximate solution is obtained. In the second stage, the original problem is converted into a generalized trust region sub-problem (GTRS), the approximate solution obtained by the IPM is used as an initial estimation of the second stage, and then an iteration solution is obtained by combining a block coordinate update method, to obtain accurate estimation values of the marine node position and the path loss factor. The node positioning method for the wireless sensor network of marine ecological environment monitoring includes the following steps:

[0083] S1, constructing a received signal strength model according to signal propagation loss and underwater acoustic propagation absorption effect;

[0084] S2, constructing a joint estimation optimization function of path loss factor and target position through Taylor expansion and other approximation operations;

[0085] S3, re-expressing the optimization function by using a penalty function, and finding an approximate solution by using an interior point method;

[0086] S4, converting the original problem into a generalized trust region subproblem;

[0087] S5, taking the approximate solution found by the interior point method as an initial estimation value of the generalized trust region subproblem, and finding an optimal solution by combining a block coordinate update method.

[0088] In the present example, the step S1 specifically comprises:

[0089] In underwater target node positioning, the RSS-based node positioning method has been widely concerned due to its low cost and the characteristics of not requiring time synchronization. However, in the underwater environment, due to the high dynamicity and complexity, the path loss factor is prone to change with the environment, thereby causing the positioning accuracy to decrease. Due to the influence of water flow, the positions of the buoy sensor node and the target node change at each moment, and the movement of the buoy is usually limited in a circle with a radius of L, where L is the anchor chain length and Dep is the water depth. In this part, a signal reception strength model is constructed according to signal propagation loss and underwater sound propagation absorption effect, and then a joint estimation optimization function is constructed according to the model.

[0090] N anchor nodes and a target node are deployed in the underwater and surface environment, and it is assumed that the position of the i th anchor node at time t is T represents transposition; the position of the target node at time t is

[0091] According to the wireless signal loss propagation model, the signal strength of the information received by the node i from the node is:

[0092]

[0093] wherein, represents the power of the target node received by the i th anchor node at time t; represents the transmission power of the target node at time t; L(l0) represents the loss value when the reference distance is l0, and k0 is usually 1 m; β represents the path loss factor; ||·|| represents the second norm; n idenotes the signal attenuation noise of the ith anchor node, assuming that the noise variance of each anchor node is equal, if it obeys a Gaussian distribution with mean zero and variance , can be expressed as α f denotes the absorption coefficient, which is obtained by using the Sorep formula at the transmission frequency f, that is:

[0094]

[0095] If the observation vector at time t is When the path loss factor β is unknown, the joint probability density function can be expressed as:

[0096]

[0097] where

[0098] By maximizing the probability density function, the ML estimation can be obtained, that is

[0099]

[0100] The above formula is very difficult to solve due to the unknown path loss factor and the high non-convexity.

[0101] The step S2 specifically comprises:

[0102] Assuming that the noise n i is small enough, let l0=1m. According to formula (1), the following approximate expression can be obtained

[0103]

[0104] Let It can be proved that when the absorption coefficient α f is small enough, especially in deep water, the absorption term Therefore, 0<||v||<<1. Therefore, for small absorption coefficient α f , the Taylor first-order expansion can be used to approximate v

[0105]

[0106] Bring formula (6) into formula (5)

[0107]

[0108] Let Then

[0109]

[0110] The distance can be obtained.

[0111]

[0112] Substitute equation (9) into equation (8)

[0113]

[0114] Equation (10) can be rewritten as

[0115]

[0116] Let Divide numerator and denominator by

[0117]

[0118] Let It can be proved that Therefore, when the absorption coefficient α f is small enough, the first order Taylor expansion of can be used to approximate equation (12) as follows:

[0119]

[0120] Substitute equation (13) into equation (11) to get

[0121]

[0122] However, since the path loss factor β is unknown, its distance cannot be obtained. By introducing an estimation parameter such that and where equation (14) can be transformed into

[0123]

[0124] Assume is small, i.e. then

[0125]

[0126] where

[0127] By performing a first order Taylor expansion on equation (16) can be further approximated as

[0128]

[0129] Therefore, the LS framework for distance is as follows:

[0130]

[0131] Let The ANLS problem can be transformed from the expansion (18) as follows:

[0132]

[0133] where

[0134]

[0135] The step S3 specifically comprises:

[0136] According to the interior point method, the problem (19) is described again by introducing a penalty function

[0137]

[0138] where θ>0 is a penalty factor, and θ is gradually reduced to zero as the iteration proceeds, and the feasible region is D={ψ i >0, i=1, 2, …, k}.

[0139] The first order gradient and the second order gradient of equation (21) are respectively

[0140]

[0141] where E=[1 1…1] T , γ=diag(ψ1, ψ2…ψ k , and the problem can be solved by using Newton iteration method to find the optimal solution KKT:

[0142] Let z k =(ψ k ) -1 , Z=diag(z1, z2…, z k ), and the KKT condition is:

[0143]

[0144] It can be written in matrix form

[0145]

[0146] According to , a linear system is constructed:

[0147]

[0148] where and are the Newton iteration directions.

[0149] A significant advantage of IP-based methods is that they do not require strictly feasible initial points; only non-negativity conditions are needed. Once an initial point satisfying the above system conditions is found, it can be followed... Perform a linear search to find new iterative values, following... Where α k It's the step size. Similarly... When all the tolerance conditions are met, the final solution ψ can be obtained. * .

[0150] Step S4 specifically includes:

[0151]

[0152] in 0 represents the identity matrix and the zero matrix.

[0153] In underwater wireless sensor networks, nodes are vulnerable to Byzantine attacks and can become faulty nodes, thus rendering the problem in (26) unsuitable for practical applications. Therefore, a regularization function is introduced. Right now

[0154]

[0155] In the formula:

[0156]

[0157] Step S5 specifically includes:

[0158] The original problem can be transformed into two subproblems, namely

[0159]

[0160] Where k represents the number of iterations.

[0161] The second problem in equation (29) is a strictly convex function, so it can be solved according to equation (30) in each iteration.

[0162]

[0163] The first problem in equation (29) is nonconvex, therefore, the Lipschitz constant λ is introduced to construct the BCU equation.

[0164]

[0165] in

[0166]

[0167] These are the given extrapolation coefficients.

[0168] According to the definition of Lipschitz constant

[0169]

[0170] The literature shows that this method can converge.

[0171] According to theorem 1, the first problem in formula (31) has a global minimum in each iteration, and we introduce the multiplier When there is a global minimum under the KKT condition

[0172]

[0173] The optimal solution can be obtained by formula (35)

[0174]

[0175] Wherein Can be obtained by formula (36)

[0176]

[0177] After obtaining the variable ψ, the accurate position coordinates x of the marine node can be obtained t And the estimated value of the path loss factor Wherein The first column of the last row of ψ, in order to further optimize the estimated value of the path loss factor, we calculate the average value of the path loss factor according to the solved position information, that is

[0178]

[0179] In the formula, The distance estimate between the estimated position of the unknown node and the anchor node.

[0180] The problem model established by the present application and the node positioning method of the marine ecological environment monitoring wireless sensor network of the present application are simulated and analyzed by MATLAB R2022a, to further introduce the implementation mode of the present application example and the advantages of the present application in the field of marine environment monitoring. For different scenes, compare the existing methods WLS, SR-LS, SR-IRLS, PM and RNLA, and take the minimum root mean square error as the evaluation index to evaluate the performance of the proposed method, that is

[0181]

[0182] Wherein, MC is the total number of Monte Carlo tests, And respectively, are the estimated values in the ith MC iteration. To simulate the high dynamicity of real underwater environment, the positions of anchor nodes and target node are randomly changed in each simulation.

[0183] The six positioning methods are compared in the following three aspects:

[0184] 1) Different number of anchor nodes;

[0185] 2) Different deployment range;

[0186] 3) Different absorption coefficient.

[0187] Figure 4 The estimation errors of position and path loss factor corresponding to different number of anchor nodes are shown. As the number of anchor nodes increases, the information for estimation of RSS increases, so the estimation errors of each method decrease with the increase of the number of anchor nodes. As can be seen from the figure, for the estimation of position, the positioning errors of other methods decrease with the increase of the number of anchor nodes, except for SR-LS and WLS. For IPM-BCU, WLS, SR-LS, the change of the number of anchor nodes is more sensitive, and in the process of the number of anchor nodes N increasing from 6 to 15, the positioning accuracy increases by nearly 60%, but the positioning accuracy of IPM-BCU is higher. SR-IRLS, IPM, ANLS are improved by 22%, 20% and 14% respectively. When the number of nodes is small, the performance of IPM-BCU is better than three of the methods, close to the other three methods. For the estimation error of path loss factor, the estimation errors of IPM-BCU and ANLS are similar, and are significantly better than WLS and SRLS. Therefore, in general, the estimation effect of IPM-BCU is significantly better than other methods.

[0188] Figure 5The figure shows the position and estimation error corresponding to different deployment ranges. As the deployment range increases, the influence of the absorption effect on the positioning accuracy gradually increases, and the position estimation error of each method increases. In the process of increasing the side length of the deployment area from 50m to 120m, the estimation error of SR-LS, WLS, IPM-BCU, IPM, RNLA and SR-IRLS increases by 500%, 500%, 216%, 202%, 200% and 147% respectively. Compared with other positioning methods, the positioning accuracy is still improved by 10% to 25%. Although the error increase of IPM-BCU is relatively large, it can be seen from the figure that the error of IPM-BCU is still the smallest. For the estimation error of the path loss factor, when the side length of the deployment area is 60m, the estimation error of SRLS and WLS decreases, but the overall error trend still increases as the deployment area increases. The final result shows that the IPM-BCU method has higher estimation accuracy for position and path loss factor, and has greater superiority compared with other methods.

[0189] Figure 6 The figure shows the position and estimation error corresponding to different absorption coefficients. As can be seen from the figure, the position estimation error of WLS and SRLS increases with the increase of the absorption coefficient, and the growth rate reaches 178% and 190% respectively. The position error of other methods is relatively stable, and the fluctuation range is not more than 10%, showing strong robustness. At the same time, we find that the positioning method we propose is the best for estimating the target position, and is the closest to the CRLB positioning scheme. The performance of the single IPM method is at a medium level. In the estimation of the path loss factor, when α f =[0,0.12], the estimation accuracy of IPM-BCU is higher than that of all methods except SR-IRLS, and when α f =[0.08,0.12], the performance of IPM-BCU is optimal. When α f =[0.12,0.2], the performance of IPM-BCU is still better than that of other methods except IPM and RNLA. As can be seen from the figure, the robustness of each method is not ideal for the estimation of the path loss factor, but our method still maintains high performance.

[0190] In summary, the positioning method for nodes of the ocean environment monitoring wireless sensor network node proposed by the application realizes high-precision and high-robust positioning of the ocean target node, and has optimal performance compared with existing positioning methods in different scenarios.

[0191] The preferred embodiments of the present application have been described above in detail. It should be understood that modifications and variations to the preferred embodiments could be made by those skilled in the art in light of the teachings above. It is therefore contemplated that the application can encompass other variations and modifications that fall within the scope of the claims.

Claims

1. A method for positioning nodes of a wireless sensor network for monitoring the marine ecological environment, characterized in that, The method steps include: A received signal strength model is constructed according to signal propagation loss and underwater acoustic propagation absorption effect; A joint estimation optimization function of a path loss factor and a target position is established; The optimization function is re-expressed by using a penalty function, and an interior point method is used to find an approximate solution of the sea node position coordinates; The original positioning problem is converted into a generalized trust region subproblem, the approximate solution found by the interior point method is used as an initial estimation value of the generalized trust region subproblem, and a block coordinate update method is used to find an optimal solution.

2. The method according to claim 1, wherein, The received signal strength model is constructed as follows: According to the wireless signal loss propagation model, the node The signal strength of the information received by the node is represented as: wherein denotes the received power of the target node at the time instant by the th anchor node; denotes the transmission power of the target node at the time instant; denotes the loss value at the reference distance ; denotes the path loss factor; denotes the second norm; denotes the signal attenuation noise of the th anchor node; denotes the absorption coefficient; is the position of the th anchor node at the time instant; is the position of the target node at the time instant.

3. The method of claim 1, wherein, The joint estimation of the path loss factor and the target position is as follows: wherein is the position of the target node at time t ; is the path loss factor; denotes the power of the target node received by the th anchor node at time ; ; denotes the loss value for a reference distance of ; ; ; is the position of the th anchor node at time ; denotes the absorption coefficient; denotes the transmit power of the target node at time t ; is the noise variance of the i th anchor node.

4. The method of claim 3, wherein, The joint estimation function of the path loss factor and the target position is optimized as an ANLS problem as follows: wherein ; ; is the position of the jth anchor node at time i ; t ; is the position of the target node at time , ; is the path loss factor; is the estimation parameter ; .

5. The method of claim 4, wherein, The optimization function is re-expressed by using a penalty function, and an interior point method is used to find an approximate solution, and the specific steps include: According to the interior point method, a penalty function is introduced to re-describe the problem: wherein, is a penalty factor, which gradually decreases to zero as the iteration is performed, the feasible region is ; A Newton iteration method is used to solve KKT to find an optimal approximate solution of the problem.

6. The method of claim 5, wherein, The specific steps of using the Newton iteration method to solve KKT to find an optimal solution of the problem include: Let The KKT conditions are then expressed as: The KKT condition is written in a matrix form: According to , a linear system is constructed: wherein and is the Newton iteration direction; Find initial point that satisfies system, and along each linear search to find new iteration value; when all conditions are satisfied, final approximate solution is found .​ 7. The method of claim 6, wherein, The original positioning problem is converted into a generalized trust region subproblem as follows: wherein , ; and denote the identity and zero matrices, respectively; is the vector of variables to be optimized, with the approximate solution found by the interior point method as its initial estimate. Introducing a regularization function : 。 8. The method of claim 5, wherein, The original positioning problem is converted into two subproblems wherein denotes the number of iterations; The first subproblem is a non-convex function, and a block coordinate update equation is constructed based on a Lipschitz constant to solve the first subproblem; The second subproblem is a strict convex function, and is solved according to the following formula in each iteration process: 。 9. The method of claim 8, wherein, The specific steps of constructing a block coordinate update equation based on a Lipschitz constant to solve the first subproblem include: wherein , is a given extrapolation coefficient, ; Introducing multipliers When there is a global minimum subject to KKT conditions An optimal solution is obtained by the following formula wherein is obtained by the formula: the variable is obtained After, the precise position coordinates of the marine node are calculated and the estimated value of the path loss factor where is the first column of the last row.

10. The method of claim 9, wherein, In order to further optimize the estimation value of the path loss factor, the average value of the path loss factor is calculated according to the solved position information: wherein, estimating a distance estimate between the unknown node's estimated position and the anchor node.

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