Target node positioning methods, equipment, and systems for observation systems in polar sea ice environments

Abstract

This invention discloses a target node localization method, device, and system for an observation system in a polar sea ice environment. The main components include: formulating the three-dimensional target localization problem as a maximum likelihood estimation problem; and transforming this problem into a second-order rotating conic optimization problem by introducing relaxation techniques. This method allows for finding the optimal position estimate of the target node under NLOS conditions through an optimization algorithm, without relying on specific NLOS error statistics. By utilizing geometric constraints, the target position is mapped onto a parabolic surface, enabling more accurate position estimates even under NLOS propagation effects, effectively reducing the impact of NLOS errors on positioning accuracy. It is particularly suitable for complex environments facing NLOS challenges and requiring high positioning accuracy. Special consideration is given to mixed propagation scenarios of LOS (line-of-sight) and NLOS (non-line-of-sight), improving the practicality of the positioning system.

Description

Technical Field

[0001] This invention belongs to the field of marine wireless network monitoring, specifically relating to a target node positioning method, equipment, and system for an observation system in a polar sea ice environment. Background Technology

[0002] In observation systems operating in polar sea ice environments, target node localization technology is crucial for oceanographic research, environmental monitoring, resource exploration, and security and defense applications. However, this field faces unique challenges, primarily including extreme natural conditions, complex sea ice movement patterns, and communication limitations. Currently, localization technologies for observation systems in polar sea ice environments mainly rely on Global Navigation Satellite Systems (GNSS) such as GPS and GLONASS, as well as underwater acoustic localization methods.

[0003] Global Navigation Satellite System (GNSS) positioning technology:

[0004] GNSS provides high-precision location information over open seas and land. However, in polar regions, especially in sea ice-covered areas, GNSS signals can be severely blocked and reflected, leading to a decrease in positioning accuracy. Furthermore, dynamic changes in sea ice, such as crack formation and ice sheet movement, can further affect the stability of positioning.

[0005] Underwater acoustic positioning methods:

[0006] Underwater acoustic positioning systems determine location by emitting sound wave signals and measuring their round-trip time. This method is relatively effective in underwater environments, but in polar sea ice environments, variations in ice thickness and irregular shapes significantly affect the sound wave propagation path, thus reducing positioning accuracy. Furthermore, underwater acoustic equipment consumes a lot of energy, and its reliability during long-term deployment in harsh environments remains a challenge.

[0007] Other auxiliary positioning technologies:

[0008] In addition to the two main methods mentioned above, data fusion techniques utilizing inertial navigation systems (INS), magnetometers, and other sensors can improve the robustness and accuracy of positioning. However, these auxiliary techniques typically need to be used in conjunction with GNSS or other external reference systems to achieve satisfactory performance.

[0009] In summary, the main problems faced by existing target node localization technologies in polar sea ice observation systems include:

[0010] 1. Limited positioning accuracy: Due to signal obstruction and interference caused by environmental factors, the positioning accuracy cannot meet the requirements of high-precision application scenarios.

[0011] 2. Insufficient stability: The dynamic changes in sea ice pose a threat to the stability and continuity of the positioning system.

[0012] Given the aforementioned technological limitations, developing a high-precision and stable target node positioning technology capable of operating in polar sea ice environments is particularly urgent. This invention aims to overcome the shortcomings of existing technologies and propose a novel positioning method adapted to the unique polar environment, with the hope of achieving breakthrough progress in polar scientific research and applications. Summary of the Invention

[0013] The technical problem to be solved by the present invention is to provide a method, device and system for target node positioning in an observation system under polar sea ice environment, which solves the problem of three-dimensional target positioning under mixed LOS / NLOS propagation conditions in the prior art.

[0014] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0015] The target node localization method for an observation system in a polar sea ice environment includes the following steps:

[0016] Step S1: Data collection, the target node collects distance measurement information from multiple anchor nodes;

[0017] Step S2: Construct a localization problem model in the NLOS environment. Based on ranging information, the localization problem is transformed into a maximum likelihood estimation problem.

[0018] Step S3: Solve for the optimal position estimate of the target node. First, a relaxation technique is introduced to transform the localization problem into a second-order rotating cone optimization problem, and a second-order rotating cone optimization model is constructed. Then, using geometric constraints, the target position is mapped onto a parabolic surface, thereby obtaining a more accurate position estimate under NLOS propagation conditions. Finally, an optimization algorithm is used to solve the constructed second-order rotating cone optimization model to obtain the optimal position estimate of the target node.

[0019] Step 2, constructing the localization problem model in the NLOS environment, specifically includes:

[0020] Step 2.1: Initialization settings. In a 3D space with mixed view distance and non-view distance, consider the existence of N anchor nodes with known coordinate positions, and set the first... The position of each anchor node is determined by coordinates. The coordinates of the target node are unknown, so we use... express;

[0021] Step 2.2, Distance Measurement: Measure the distance between the target node and the first node in both LOS and hybrid LOS / NLOS environments. The distance between anchor nodes;

[0022] Step 2.3: Use the approximate expression for measurement noise to establish a maximum likelihood estimate for the unknown location under the combined NLOS error and measurement noise, forming a maximum likelihood estimate for the unknown location. Minimization of the estimation problem.

[0023] Step 3.1: A relaxation technique was used to address the unknown location. The minimization estimation problem is transformed into a second-order cone programming problem;

[0024] Step 3.2: Define the cost function and apply inequality constraints;

[0025] Step 3.3: Apply the rotating cone representation of the inequality to convert the nonlinear inequality into a linear matrix inequality;

[0026] Step 3.4: Considering the 3σ rule, a correction term is introduced into the linear matrix inequality, and it is transformed into a rotating cone expression to obtain a second-order cone programming model for a structured optimization problem.

[0027] Step 3.5: Solve the second-order cone programming model to obtain the optimal location estimate of the target node.

[0028] In step 2.2, the target node and the... The distance between anchor nodes is calculated in a LOS environment using the following formula:

[0029] in Represents the true distance between the i-th anchor node and the target node, denoted by . express Norm, The measurement noise is assumed to be an independent and identically distributed Gaussian random variable with a mean of 0 and a variance of . ,Right now ;

[0030] The following formula is used to calculate in a mixed LOS / NLOS environment:

[0031]

[0032] in, and Let these represent the line-of-sight connectivity set and the non-line-of-sight connectivity set, respectively, and the non-line-of-sight error. It exists under NLOS conditions, and it is assumed that... This indicates that the non-line-of-sight error is much larger than the measurement noise. The maximum value of the non-line-of-sight error is denoted as... ,Right now .

[0033] In step 2.3, using The approximate expression for the unknown position is established. In combined NLOS error and measuring noise The maximum likelihood estimate is given below.

[0034] Step 3.3 The definition expression of the rotating cone is as follows:

[0035]

[0036] in, Indicates length is vector, They are vectors The first and second elements.

[0037] After obtaining the optimal location estimate of the target node, the estimate is verified by simulation, the performance of the positioning method is evaluated, and the actual location of the target node is determined based on the estimated location.

[0038] A target node positioning device for polar sea ice environments, wherein the device uses the target node positioning method to obtain the actual position of the target node.

[0039] The observation system in the polar sea ice environment includes the target node positioning device in the polar sea ice environment, which is used for observation and target node positioning in the polar sea ice environment.

[0040] A computer-readable storage medium storing computer-readable instructions that, when executed by a processor, invoke all or part of the steps of the method.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. This invention specifically considers mixed propagation scenarios of LOS (line of sight) and NLOS (non-line of sight). Through appropriate relaxation and constraints, it can effectively cope with the complexity of signal propagation in real environments and improve the practicality of the positioning system.

[0043] 2. By introducing a 2σ parameter based on the 3σ rule, the distance constraint remains effective under non-line-of-sight (NLOS) conditions in most cases, thereby enhancing the robustness of the positioning algorithm to measurement errors and NLOS effects. Through relaxation techniques and the introduction of the rotating cone expression, the originally non-convex problem is transformed into a convex optimization problem, i.e., SOCP. This ensures that the optimization algorithm can find the global optimum, avoiding the risk of getting trapped in local optima, thus improving positioning accuracy.

[0044] 3. This method can effectively handle measurement errors, especially NLOS errors, and can provide stable and accurate positioning results even when the communication of the observation system is affected by the harsh environment of polar sea ice. Attached Figure Description

[0045] Figure 1 This is a flowchart of the positioning optimization method based on second-order rotating cone planning of the present invention.

[0046] Figure 2 This diagram illustrates the comparison of the root mean square error (RMSE) between the positioning method proposed in this invention and existing positioning methods under different maximum non-line-of-sight (NLOS) errors. Detailed Implementation

[0047] The structure and working process of the present invention will be further described below with reference to the accompanying drawings.

[0048] This solution addresses the limitations of traditional techniques in handling NLOS (Non-Line-of-Sight) errors, primarily including:

[0049] 1) Reliance on prior information about NLOS error: Many traditional methods, in attempting to mitigate the impact of NLOS error, assume some prior knowledge about the NLOS error, such as its statistical characteristics or distribution. However, in practical applications, this prior information is often difficult to obtain accurately. NLOS conditions are caused by environmental factors, such as buildings, terrain, and weather conditions, all of which are dynamically changing, making it difficult to accurately predict prior information about NLOS error.

[0050] 2) Environmental Dependence of Machine Learning Methods: While machine learning methods can effectively identify and compensate for NLOS errors in certain situations, their performance is highly dependent on the representativeness of the training data. If the training data does not cover all possible environmental conditions, the machine learning model may not work accurately in unseen scenarios. Furthermore, updating and maintaining machine learning models requires continuous data acquisition and computing resources, which may be impractical in some real-time positioning systems.

[0051] This provides a more efficient, accurate, and robust positioning solution, particularly suitable for complex environments facing NLOS challenges and requiring high positioning accuracy. It specifically considers mixed propagation scenarios of LOS (line-of-sight) and NLOS (non-line-of-sight), effectively addressing the complexity of signal propagation in real-world environments through appropriate relaxation and constraints, thus improving the practicality of the positioning system. The main innovations include the following two aspects:

[0052] 1. Problem Modeling and Optimization Framework: The 3D target localization problem is formulated as a maximum likelihood estimation problem. By introducing relaxation techniques, this problem is transformed into a second-order rotating conical optimization problem. This approach allows for finding the optimal position estimate of the target node under NLOS conditions through optimization algorithms, without relying on specific NLOS error statistics.

[0053] 2. Geometric constraints and parabolic surface mapping: By utilizing geometric constraints, the target position is mapped onto a parabolic surface. Even under the NLOS propagation effect, a more accurate position estimate can be calculated, effectively reducing the impact of NLOS error on positioning accuracy.

[0054] The target node localization method for an observation system in a polar sea ice environment includes the following steps:

[0055] Step S1: Data collection, the target node collects distance measurement information from multiple anchor nodes;

[0056] Step S2: Construct a localization problem model in the NLOS environment. Based on ranging information, the localization problem is transformed into a maximum likelihood estimation problem.

[0057] Step S3: Solve for the optimal position estimate of the target node. First, a relaxation technique is introduced to transform the localization problem into a second-order rotating cone optimization problem, and a second-order rotating cone optimization model is constructed. Then, using geometric constraints, the target position is mapped onto a parabolic surface, thereby obtaining a more accurate position estimate under NLOS propagation conditions. Finally, an optimization algorithm is used to solve the constructed second-order rotating cone optimization model to obtain the optimal position estimate of the target node.

[0058] Specific embodiments, such as Figure 1 , Figure 2 As shown,

[0059] The rotational second-order cone optimization method for mixed view distance scenes and non-view distance scenes described in this embodiment includes the following steps:

[0060] Step S1. Data Collection. The target node collects distance measurement information from multiple anchor nodes, including but not limited to Time of Arrival (TOA), Time Difference of Arrival (TDOA), Angle of Arrival (AOA), or Received Signal Strength (RSS).

[0061] Step S2: Construct a localization problem model under NLOS conditions. Based on ranging information, the localization problem is transformed into a maximum likelihood estimation problem. By giving a proposition and proving that the inner cost function has a good estimate in the worst case of NLOS error, the target localization problem in the best case of NLOS is thus formulated as an optimization problem.

[0062] Step S3: Solve for the optimal position estimate of the target node. First, a relaxation technique is introduced to transform the localization problem into a second-order rotating conic optimization problem. Then, using geometric constraints, the target position is mapped onto a parabolic surface, thereby obtaining a more accurate position estimate under NLOS propagation conditions. Finally, an advanced optimization algorithm is used to solve the constructed RotSOCP model to obtain the optimal position estimate of the target node.

[0063] Step S4: Performance Evaluation and Simulation Verification. Comparative experiments are conducted to verify the ability of the method of this invention to handle NLOS errors and measurement noise. Performance is compared with existing algorithms to confirm the superiority of this method.

[0064] Through the above steps, this invention solves the problem of target node positioning in observation systems under polar sea ice conditions, improves the robustness and accuracy of the positioning system, and provides strong support for scientific research and technological applications in related fields.

[0065] Following the above method, step S2, modeling the localization problem in the NLOS environment, specifically involves:

[0066] Basic settings and distance measurement in a LOS environment: Considering N anchor nodes with known coordinates in 3D space, including mixed line-of-sight and non-line-of-sight measurements, the first... The position of each anchor node is determined by coordinates. This indicates that the coordinates of the target node are unknown, represented by... This means that, under ideal line-of-sight (LOS) conditions, the measured distance between them is: the distance between the target node and the _th ... The distance between anchor nodes can be measured using the following formula:

[0067] (1)

[0068] in Represents the true distance between the i-th anchor node and the target node, denoted by . express Norm, The measurement noise is assumed to be an independent and identically distributed Gaussian random variable with a mean of 0 and a variance of . ,Right now .

[0069] Distance measurement in hybrid LOS / NLOS environments: In polar sea ice environments, positioning system signals may propagate non-line-of-sight (NLOS) signals. NLOS propagation introduces additional measurement errors, i.e., NLOS errors, denoted by the symbol [symbol missing]. This indicates that, under NLOS conditions, in addition to measurement noise, non-line-of-sight errors... This has become a key factor affecting distance measurement. The existence of non-line-of-sight (LOS) error causes distance measurements to deviate significantly from the true value, which is the main reason for the reduced positioning accuracy in NLOS environments. Depending on whether the anchor node is in LOS state, the distance measurement can be expressed as:

[0070] (2)

[0071] in, and Let these represent the line-of-sight connectivity set and the non-line-of-sight connectivity set, respectively. Non-line-of-sight error. It exists under NLOS conditions, and it is assumed that... This indicates that the non-line-of-sight error is much larger than the measurement noise. The maximum value of the non-line-of-sight error is denoted as... ,Right now .

[0072] Step S2:

[0073] The above expression (2) can be simplified to:

[0074] (3)

[0075] It is worth noting that for anchor nodes belonging to the LOS set, i.e. Non-line-of-sight error .

[0076] Square both sides of equation (3), and then perform mathematical transformations to obtain:

[0077]

[0078] Here we assume Compared to other terms, it is very small and can be ignored, thus the following formula is obtained from (4):

[0079]

[0080] Next, using n i To establish an approximate expression for the unknown position x in the joint NLOS error e i and measurement noise n i The maximum likelihood estimation is performed. This typically involves minimizing a cost function that reflects the difference between the observed data and the model. In this example, the cost function is...

[0081]

[0082] The final step is to consider the worst-case scenario of the NLOS error, which typically means that when estimating the location, we want to ensure that the estimation is still reasonable even with the largest NLOS error. This leads to a more complex optimization problem, where we first maximize e i The influence of this is then considered, and the minimum value for the unknown position x is calculated, i.e.:

[0083]

[0084] The entire process begins with raw observation data, gradually constructs a mathematical model of the localization problem that takes into account NLOS error, and ultimately forms an optimization problem with the goal of minimizing the position estimate while taking into account observation noise and potential NLOS error.

[0085] To improve the computational efficiency of the maximum likelihood (ML) problem, a scaling technique is introduced to simplify the handling of the non-line-of-sight (NLOS) error term. The NLOS error term e i The range is [0, e] m ], where e m This is the maximum value of the NLOS error. By using e i Subtract its midpoint It can adjust its bias center to zero, that is: This transformation makes e i Adjusted version It is numerically closer to zero, which facilitates subsequent mathematical processing. Meanwhile, the observation distance r... i Similar adjustments are needed to obtain... This adjustment simplifies the form of problem (7), transforming it into:

[0086]

[0087] Where the function Defined as:

[0088]

[0089] The piecewise function can be used to express this as:

[0090]

[0091] Regarding the internal maximization problem of equation (8), that is, how to solve for the maximum value of equation (10), the following proposition holds:

[0092] Proposition: Internal Maximization Problem Regarding variables The optimal value is in The optimal solution to the internal maximization problem is obtained at that time. In other words, the optimal solution to the internal maximization problem is obtained at that time. Exactly equal to Right now

[0093] This proposition can be proven through mathematical calculation.

[0094] This proposition reveals that in the optimization problem (8), for each beacon... NLOS error The optimal choice is to minimize its adjusted range. This means that when dealing with NLOS error, a conservative estimate is preferred, assuming the worst-case NLOS error scenario. This finding simplifies the calculation process because for each beacon, it is no longer necessary to iterate through all possible values. To find the maximum value Instead of a specific point, it can be set directly. hour It reaches its maximum value. This provides an important simplification step for solving optimization problems, thereby improving computational efficiency. The equivalent expression of equation (8) obtained through the proposition is:

[0095] (11)

[0096] The expression (8) for the worst-case NLOS error has been transformed into (11). However, since the problem is non-convex, direct solution is very difficult and may not find a globally optimal solution. To overcome this challenge, a relaxation technique is used to transform the problem into a more tractable form, namely the second-order cone programming (SOCP) model.

[0097] First, the cost function defined in equation (11) is:

[0098] (12)

[0099] In the formula for (13)

[0100] as well as (14)

[0101] Then, the original equations (12) and (14) are converted into inequalities:

[0102] (15)

[0103] (16)

[0104] This is a common relaxation technique that allows for the replacement of complex equality constraints with simpler inequality constraints. This avoids directly addressing the nonlinearity and nonconvexity of the original problem.

[0105] Next, these inequalities are represented using a rotating cone. A rotating cone is a special type of second-order cone used to transform nonlinear inequalities into linear matrix inequalities (LMIs), which is very useful in optimization problems. For inequalities (15) and (16), the following vectors are constructed respectively:

[0106] (17)

[0107] (18)

[0108] They belong to the corresponding conical space of revolution. and The definition of a rotating cone is:

[0109] (19)

[0110] If the vector belongs to this space, then a specific nonlinear inequality condition is satisfied. Considering that the observation distance under NLOS conditions may be affected by a large error, the 3σ rule is further considered to ensure that the inequality is reviewed in equation (3) and the given assumptions. Therefore, we know that there is an inequality in the LOS environment.

[0111] (20)

[0112] The inequality holds. Considering that the observation distance under NLOS conditions may be affected by a large error, the 3σ rule is further considered to ensure that inequality (20) holds in most cases. To this end, a correction term is introduced. And the inequality was obtained:

[0113] (twenty one)

[0114] Similarly, this inequality is also transformed into a cone of revolution expression:

[0115] (twenty two)

[0116] This further enhances the solvability of the problem.

[0117] Ultimately, this leads to a structured optimization problem:

[0118] (twenty three)

[0119] Here, the cost function minimizes the sum of weighted squared errors across all observations. The constraints ensure that the variables... , , as well as Defined according to equations (13), (17), (18) and (22), it provides a structured approach for handling mixed LOS / NLOS propagation in localization problems.

[0120] This method not only provides an effective approach to localization problems under NLOS conditions, but also makes the solution more stable and faster due to the presence of the rotating cone representation, especially when dealing with large-scale datasets. Furthermore, by introducing the 2s parameter of the 3s rule, we enhance the algorithm's robustness in environments with high noise and uncertainty. This method has broad application prospects in fields such as wireless communication, robot navigation, and the Internet of Things.

[0121] To verify the above method, the root mean square error (RMSE) of the positioning method proposed in this invention is compared with that of existing positioning methods under different maximum non-line-of-sight (NLOS) errors. Specifically:

[0122] Experimental conditions: The standard deviation of ranging noise was fixed at 0.7 meters, and 3000 Monte Carlo simulations were performed to ensure the reliability of the statistical results. In each simulation run, the number of NLOS links was randomly varied to simulate the uncertainty of NLOS conditions in a real-world environment.

[0123] The horizontal axis in the graph represents the maximum NLOS error, in meters. This reflects the maximum possible NLOS measurement error under NLOS conditions during simulation. The vertical axis represents RMSE, also in meters. RMSE is an important indicator of positioning accuracy; the smaller the value, the smaller the average deviation between the positioning result and the actual position, and the higher the positioning accuracy.

[0124] Comparison Results: As shown in the figure, the RMSE of all methods increases with the increase of the maximum NLOS error, because a larger NLOS error directly affects positioning accuracy. However, it can be seen that the RMSE growth rate of the RotSOCP method is slower than that of the other three methods, especially when the NLOS error is large, its advantage is more obvious.

[0125] Figure 2 This invention clearly demonstrates that the RotSOCP method proposed in this paper exhibits higher robustness and positioning accuracy compared to the other three methods in handling NLOS errors. Even with large NLOS errors, the RotSOCP method maintains a low RMSE, demonstrating good anti-interference capability.

[0126] In summary, Figure 2This intuitively demonstrates the superior performance of the present invention compared to existing technologies under NLOS conditions, especially in harsh environments with large NLOS errors, where it can still maintain high positioning accuracy.

[0127] For example:

[0128] The present invention will be further described below with reference to the accompanying drawings, but this does not constitute any limitation on the present invention. Any limited modifications made within the scope of the claims of the present invention are still within the scope of the claims of the present invention. The comparison algorithms used in the simulation diagram are shown in Table 1:

[0129] Table 1 Comparison of Algorithms

[0130]

[0131] Table 1 summarizes several positioning methods used to mitigate the effects of non-line-of-sight (NLOS) errors, aiming to compare their principles, characteristics, and applicable scenarios. The following is a detailed description of each method:

[0132] The Robust Second Order Cone Relaxation (RSOCR) algorithm works by jointly estimating the anchor node coordinates and the NLOS error upper bound to construct a least squares problem. Due to the non-convexity of the problem, relaxation techniques are further applied to construct a Robust Second Order Cone Programming (SOCP) model to solve for the position of the target node.

[0133] The robust semidefinite programming (RSDP) algorithm is based on the principle of introducing a balance parameter for NLOS error. This parameter, combined with the coordinates of the anchor node, forms a new robust weighted least square (RWLS) problem. The RWLS problem is then transformed into a non-convex optimization problem using the S-principle, and finally relaxed into a semidefinite programming (SDP) problem to solve for the coordinates of the target node.

[0134] The semidefinite programming (SDP) algorithm is based on constrained least squares optimization and solves for the coordinates of the target node by relaxing it to semidefinite programming.

[0135] Each approach offers a unique solution to the localization challenges in NLOS environments, aiming to improve localization accuracy and robustness through different relaxation and optimization strategies.

[0136] [Implementation Process in Brief]

[0137] 1. Collect TOA data: Receive TOA estimates for the target node from multiple anchor nodes.

[0138] 2. Calculate the initial distance: Estimate the distance from the anchor node to the target node based on the TOA.

[0139] 3. Construct the optimization problem: Transform the initial distance problem into the form of an SOCP problem.

[0140] 4. Introduce relaxation techniques: Use the rotation cone expression to relax non-convex constraints.

[0141] 5. Solve SOCP: Use convex optimization algorithms to obtain the optimization results.

[0142] 6. Post-processing: Analyze the optimization results to obtain the final positioning coordinates.

[0143] 7. Verification and Feedback: Evaluate positioning accuracy and adjust parameters and retry if necessary.

[0144] Based on the above method, this solution also proposes a target node positioning device in a polar sea ice environment, wherein the device uses the target node positioning method to obtain the actual position of the target node.

[0145] The observation system in the polar sea ice environment includes the target node positioning device in the polar sea ice environment, which is used for observation and target node positioning in the polar sea ice environment.

[0146] A computer-readable storage medium storing computer-readable instructions that, when executed by a processor, invoke all or part of the steps of the method.

[0147] 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.

[0148] It should be understood that this solution is not limited to the specific embodiments described above. Devices and structures not described in detail herein should be understood as being implemented in a manner common to the art. Any person skilled in the art can make many possible variations and modifications to this solution, or modify it into equivalent embodiments, without departing from the scope of this solution, using the methods and techniques disclosed above. This does not affect the substantive content of this solution. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of this solution, without departing from its scope, still fall within the protection scope of this solution.

Claims

1. A target node localization method for an observation system in a polar sea ice environment, characterized in that: Includes the following steps: Step S1: Data collection, the target node collects distance measurement information from multiple anchor nodes; Step S2: Construct a localization problem model in the NLOS environment. Based on ranging information, the localization problem is transformed into a maximum likelihood estimation problem. The specific steps in constructing the localization problem model in the NLOS environment include: Step 2.1: Initialization settings. In a 3D space with mixed view distance and non-view distance, consider the existence of N anchor nodes with known coordinate positions, and set the first... The position of each anchor node is determined by coordinates. The coordinates of the target node are unknown, so we use... express; Step 2.2, Distance Measurement: Measure the distance between the target node and the first node in both LOS and hybrid LOS / NLOS environments. The distance between anchor nodes; Step 2.3: Use the approximate expression for measurement noise to establish a maximum likelihood estimate for the unknown location under the combined NLOS error and measurement noise, forming a maximum likelihood estimate for the unknown location. Minimization estimation problem; Step S3: Solve for the optimal position estimate of the target node. First, a relaxation technique is introduced to transform the localization problem into a second-order rotating conical optimization problem, constructing a second-order rotating conical optimization model. Then, using geometric constraints, the target position is mapped onto a parabolic surface, thereby obtaining a more accurate position estimate under NLOS propagation conditions. Finally, an optimization algorithm is used to solve the constructed second-order rotating conical optimization model to obtain the optimal position estimate of the target node. The specific process of solving for the optimal position estimate of the target node is as follows: Step 3.1: A relaxation technique was used to address the unknown location. The minimization estimation problem is transformed into a second-order cone programming problem; Step 3.2: Define the cost function and apply inequality constraints; Step 3.3: Apply the rotating cone representation of the inequality to convert the nonlinear inequality into a linear matrix inequality; Step 3.4: Considering the 3σ rule, a correction term is introduced into the linear matrix inequality, and it is transformed into a rotating cone expression to obtain a second-order cone programming model for a structured optimization problem. Step 3.5: Solve the second-order cone programming model to obtain the optimal location estimate of the target node.

2. The target node positioning method of the observation system in the polar sea ice environment according to claim 1, characterized in that: In step 2.2, the target node and the... The distance between anchor nodes is calculated in a LOS environment using the following formula: in Represents the true distance between the i-th anchor node and the target node, denoted by . express Norm, The measurement noise is assumed to be an independent and identically distributed Gaussian random variable with a mean of 0 and a variance of . ,Right now ; The following formula is used to calculate in a mixed LOS / NLOS environment: in, and Let these represent the line-of-sight connectivity set and the non-line-of-sight connectivity set, respectively, and the non-line-of-sight error. It exists under NLOS conditions, and it is assumed that... This indicates that the non-line-of-sight error is much larger than the measurement noise. The maximum value of the non-line-of-sight error is denoted as... ,Right now .

3. The target node positioning method for an observation system in a polar sea ice environment according to claim 2, characterized in that: In step 2.3, using The approximate expression for the unknown position is established. In combined NLOS error and measuring noise The maximum likelihood estimate is given below.

4. The target node positioning method of the observation system in the polar sea ice environment according to claim 1, characterized in that: Step 3.3 The definition expression of the rotating cone is as follows: in, Indicates length is vector, They are vectors The and the Each element.

5. The target node positioning method of the observation system in the polar sea ice environment according to claim 1, characterized in that: After obtaining the optimal location estimate of the target node, the estimate is verified by simulation, the performance of the positioning method is evaluated, and the actual location of the target node is determined based on the estimated location.

6. A target node positioning device in polar sea ice environments, characterized in that: The device uses the target node positioning method according to any one of claims 1 to 5 to obtain the actual position of the target node.

7. An observation system for polar sea ice environments, characterized by: The device includes the target node positioning device in the polar sea ice environment as described in claim 6, which is used for observation and target node positioning in the polar sea ice environment.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-readable instructions, which, when executed by a processor, invoke all or part of the steps of the method according to any one of claims 1 to 5.

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