Target node positioning method, device and system for observation system in polar sea ice environment

Abstract

The invention discloses a target node positioning method, device and system for an observation system in a polar sea ice environment, and the method mainly comprises the steps: expressing a three-dimensional target positioning problem as a maximum likelihood estimation problem, and converting the problem into a rotary second-order cone optimization problem through introducing a relaxation technology. This approach allows the optimal position estimate of the target node to be found through an optimization algorithm under NLOS conditions without relying on specific NLOS error statistics. According to the method, the target position is mapped to the paraboloid by using the geometric constraint condition, so that more accurate position estimation can be calculated even under the NLOS propagation effect, and the influence of NLOS errors on the positioning accuracy is effectively reduced. The method is especially suitable for complex environments facing NLOS challenges and requiring high positioning precision. A mixed propagation scene of LOS (Line Of Sight) and NLOS (Non Line Of Sight) is especially considered, and the practicability of the positioning system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of marine wireless network monitoring, and in particular relates to a method, device and system for positioning a target node of an observation system in a polar sea ice environment. Background Art

[0002] In observation systems under polar sea ice environments, target node positioning technology is essential for achieving oceanographic research, environmental monitoring, resource exploration, and security and defense applications. However, the technology in this field faces unique challenges, mainly including extreme natural conditions, complex sea ice movement patterns, and communication limitations. Currently, the positioning technology used for observation systems under polar sea ice environments mainly relies on global navigation satellite systems (GNSS) such as GPS, GLONASS, etc., as well as underwater acoustic positioning methods.

[0003] Global Navigation Satellite System (GNSS) Positioning Technology: GNSS provides high-precision position information in the open ocean and on land. However, in polar regions, especially in areas covered by sea ice, GNSS signals may be severely blocked and reflected, resulting in reduced positioning accuracy. In addition, dynamic changes in sea ice, such as crack formation and ice sheet movement, can further affect the stability of positioning.

[0004] Underwater acoustic positioning method: Underwater acoustic positioning systems determine location by emitting acoustic signals and measuring their round-trip time. This method is relatively effective in underwater environments, but in polar sea ice environments, changes in ice thickness and irregular shapes can significantly affect the propagation path of acoustic waves, thereby reducing positioning accuracy. At the same time, underwater acoustic equipment has high energy consumption, and long-term deployment in harsh environments is a challenge in terms of reliability.

[0005] Other auxiliary positioning technologies: In addition to the two main methods mentioned above, there are also data fusion techniques that use inertial navigation systems (INS), magnetometers and other sensors to improve the robustness and accuracy of positioning. However, these auxiliary technologies usually need to be used in conjunction with GNSS or other external reference systems to achieve satisfactory performance.

[0006] In summary, the main problems faced by the existing target node positioning technology of the observation system in the polar sea ice environment include: 1. Limited positioning accuracy: Due to signal blocking and interference caused by environmental factors, the positioning accuracy cannot meet the application scenarios with high precision requirements.

[0007] 2. Insufficient stability: The dynamic changes in sea ice pose a threat to the stability and sustainability of the positioning system.

[0008] In view of the above technical limitations, it is particularly urgent to develop a high-precision and stable target node positioning technology in the polar sea ice environment. The present invention aims to solve the defects of the prior art and propose a new positioning method adapted to the special polar environment, in order to achieve breakthrough progress in polar scientific research and application fields. Summary of the invention

[0009] The technical problem to be solved by the present invention is to provide a method, device and system for positioning a target node of an observation system in a polar sea ice environment, which solves the problem of three-dimensional target positioning under mixed LOS / NLOS propagation conditions in the prior art.

[0010] The present invention adopts the following technical solutions to solve the above technical problems: The target node positioning method of the observation system in the polar sea ice environment includes the following steps: Step S1, data collection, the target node collects distance measurement information from multiple anchor nodes; Step S2: construct a positioning problem model in the NLOS environment, and transform the positioning problem into a maximum likelihood estimation problem based on ranging information; Step S3, solve the optimal position estimate of the target node. First, introduce relaxation technology to transform the positioning problem into a rotating second-order cone optimization problem and construct a rotating second-order cone optimization model. Then, use geometric constraints to map the target position onto a parabola, so as to obtain a more accurate position estimate under NLOS propagation conditions. Finally, use the optimization algorithm to solve the constructed rotating second-order cone optimization model to obtain the optimal position estimate of the target node.

[0011] In step 2, building a positioning problem model in the NLOS environment specifically includes: Step 2.1, initialization setting, in the three-dimensional space with mixed line-of-sight and non-line-of-sight, consider that there are N anchor nodes with known coordinates, set the first The position of the anchor node is given by the coordinates ; The coordinates of the target node are unknown, so use express; Step 2.2: Distance measurement: measure the distance between the target node and the first node in the LOS environment and the mixed LOS / NLOS environment. The distance between anchor nodes; Step 2.3: Use the approximate expression of the measurement noise to establish the maximum likelihood estimate of the unknown position under the combined NLOS error and measurement noise, forming a maximum likelihood estimate of the unknown position. Minimization estimation problem.

[0012] Step 3.1: Use relaxation technology to The estimation problem of minimization is transformed into a second-order cone programming problem; Step 3.2, define the cost function and use inequality constraints; Step 3.3, apply the rotating cone representation to transform the nonlinear inequality into a linear matrix inequality; Step 3.4, considering the 3σ rule, introduce a correction term into the linear matrix inequality and convert it into a rotation cone expression to obtain a second-order cone programming model for the structured optimization problem; Step 3.5: Solve the second-order cone programming model to obtain the optimal position estimate of the target node.

[0013] In step 2.2, the target node and The distance between anchor nodes in the LOS environment is calculated using the following formula:

[0014] in Represents the true distance between the i-th anchor node and the target node, symbol express norm, represents the measurement noise, which is assumed to be an independent and identically distributed Gaussian random variable with mean 0 and variance ,Right now ; In a mixed LOS / NLOS environment, the following formula is used for calculation:

[0015] in, and They represent the line-of-sight connection set and the non-line-of-sight connection set, and the non-line-of-sight error Under NLOS conditions, and assuming , indicating 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 recorded as ,Right now .

[0016] In step 2.3, use The approximate expression for the unknown position is established The joint NLOS error and measurement noise The maximum likelihood estimate of .

[0017] Step 3.3 The definition expression of the rotating cone is as follows:

[0018] in, Indicates the length vector, Respectively, vector The first and second elements of .

[0019] After obtaining the best position estimate of the target node, the estimated value is simulated and verified, the positioning method is performance evaluated, and the actual position of the target node is determined based on the estimated position.

[0020] A target node positioning device in a polar sea ice environment, wherein the device applies the target node positioning method to obtain the actual position of the target node.

[0021] 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.

[0022] A computer-readable storage medium stores computer-readable instructions, which, when executed by a processor, call all or part of the steps of the method.

[0023] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention particularly considers the 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.

[0024] 2. The 2σ parameter is introduced based on the 3σ rule to ensure that the distance constraint under non-line-of-sight (NLOS) conditions is still valid in most cases, thereby enhancing the robustness of the positioning algorithm to measurement errors and NLOS effects. Through the introduction of relaxation technology and rotating cone expressions, the original non-convex problem is converted into a convex optimization problem, namely SOCP, which ensures that the optimization algorithm can find the global optimal solution and avoid the risk of falling into the local optimum, thereby improving the positioning accuracy.

[0025] 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 The present invention is a flow chart of the positioning method based on the rotational second-order cone programming optimization.

[0027] Figure 2 This is a schematic diagram of the root mean square error (RMSE) comparison results between the positioning method proposed in the present invention and the existing positioning method under different non-line-of-sight (NLOS) error maximum values. DETAILED DESCRIPTION

[0028] The structure and working process of the present invention will be further described below in conjunction with the accompanying drawings.

[0029] This solution addresses the fact that traditional technologies do have some limitations when dealing with NLOS (Non-Line-of-Sight) errors, mainly including: 1) Reliance on prior information of NLOS errors: Many traditional methods assume some prior knowledge of NLOS errors, such as their statistical properties or distribution, when trying to mitigate the impact of NLOS errors. However, in practical applications, such prior information is often difficult to obtain accurately. NLOS conditions are caused by environmental factors such as buildings, terrain, and weather conditions, which are all dynamically changing, making it difficult to accurately predict prior information of NLOS errors.

[0030] 2) Environmental dependence of machine learning methods: Although machine learning methods can effectively identify and compensate for NLOS errors in some cases, 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. In addition, the update and maintenance of machine learning models require continuous data collection and computing resources, which may be impractical in some real-time positioning systems.

[0031] It provides a more efficient, accurate and robust positioning solution, especially for complex environments that face NLOS challenges and require high positioning accuracy. It takes into account the 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. The main innovations include the following two aspects: 1. Problem modeling and optimization framework: The 3D target positioning problem is formulated as a maximum likelihood estimation problem, which is converted into a rotational second-order cone optimization problem by introducing a relaxation technique. This approach allows the optimization algorithm to find the best position estimate of the target node under NLOS conditions without relying on specific NLOS error statistics.

[0032] 2. Geometric constraints and parabola mapping: By using geometric constraints, the target position is mapped onto the parabola. Even under the NLOS propagation effect, a more accurate position estimate can be calculated, effectively reducing the impact of NLOS errors on positioning accuracy.

[0033] The target node positioning method of the observation system in the polar sea ice environment includes the following steps: Step S1, data collection, the target node collects distance measurement information from multiple anchor nodes; Step S2: construct a positioning problem model in the NLOS environment, and transform the positioning problem into a maximum likelihood estimation problem based on ranging information; Step S3, solve the optimal position estimate of the target node. First, introduce relaxation technology to transform the positioning problem into a rotating second-order cone optimization problem and construct a rotating second-order cone optimization model. Then, use geometric constraints to map the target position onto a parabola, so as to obtain a more accurate position estimate under NLOS propagation conditions. Finally, use the optimization algorithm to solve the constructed rotating second-order cone optimization model to obtain the optimal position estimate of the target node.

[0034] Specific embodiments, such as Figure 1 , Figure 2 As shown, The rotating second-order cone optimization method for mixed line-of-sight scenes and non-line-of-sight scenes described in this embodiment includes the following steps: 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).

[0035] Step S2: Construct a positioning problem model in the NLOS environment. Based on the ranging information, the positioning 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 positioning problem in the best case of NLOS is expressed as an optimization problem.

[0036] Step S3: Solve the optimal position estimate of the target node. First, the relaxation technique is introduced to transform the positioning problem into a rotational second-order cone optimization problem; then, the target position is mapped onto a parabola using geometric constraints to obtain 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.

[0037] Step S4: Performance evaluation and simulation verification. Through comparative experiments, the ability of the method of the present invention in processing NLOS errors and measurement noise is verified, and the performance is compared with the existing algorithms to confirm the superiority of the method.

[0038] Through the above steps, the present invention solves the problem of positioning the target nodes of the observation system in the polar sea ice environment, improves the robustness and accuracy of the positioning system, and provides strong support for scientific research and technological applications in related fields.

[0039] According to the above method, the positioning problem modeling in step S2 NLOS environment is specifically as follows: Basic settings and distance measurement in LOS environment: mixed line-of-sight and non-line-of-sight In three-dimensional space, consider the existence of N anchor nodes with known coordinates. The position of the anchor node is given by the coordinates Indicates that the coordinates of the target node are unknown, using Indicates that the measured distance between them is: Under ideal line of sight (LOS) conditions, the distance between the target node and the The distance measurement between anchor nodes can be given by the following formula: (1) in Represents the true distance between the i-th anchor node and the target node, symbol express norm, represents the measurement noise, which is assumed to be an independent and identically distributed Gaussian random variable with mean 0 and variance ,Right now .

[0040] Distance measurement in mixed LOS / NLOS environment: In polar sea ice environment, the signal of the positioning system may produce non-line-of-sight (NLOS) propagation, which will bring additional measurement errors, namely NLOS errors, which are represented by the symbol In NLOS conditions, in addition to the measurement noise, the non-line-of-sight error It has become a key factor affecting distance measurement. The existence of non-line-of-sight error makes the distance measurement significantly deviate from the true value, which is the main reason for the reduction of positioning accuracy in NLOS environment. Depending on whether the anchor node is in LOS state, the distance measurement can be expressed as: (2) in, and They represent the line-of-sight connection set and the non-line-of-sight connection set respectively. Under NLOS conditions, and assuming , indicating 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 recorded as ,Right now .

[0041] Step S2: The above expression (2) can be simplified as follows: (3) It is worth noting that for the anchor nodes belonging to the LOS set, that is, , non-line-of-sight error .

[0042] Square both sides of (3), and then perform mathematical transformation to obtain:

[0043] Here we assume Compared with other terms, it is very small and can be ignored, so the following formula is obtained from (4): Next, using n i The approximate expression for the joint NLOS error e at the unknown position x is established by i and measurement noise n i This usually involves minimizing a cost function that reflects the difference between the observed data and the model. In this case, the cost function is The final step is to consider the worst case NLOS error, which generally means that when estimating a position, you want to ensure that even under the largest NLOS error, the estimate is still reasonable. This leads to a more complex optimization problem, where you first maximize e i The influence of , and then seek to minimize the unknown position x, that is: The whole process starts from the raw observation data, gradually builds a mathematical model of the positioning problem taking into account NLOS errors, and finally forms an optimization problem whose goal is to minimize the position estimate while taking into account observation noise and potential NLOS errors. In order to improve the computational efficiency of the maximum likelihood (ML) problem, a scaling trick is introduced to simplify the treatment of non-line-of-sight (NLOS) error terms. i The range is [0,e m ], where e m is the maximum value of the NLOS error. i Subtract the midpoint of the interval Its offset center can be adjusted to zero, that is: This transformation makes e i Adjusted version of The value is closer to zero, which is convenient for subsequent mathematical processing. i Similar adjustments need to be made to obtain This adjustment simplifies the form of problem (7) into: The function Defined as: The expression of piecewise function can be written as: Regarding the internal maximization problem of equation (8), that is, how to solve the maximum value of equation (10), we have the following proposition: Proposition: Internal maximization problem About variables The optimal value of In other words, the optimal solution to the internal maximization problem is is exactly equal to Right now

[0044] This proposition can be proved by mathematical calculation.

[0045] This proposition reveals that in the optimization problem (8), for each beacon , NLOS error The optimal choice of is to take the minimum value within its adjusted range. This means that when dealing with NLOS errors, a conservative estimate is preferred, that is, assuming the most unfavorable NLOS error situation. This discovery simplifies the calculation process because for each beacon, it is no longer necessary to traverse all possible value to find the maximum point, but can be set directly hour reaches its maximum value. This provides an important simplification step for solving the optimization problem, thereby improving the computational efficiency. The equivalent expression of formula (8) is obtained by the proposition: (11) For the worst-case NLOS error expression (8), it has been transformed into (11). However, since the problem is non-convex, a direct solution will be very difficult and may not find the global 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.

[0046] First, define the cost function of formula (11) as: (12) In the formula for (13) as well as (14) Then, the original equations (12) and (14) are converted into inequality form: (15) (16) This is a common relaxation technique that allows replacing complex equality constraints with simpler inequality constraints. This avoids dealing directly with nonlinearities and nonconvexities in the original problem.

[0047] Next, we use the rotating cone to represent these inequalities. The rotating cone is a special second-order cone that is used to transform nonlinear inequalities into linear matrix inequalities (LMI), which is very useful in optimization problems. For inequalities (15) and (16), the following vectors are constructed respectively: (17) (18) They belong to the corresponding rotating cone space and , the definition expression of the rotating cone is: (19) If the vector belongs to this space, then it satisfies a specific nonlinear inequality condition. Considering that the observed distance under NLOS conditions may be affected by large errors, the 3σ rule is further considered to ensure that the inequality recalls equation (3) and the given assumptions , then we know that in the LOS environment there is an inequality (20) Considering that the observation distance under NLOS conditions may be affected by large errors, the 3σ rule is further considered to ensure that inequality (20) holds true in most cases. To this end, a correction term is introduced And we get the inequality: (twenty one) Likewise, this inequality is converted to a rotating cone expression: (twenty two) This further enhances the solvability of the problem.

[0048] Finally, we get a structured optimization problem: (twenty three) The cost function is to minimize the sum of weighted squared errors of all observations. Here, the constraints ensure that the variables , , as well as It is defined according to equations (13), (17), (18) and (22), and provides a structured approach to handle mixed LOS / NLOS propagation situations in positioning problems.

[0049] This method not only provides an effective way to deal with the localization problem under NLOS conditions, but also makes the solution of the problem more stable and faster due to the existence of the rotation cone representation, especially when dealing with large-scale datasets. In addition, by introducing the 2s parameter of the 3s rule, we also increase the robustness of the algorithm in the face of high noise and uncertainty environments. This method has broad application prospects in fields such as wireless communications, robot navigation, and Internet of Things applications.

[0050] In order to verify the above method, the root mean square error (RMSE) of the positioning method proposed in the present invention and the existing positioning method under different non-line-of-sight (NLOS) error maximum values ​​is compared. Specifically: Experimental conditions: The standard deviation of the ranging noise was set to be 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 changed to simulate the uncertainty of NLOS conditions in the real environment.

[0051] The horizontal axis in the figure represents the maximum value of the NLOS error, in meters. This reflects the maximum possible NLOS measurement error under NLOS conditions during the simulation process; the vertical axis in the figure represents RMSE, also in meters. RMSE is an important indicator for measuring positioning accuracy. The smaller its value, the smaller the average deviation between the positioning result and the true position, and the higher the positioning accuracy.

[0052] Comparison results: As can be seen from the figure, as the maximum NLOS error increases, the RMSE of all methods increases, because a larger NLOS error will directly affect the 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.

[0053] Figure 2 It is clearly shown that the RotSOCP method proposed in this paper has higher robustness and positioning accuracy than the other three methods in dealing with NLOS errors. When the NLOS error is large, the RotSOCP method can still maintain a low RMSE, showing good anti-interference ability.

[0054] In summary, Figure 2 The superior performance of the present invention over the prior art in processing NLOS conditions is intuitively demonstrated, especially in harsh environments with large NLOS errors, where high positioning accuracy can still be maintained.

[0055] For example: The present invention is further described below in conjunction with the accompanying drawings, but does not constitute any limitation to the present invention. Any limited number of 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: Table 1 Comparison of algorithms

[0056] Table 1 summarizes several positioning methods used to mitigate the impact of non-line-of-sight (NLOS) errors, aiming to compare their principles, characteristics, and applicable scenarios. The following is a detailed introduction to each method: The Robust Second Order Cone Relaxation (RSOCR) algorithm is based on the principle of jointly estimating the anchor node coordinate position and the NLOS error upper bound to construct a least squares problem. Due to the non-convexity of the problem, relaxation technology is further applied to construct a second-order cone programming (SOCP) model to solve the position of the target node.

[0057] The robust semidefinite programming (RSDP) algorithm is based on the principle of introducing a balance parameter of the NLOS error, combining the anchor node coordinate position and this parameter to form a new robust weighted least square (RWLS) problem, which is converted into a non-convex optimization problem through the S principle and then relaxed into a semidefinite programming (SDP) to solve the coordinate position of the target node.

[0058] The semidefinite programming (SDP) algorithm is based on constrained least squares optimization and solves the coordinate position of the target node by relaxing to semidefinite programming.

[0059] Each method proposes a unique solution to the positioning challenges in NLOS environments, aiming to improve the accuracy and robustness of positioning through different relaxation and optimization strategies.

[0060]

Brief description of implementation process

[0061] 2. Calculate the preliminary distance: Estimate the distance from the anchor node to the target node based on TOA.

[0062] 3. Construct the optimization problem: Convert the preliminary distance into the SOCP problem form.

[0063] 4. Introduce relaxation technology: Use rotating cone expressions to relax non-convex constraints.

[0064] 5. Solve SOCP: Use convex optimization algorithm to obtain the optimization result.

[0065] 6. Post-processing: Analyze the optimization results and obtain the final positioning coordinates.

[0066] 7. Verification and feedback: Evaluate positioning accuracy and adjust parameters and try again if necessary.

[0067] Based on the above method, this solution also proposes a target node positioning device in a polar sea ice environment, and the device applies the target node positioning method to obtain the actual position of the target node.

[0068] 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.

[0069] A computer-readable storage medium stores computer-readable instructions, which, when executed by a processor, call all or part of the steps of the method.

[0070] If the above functions are implemented in the form of 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 the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0071] It should be understood that the present solution is not limited to the above-mentioned specific implementation methods, and the devices and structures not described in detail should be understood to be implemented in a common manner in the art; any technician familiar with the art can use the above-disclosed methods and technical contents to make many possible changes and modifications to the technical solution of the present solution without departing from the scope of the technical solution of the present solution, or modify it into an equivalent embodiment with equivalent changes, which does not affect the essential content of the present solution. Therefore, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present solution without departing from the content of the technical solution of the present solution still falls within the scope of protection of the technical solution of the present solution.

Claims

1. A target node positioning method for an observation system in a polar sea ice environment, characterized by: The steps include: Step S1, data collection, the target node collects distance measurement information from multiple anchor nodes; Step S2: construct a positioning problem model in the NLOS environment, and transform the positioning problem into a maximum likelihood estimation problem based on ranging information; Step S3, solve the optimal position estimate of the target node. First, introduce relaxation technology to transform the positioning problem into a rotating second-order cone optimization problem and construct a rotating second-order cone optimization model. Then, use geometric constraints to map the target position onto a parabola, so as to obtain a more accurate position estimate under NLOS propagation conditions. Finally, use the optimization algorithm to solve the constructed rotating second-order cone optimization model to obtain the optimal position 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 is characterized by: In step 2, building a positioning problem model in the NLOS environment specifically includes: Step 2.1, initialization setting, in the three-dimensional space with mixed line-of-sight and non-line-of-sight, consider that there are N anchor nodes with known coordinates, set the first The position of the anchor node is given by the coordinates ; The coordinates of the target node are unknown, so use express; Step 2.2: Distance measurement: measure the distance between the target node and the first node in the LOS environment and the mixed LOS / NLOS environment. The distance between anchor nodes; Step 2.3: Use the approximate expression of the measurement noise to establish the maximum likelihood estimate of the unknown position under the combined NLOS error and measurement noise, forming a maximum likelihood estimate of the unknown position. Minimization estimation problem.

3. The target node positioning method of the observation system in the polar sea ice environment according to claim 2 is characterized by: The specific process of solving the optimal position estimation of the target node in step 3 is as follows: Step 3.1: Use relaxation technology to The estimation problem of minimization is transformed into a second-order cone programming problem; Step 3.2, define the cost function and use inequality constraints; Step 3.3, apply the rotating cone representation to transform the nonlinear inequality into a linear matrix inequality; Step 3.4, considering the 3σ rule, introduce a correction term into the linear matrix inequality and convert it into a rotation cone expression to obtain a second-order cone programming model for the structured optimization problem; Step 3.5: Solve the second-order cone programming model to obtain the optimal position estimate of the target node.

4. The target node positioning method of the observation system in the polar sea ice environment according to claim 2 is characterized by: In step 2.2, the target node and The distance between anchor nodes in the LOS environment is calculated using the following formula: in Represents the true distance between the i-th anchor node and the target node, symbol express norm, represents the measurement noise, which is assumed to be an independent and identically distributed Gaussian random variable with mean 0 and variance ,Right now ; In a mixed LOS / NLOS environment, the following formula is used for calculation: in, and They represent the line-of-sight connection set and the non-line-of-sight connection set, and the non-line-of-sight error Under NLOS conditions, and assuming , indicating 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 recorded as ,Right now .

5. The target node positioning method of the observation system in the polar sea ice environment according to claim 4 is characterized by: In step 2.3, use The approximate expression for the unknown position is established The joint NLOS error and measurement noise The maximum likelihood estimate of .

6. The target node positioning method of the observation system in the polar sea ice environment according to claim 3 is characterized by: Step 3.3 The definition expression of the rotating cone is as follows: in, Indicates the length vector, Respectively, vector No. and elements.

7. The target node positioning method of the observation system in the polar sea ice environment according to claim 1 is characterized by: After obtaining the best position estimate of the target node, the estimated value is simulated and verified, the positioning method is performance evaluated, and the actual position of the target node is determined based on the estimated position. 8.Target node positioning equipment in polar sea ice environment, characterized by: The device applies the target node positioning method described in any one of claims 1 to 7 to obtain the actual position of the target node.

9. Observation system in polar sea ice environment, characterized by: It includes the target node positioning device in the polar sea ice environment as described in claim 8, which is used for observation and target node positioning in the polar sea ice environment.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-readable instructions, and when the computer-readable instructions are executed by a processor, all or part of the steps of the method described in any one of claims 1 to 7 are called.

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