An anchor node malicious resistance target node positioning method, device and equipment

Abstract

The application provides an anti-malicious anchor node target node positioning method, device and equipment, and belongs to the field of network security and signal processing. The method comprises the following steps: acquiring the received signal strength measurement data between nodes, establishing a received signal strength nonlinear measurement model containing an unknown attack strength parameter, further converting the multiplicative noise item in the established model into an explicit additive equivalent noise item, constructing an optimization model with the weighted residual square sum minimization as an objective function, introducing an L1 norm regularization term for the attack strength parameter, coupling the identification of the malicious anchor node and the position estimation of the target node into the same optimization problem to obtain an initial optimization model, introducing an auxiliary variable for relaxing the non-convex item, converting the non-convex constraint into a convex constraint and solving the same to determine the target node position, and providing a reliable basis for subsequent network security maintenance and node trust management.

Description

Technical Field

[0001] This invention belongs to the field of network security and signal processing, and specifically relates to a method, apparatus and device for locating target nodes against malicious anchor nodes. Background Technology

[0002] With the rapid development of IoT technology, the demand for location-based services is growing. Among various positioning technologies, received signal strength (RSS) based positioning methods have been widely used due to their lack of additional hardware support, low cost, and ease of implementation. Traditional RSS positioning algorithms, such as maximum likelihood estimation (ML) and least squares (LS), typically assume that the network environment is "cooperative" and "trustworthy," meaning that the location and transmission power of all anchor nodes (base stations) are precisely known and operate strictly according to the protocol.

[0003] However, in real-world applications, particularly in positioning scenarios such as military reconnaissance, illegal radio surveillance, or open public networks, network security faces significant challenges. Attackers may compromise some anchor nodes or masquerade as normal anchor nodes by placing malicious nodes to launch signal spoofing attacks. Such attacks typically involve maliciously altering the anchor node's transmit power (different from the nominal power P0), causing a significant deviation in the RSS value measured at the receiver. Traditional positioning algorithms cannot distinguish whether this deviation is caused by path loss or introduced by the attack, thus misinterpreting the attack deviation as a distance change, resulting in positioning results that are severely off-target from the true location.

[0004] Most existing methods for locating malicious attacks rely on authentication, historical reputation databases, or dedicated hardware detection mechanisms, which are difficult to implement in dynamically deployed or non-cooperative scenarios. Furthermore, existing robust localization methods typically treat malicious node detection and target localization as two independent stages, allowing detection errors to accumulate and propagate to the localization stage, impacting overall accuracy. Additionally, RSS localization is a highly nonlinear, non-convex optimization problem; traditional iterative algorithms such as Newton's method and gradient descent are prone to getting trapped in local optima and lack a mathematical framework for jointly estimating attack parameters, making it impossible to diagnose attack behavior simultaneously with localization. This results in poor robustness of existing wireless sensor network localization methods in the presence of malicious anchor node transmit power attacks, a heavy reliance on prior reputation information, and an inability to achieve coordinated optimization of attack identification and target localization. Summary of the Invention

[0005] To address the problems of poor robustness, reliance on prior reputation information, and inability to achieve coordinated optimization of attack identification and target localization in existing technologies when malicious anchor node attacks exist, this invention provides a target node localization method, apparatus, and device that resists malicious anchor node attacks.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for locating target nodes that resist malicious anchor nodes, the method comprising: The system acquires received signal strength measurement data between a target node and multiple anchor nodes at known locations within the monitored network area, as well as received signal strength measurement data between each anchor node; wherein, the target node is a node to be located with an unknown location, and there is an unknown number of malicious anchor nodes in the network whose transmission power has been tampered with. Based on the received signal strength measurement data, a nonlinear measurement model of received signal strength is established, which includes the position vector of the target node and unknown attack strength parameters. The attack strength parameters are used to characterize the deviation of the transmission power of each anchor node from the nominal value. The multiplicative noise term in the nonlinear measurement model of the received signal strength is transformed into an explicit additive equivalent noise term; An optimization model is constructed using the variance of the additive equivalent noise term, with the objective function being to minimize the weighted sum of squared residuals of the received signal strength measurements. Furthermore, a parameter specific to the attack strength is introduced into the objective function. The norm regularization term utilizes the sparsity of the distribution of malicious anchor nodes in the network to construct the joint estimation of the target node's position vector and the attack strength parameter into the same optimization problem, thus obtaining the initial optimization model. The non-convex constraints in the initial optimization model are transformed into convex constraints, thereby reconstructing a convex optimization problem. The convex optimization problem is solved to jointly obtain the estimated position vector of the target node and the estimated attack strength parameters of each anchor node. The estimated position vector is used as the positioning result of the target node, and the malicious anchor nodes in the network are synchronously identified based on the degree of deviation between the estimated attack strength parameters and their corresponding nominal values.

[0007] Optionally, for the link between the target node and the anchor node at a known location, the received signal strength measurement data is represented as the nominal transmit power minus the path loss term, plus the unknown attack strength parameter and noise term; For mutual measurement links between anchor nodes at known locations, the measured value is expressed as the nominal transmit power minus the path loss term corresponding to the known distance, plus the unknown attack strength parameter and noise term; The attack strength parameter is zero at normal anchor nodes, non-zero at malicious anchor nodes, and is sparsity across the entire network.

[0008] Optionally, an exponential transformation is performed on the nonlinear measurement model of the received signal strength, and a first-order Taylor series expansion is performed on the multiplicative error term containing noise, transforming the multiplicative noise term in the original model into an explicit additive equivalent noise term, as shown in the formula: ; in, The transformed additive equivalent noise term, , , The preset reference distance, For the first Attack strength parameters for each anchor node, This is the path loss index. It is Gaussian noise with zero mean.

[0009] Optionally, the objective function of the optimization model consists of three parts: The first part is the weighted sum of squared residuals determined based on the target-anchor node link, which is used to constrain the accuracy of the target node location estimation; The second part is based on the weighted sum of squared residuals determined by the anchor node-anchor node link, which uses the known real distance between anchor nodes to provide a consistency constraint for the estimation of attack strength parameters. The third part is The norm regularization term, applied to the attack strength parameter vector, is used to push the attack strength parameters of most anchor nodes toward zero during the optimization process, allowing only a few non-zero values ​​to exist, thereby enabling the identification of sparse malicious attacks.

[0010] Optionally, the weighting coefficients in the weighted residual sum of squares are determined by the variance of the additive equivalent noise term, such that links with larger variances of the additive equivalent noise term contribute less weight in the optimization.

[0011] Optionally, for the initial optimization model, auxiliary variables are introduced to relax the non-convex terms. Through positive semidefinite relaxation and second-order cone programming techniques, the non-convex constraints in the initial optimization model are transformed into convex constraints, including: The non-convex constraints include a first non-convex equality constraint formed by the inner product of the target node position vectors, and a second non-convex equality constraint formed by the squared term of the attack strength parameter in the weight expression. The auxiliary variables include non-negative scalar variables used to replace the vector inner product in the first non-convex equality constraint, and scalar variables used to replace the squared terms in the second non-convex equality constraint; By introducing the auxiliary variables, a positive semidefinite matrix inequality is constructed using nonnegative scalar variables and the target node position vector to achieve positive semidefinite relaxation of the position constraints; and a second-order cone constraint is constructed using the attack strength parameter and its corresponding scalar variable to achieve second-order cone relaxation of the weight parameter constraint.

[0012] Optionally, the synchronous identification of malicious anchor nodes in the network based on the degree of deviation between the estimated attack strength parameter and its corresponding nominal value includes: Calculate the absolute value of the deviation between the estimated attack strength parameter of each anchor node and its corresponding normal state nominal value; when the absolute value of the deviation of any anchor node exceeds the preset judgment threshold, the anchor node is identified as a malicious anchor node. Based on the location vector estimate output by the initial optimization model, the identified malicious anchor nodes are removed from the currently monitored network area, or their credibility coefficient is dynamically lowered according to the deviation of their attack strength parameter estimate, so as to perform secondary positioning optimization of the target node location.

[0013] A target node positioning device for resisting malicious anchor nodes, the device comprising: The acquisition module is used to acquire received signal strength measurement data between a target node and multiple anchor nodes at known locations within the monitored network area, as well as received signal strength measurement data between each anchor node; wherein, the target node is a node to be located with an unknown location, and there is an unknown number of malicious anchor nodes in the network whose transmission power has been tampered with; The construction module is used to establish a nonlinear measurement model of the received signal strength based on the received signal strength measurement data, which includes the position vector of the target node and unknown attack strength parameters. The attack strength parameters are used to characterize the deviation of the transmission power of each anchor node from the nominal value. The conversion module is used to convert the multiplicative noise term in the nonlinear measurement model of the received signal strength into an explicit additive equivalent noise term; The joint module is used to construct an optimization model with the objective function of minimizing the weighted sum of squared residuals of received signal strength measurements, utilizing the variance of the additive equivalent noise term, and introducing parameters specific to the attack strength into the objective function. The norm regularization term utilizes the sparsity of the distribution of malicious anchor nodes in the network to construct the joint estimation of the target node's position vector and the attack strength parameter into the same optimization problem, thus obtaining the initial optimization model. The identification module is used to transform the non-convex constraints in the initial optimization model into convex constraints, thereby reconstructing it into a convex optimization problem; solve the convex optimization problem to jointly obtain the estimated position vector of the target node and the estimated attack strength parameters of each anchor node; use the estimated position vector as the positioning result of the target node, and realize the synchronous identification of malicious anchor nodes in the network based on the degree of deviation between the estimated attack strength parameters and their corresponding nominal values.

[0014] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for locating target nodes against malicious anchor nodes.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned method for locating a target node against malicious anchor nodes.

[0016] The target node localization method against malicious anchor nodes provided by this invention has the following beneficial effects: This invention leverages the inherent sparsity of malicious attacks in networks by introducing a regularization term into the objective function. This allows the algorithm to automatically distinguish between legitimate and malicious anchor nodes based solely on a single received signal strength measurement, without requiring any prior reputation information or historical data accumulation. Simultaneously, it achieves high-precision target node localization. Secondly, it transforms the original highly nonlinear, non-convex localization problem into a globally solvable convex optimization problem, effectively avoiding the pitfalls of traditional iterative algorithms that easily get trapped in local optima. This ensures the stability and reliability of the solution results. Thus, in complex attack environments, regardless of changes in the attack intensity of malicious anchor nodes, the number of attacked nodes, or fluctuations in measurement noise, this method significantly suppresses the negative impact of attacks on localization accuracy, maintaining high localization stability. It can identify attacked nodes in the network with high accuracy and completeness, providing a reliable basis for subsequent network security maintenance and node trust management. In summary, this invention significantly improves the localization robustness of wireless sensor networks in non-cooperative environments while reliably identifying attacked anchor nodes, providing effective support for subsequent network security maintenance and node trust management. Attached Figure Description

[0017] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a target node location method for resisting malicious anchor nodes provided by the present invention.

[0019] Figure 2 This invention provides a schematic diagram of a target positioning wireless sensor network and a malicious anchor node attack scenario.

[0020] Figure 3 This invention provides an analysis diagram of the relative error of RSS model linearization and the effective working area boundary.

[0021] Figure 4 This is a comparison chart of the positioning errors of the method of the present invention and the traditional method under different attack intensity limits.

[0022] Figure 5 This is a comparison chart of the positioning errors of the method of the present invention and the traditional method under different malicious anchor nodes.

[0023] Figure 6 This is a comparison chart of the positioning errors of the method of the present invention and the traditional method under different noise standard deviations.

[0024] Figure 7 This is a comparison chart of the recall rates of the method of this invention and the traditional method under different attack intensity limits.

[0025] Figure 8 This is a comparison chart of the accuracy of the method of the present invention and the traditional method under different attack intensity limits.

[0026] Figure 9 This is a comparison chart of the recall rates of the method of this invention and the traditional method under different numbers of malicious anchor nodes.

[0027] Figure 10 This is a comparison chart of the accuracy of the method of the present invention and the traditional method under different malicious anchor nodes.

[0028] Figure 11 This is a comparison chart of the accuracy of the method of the present invention and the traditional method under different noise standard deviations.

[0029] Figure 12 This is a comparison chart of the recall rates of the method of this invention and the traditional method under different noise standard deviations.

[0030] Figure 13 A block diagram of a target node positioning device for resisting malicious anchor nodes provided by the present invention. Detailed Implementation

[0031] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0032] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0033] First, this invention provides a target node localization method that resists malicious anchor nodes, specifically as follows: Figure 1 As shown, it includes the following steps: S101. Obtain the received signal strength measurement data between the target node and multiple anchor nodes at known locations within the monitored network area, as well as the received signal strength measurement data between each anchor node.

[0034] The target node is a node whose location is unknown and needs to be located. There is an unknown number of malicious anchor nodes in the network whose transmission power has been tampered with. The specific details of each node are as follows: Figure 2 As shown.

[0035] In this step, for the link between the target node and an anchor node at a known location, the received signal strength measurement data is represented as the nominal transmit power minus the path loss term, plus the unknown attack strength parameter and noise term. For the mutual measurement link between anchor nodes at known locations, the measurement value is represented as the nominal transmit power minus the path loss term corresponding to the known distance, plus the unknown attack strength parameter and noise term. The attack strength parameter is zero at normal anchor nodes and non-zero at malicious anchor nodes, and it exhibits sparsity across the entire network. For both types of measurement links, the attack strength parameter for the same anchor node is the same, but the noise term in these two types of links can be the same or different.

[0036] S102. Based on the received signal strength measurement data, establish a nonlinear measurement model for received signal strength that includes the position vector of the target node and unknown attack strength parameters.

[0037] Among them, the attack strength parameter is used to characterize the deviation of the transmission power of each anchor node from the nominal value.

[0038] In this step, a received signal strength measurement equation that includes shadow fading noise and unknown attack strength parameters can be established based on the log-normal shadow fading model.

[0039] S103. The multiplicative noise term in the nonlinear measurement model of the received signal strength is transformed into an explicit additive equivalent noise term.

[0040] In this step, an exponential transformation is performed on the nonlinear measurement model of the received signal strength, and a first-order Taylor series expansion is performed on the multiplicative error term containing noise. The multiplicative noise term in the original model is transformed into an explicit additive equivalent noise term to construct an approximate observation equation containing the quadratic form of the target node position.

[0041] For example, by performing an algebraic transformation on the nonlinear measurement model of received signal strength and then taking an exponential transformation at both ends, the additive measurement noise in the original model is transformed into an exponential multiplicative error term. A first-order Taylor series expansion is applied to the exponential multiplicative error term for linearization approximation, and algebraic term reconstruction is performed. The implicit coupled nonlinear relationship between the nonlinear measurement model of received signal strength and distance, attack strength parameter and noise after exponential transformation is separated into an approximate observation equation containing the effective observation in the quadratic form of the target node position, the principal value term of the attack strength parameter and the additive equivalent noise term.

[0042] S104. Construct an optimization model using the variance of the additive equivalent noise term, with the objective function being to minimize the weighted sum of squared residuals of the received signal strength measurements. Introduce parameters specific to the attack strength into the objective function. The norm regularization term utilizes the sparsity of the distribution of malicious anchor nodes in the network to construct the joint estimation of the target node's position vector and the attack strength parameter into the same optimization problem, thus obtaining the initial optimization model.

[0043] In this step, the objective function of the optimization model consists of three parts: the first part is the weighted sum of squared residuals determined based on the target-anchor node link, used to constrain the accuracy of the target node location estimation; the second part is the weighted sum of squared residuals determined based on the anchor node-anchor node link, using the known true distance between anchor nodes to provide a consistency constraint on the estimation of attack strength parameters; the third part is... The norm regularization term, applied to the attack strength parameter vector, is used to push the attack strength parameters of most anchor nodes toward zero during the optimization process, allowing only a few non-zero values ​​to exist, thereby enabling the identification of sparse malicious attacks.

[0044] The weight coefficients in the weighted residual sum of squares are determined by the variance of the additive equivalent noise, so that links with larger noise variances contribute less weight in the optimization, thereby reducing the interference of abnormal measurements on the positioning results.

[0045] S105. Transform the non-convex constraints in the initial optimization model into convex constraints, thereby reconstructing it into a convex optimization problem; solve the convex optimization problem to jointly obtain the estimated position vector of the target node and the estimated attack strength parameters of each anchor node; use the estimated position vector as the positioning result of the target node, and based on the degree of deviation between the estimated attack strength parameters and their corresponding nominal values, realize the synchronous identification of malicious anchor nodes in the network.

[0046] In this step, the non-convex constraints first include a first non-convex equality constraint formed by the inner product of the target node position vectors, and a second non-convex equality constraint formed by the squared term of the attack strength parameter in the weight expression. Auxiliary variables include non-negative scalar variables used to replace the inner product of the vectors in the first non-convex equality constraint, and scalar variables used to replace the squared term in the second non-convex equality constraint. By introducing auxiliary variables, a positive semi-definite matrix inequality is constructed using the non-negative scalar variables and the target node position vectors to achieve positive semi-definite relaxation of the position constraints. Furthermore, a second-order cone constraint is constructed using the attack strength parameter and its corresponding scalar variable to achieve second-order cone relaxation of the weight parameter constraint. The principle is to relax the position constraints in the original optimization problem into positive semi-definite matrix inequality constraints and relax the weight parameter constraints into second-order cone constraints, ensuring that the transformed optimization problem is a strictly convex optimization problem and can be solved globally.

[0047] Secondly, the convex optimization problem is solved to jointly obtain the estimated position vector of the target node and the estimated attack strength parameters of each anchor node. Taking advantage of the adaptive robustness of the sparse regularization term in the convex optimization problem, the estimated position vector is used as the localization result of the target node. The malicious anchor nodes in the network are identified based on the degree of deviation between the estimated attack strength parameters and their corresponding nominal values, and the target node is then precisely located a second time.

[0048] In one embodiment, the specific steps for identifying malicious anchor nodes in the network and optimizing the target node location based on the attack strength parameter estimate include: First, calculate the absolute value of the deviation between the estimated attack strength parameter of each anchor node and its corresponding normal state nominal value; when the absolute value of the deviation of any anchor node exceeds the preset judgment threshold, the anchor node is judged to be a malicious anchor node.

[0049] Secondly, since the advantage of this method is that it can locate the target node and identify which nodes are malicious anchor nodes based on a single experiment, the identified malicious anchor nodes are removed from the observation set of the current positioning system based on the preliminary joint output of the target node position estimate of the initial optimization model, or their weight in the approximate observation equation is dynamically reduced according to the degree of deviation of their attack parameters. On this basis, a second fine calculation of the target node position is performed, thereby outputting the final high-precision positioning result.

[0050] By employing the aforementioned method and leveraging the inherent sparsity of malicious attacks within networks, a regularization term is introduced into the objective function. This allows the algorithm to automatically distinguish between legitimate and malicious anchor nodes based solely on a single received signal strength measurement, without requiring any prior reputation information or historical data accumulation. Simultaneously, it achieves high-precision target node localization. By introducing auxiliary variables and employing semidefinite relaxation and second-order cone programming techniques, this method transforms the original highly nonlinear, non-convex localization problem into a globally solvable convex optimization problem. This effectively avoids the pitfalls of traditional iterative algorithms that easily get trapped in local optima, ensuring the stability and reliability of the solution results. In complex real-world attack environments, regardless of variations in the attack intensity of malicious anchor nodes, the number of attacked nodes, or fluctuations in measurement noise, this method significantly suppresses the negative impact of attacks on localization accuracy, maintaining high localization stability. It can identify attacked nodes in the network with high accuracy and completeness, providing a reliable basis for subsequent network security maintenance and node trust management.

[0051] It should be noted that, considering the limited energy and computing power of the underlying physical nodes in wireless sensor networks, the hybrid SDP-SOCP anti-attack localization algorithm proposed in this invention is mainly deployed on aggregation nodes, edge gateways, or cloud servers with sufficient computing and storage resources. The underlying sensors are only responsible for the ranging signal acquisition and data transmission of blind nodes. Therefore, the computational complexity of the algorithm will not negatively affect the lifecycle of the underlying network, which is fully in line with the modern cloud-edge collaborative IoT architecture. Although the hybrid SDP-SOCP relaxation framework is introduced, which expands the dimension compared to traditional linear baseline algorithms (such as SWLS), the constructed model strictly maintains the mathematical properties of convex optimization. This means that there is no local optimum trap in this problem, and the global optimal solution can be obtained efficiently and stably in polynomial time using mature modern interior-point methods, meeting the real-time requirements of most practical positioning systems. Furthermore, the design of this invention is based on positioning scenarios with high security requirements (such as industrial control, critical security, or military sensing). In such scenarios, the high reliability and resilience of the positioning results have absolute priority. This invention achieves robustness against system crashes under extremely high-intensity malicious attacks by trading controllable computing resources. This trade-off is extremely necessary and valuable in practical engineering applications.

[0052] In summary, this invention significantly improves the robustness of wireless sensor networks in non-cooperative environments while also possessing good engineering practicality and deployment flexibility.

[0053] Based on the above method, the present invention also provides an implementation step.

[0054] Step 1: Network initialization and data acquisition.

[0055] Within the monitoring area, the received signal strength (RSS) data between the target node and multiple anchor nodes, as well as the received signal strength (RSS) data between each anchor node, are acquired. The anchor node locations are known, while the target node locations are unknown. There is an unknown number of attacked anchor nodes in the network. Attacked anchor nodes are considered malicious anchor nodes, and their transmit power parameters have been tampered with.

[0056] Step 2: Construct an RSS nonlinear measurement model that includes attack parameters.

[0057] Based on the log-normal shadow fading model, an RSS measurement equation is established that includes shadow fading noise and unknown attack strength parameters.

[0058] Among them, for the target node With the Links between anchor nodes:

[0059]

[0060] For the The anchor node and the first Mutual testing links between anchor nodes:

[0061] Among them, set , The set of communication links between the target node and the anchor node. , This is the set of communication links between anchor nodes. The node communication radius; For the set of anchor node indexes, For the target node From anchor node The received signal strength at that location; For anchor nodes From anchor node The received signal strength at that location; For anchor nodes The nominal transmit power, This is the path loss index. For the target node and the The distance between anchor nodes; For the first The anchor node and the first The distance between anchor nodes; For reference distance; For the first The attack strength parameter of each anchor node, when the anchor node is not under attack. ; and It is Gaussian noise with zero mean.

[0062] Step 3: Model linearization approximation.

[0063] Introduce variables related to attack strength parameters The RSS nonlinear measurement model is first subjected to algebraic transformation, then exponential transformation, and a first-order Taylor series expansion is performed on the multiplicative error terms containing noise to construct an approximate observation equation in quadratic form containing the target node position. The relative error of the RSS model linearization and the effective working area boundary analysis diagram are shown below. Figure 3 As shown.

[0064] ; ; in, For the nominal transmission power, and for simplicity, we assume that all anchor nodes have the same nominal transmission power, denoted as . .

[0065] Define the measurement transformation quantity and attack factors Perform an exponential transformation on both sides of the original RSS equation and use the first-order Taylor expansion. The following approximate observation equation is derived:

[0066] Similarly, links between anchor nodes also have a similar form:

[0067] in, The variance of the additive equivalent noise term after link transformation of the anchor node and the target node is given. and Related; The variance of the additive equivalent noise term after the link transformation between anchor nodes is given. and Related; It is a constant. It is related to the amount of attack.

[0068] Step 4: Construct a sparse regularized weighted least squares optimization model.

[0069] Based on this approximate observation equation, the variance of the additive equivalent noise term is used to determine the weighting coefficients, and an optimization problem is constructed with the goal of minimizing the weighted sum of squared residuals of the links between the target node and the anchor node, as well as the links between the anchor nodes. At the same time, an L1 norm regularization term is introduced into the objective function to address the deviation of the attack strength parameter vector and its auxiliary variable vector from the normal nominal value, thereby making full use of the sparse distribution of malicious attacks in the network to complete the construction of the joint estimation objective function.

[0070] The optimization objective function constructed in this step is:

[0071] in, and These are the target-anchor node link set and the anchor node-anchor node link set, respectively. and For corresponding and Weighted residual proxy variables after two types of link relaxation; The target node vector; For sparse regularization weight parameters; , These are the L1 norm sparse regularization terms applied to the attack strength parameter vector and its corresponding auxiliary variable vector, respectively.

[0072] Step 5: Introduce boundary constraints.

[0073] against and The value has boundaries, so we introduce an attack value boundary auxiliary variable. Through the and By imposing effective boundary constraints, the attack range can be limited to conform to the actual attack range, while making the feasible region a bounded convex set, thus ensuring that there is a unique solution to the optimization problem.

[0074] Introducing boundary auxiliary variables ,right and Apply effective boundary constraints: ; in, , , , Both are M*1 real-valued vectors. This is the preset upper limit of attack strength.

[0075] Step 6: Semidefinite relaxation (SDR) and convex optimization solution.

[0076] For non-convex terms in the optimization model, positional auxiliary variables are introduced. and attack parameters auxiliary variables By constructing semi-positive definite matrix inequality constraints (LMI) and second-order cone constraints (SOCP), the highly nonlinear non-convex optimization problem is strictly relaxed into a globally solvable convex optimization problem.

[0077] Among them, semidefinite relaxation and convex optimization transformations include: (1) Introducing auxiliary variables Relaxing position constraints For positive semidefinite constraints: .

[0078] (2) Introducing auxiliary variables Handling non-convex terms in weights , will constrain relaxation Construct a second-order cone constraint: .

[0079] (3) Transform the residual constraint into a second-order cone form:

[0080]

[0081] Step 7: Joint estimation and malicious node identification.

[0082] This rigorous convex optimization problem is solved using a convex optimization solver (such as the CVX toolkit), and the estimated position coordinates of the target node and the estimated attack parameters of each anchor node are obtained jointly. And based on the estimated attack parameters, malicious anchor nodes in the network are identified.

[0083] Calculate attack parameter estimates The absolute value of the deviation from its normal nominal value (1 in this embodiment); if ,in If the preset threshold is used, then the first... If an anchor node is identified as malicious, it will be removed or have its weight reduced during subsequent location analysis.

[0084] Furthermore, the present invention also provides embodiments based on the above-described implementation steps.

[0085] Example 1: System Model and Problem Description.

[0086] Consider a two-dimensional wireless sensor network containing one target node whose location is unknown. and M anchor nodes with known locations Define a set, i=1,…,M. , The set of communication links between the target and the anchor node. , This is the set of communication links between anchor nodes.

[0087] Assuming some anchor nodes are malicious, their transmission power deviates from the nominal value. The RSS measurement model is as follows: For the target-anchor node link:

[0088] For anchor node-anchor node links:

[0089] in, For the target node anchor node The received signal strength value at the location; For anchor nodes From anchor node The received signal strength value at the location; The path loss index; For anchor nodes and target node The distance between two points; For anchor nodes and anchor node The distance between two points; For reference distance; and All are independent and identically distributed zero-mean Gaussian random noise, i.e. , ; These are attack parameters. If the anchor node... Normal, then If it is malicious, then .

[0090] Example 2: Detailed algorithm derivation steps.

[0091] Step 1: Model transformation and linearization.

[0092] To handle nonlinear terms, we introduce variable substitution: Let , and attack factors Obviously, when hour, The original RSS equation can be rewritten as:

[0093] Rearranging the terms, we get:

[0094] Due to noise It remains nonlinear, utilizing a first-order Taylor expansion. (when When smaller):

[0095] Substituting into the above equation and ignoring higher-order errors, we obtain the approximate observation equation:

[0096] Similarly, links between anchor nodes also have a similar form:

[0097] Step 2: Construct the weighted least squares (WLS) objective function.

[0098] The core optimization objective of this invention is to jointly solve for the target node vector. and attack strength parameter vector This minimizes the weighted sum of squared residuals. Define the distance residual of the target-anchor node link. According to the theory of weighted least squares (WLS), to obtain the optimal estimate, the weighting coefficients of each link should theoretically be the reciprocal of the variance of the corresponding additive equivalent noise term. The optimization objective is to minimize... The reciprocal of the weights approximates the corresponding additive equivalent noise variance: ; ; Since the variance mentioned above includes the square of the attack strength parameter to be solved, the denominator of the squared residual term must contain a non-convex variable. Substitute the reciprocals of the aforementioned variances as weights into the weighted least squares objective function, and introduce an algebraic simplification constant. .

[0099] The constructed weighted least squares objective function is:

[0100] in To simplify constants, and The substitution variable is derived from the received signal strength (RSS) measurement, satisfying... , ; This is the equivalent attack strength parameter.

[0101] Step 3: Introduce sparse regularization.

[0102] Because malicious nodes in a network are usually in the minority, the actual physical attack vector is... It possesses inherent sparsity, which in turn makes the corresponding attack strength parameter vector... Most elements in the function should theoretically be equal to the nominal value of 1 in the normal state. Based on this, this invention introduces attack parameters and their auxiliary variables into the objective function. Norm regularization term , This mechanism utilizes The non-smoothness penalty property of the norm forces the optimization solver to include node parameters that have not been significantly affected by attacks during iterative optimization. Strict constraints are applied and the algorithm converges to a nominal value of 1; parameters are only allowed to deviate from 1 if the residual term caused by outlier measurements is sufficient to overcome the regularization penalty weight. This approach achieves automatic identification and robust suppression of sparse malicious nodes from a mathematical mechanism, without requiring any prior reputation information.

[0103] Step 4: Joint relaxation of semidefinite and second-order cone and reconstruction of convex optimization model.

[0104] Regarding the non-convex optimization objective function for the initial height constructed above, there are mainly two types of non-convex challenges: 1. Squared distance The expanded non-convex quadratic equation contains the target node position vector. .

[0105] 2. Non-convex quadratic equation terms in the denominator of the weights that include the attack strength parameter. .

[0106] Therefore, the present invention adopts the following combined relaxation and reconstruction strategy: (1) Relaxation of position variables: Introduce non-convex equality constraints scalar and will constrain Relaxation is a positive semidefinite inequality constraint Using Schul's complement lemma, this is equivalent to the linear matrix inequality (LMI): ; At this point, the squared distance term of the originally non-convex term This can be equivalently replaced with information about the optimization variables. and Affine form: .

[0107] (2) Attack variable second-order cone relaxation: In order to handle the objective function containing The term introduces auxiliary variables. = Non-convex constraints Relaxation is an inequality constraint This relaxation condition can be expressed in standard form as the following second-order cone (SOCP) constraint: ; (3) Upper bound proxy transformation of objective function: In order to eliminate the non-convexity of the objective function caused by the weighted residual, an upper bound proxy variable is introduced. and The original problem is equivalently transformed into minimizing the sum of proxy variables. And apply the following second-order cone inequality constraint to this end: , .

[0108] Through this transformation, the optimization solver, when minimizing the objective function, will force the above inequality constraints to reach a compact state, thus forcing... and The sum of the factors should be minimized to approximate the original constraint problem.

[0109] Step 5: Attack value boundary constraints.

[0110] Based on the physical upper limit of node transmit power in practical wireless sensor networks, a preset attack strength boundary vector parameter is introduced. , for the attack strength parameter vector and its auxiliary variable vector Apply linear inequality boundary constraints, with the constraint boundaries being... , By using two effective boundary constraints, the attack on the model can be limited to a reasonable range that conforms to the actual attack scenario. At the same time, the feasible region becomes a bounded convex set, which guarantees the existence of the global optimal solution from the perspective of optimization theory and significantly improves the stability of the numerical solution process.

[0111] Step 6: Final joint relaxation convex optimization solution model.

[0112] Based on the above derivation, the original highly nonlinear non-cooperative localization problem is transformed into the following globally solvable strictly convex optimization problem. The final optimization objective function is: (15) in, , , , All are M*1 real-valued vectors.

[0113] Step 7: Joint estimation, malicious node identification and secondary precise localization.

[0114] First, the convex optimization model constructed in step 6 is input into an interior-point method optimization solver (such as the CVX toolkit) for solving, and the position vector estimate of the target node is obtained jointly. and estimated attack strength parameters for each anchor node. .

[0115] Because this invention creatively introduces a parameter targeting the attack into the objective function. The norm sparsity regularization term automatically suppresses abnormal residual weights in the attacked link during the iterative process of minimizing the objective function in the solver. Therefore, the initial joint output position estimate of the solver... It already possesses extremely strong robustness against sparse malicious attacks, and this embodiment directly uses it as the final location result of the system.

[0116] Meanwhile, as an additional diagnostic benefit of this joint optimization model, the system can use the obtained attack parameter estimates... Simultaneously identify malicious anchor nodes in the network. The specific decision rule is: calculate the absolute value of the deviation between the estimated attack parameters of each anchor node and its normal state nominal value (1 in this embodiment). If... ( If the threshold is set to 0, then the first... The anchor nodes are malicious anchor nodes, thus providing data support for network security early warning of the upper layer network.

[0117] Example 3: Simulation verification.

[0118] To verify the effectiveness of this method, 8 anchor nodes and 1 target node were randomly deployed within a 100m × 100m area. One-third (rounded up) of the total number of anchor nodes were randomly selected as malicious nodes, and the attack obedience probability density was... The distribution of the path loss index. The simulation physical environment parameters are set as follows: Path loss index. Standard deviation of background noise Attack generation parameters Reference distance Sparse regularization weight parameters Log-normal shadowing fading noise standard deviation In the simulation, the attack threshold was changed separately. The noise standard deviation σ and the number of malicious anchor nodes were considered. A Monte Carlo repeatability experiment was conducted for each scenario, with 1000 runs. Simulation results show:

[0119] like Figure 4 As shown, compared with the SWLS and R-SOCP algorithms, the algorithm proposed in this invention has a significantly lower positioning error than the SWLS and RSOCP algorithms when facing attacks of different intensities, and the error increases slowly with the attack intensity. Therefore, the method proposed in this invention can significantly suppress the growth of positioning error and has better anti-attack performance and stability.

[0120] like Figure 5 As shown, compared with SWLS and R-SOCP algorithms, the algorithm proposed in this invention has the smallest increase in positioning error when the number of malicious anchor nodes increases, and still maintains high accuracy in scenarios with multiple malicious nodes. Therefore, the method proposed in this invention can significantly suppress the growth of positioning error and has better anti-attack performance and stability.

[0121] like Figure 6 As shown, compared with SWLS and R-SOCP algorithms, the algorithm proposed in this invention has a lower positioning error than the comparison algorithm when facing attacks with a noise standard deviation of less than 3.5 dB. It can significantly suppress the growth of positioning error and has better anti-attack performance and stability.

[0122] like Figure 7 As shown, compared with the SWLS and R-SOCP algorithms, the algorithm proposed in this invention can more comprehensively determine the location of malicious anchor nodes when facing different attack strength limits. As the attack strength limit increases, it has a higher recall rate in the search for malicious anchor nodes.

[0123] like Figure 8 As shown, compared with the SWLS and R-SOCP algorithms, the algorithm proposed in this invention can more accurately determine the location of malicious anchor nodes when facing attacks of different intensities, and has higher accuracy in searching for malicious anchor nodes.

[0124] like Figure 9 As shown, compared with the SWLS and R-SOCP algorithms, the algorithm proposed in this invention can more comprehensively determine the location of malicious anchor nodes when faced with different numbers of malicious anchor nodes, and has a higher recall rate in the search for malicious anchor nodes.

[0125] like Figure 10 As shown, compared with the SWLS and R-SOCP algorithms, the algorithm proposed in this invention has higher accuracy in identifying malicious anchor nodes when facing attacks from different malicious anchor nodes.

[0126] like Figure 11 As shown, compared with the SWLS and R-SOCP algorithms, the algorithm proposed in this invention has higher accuracy in identifying malicious anchor nodes when facing attacks with different noise standard deviations.

[0127] like Figure 12 As shown, compared with the SWLS algorithm, the algorithm proposed in this invention can more comprehensively determine the location of malicious anchor nodes when faced with different noise standard deviations, and has a higher recall rate in the search for malicious anchor nodes.

[0128] Based on the above figures, by Figure 4 and Figure 5 It is evident that as the attack intensity and malicious node density increase, the NRMSE of the comparative algorithm deteriorates significantly, while the positioning error of the secure positioning method proposed in this invention remains at an extremely low level (within approximately 3.5m). Furthermore, in Figure 8 and Figure 10 In this process, the precision of the proposed algorithm remains constant at 1. Based on the prior physical assumption that malicious controlled nodes typically occupy a minority (i.e., possess spatial sparsity) in real-world IoT scenarios, this demonstrates that the constructed hybrid SDP-SOCP model can effectively leverage the strong sparsity-inducing properties of the L1 norm, achieving not only effective suppression of malicious attack energy but also high reliability.

[0129] Figure 6 and Figure 12The performance evolution of each algorithm under different shadow fading noise intensities σ is revealed. In the low to medium noise region (σ <= 3dB), the proposed algorithm maintains the best localization and recognition performance. However, due to the model's sensitivity to strong noise, when the noise floor crosses a critical threshold (e.g., σ > 3.5dB), the localization error of the proposed algorithm increases sharply and gradually deteriorates compared to the R-SOCP algorithm, accompanied by a rapid decrease in the recall index and a significant increase in NRMSE.

[0130] This is mainly due to two underlying physical and mathematical mechanisms: First, the extremely high background noise produces a "masking effect," making it difficult for low- to medium-intensity malicious attacks to be separated from the violent random fluctuations of the channel, resulting in an increase in the false alarm rate; Second, as shown in the linearization error analysis diagram above, the excessively large noise variable exceeds the effective approximation interval of the first-order Taylor expansion of the logarithmic distance observation model, and the sharp amplification of the truncation error dominates the final position calculation deviation.

[0131] The above results demonstrate that the secure location method proposed in this invention is highly suitable for robust location and effective defense against high-intensity, multi-node concurrent malicious attacks in conventional shadow fading environments (σ<=3.5dB).

[0132] Figure 9 The results show that the proposed algorithm's recall remains at an extremely high level close to 1.0 when facing attacks of different scales, proving that the joint optimization framework has a very strong fault tolerance limit and stability against "multi-node concurrent attacks".

[0133] Of particular note is Figure 7 The nonlinear evolution of recall with attack strength Δ is investigated. When the attack strength is in a weak range (Δ <= 2dB), a severe "noise masking effect" is triggered because the magnitude of the attack deviation completely coincides with the background fluctuation of environmental shadow fading noise (σ = 1dB). Within this range, the proposed algorithm exhibits extremely strong "recognition restraint." To ensure a zero false alarm rate (e.g., ...), the algorithm... Figure 8 As shown in the diagram, the algorithm's regularization term smooths minor attacks into natural noise, resulting in a low Recall. However, as the error analysis above shows, such weak attacks cannot cause substantial damage to the system. Once the attack strength breaks through the ambiguity of the noise masking (e.g., Δ≥3dB), the Recall of the proposed algorithm begins to rise rapidly, quickly increasing to above 0.9 in the medium-to-high attack strength region (Δ=5dB), and finally stabilizing at an extremely high level close to 1.0 for strong attacks (Δ≥9dB). This nonlinear evolution characteristic fully demonstrates that the proposed algorithm achieves a reasonable adaptive balance between 'attack recognition sensitivity' and 'system false alarm control'.

[0134] This demonstrates that the present invention maintains high-precision positioning and strong malicious anchor node identification capabilities even under strong attacks and a certain degree of noise interference, especially under conditions of high attack thresholds or multiple malicious nodes, where its identification performance advantage is even more pronounced. In summary, the present invention can achieve both high-precision positioning and reliable identification of attacked anchor nodes in non-cooperative environments, providing effective support for network security early warning.

[0135] Secondly, the present invention also provides a target node positioning device that resists malicious anchor nodes, such as Figure 13 As shown, it includes: The acquisition module 201 is used to acquire the received signal strength measurement data between the target node and multiple anchor nodes at known locations within the monitored network area, as well as the received signal strength measurement data between each anchor node; wherein, the target node is a node to be located with an unknown location, and there is an unknown number of malicious anchor nodes in the network whose transmission power has been tampered with.

[0136] The construction module 202 is used to establish a nonlinear measurement model of the received signal strength based on the received signal strength measurement data, which includes the position vector of the target node and the unknown attack strength parameter. The attack strength parameter is used to characterize the deviation of the transmission power of each anchor node from the nominal value.

[0137] The conversion module 203 is used to convert the multiplicative noise term in the nonlinear measurement model of the received signal strength into an explicit additive equivalent noise term.

[0138] Joint module 204 is used to construct an optimization model using the variance of the additive equivalent noise term, with the objective function being to minimize the weighted sum of squared residuals of the received signal strength measurements, and to introduce parameters specific to the attack strength into the objective function. The norm regularization term utilizes the sparsity of the distribution of malicious anchor nodes in the network to construct the joint estimation of the target node's position vector and the attack strength parameter into the same optimization problem, thus obtaining the initial optimization model.

[0139] The identification module 205 is used to transform the non-convex constraints in the initial optimization model into convex constraints, thereby reconstructing it into a convex optimization problem; solve the convex optimization problem, and jointly obtain the estimated value of the target node's position vector and the estimated value of the attack strength parameter of each anchor node; use the estimated value of the position vector as the positioning result of the target node, and realize the synchronous identification of malicious anchor nodes in the network based on the degree of deviation between the estimated value of the attack strength parameter and its corresponding nominal value.

[0140] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 The steps of a target node location method that resists malicious anchor nodes are provided.

[0141] This invention also provides a computer device. At the hardware level, the computer device includes a processor, an internal bus, a network interface, memory, and non-volatile memory, and may also include other hardware required for various operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above-mentioned functions. Figure 1 The steps of a target node location method that resists malicious anchor nodes are provided.

[0142] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0143] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0144] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0145] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0146] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail in this specification, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are covered within the protection scope of the patent of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A target node localization method resistant to malicious anchor nodes, characterized in that, The method includes: The system acquires received signal strength measurement data between a target node and multiple anchor nodes at known locations within the monitored network area, as well as received signal strength measurement data between each anchor node; wherein, the target node is a node to be located with an unknown location, and there is an unknown number of malicious anchor nodes in the network whose transmission power has been tampered with. Based on the received signal strength measurement data, a nonlinear measurement model of received signal strength is established, which includes the position vector of the target node and unknown attack strength parameters. The attack strength parameters are used to characterize the deviation of the transmission power of each anchor node from the nominal value. The multiplicative noise term in the nonlinear measurement model of the received signal strength is transformed into an explicit additive equivalent noise term; An optimization model is constructed using the variance of the additive equivalent noise term, with the objective function being to minimize the weighted sum of squared residuals of the received signal strength measurements. Furthermore, a parameter specific to the attack strength is introduced into the objective function. The norm regularization term utilizes the sparsity of the distribution of malicious anchor nodes in the network to construct the joint estimation of the target node's position vector and the attack strength parameter into the same optimization problem, thus obtaining the initial optimization model. The non-convex constraints in the initial optimization model are transformed into convex constraints, thereby reconstructing a convex optimization problem. The convex optimization problem is solved to jointly obtain the estimated position vector of the target node and the estimated attack strength parameters of each anchor node. The estimated position vector is used as the positioning result of the target node, and the malicious anchor nodes in the network are synchronously identified based on the degree of deviation between the estimated attack strength parameters and their corresponding nominal values.

2. The method according to claim 1, characterized in that, For the link between the target node and the anchor node at a known location, the received signal strength measurement data is represented as the nominal transmit power minus the path loss term, plus the unknown attack strength parameter and noise term; For mutual measurement links between anchor nodes at known locations, the measured value is expressed as the nominal transmit power minus the path loss term corresponding to the known distance, plus the unknown attack strength parameter and noise term; The attack strength parameter is zero at normal anchor nodes, non-zero at malicious anchor nodes, and is sparsity across the entire network.

3. The method according to claim 1, characterized in that, Transforming the multiplicative noise term in the nonlinear measurement model of the received signal strength into an explicit additive equivalent noise term includes: An exponential transformation is performed on the nonlinear measurement model of the received signal strength, and a first-order Taylor series expansion is performed on the multiplicative error term containing noise, transforming the multiplicative noise term in the original model into an explicit additive equivalent noise term.

4. The method according to claim 1, characterized in that, The objective function of the optimization model consists of three parts: The first part is the weighted sum of squared residuals determined based on the target-anchor node link, which is used to constrain the accuracy of the target node location estimation; The second part is based on the weighted sum of squared residuals determined by the anchor node-anchor node link, which uses the known real distance between anchor nodes to provide a consistency constraint for the estimation of attack strength parameters. The third part is The norm regularization term, applied to the attack strength parameter vector, is used to push the attack strength parameters of most anchor nodes toward zero during the optimization process, allowing only a few non-zero values ​​to exist, thereby enabling the identification of sparse malicious attacks.

5. The method according to claim 4, characterized in that, The weighting coefficients in the weighted residual sum of squares are determined by the variance of the additive equivalent noise term, so that links with larger variances of the additive equivalent noise term contribute less weight in the optimization.

6. The method according to claim 1, characterized in that, For the initial optimization model, auxiliary variables are introduced to relax non-convex terms. Through positive semidefinite relaxation and second-order cone programming techniques, the non-convex constraints in the initial optimization model are transformed into convex constraints, including: The non-convex constraints include a first non-convex equality constraint formed by the inner product of the target node position vectors, and a second non-convex equality constraint formed by the squared term of the attack strength parameter in the weight expression. The auxiliary variables include non-negative scalar variables used to replace the vector inner product in the first non-convex equality constraint, and scalar variables used to replace the squared terms in the second non-convex equality constraint; By introducing the auxiliary variables, a positive semidefinite matrix inequality is constructed using nonnegative scalar variables and the target node position vector to achieve positive semidefinite relaxation of the position constraints; and a second-order cone constraint is constructed using the attack strength parameter and its corresponding scalar variable to achieve second-order cone relaxation of the weight parameter constraint.

7. The method according to claim 1, characterized in that, Based on the degree of deviation between the estimated attack strength parameter and its corresponding nominal value, the synchronous identification of malicious anchor nodes in the network includes: Calculate the absolute value of the deviation between the estimated attack strength parameter of each anchor node and its corresponding normal state nominal value; when the absolute value of the deviation of any anchor node exceeds the preset judgment threshold, the anchor node is identified as a malicious anchor node. Based on the position vector estimate output by the initial optimization model, the identified malicious anchor nodes are removed, or their credibility coefficient is dynamically lowered according to the deviation of their attack strength parameter estimate, so as to perform secondary positioning optimization of the target node position.

8. A target node positioning device for resisting malicious anchor nodes, characterized in that, The device includes: The acquisition module is used to acquire received signal strength measurement data between a target node and multiple anchor nodes at known locations within the monitored network area, as well as received signal strength measurement data between each anchor node; wherein, the target node is a node to be located with an unknown location, and there is an unknown number of malicious anchor nodes in the network whose transmission power has been tampered with; The construction module is used to establish a nonlinear measurement model of the received signal strength based on the received signal strength measurement data, which includes the position vector of the target node and unknown attack strength parameters. The attack strength parameters are used to characterize the deviation of the transmission power of each anchor node from the nominal value. The conversion module is used to convert the multiplicative noise term in the nonlinear measurement model of the received signal strength into an explicit additive equivalent noise term; The joint module is used to construct an optimization model with the objective function of minimizing the weighted sum of squared residuals of received signal strength measurements, utilizing the variance of the additive equivalent noise term, and introducing parameters specific to the attack strength into the objective function. The norm regularization term utilizes the sparsity of the distribution of malicious anchor nodes in the network to construct the joint estimation of the target node's position vector and the attack strength parameter into the same optimization problem, thus obtaining the initial optimization model. The identification module is used to transform the non-convex constraints in the initial optimization model into convex constraints, thereby reconstructing it into a convex optimization problem; solve the convex optimization problem to jointly obtain the estimated position vector of the target node and the estimated attack strength parameters of each anchor node; use the estimated position vector as the positioning result of the target node, and realize the synchronous identification of malicious anchor nodes in the network based on the degree of deviation between the estimated attack strength parameters and their corresponding nominal values.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method described in any one of claims 1 to 7.

10. A computer device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1 to 7.

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