RSS positioning method based on directional gain correction

Abstract

The invention relates to an RSS (Received Signal Strength) positioning method based on directional gain correction, and aims to solve the problem that a traditional positioning method based on Received Signal Strength performs target positioning under the condition of neglecting antenna directional gain and easily generates system errors in a three-dimensional space. The invention designs an RSS (Received Signal Strength) positioning method based on directional gain correction, which comprises the following steps of: firstly, introducing an antenna directional gain item into a classic logarithmic path loss model so as to more accurately describe the relationship between signal intensity and a space direction; an optimization problem is solved by using an iterative algorithm, and in each iteration, local fixed parameter optimization is performed on the directional gain, and an original non-convex positioning problem is converted into a solvable convex SDP problem. Simulation experiment results show that the positioning precision of the method can approach the Cramer-Rao lower bound, and high robustness is still kept under the condition of serious shadow fading.

Description

Technical Field

[0001] This invention relates to the field of wireless positioning and signal processing technology, and in particular to a positioning method based on Received Signal Strength (RSS) correction. Background Technology

[0002] In recent years, with the rapid development of Wireless Sensor Networks (WSN), Internet of Things (IoT), and Smart Space technologies, the demand for Location-Based Services (LBS) in fields such as indoor and outdoor navigation, asset tracking, smart logistics, and emergency rescue has been increasing. While traditional satellite positioning systems (such as GPS and BeiDou) can provide high-precision location estimation in outdoor environments, satellite signals are significantly attenuated in complex indoor environments due to walls, obstacles, and multipath effects, making it difficult to meet indoor positioning requirements. Therefore, how to achieve high-precision, low-cost wireless positioning in complex environments without satellite signal coverage has become a current research hotspot.

[0003] Among numerous wireless positioning methods, the Received Signal Strength (RSS) method is widely used due to its low hardware requirements, simple implementation, and controllable cost. The RSS positioning method measures the signal power received by the device, estimates the distance between the receiver and transmitter using a logarithmic distance path loss model, and combines this with geometric constraints to calculate the target location. Compared to Time of Arrival (TOA) and Time Difference of Arrival (TDOA) methods that require high time synchronization accuracy, or Angle of Arrival (AOA) methods that require complex antenna array structures, the RSS positioning method has significant advantages in terms of system complexity, energy consumption, and deployment flexibility, making it particularly suitable for resource-constrained terminal devices and existing Wi-Fi infrastructure environments.

[0004] However, traditional RSS positioning methods typically assume that wireless signal propagation is isotropic, meaning that the transmitting and receiving antennas have the same gain in all directions. This assumption often fails in practical applications. Due to the inherent directional gain characteristics of antennas, their radiated power is unevenly distributed in space, leading to significant differences in received signal strength in different directions at the same distance. Furthermore, factors such as antenna elevation angle, polarization, installation orientation, and environmental reflections also affect signal strength, introducing systematic errors into 3D positioning scenarios and causing the positioning results to deviate from the true location. This cumulative error effect is particularly pronounced in complex building environments with significant elevation differences or multiple floors.

[0005] Therefore, how to effectively overcome the positioning errors caused by signal multipath, obstruction and antenna directivity in complex indoor environments, and improve the accuracy and stability of RSS-based positioning, has become a key technical problem that urgently needs to be solved in the field of wireless positioning and signal processing. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide an RSS positioning method based on directional gain correction, which can perform gain correction on RSS measurement values ​​by establishing directional gain models of the transmitter and receiver, thereby effectively eliminating systematic errors caused by antenna directivity and improving the accuracy and robustness of target positioning in complex three-dimensional space.

[0007] The technical solution adopted in this invention is an RSS positioning method based on directional gain correction, which includes the following steps: S1. Introduce the transmit and receive antenna directional gain parameter into the classical logarithmic path loss model to construct an improved RSS measurement model that includes directional gain. S2. Deploy a wireless sensor network in three-dimensional space, the wireless sensor network including a target node with an unknown location and M For each receiving node with a known location, the RSS observation values ​​between the target node and each receiving node are obtained according to the improved RSS measurement model. The corresponding pitch angle parameters are calculated by combining the spatial geometric relationship, and the directional gain of each receiving node is obtained based on the pitch angle parameters. S3. Take the average of the positions of all receiving nodes to obtain the initial target position estimate; S4. Using the initial target position estimate as the current target position estimate, and based on the RSS observations and the directional gain of each receiving node, perform target position estimation iteratively until the convergence condition is met; wherein, the iterative target position estimation specifically involves: S4.1 Based on the current target position estimate, perform local fixed parameter optimization on the directional gain of each receiving node to obtain the optimized directional gain, and correct the RSS observation to obtain the corrected RSS observation. S4.2. Construct a positioning optimization problem based on the corrected RSS observations. Based on the positioning optimization problem, construct an equivalent convex constraint problem by discarding the rank-one constraint and using the Schur complement method. S4.3 Solve the convex constraint problem to obtain the target position estimation result for the current iteration. S4.4 Determine whether the target position estimation result of the current iteration meets the convergence condition; if it does, output the result as the final three-dimensional spatial coordinates of the target node; if it does not, take the target position estimation result of the current iteration obtained in step S4.3 as the current target position estimate, and return to step S4.1 to continue executing the next iteration.

[0008] The beneficial effects of this invention are as follows: By introducing a directional gain correction model based on elevation angle (i.e., an improved RSS measurement model) into the traditional RSS-based positioning framework, this invention effectively compensates for measurement errors caused by uneven radiation intensity distribution of the antenna at different elevation angles, resulting in more accurate RSS positioning. The directional gain correction model utilizes the elevation angle dependence of the antenna gain to perform directional correction on the received signal, making the measured RSS value closer to the actual situation. Simultaneously, this invention uses an iterative algorithm to solve the optimization problem. In each iteration, by optimizing the directional gain with locally fixed parameters, the original non-convex positioning problem is transformed into a solvable convex semi-definite programming (SDP) problem, achieving efficient solution. This invention achieves positioning accuracy approaching the Cramer-Rao lower bound under low measurement noise conditions and maintains high robustness even under shadow fading and severe measurement noise. Compared to traditional methods, it significantly reduces systematic bias and positioning errors, providing an efficient technical solution for indoor positioning, IoT node positioning, and other applications.

[0009] Preferably, in step S1, the improved RSS measurement model including directional gain is specifically expressed as follows: ; in, Indicates the distance of the receiving end. Average received power at that location Indicates the reference distance The received power at that location, This represents the path loss index. , This indicates log-normal shadowing fading. This represents the receive directional gain parameter. This represents the directional gain parameter of the transmitting antenna. , The pitch angle is the angle between the vertical direction (z-axis) and the line connecting the transmitter and receiver.

[0010] Preferably, in step S2, the RSS observation values ​​between the target node and each receiving node are specifically represented as follows: ; in, This represents the directional gain of the i-th receiving node. ; This indicates log-normal shadowing fading; Preferably, both the receiving node and the target node use vertical dipole antennas, and are placed vertically; the elevation angle parameter... Specifically, it is expressed as follows: ; in, This represents the Euclidean distance between the target node and the i-th receiving node. This represents the horizontal distance between the target node and the i-th receiving node; , Indicates the location of the target node; , This indicates the position of the i-th receiving node. .

[0011] Preferably, the specific process of optimizing the directional gain of each receiving node by local fixed parameters is as follows: Let the first... k The target position estimate at the next iteration is Based on the aforementioned target location estimate Calculate the first k+1 During the nth iteration i The elevation angles of the receiving nodes are: Based on the first k+1 Pitch angle at the next iteration The optimized directional gain is obtained, specifically expressed as: .

[0012] As a preferred embodiment, the corrected RSS observations are specifically expressed as follows: ; in, This represents the reference power value after stripping the directional gain.

[0013] As a preferred option, the specific process of step S4.2 is as follows: Based on the reference power value after stripping the directional gain and corrected RSS observations The physical distance relationship of the i-th receiving node in the (k+1)-th iteration is obtained, specifically expressed as: ; in, , This represents the distance measurement value in this round. When the noise is low, the noise term is considered. Perform a first-order Taylor expansion, i.e. The distance relationship then transforms into: , The equivalent noise of the i-th sensor in the distance domain is expressed as follows: ; Based on the aforementioned physical distance relationships, a positioning optimization problem is constructed, specifically expressed as: ; Among them, the physical distance relationship vector in the (k+1)th iteration Distance measurement vector Weight matrix It is the inverse of the noise covariance. ; ; definition , ,get: ; Depend on satisfy and The equivalent optimization problem of the positioning optimization problem is obtained, specifically expressed as: ; Where i and j represent the indices of the receiving node, and their values ​​range from 1 to 10. ;matrix diagonal elements square of the corresponding distance off-diagonal elements This represents the intersection term between node i and node j, corresponding to ; By performing semidefinite relaxation on the equivalent optimization problem, discarding the rank-one constraint, and using Schur's complement to represent the positive semidefinite constraint, we obtain the equivalent convex constraint problem: ; in, Represents the three-dimensional identity matrix; Solving the equivalent convex constraint problem yields the target position estimate for the (k+1)th iteration. .

[0014] Preferably, the convergence condition in step S4.4 is as follows: ; in, This indicates the set convergence threshold. Attached Figure Description

[0015] Figure 1 This is a flowchart of an RSS positioning method based on directional gain correction according to the present invention; Figure 2 For the simulation experiments in this invention Spatial distribution effect diagram; Figure 3 This is a schematic diagram comparing the average positioning error with CRLB for different numbers of receiving nodes in the simulation experiment of this invention; Figure 4 The simulation experiments in this invention are conducted in different... A diagram showing the comparison between the average positioning error and CRLB. Detailed Implementation

[0016] The invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can implement it based on the description. The scope of protection of the invention is not limited to these specific embodiments.

[0017] This invention relates to an RSS positioning method based on directional gain correction, particularly suitable for RSS positioning that considers directional gain. In this application scenario, the receiving node receives the RSS value of the target node, and the system locates the target node's position based on the RSS value including directional gain. Figure 1 As shown, the method includes the following steps: Step 1: Introduce the transmit and receive antenna directional gain parameter into the classic logarithmic path loss model to construct an improved RSS measurement model that includes directional gain.

[0018] Step one includes the following steps: S1.1 Introducing the transmit and receive antenna directional gain parameter into the classical logarithmic path loss model. as well as ; S1.2. According to the antenna type, adjust the directional gain parameters of the transceiver antenna. as well as Perform modeling and merge into .

[0019] In step S1.1, the expression for the improved RSS measurement model obtained by introducing the transmit and receive antenna directional gain parameter into the classical logarithmic path loss model is as follows: ; in, Indicates the distance of the receiving end. Average received power at the location (in dBm). (dB) represents the reference distance (Generally, the receiving power at a distance of 1 meter) This is the path loss exponent, typically between 2 and 5. Representing log-normal shadowing fading, the transmit and receive antenna directional gain parameters are respectively... and .

[0020] In step S1.2, since vertical dipole antennas are widely used in WSNs due to their simple structure and stable radiation characteristics, all transceiver antennas are vertical dipole antennas and are placed vertically. The expression for modeling the directional gain of the transceiver antenna is: ; in The pitch angle represents the angle between the vertical direction (z-axis) and the line connecting the transmitter and receiver, i.e., the pitch angle. is the antenna's maximum gain constant.

[0021] Since the two are identical, merging them yields: .

[0022] Step 2: Deploy several receiving nodes with known locations in three-dimensional space, obtain the RSS observation values ​​between the target node and each receiving node, and calculate the corresponding pitch angle parameters in combination with spatial geometric relationships, thereby obtaining the directional gain of each receiving node.

[0023] Step two includes the following steps: S2.1. Based on the improved RSS measurement model, obtain the RSS observation values ​​between the target node and each receiving node; S2.2 Calculate the corresponding pitch angle parameters based on spatial geometric relationships. ; In step S2.1, the expression for the RSS observation values ​​between the target node and each receiving node is: ; The system is a three-dimensional wireless sensor network, which includes a target node with an unknown location and M There are 1 receiving node with a known location. The location of the unknown target node is denoted as . , No. i The location of each receiving node is represented as follows: , , Indicates the first i The RSS value received by each receiving node. For the first i Directional gain of each receiving node This represents a log-normal shadowing fading.

[0024] In step S2.2, since the vertical dipole antenna has a uniform radiation mode in the horizontal plane, its directional gain only changes with the elevation angle. The pitch angle parameter changes. Based on spatial geometric relationships, it can be represented as the target node and the... i The angle between the horizontal distances of the receiving nodes is expressed as: ; in For the target node and the first i Euclidean distance between receiving nodes For the target node and the first i The horizontal distance between the receiving nodes. That is, the first... i The expression for the directional gain of each receiving node is: .

[0025] Step 3: Begin the iterative process based on the initial position.

[0026] Step three includes the following steps: S3.1. Average the positions of all receiving nodes to obtain the initial target position estimate. ; S3.2, Based on the initial target position estimate The iteration begins by optimizing the directional gain of each receiving node using local fixed parameters and correcting the RSS value, denoted as . .

[0027] In step S3.2, during the first iteration, the estimated value of the target position is... To address the nonlinearity issue caused by directional gain, the directional gain is estimated using the initial position. Converting this into an expression representing positional relationships, the directional gain of each receiving node during the first iteration can be expressed as: ; The RSS value of each receiving node in the first iteration is corrected, denoted as . : ; Step 4: Construct a localization optimization problem based on the corrected RSS values ​​from the first iteration, and transform it into an SDP problem using semidefinite relaxation.

[0028] Step four includes the following steps: S4.1 Construct a weighted least squares (WLS) problem, which is the aforementioned localization optimization problem; S4.2, Problem of constructing SDP.

[0029] A set of raw received power measured from each receiving node Estimate the target location The maximum likelihood estimate is constructed in the following form: Due to the directional gain term The logarithm of the distance Since it is non-convex, it is difficult to solve directly using ML estimation. Therefore, the idea of ​​this invention is to separate the two sources of non-convexity. Among them, the directional gain term In each iteration, local fixed parameter optimization is performed according to the method in step three. Next, [the following is...] By performing relaxation, a solvable convex optimization problem is constructed.

[0030] In step S4.1, in the first iteration, the distance relationship expression for the i-th receiving node is: ; Among them, the distance measurement value is defined as When the noise level is low, the noise level is low. Performing a first-order Taylor expansion, we obtain ,in This represents the equivalent noise in the distance domain.

[0031] Construct a localization optimization problem (weighted least squares problem), expressed as: ; in, It is a distance relationship vector. For distance measurement vectors, the weight matrix is... The inverse of the noise covariance is given by achievable The expression is: ; in, .

[0032] In step S4.2, to construct an SDP problem, let ,So Define a condition that must be satisfied. A symmetric matrix, and The weighted least squares problem described in step S4.1 can be transformed into the following problem: ; Where i and j represent the indices of the receiving node, and their values ​​range from 1 to 10. .matrix diagonal elements square of the corresponding distance off-diagonal elements This represents the intersection term between node i and node j, corresponding to .

[0033] Due to the presence of the rank-1 constraint, the optimization problem is non-convex. Utilizing the SDP approach, the rank-1 constraint is discarded, and the Schur complement is used to represent the positive semidefinite constraint. The final SDP solution is expressed as follows: ; in, Represents the three-dimensional identity matrix.

[0034] The target position estimate for the first round of iterations is obtained by solving the SDP problem. .

[0035] Step 5: Set the iteration conditions. If the iteration termination condition is not met, enter the loop.

[0036] Step five includes the following steps: S5.1 Set the iteration termination condition as follows: the difference between the target position estimate and the initial position estimate in the first iteration satisfies... , can be represented as: in, The convergence threshold is set to 1. When the position is estimated in the first iteration If the condition is met, skip step six and proceed to step seven; otherwise, begin step six.

[0037] Step 6: Repeat the iteration process until the iteration termination condition is met.

[0038] Step six includes the following steps: S6.1 Update directional gain.

[0039] S6.2. Based on the new directional gain, construct the WLS problem.

[0040] S6.3 Transform the WLS problem into a solvable SDP form.

[0041] S6.4 If the obtained position estimate satisfies the iteration termination condition, the obtained position estimate is the target node position obtained from the localization; otherwise, repeat step six.

[0042] In step S6.1, the first k During +1 iterations, the estimated value of the target position is To address the nonlinearity issue caused by directional gain, the directional gain is passed through the first... k The position estimate obtained in the next iteration Convert to an expression representing positional relationships, the first... k The directional gain of each receiving node during the +1 iteration can be expressed as: ; For the k The RSS value of each receiving node in the +1 iteration process is corrected, denoted as . : In step S6.2, at the first k During the +1 iterations, the distance relationship expression for the i-th sensor is: ; Among them, the distance measurement value in this round is defined as When the noise level is low, the noise level is low. Performing a first-order Taylor expansion, we obtain the result of this iteration. ,in This represents the equivalent noise in the distance domain.

[0043] Construct the weighted least squares problem, expressed as: ; Among them, the physical distance relationship vector in the (k+1)th iteration Distance measurement vector Weight matrix The inverse of the noise covariance is given by achievable The expression is: ; in, .

[0044] Defined in step S6.3 , ,So , satisfy and The equivalent optimization problem of the positioning optimization problem is obtained, specifically expressed as: Where i and j represent the indices of the receiving node, and their values ​​range from 1 to 10. .matrix diagonal elements square of the corresponding distance off-diagonal elements This represents the intersection term between node i and node j, corresponding to .

[0045] Due to the presence of the rank-1 constraint, the optimization problem is non-convex. Utilizing the SDP approach, the rank-1 constraint is discarded, and the Schur complement is used to represent the positive semidefinite constraint. The final SDP solution is expressed as follows: in, Represents the three-dimensional identity matrix.

[0046] The first step is to obtain the solution by solving the SDP problem. k The target position is estimated in +1 iterations. .

[0047] In step S6.4, the iteration termination condition is set to the first iteration. k +1 round of iteration target position estimation and the first k The difference in position estimates from round iterations satisfies , can be represented as: in, The convergence threshold is set to 1. The maximum number of iterations is set to 100 rounds. If the position estimate in the (k+1)th iteration satisfies either of the above two conditions, the iteration process ends and proceeds to step seven; otherwise, step six is ​​repeated.

[0048] Step 7: Obtain the target node position .

[0049] The following simulation experiments further illustrate the feasibility and effectiveness of the RSS positioning method based on directional gain correction of this invention.

[0050] This invention considers a three-dimensional indoor positioning system, the system area being a The system comprises a cube-shaped region. Ten receiver nodes are randomly generated within this region, and the target location is set... Set reference distance Received power at the location The path loss index is -30dBm. The maximum directivity gain of the antenna is 3. It is 3dB.

[0051] Based on the above parameter settings, simulation experiments tested the method of the present invention under different numbers of receiving nodes and different shadow fading standard deviations. Performance under both scenarios.

[0052] Figure 2 The present invention provides the results regarding the standard deviation of shadow fading and the number of receiving nodes. The spatial distribution effect of 1000 Monte Carlo simulation experiments is shown. The average estimated position is (2.421, 5.662, 8.498) m, and the average estimation error is 0.736 m.

[0053] Figure 3 The localization performance of the method of this invention is demonstrated under different numbers of receiving nodes. In the experiment, 13 receiving nodes were randomly distributed in three-dimensional space, and the first 8 to 13 receiving nodes were selected for the experiment, with shadow fading being considered. ,Pick For each receiving node, 1000 Monte Carlo simulations were performed, and the RMSE of the resulting positioning error was calculated. Figure 3 It can be seen that the positioning error decreases as the number of receiving nodes increases. When the number of receiving nodes reaches 10, the rate of performance increase slows down, indicating that the positioning accuracy of the system has approached the lower limit of the algorithm under the current noise conditions.

[0054] Figure 4 Showing different Below is a comparison of the RMSE results between the method of this invention and CRLB. In the experiment, the number of receiving nodes was 10, and their positions were fixed, with shadow fading... , The range of values ​​is The step size is 5dB, each Perform 1000 Monte Carlo simulations and calculate the RMSE of the resulting positioning error. Figure 4 As can be seen, the positioning error increases approximately exponentially with the increase of the standard deviation of shadow fading. Under low noise conditions ( The RMSE of the method in this invention almost coincides with the CRLB curve, indicating that the algorithm can approach the theoretical optimal performance in low-noise environments. When the signal-to-noise ratio is low ( Despite the fact that measurement randomness introduced by shadow fading dominates the error, this method still shows strong robustness.

Claims

1. An RSS positioning method based on directional gain correction, characterized in that, The method includes the following steps: S1. Introduce the transmit and receive antenna directional gain parameter into the classical logarithmic path loss model to construct an improved RSS measurement model that includes directional gain. S2. Deploy a wireless sensor network in three-dimensional space, the wireless sensor network including a target node with an unknown location and M For each receiving node with a known location, the RSS observation values ​​between the target node and each receiving node are obtained according to the improved RSS measurement model. The corresponding pitch angle parameters are calculated by combining the spatial geometric relationship, and the directional gain of each receiving node is obtained based on the pitch angle parameters. S3. Take the average of the positions of all receiving nodes to obtain the initial target position estimate; S4. Using the initial target position estimate as the current target position estimate, and based on the RSS observations and the directional gain of each receiving node, perform target position estimation iteratively until the convergence condition is met; wherein, the iterative target position estimation specifically involves: S4.1 Based on the current target position estimate, perform local fixed parameter optimization on the directional gain of each receiving node to obtain the optimized directional gain, and correct the RSS observation to obtain the corrected RSS observation. S4.

2. Construct a positioning optimization problem based on the corrected RSS observations. Based on the positioning optimization problem, construct an equivalent convex constraint problem by discarding the rank-one constraint and using the Schur complement method. S4.3 Solve the convex constraint problem to obtain the target position estimation result for the current iteration. S4.4 Determine whether the target position estimation result of the current iteration meets the convergence condition; if it does, output the result as the final three-dimensional spatial coordinates of the target node; if it does not, take the target position estimation result of the current iteration obtained in step S4.3 as the current target position estimate, and return to step S4.1 to continue executing the next iteration.

2. The RSS positioning method based on directional gain correction according to claim 1, characterized in that, In step S1, the improved RSS measurement model including directional gain is specifically expressed as follows: ； in, Indicates the distance of the receiving end. Average received power at that location Indicates the reference distance The received power at that location, This represents the path loss index. , This indicates log-normal shadowing fading. This represents the receive directional gain parameter. This represents the directional gain parameter of the transmitting antenna. , The pitch angle is the angle between the vertical direction and the line connecting the transmitter and receiver.

3. The RSS positioning method based on directional gain correction according to claim 2, characterized in that, In step S2, the RSS observation values ​​between the target node and each receiving node are specifically represented as follows: ； in, This represents the directional gain of the i-th receiving node. ; This represents the fading of the log-normal shadow.

4. The RSS positioning method based on directional gain correction according to claim 3, characterized in that, The transmitting and receiving antennas corresponding to both the receiving node and the target node are vertical dipole antennas, and are placed vertically; the elevation angle parameter... Specifically, it is expressed as follows: ； in, This represents the Euclidean distance between the target node and the i-th receiving node. This represents the horizontal distance between the target node and the i-th receiving node; , Indicates the location of the target node; , This indicates the position of the i-th receiving node. .

5. The RSS positioning method based on directional gain correction according to claim 4, characterized in that, In step S4.1, the specific process of optimizing the directional gain of each receiving node using local fixed parameters is as follows: Let the first... k The target position estimate at the next iteration is Based on the aforementioned target location estimate Calculate the first k+1 During the nth iteration i The elevation angles of the receiving nodes are: Based on the first k+1 Pitch angle at the next iteration The optimized directional gain is obtained, specifically expressed as: .

6. The RSS positioning method based on directional gain correction according to claim 5, characterized in that, The corrected RSS observations are specifically represented as follows: ； in, This represents the reference power value after stripping the directional gain.

7. The RSS positioning method based on directional gain correction according to claim 6, characterized in that, The specific process of step S4.2 is as follows: Based on the reference power value after stripping the directional gain and corrected RSS observations The physical distance relationship of the i-th receiving node in the (k+1)-th iteration is obtained, specifically expressed as: ； in, , This represents the distance measurement value in this round; Based on the aforementioned physical distance relationships, a positioning optimization problem is constructed, specifically expressed as: ； in, , This represents the physical distance relationship vector in the (k+1)th iteration. , Represents a vector of distance measurement values. , The weight matrix is ​​the inverse of the noise covariance. ; definition , ,get: ; Depend on satisfy and The equivalent optimization problem of the positioning optimization problem is obtained, specifically expressed as: ； Where i and j represent the indices of the receiving node, and their values ​​range from 1 to 10. ;matrix diagonal elements square of the corresponding distance off-diagonal elements This represents the intersection term between node i and node j, corresponding to ; By performing semidefinite relaxation on the equivalent optimization problem, discarding the rank-one constraint, and using Schur's complement to represent the positive semidefinite constraint, we obtain the equivalent convex constraint problem: ； in, Represents the three-dimensional identity matrix; Solving the equivalent convex constraint problem yields the target position estimate for the (k+1)th iteration. .

8. The RSS positioning method based on directional gain correction according to claim 7, characterized in that, In step S4.4, the convergence condition is specifically as follows: ； in, This indicates the set convergence threshold.

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