An improved DV-Hop positioning method based on adaptive inverse optimization mechanism

Abstract

The application discloses an improved DV-Hop positioning method based on an adaptive inverse optimization mechanism, and on the basis of an existing improved DV-Hop algorithm, a method for adaptively obtaining a target node hop threshold value is provided, anchor nodes are optimally selected, and data with poor quality is discarded, so that the coordinates of the target node are inversely optimized, and the overfitting state of the objective function is eliminated in the correction stage of estimating the position. The application can well adapt to irregular network environments and effectively improve the positioning precision in an anisotropic network.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless sensor network positioning, and particularly relates to an improved DV-Hop positioning method based on an adaptive inverse optimization mechanism. BACKGROUND

[0002] Wireless sensor network (WSN) is a wireless network formed by a large number of sensors with small volume, low energy consumption, low cost and computing, communication, storage and even mobile capabilities in a self-organizing and multi-hop manner. These sensors can autonomously perceive the environment, acquire and process data, and finally deliver the data to users. The dynamic perception, processing and delivery capabilities of wireless sensor network make it receive attention and research from scholars and experts in many countries around the world.

[0003] In many applications of wireless sensor network, sensor nodes are randomly deployed. If the positions of the sensors are unknown, the monitoring data can not be meaningful. The most basic positioning method is to equip each sensor node with a global positioning system (GPS), but this not only leads to high cost of the entire system, but also significantly increases power consumption. In addition, the positioning effect of GPS is poor in indoor and complex environments. Another positioning scheme is to use node positioning algorithm, in which a small number of sensor nodes are equipped with a positioning module, and then the positions of the remaining sensor nodes are calculated by using the known information in the network.

[0004] Wireless sensor network node positioning algorithm is one of the supporting technologies of sensor network application, and is also a hotspot of wireless sensor network research. An effective positioning algorithm can use various information to infer the specific positions of each node in the wireless sensor network, and has universal application in positioning-related fields such as target tracking, intelligent transportation and environmental monitoring.

[0005] According to whether special equipment is needed to measure the distance or angle between sensor nodes, the positioning algorithm can be divided into ranging-based positioning algorithm and non-ranging-based positioning algorithm. The ranging-based positioning algorithm needs to measure the distance or angle between sensor nodes, and has higher requirements for hardware, such as RSSI (Received Signal Strength Indicator), TOA (Time of Arrival), TDOA (Time Difference of Arrival), AOA (Angle of Arrival) and the like. The non-ranging-based positioning algorithm exchanges information according to network connectivity or multi-hop routing, such as centroid algorithm, DV-Hop (Distance Vector-Hop) algorithm, APIT (Approximate Point in Triangulation) algorithm and the like.

[0006] As one of the most commonly used positioning algorithms in wireless sensor networks, DV-Hop algorithm estimates the distance between the target node and multiple beacon nodes by the interaction and forwarding of existing information in the network, and then calculates the position of the target node. The algorithm is simple and low cost, but in practical application, the sensor nodes are distributed in complex and harsh environment, due to the existence of obstacles, the network hole and other extremely irregular node distribution phenomena are easy to appear, the positioning accuracy of DV-Hop algorithm will be significantly reduced. SUMMARY

[0007] In view of the poor performance of the DV-Hop positioning method in the irregular network environment in practical application, the application provides an improved DV-Hop positioning method based on an adaptive inverse optimization mechanism, which corrects the average hop distance of the node, obtains the hop threshold value by the coordinates of the to-be-solved node, discards the data with poor quality, eliminates the overfitting state of the objective function and further reduces the positioning error through weighted iteration, thereby effectively improving the positioning accuracy of the method in anisotropic network.

[0008] An improved DV-Hop positioning method based on an adaptive inverse optimization mechanism, comprising the following steps:

[0009] Step 1, initializing the wireless sensor network: each anchor node broadcasts a data packet containing its own position, hop count and label information to the entire network;

[0010] Step 2, obtaining the minimum hop count between sensor nodes: when each sensor node receives the data packet, the hop count value in the data packet is increased by 1, then the content in the data packet is recorded, and the data packet is forwarded to the neighbor node, until all sensor nodes receive the information, if a sensor node receives a data packet from the same anchor node, then the hop count value is compared and the smaller hop count information is saved;

[0011] Step 3, calculating the initial value of the average hop distance of the anchor node: based on the actual distance and the minimum hop count between the anchor nodes, the average hop distance of the anchor node is calculated by using the least mean square error criterion;

[0012] Step 4, correcting the average hop distance of the anchor node: the average hop distance of the anchor node is corrected according to the error setting of the weighted factor of the estimated distance between the anchor nodes;

[0013] Step 5, calculating the average hop distance of the unknown node: considering the influence of r anchor nodes around the unknown node, the corresponding weight is designed, and the average hop distance of the unknown node is calculated by using the least mean square error criterion;

[0014] Step 6, calculating the estimated position of the unknown node: calculating the distance between the unknown node and the m anchor nodes according to the average hop distance of the unknown node and the minimum hop number between the nodes, and obtaining the estimated position of the unknown node by using the least square method;

[0015] Step 7, judging whether the estimated position is the first estimated position of the unknown node, if yes, directly entering step 8, if not, entering step 11, and taking the estimated position as the initial value (x0, y0) of the subsequent iteration;

[0016] Step 8, reversely and adaptively obtaining the hop number threshold of the unknown node: based on the current estimated position of the unknown node and the maximum communication radius of the node, calculating and returning the hop number of the unknown node to the maximum distance of the monitoring area, and further performing the upward rounding operation on the result, and setting the result as the hop number threshold of the unknown node;

[0017] Step 9, discarding the data with poor quality: discarding the anchor nodes with the hop number to the unknown node greater than the hop number threshold of the unknown node, and using the remaining anchor nodes to participate in the subsequent steps;

[0018] Step 10, entering step 5 for secondary calculation, and using the anchor node set within the hop number threshold of the unknown node to replace the r anchor nodes in step 5 and the m anchor nodes in step 6;

[0019] Step 11, eliminating the overfitting state of the objective function and iteratively updating the estimated position of the unknown node: using only the anchor nodes within the hop number threshold of the unknown node to design the objective function, preventing the overfitting state; weighting the objective function, and iteratively updating the estimated position of the unknown node;

[0020] Step 12, obtaining the final position of the unknown node: iteratively updating the coordinates of the unknown node until the iteration condition is met, taking the last calculation result as the final position of the unknown node, and ending the positioning.

[0021] The beneficial effects achieved by the present application are:

[0022] (1) The method not only corrects the average hop distance of the node, but also reversely obtains the hop number threshold through the coordinates of the node to be solved, optimally selects the anchor nodes, discards the data with poor quality, eliminates the overfitting state of the objective function, and finally obtains the optimal estimated position of the node to be solved by using the weighted iteration.

[0023] (2) The method effectively improves the positioning accuracy of the node in the irregular network topology in actual application. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The method flowchart in the embodiment of the present application.

[0025] Figure 2A node distribution schematic diagram of a square monitoring area in an embodiment of the present application.

[0026] Figure 3 A node distribution schematic diagram of an H-shaped monitoring area in an embodiment of the present application.

[0027] Figure 4 A node distribution schematic diagram of a C-shaped monitoring area in an embodiment of the present application.

[0028] Figure 5 A positioning error diagram of the present method and the existing DV-Hop algorithm under different anchor node ratios in a square monitoring area in an embodiment of the present application.

[0029] Figure 6 A positioning error diagram of the present method and the existing DV-Hop algorithm under different anchor node ratios in an H-shaped monitoring area in an embodiment of the present application.

[0030] Figure 7 A positioning error diagram of the present method and the existing DV-Hop algorithm under different anchor node ratios in a C-shaped monitoring area in an embodiment of the present application. DETAILED DESCRIPTION

[0031] The technical solutions of the present application are further described in detail below in combination with the accompanying drawings of the specification.

[0032] As shown in Figure 1 , the present application provides an improved DV-Hop positioning method based on an adaptive inverse optimization mechanism, and the specific process is as follows.

[0033] Step 1: Initialize the wireless sensor network: each anchor node broadcasts a data packet containing its own position, hop count and label information to the entire network. All anchor nodes in the network are configured with GPS modules.

[0034] Step 2: Obtain the minimum hop count between sensor nodes: each sensor node increases the hop count value in the received data packet by 1, then records the contents in the data packet, and forwards it to the neighbor nodes until all sensor nodes receive the information. If a sensor node receives a data packet originating from the same anchor node, compare and save the hop count information with the smaller hop count value.

[0035] Step 3: Calculate the initial value of the average hop distance of the anchor nodes: based on the actual distance between the anchor nodes and the minimum hop count, the average hop distance of the anchor nodes is calculated using the least mean square error criterion.

[0036] The mean square error e of the estimated distance between anchor node i and the remaining anchor nodes is expressed as:

[0037]

[0038] where m is the number of anchor nodes in the network, D ij is the actual distance between anchor node i and anchor node j, h ij is the minimum hop count between anchor node i and anchor node j.

[0039] Let The initial average hop count of anchor node i is:

[0040]

[0041] Step 4: Correct the average hop count of anchor nodes: set the weighting factor according to the error of the estimated distance between anchor nodes, so as to correct the average hop count of anchor nodes.

[0042] The calculation of the average hop count of anchor node i in the actual wireless sensor network is affected differently by the remaining anchor nodes, and a corresponding weight needs to be designed to improve the reliability of the average hop count calculation. Set the weighting factor w ij :

[0043]

[0044] Then the mean square error e' of the estimated distance between anchor node i and the remaining anchor nodes after weighting is expressed as:

[0045]

[0046] Let The corrected average hop count of anchor node i is:

[0047]

[0048] Step 5: Calculate the average hop count of unknown nodes: consider the influence of the r anchor nodes around the unknown node, design a corresponding weight, and calculate the average hop count of the unknown node using the least mean square error criterion.

[0049] The mean square error ε of the estimated distance between the unknown node and the r nearest anchor nodes around it is expressed as:

[0050]

[0051] where λ s is the weight corresponding to anchor node s, h us is the hop count between unknown node u and anchor node s, hopsize s ' is the corrected average hop count of anchor node s.

[0052] According to the connectivity between anchor nodes in the network, the hop count between unknown node u and anchor node s, and the average distance error per hop of anchor node s, set the weight λs :

[0053]

[0054] where h sj is the hop number between anchor node s and anchor node j, θ s represents the average distance error of anchor node s per hop:

[0055]

[0056] where D sj is the actual distance between anchor node s and anchor node j.

[0057] Let The average hop size of unknown node u can be obtained as:

[0058]

[0059] where the simplified weight of anchor node s and its normalized value are:

[0060]

[0061] Step 6: Calculate the estimated position of the unknown node: Calculate the distance between the unknown node and the m anchor nodes according to the average hop size of the unknown node and the minimum hop number between nodes, and obtain the estimated position of the unknown node using the least squares method.

[0062] The specific operation steps of the least squares method to obtain the estimated position of the unknown node are:

[0063] The estimated distance between the unknown node u and the m anchor nodes is:

[0064] d ui = hopsize u ·h ui , i = 1, 2, …, m

[0065] where h ui is the hop number between the unknown node u and anchor node i.

[0066] Thus, the distance equation set between the unknown node u and the m anchor nodes is obtained as:

[0067]

[0068] where (x i , y i ) is the coordinate of anchor node i, i = 1, 2, …, m, and (x u , y u ) is the coordinate of the unknown node u to be solved.

[0069] Subtracting the m-th term from the first m-1 terms of the equation set, we have:

[0070]

[0071] The matrix form is AX = b, where A, X and b are as follows:

[0072]

[0073] Thus, the coordinates of the unknown node can be obtained by the least square method:

[0074] X = (A T A) -1 A T b

[0075] Step 7, determine whether the estimated position is the first estimated position of the unknown node. If yes, directly go to step 8, if not, go to step 11, and set the estimated position as the initial value (x0, y0) of subsequent iteration.

[0076] Step 8: reverse adaptive acquisition of the hop threshold of the unknown node: based on the current estimated position of the unknown node and the maximum communication radius of the node, calculate and return the hop number of the unknown node to the maximum distance of the monitoring area, and further take the upward rounding operation, set the result as the hop threshold of the unknown node.

[0077] According to the maximum distance d m from the current estimated position of the unknown node to the boundary of the monitoring area, combined with the maximum communication radius R of the node, the hop threshold h t of the unknown node is obtained:

[0078]

[0079] Where represents the upward rounding.

[0080] The hop threshold of the unknown node is calculated according to the current estimated position of the unknown node, and its feasibility is explained as follows: although there is an error between the estimated position of the unknown node calculated in step 6 and the actual position, compared with the maximum communication radius of the node, the error is small, and due to the upward rounding operation in the calculation, the influence of the deviation of the estimated position on the calculation of the hop threshold of the unknown node can be ignored.

[0081] Step 9: Discard the data with poor quality: discard the anchor nodes whose hop count to the unknown node is greater than the hop count threshold of the unknown node, and use the remaining anchor nodes to participate in the subsequent steps. Ideally, the average distance per hop is close to the communication radius. If the hop count of the anchor node to the unknown node is greater than the hop count threshold of the unknown node, it indicates that the node distribution between the two is extremely irregular, and even there is a network hole, so the positioning of the unknown node by such anchor nodes will produce a larger error.

[0082] Step 10, go to step 5 for secondary calculation, the calculation of the average hop distance of the unknown node in step 5 only uses a few anchor nodes, so the amount of information it can provide is limited. However, if all anchor nodes are used, the error will easily increase. Therefore, the anchor node set within the hop count threshold of the unknown node is used to replace the r anchor nodes in step 5 and the m anchor nodes in step 6.

[0083] Step 11: Eliminate the overfitting state of the objective function and iteratively update the estimated position of the unknown node: only use the anchor nodes within the hop count threshold of the unknown node to design the objective function to prevent overfitting. The objective function is weighted and the estimated position of the unknown node is iteratively updated.

[0084] Generally, the deviation of the estimated distance between the unknown node and all anchor nodes is minimized as the objective function, but the anchor nodes with larger errors are mixed in, which easily leads to a decrease in positioning accuracy. The present application only selects anchor nodes within the hop count threshold of the unknown node, effectively avoiding the overfitting state of the objective function, thereby achieving more accurate positioning. Therefore, the objective function is the minimum value of the square of the deviation of the estimated distance between the unknown node and the anchor node:

[0085]

[0086] where (x, y) is the unknown node coordinates to be solved, l is the number of anchor nodes within the hop count threshold of the unknown node, (x i ,y i ) is the coordinates of anchor node i, d ui is the estimated distance from the unknown node u to the anchor node i, is the weight of the anchor node i according to its own per-hop accuracy and the normalized value:

[0087]

[0088] Since the objective function is a nonlinear function of (x, y), it cannot be directly solved linearly, so the Taylor expansion formula is used to approximate the nonlinear term.

[0089] The first-order Taylor expansion at the initial coordinates (x0, y0) is:

[0090]

[0091] At the same time, let

[0092]

[0093] Substituting the linearized objective function:

[0094]

[0095] The partial derivatives of the above formula with respect to x and y are taken respectively, and the partial derivatives are set to zero, to obtain the updated coordinates of the unknown node. Thus far, the estimated position of the unknown node is updated once.

[0096] Step 12: Obtain the final position of the unknown node: iteratively update the coordinates of the unknown node until the iteration condition is met, take the final calculation result as the final position of the unknown node, and end the positioning.

[0097] The iteration condition is:

[0098]

[0099] Where (x0, y0) is the initial iteration value of the unknown node coordinates, I t is the iteration threshold, which is set to 0.25 meters in the present application.

[0100] If the calculated estimated position (x, y) meets the iteration condition, then (x, y) is taken as the final estimated position of the unknown node, otherwise (x, y) is assigned to (x0, y0) and the next iteration is performed.

[0101] In order to verify the real effect of the above method, the following is a simulation experiment analysis of a DV-Hop positioning method based on an adaptive inverse optimization mechanism (ARODV-Hop) of the present application under different network topologies. The positioning error of the method of the present application, the classical DV-Hop algorithm and the An enhanced nonlinear iterative localization algorithm for DV_Hop with uniform calculation criterion (NWIDV-Hop) proposed by Chen et al. in 2021 under different anchor node ratios is compared.

[0102] The experimental parameters are set as follows:

[0103] In the network area with the side length of 100m*100m, 100 sensor nodes are randomly distributed, the maximum communication radius of the nodes is 30m, the anchor node proportion is 20%-45%, and the parameter r=5 is set. Meanwhile, in order to eliminate the randomness error as much as possible, all the simulation results are the average values of 100 repeated runs in the same environment.

[0104] Figure 2 Figure 3 and Figure 4 are the node distribution diagrams of square, H-shaped and C-shaped monitoring areas respectively, wherein "*" represents an anchor node and "o" represents an unknown node.

[0105] Experiment 1: Comparison of positioning errors of the method of the application and the existing DV-Hop algorithm under different anchor node proportions in a square topology structure.

[0106] As shown in Figure 5 , in the square topology structure, the positioning error of the algorithm of the application is reduced by about 49.66% and 2.41% than the classic DV-Hop algorithm and NWIDV-Hop algorithm respectively when the anchor node proportion is 25% in comparison with the existing DV-Hop positioning method under different anchor node proportions.

[0107] Experiment 2: Comparison of positioning errors of the method of the application and the existing DV-Hop algorithm under different anchor node proportions in an H-shaped topology structure.

[0108] As shown in Figure 6 , in the H-shaped topology structure, the positioning error of the algorithm of the application is reduced by about 48.92% and 7.33% than the classic DV-Hop algorithm and NWIDV-Hop algorithm respectively when the anchor node proportion is 25% in comparison with the existing DV-Hop positioning method under different anchor node proportions.

[0109] Experiment 3: Comparison of positioning errors of the method of the application and the existing DV-Hop algorithm under different anchor node proportions in a C-shaped topology structure.

[0110] As shown in Figure 7 , in the C-shaped topology structure, the positioning error of the algorithm of the application is reduced by about 56.77% and 21.79% than the classic DV-Hop algorithm and NWIDV-Hop algorithm respectively when the anchor node proportion is 25% in comparison with the existing DV-Hop positioning method under different anchor node proportions.

[0111] ​In summary, the application optimally selects anchor nodes by reversely obtaining the hop threshold of the node to be solved, discards data with poor quality, and eliminates the overfitting state of the objective function on the basis of the existing improved DV-Hop algorithm. The method can well adapt to irregular network environment and effectively improve the positioning accuracy of the algorithm in anisotropic network.

[0112] The above merely describes the preferred embodiments of the present application, and the protection scope of the present application is not limited to the above-described embodiments, but any equivalent modifications or changes made by those skilled in the art according to the disclosed content of the present application shall be included in the protection scope recorded in the claims.

Claims

1. An improved DV-Hop localization method based on adaptive inverse optimization mechanism, characterized in that: The method comprises the following steps: Step 1, initializing the wireless sensor network: each anchor node broadcasts a data packet containing its own position, hop count and label information to the whole network; Step 2, obtaining the minimum hop count between sensor nodes: each sensor node increases the hop count value in the received data packet by 1, then records the content in the data packet, and forwards it to the neighbor nodes, until all sensor nodes receive the information, if a sensor node receives data packets from the same anchor node, then the hop count values are compared and the hop count information with the smaller hop count value is saved; Step 3, calculating the initial value of the average hop distance of the anchor nodes: based on the actual distance and the minimum hop count between the anchor nodes, the average hop distance of the anchor nodes is calculated by using the least mean square error criterion; Step 4, correcting the average hop distance of the anchor nodes: a weighting factor is set according to the error of the estimated distance between the anchor nodes, so as to correct the average hop distance of the anchor nodes; Step 5, calculating the average hop distance of the unknown node: considering the influence of r anchor nodes around the unknown node, the corresponding weight is designed, and the average hop distance of the unknown node is calculated by using the least mean square error criterion; Step 6, calculating the estimated position of the unknown node: the distances between the unknown node and m anchor nodes are calculated according to the average hop distance of the unknown node and the minimum hop count between the nodes, and the estimated position of the unknown node is obtained by using the least square method; Step 7, judging whether the estimated position is the first estimated position of the unknown node, if yes, directly entering step 8, if not, entering step 11, and taking the estimated position as the initial value (x0, y0) of subsequent iteration; Step 8, obtaining the hop count threshold of the unknown node in reverse adaptation: based on the current estimated position of the unknown node and the maximum communication radius of the node, the hop count of the unknown node to the maximum distance of the monitoring area is calculated and returned, and further rounding up operation is performed on it, and the result is set as the hop count threshold of the unknown node; Step 9, discarding data with poor quality: discarding the anchor nodes whose hop count to the unknown node is greater than the hop count threshold of the unknown node, and using the remaining anchor nodes to participate in the subsequent steps; Step 10, entering step 5 for secondary calculation, and replacing the r anchor nodes in step 5 and the m anchor nodes in step 6 with the anchor node set within the hop count threshold of the unknown node; Step 11, eliminating the overfitting state of the objective function and iteratively updating the estimated position of the unknown node: only using the anchor nodes within the hop count threshold of the unknown node to design the objective function, so as to prevent the overfitting state; weighting the objective function and iteratively updating the estimated position of the unknown node; Step 11 specifically: selecting the anchor nodes within the hop count threshold of the unknown node, and the objective function is the minimum value of the square of the estimated distance deviation between the unknown node and the anchor nodes: where (x, y) is the unknown node coordinate to be solved, / is the number of anchor nodes within the unknown node hop count threshold, (x i ,y i ) is the coordinate of anchor node i, d ui is the estimated distance from unknown node u to anchor node i, is the weight of anchor node i according to its own per-hop accuracy after normalization: where θ i defined as the average distance error per hop of anchor node i; using the Taylor expansion formula to approximate the nonlinear term of the objective function; The first order Taylor expansion at the initial coordinates (x0, y0) is: At the same time, let Substituting the linearized objective function is obtained: Taking the partial derivative of the above formula with respect to x and y respectively and making the partial derivative zero, the updated coordinates of the unknown node are obtained; thus, the estimated position of the unknown node is updated once. Step 12, obtaining the final position of the unknown node: iteratively updating the coordinates of the unknown node until the iteration condition is met, taking the final calculation result as the final position of the unknown node, and ending the positioning; The iteration condition in step 12 is: where (x0, y0) is the initial iteration value of the unknown node coordinates, I t is the iteration threshold value; If the calculated estimated position (x, y) meets the iteration condition, then (x, y) is taken as the final estimated position of the unknown node, otherwise (x, y) is assigned to (x0, y0) and the next iteration is performed. 2.The improved DV-Hop positioning method based on adaptive inverse optimization mechanism according to claim 1, characterized in that: In step 1, all anchor nodes in the wireless sensor network are configured with GPS modules. 3.The improved DV-Hop localization method based on adaptive inverse optimization mechanism according to claim 1, characterized in that: The initial value of the average hop distance of the anchor node in step 3 is specifically: the mean square error e of the estimated distance between anchor node i and the remaining anchor nodes is expressed as: where m is the number of anchor nodes in the network, D ij is the actual distance between anchor node i and anchor node j, h ij is the minimum hop count between anchor node i and anchor node j; Let The average hop count initial value of the anchor node i is obtained as 4. The improved DV-Hop localization method based on adaptive inverse optimization mechanism according to claim 3, characterized in that: The average hop distance of the modified anchor node in step 4 is specifically: the calculation of the average hop distance of anchor node i in the actual wireless sensor network is affected differently by the remaining anchor nodes, and a corresponding weight needs to be designed to improve the reliability of the average hop distance calculation, and a weighting factor w is set according to the error of the estimated distance and the actual distance from anchor node i to anchor node j ij : Then the weighted mean square error e' of the estimated distance between anchor node i and the remaining anchor nodes is expressed as: where hopsize i is the corrected average hop size for anchor node i; Let The average hop distance of the modified anchor node i is obtained as 5. The improved DV-Hop localization method based on adaptive inverse optimization mechanism according to claim 4, characterized in that: In step 5, the average hop distance of the unknown node is calculated as: the mean square error ε of the estimated distance between the unknown node and the surrounding nearest r anchor nodes is expressed as: where λ s is the weight corresponding to anchor node s, h us is the hop count between unknown node u and anchor node s, hopsize u is the average hop distance of unknown node u, hopsize s ′ is the corrected average hop distance of anchor node s; According to the connectivity between anchor nodes in the network, the hop number between the unknown node u and the anchor node s, and the average distance error per hop of the anchor node s, a weight λ is set s : where h sj is the number of hops between anchor node s and anchor node j, θ s denotes the average distance error per hop of anchor node s: where D sj is the actual distance between anchor node s and anchor node j; Let The average hop distance of unknown node u is obtained as: Where the simplified weight of anchor node s and its normalized value are respectively:

6. The improved DV-Hop localization method based on adaptive inverse optimization mechanism according to claim 5, characterized in that: The step 8 specifically comprises: obtaining the hop threshold value according to the unknown node in reverse, that is, obtaining the hop threshold value h of the unknown node according to the maximum distance d from the current estimated position of the unknown node to the boundary of the monitoring area and the maximum communication radius R of the node. m t ​​ wherein denotes the ceiling function.

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