Distributed iterative convex optimization node localization method based on multi-hop strategy

Abstract

The present invention provides a distributed iterative convex optimization node positioning method based on a multi-hop strategy, that is, according to the classic DV-hop multi-hop strategy, the distance between the unknown node and the anchor node is obtained, and then the node positioning problem can be converted into an optimization problem for solution. The following steps are included: first, the node positioning problem is converted into a minimum-maximum error problem according to the minimum-maximum criterion; then, considering the difficulty of directly solving non-convex problems, the present invention introduces auxiliary variables, gives an optimization problem with non-convex constraints, and converts non-convex constraints into convex constraints through first-order Taylor expansion; finally, a continuous convex approximation method for iteratively solving the non-convex optimization problem of node positioning is given, thereby realizing high-precision positioning of unknown nodes. The present invention can ensure the estimation accuracy of unknown nodes when the anchor nodes are sparsely distributed, and at the same time can reduce the deployment of anchor nodes, reduce energy consumption and save costs.

Description

Technical Field

[0001] The invention relates to the field of wireless sensor node positioning, and in particular to a distributed iterative convex optimization node positioning method based on a multi-hop strategy. Background Art

[0002] Wireless sensor networks (WSN) consist of a large number of sensor nodes deployed in the monitoring area. Due to its simplicity, reliability, easy deployment and self-organization, it is widely used in search and rescue, disaster relief, target tracking and intelligent environment detection. In the above applications, monitoring data with sensor locations is of great significance. Although the Global Navigation Satellite System (GPS) can provide sensors with their own location information, it is unrealistic to equip each node in WSN with GPS due to its price and energy consumption. In addition, in some special applications, such as underwater sensor networks, underwater sensor nodes cannot use GPS devices. Therefore, the current positioning of unknown nodes in WSN mainly relies on the collaborative positioning of nodes with known location information (anchor nodes).

[0003] Unknown node collaborative positioning methods can be divided into two categories: ranging-based and non-ranging-based. Based on ranging methods, such as TOA (time of arrival) or AOA (angle of arrival), node position estimation is achieved by measuring the distance between nodes and using the principle of multilateral positioning. However, this method requires the nodes to be located to have distance measurement equipment, resulting in higher energy consumption and increased total cost. Unlike ranging-based methods that directly measure the distance between nodes, non-ranging node positioning methods obtain the distance between nodes based on network connectivity and do not require additional hardware measurement equipment. Therefore, the influence of measurement errors on positioning accuracy is avoided, which can effectively reduce network energy consumption.

[0004] At present, the classic non-distance measurement method mainly includes DV-hop (distance vector-hop). This method uses the shortest path of multiple hops to estimate the distance between nodes. It does not need to equip the nodes with special distance detection units. It can estimate the position of unknown nodes only by using network connectivity. At the same time, this method is widely used in many fields because it is simple, reliable and easy to implement. However, there is a large deviation in the strategy of approximating the straight-line distance between nodes by multi-hop distance. Recently, an improved algorithm for the DV-hop algorithm has appeared. CC-DV-hop (correct coordinate distance vector-hop) corrects the position estimation of unknown nodes by selecting anchor nodes with large contributions, but this improved algorithm is still based on linear least squares to estimate the position of unknown nodes, resulting in low positioning accuracy. However, an improved PSO-DV-hop algorithm based on PSO (particle swarm optimization) optimization improves the positioning accuracy of unknown nodes by minimizing the cumulative error, but this optimization algorithm is prone to fall into the local optimal solution and the positioning effect is poor. At the same time, the positioning accuracy decreases significantly when the anchor nodes are sparsely distributed. Although the above node positioning methods can estimate the position of unknown nodes, they still fail to achieve the best positioning performance. Summary of the invention

[0005] The purpose of the present invention is to provide a distributed iterative convex optimization node positioning method based on a multi-hop strategy, which can better improve the positioning accuracy of unknown nodes in a sparse anchor node distribution network.

[0006] The technical solution adopted by the present invention is:

[0007] The distributed iterative convex optimization node positioning method based on multi-hop strategy mainly includes the following specific steps:

[0008] Step 1: Initialize parameters;

[0009] Step 2: Calculate the distance between the unknown node and the anchor node:

[0010] Using the average hop distance of anchor nodes, the distance between nodes is estimated by multiplying the average hop distance by the minimum hop number. The specific steps are as follows:

[0011] Step 2.1: Calculate the average hop distance of the anchor node. Specifically:

[0012] According to the network connectivity, anchor node a broadcasts a data packet containing its own information to the network. The data packet information includes the anchor node ID, location coordinates (x i ,y i ) and the initial hop value h of 0, that is, ID = a, x a =(x a ,y a),h=0,a=1,…,m, where m is the number of anchor nodes. When the adjacent node receives this data packet, it compares it with the locally stored data, selectively saves the data packet with the smallest hop value, and broadcasts the hop value in this data packet plus 1 to the remaining adjacent nodes. The average hop distance can be calculated based on the data packet information stored locally by anchor node a And broadcast to the network.

[0013]

[0014] in, Respectively represent The distance and minimum hop value between the anchor node and the a-th anchor node, The calculation is as follows:

[0015]

[0016] Among them, ||·||2 represents the l2 norm, x a Respectively represent The position coordinates of the anchor node and the ath anchor node, and m represents the number of anchor nodes.

[0017] Step 2.2: Calculate the distance between the unknown node and the anchor node: According to the average hop distance broadcasted in step 2.1, the unknown node obtains the average hop distance of the anchor node a (a = 1, ..., m), where m is the number of anchor nodes, and then calculates the minimum hop number h between the unknown node u (u = 1, ..., n) and the anchor node au , where n is the number of unknown nodes, so that the distance between the unknown node and the anchor node can be easily obtained

[0018]

[0019] in, represents the average hop distance of the a-th anchor node, h au Indicates the minimum hop value between the a-th anchor node and the u-th unknown node.

[0020] Step 3: Construct an objective function to minimize the maximum error. Specifically:

[0021] According to step 2.1 and step 2.2, we can get the position node position x a and estimated distance The node location problem can be constructed as the following problem of minimizing the maximum error using the norm approximation method:

[0022]

[0023] Among them, x urepresents the variable to be optimized for the uth unknown node position coordinate, x a represents the position coordinate of the ath anchor node, ||·||2 represents the l2 norm, |·| represents the absolute value, and m represents the number of anchor nodes. represents the estimated distance between the a-th anchor node and the u-th unknown node.

[0024] Step 4: Solve the objective function to estimate the position coordinates of the unknown nodes, which specifically includes the following steps:

[0025] Step 4.1: Convert the non-convex objective function into a convex objective function by introducing auxiliary variables. Specifically:

[0026] According to the objective function of minimizing the maximum error constructed in step 3, due to the non-convexity of the objective function, let is the maximum error, the original problem can be transformed into the following optimization problem:

[0027] Objective function:

[0028] Constraints:

[0029]

[0030] Among them, ||·||2 represents the l2 norm, x u represents the coordinate variable of the uth unknown node to be optimized, t represents the maximum error of the distance from the unknown node to the anchor node, x a represents the position coordinates of the ath anchor node, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0031] Step 4.2: Convert the non-convex constraints into convex constraints. Specifically:

[0032] According to the optimization problem with non-convex constraints in step 4.1, according to the definition of convex problem, the following inequality is a non-convex constraint:

[0033]

[0034] Among them, ||·||2 represents the l2 norm, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinate of the ath anchor node, t represents the maximum error of the distance from the unknown node to the anchor node, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0035] Using Taylor expansion and omitting higher-order terms, the inequality is linearized to:

[0036]

[0037] Among them, ||·||2 represents the l2 norm, (·) T represents transpose, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the a-th anchor node and the unknown node u.

[0038] Then the non-convex constraint can be transformed into a convex constraint:

[0039]

[0040] Among them, ||·||2 represents the l2 norm, (·) T represents transpose, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0041] Step 4.3: Continuous convex approximation iterative optimization estimates the unknown node position coordinates, specifically:

[0042] According to steps 4.1 and 4.2, we get the following convex optimization problem: given the initial optimization value of the unknown node u Iterative solution and will As the initial value of the next iteration, we can get The optimization is iterated in this way until the accuracy threshold ∈ is met.

[0043] Objective function:

[0044] Constraints:

[0045]

[0046] Among them, ||·||2 represents the l2 norm, (·) T represents transposition, t represents the maximum distance error between the unknown node and the anchor node, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0047] Beneficial effects of the present invention:

[0048] Through the above technical scheme, the present invention aims at the problem of low positioning accuracy of unknown nodes caused by sparse distribution of anchor nodes in the network, and proposes a distributed iterative convex optimization node positioning method based on a multi-hop strategy. First, the node positioning problem is converted into a minimum-maximum error problem according to the minimum-maximum criterion. Secondly, considering the difficulty of solving non-convex problems, the present invention introduces auxiliary variables to give an optimization problem with non-convex constraints, and converts the non-convex constraints into convex constraints through a first-order Taylor expansion. Finally, a continuous convex approximation method for iteratively solving the non-convex optimization problem of node positioning is given, thereby achieving high-speed positioning of unknown nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0050] Figure 1 is a flow chart of the present invention;

[0051] Figure 2 Distribution map of unknown nodes and anchor nodes;

[0052] Figure 3 Simulation comparison of different algorithms for unknown node positioning error. DETAILED DESCRIPTION

[0053] like Figure 1 As shown, the present invention comprises the following steps:

[0054] Step 1: Initialize parameters;

[0055] Step 2: Calculate the distance between the unknown node and the anchor node:

[0056] Using the average hop distance of anchor nodes, the distance between nodes is estimated by multiplying the average hop distance by the minimum hop number. The specific steps are as follows:

[0057] Step 2.1: Calculate the average hop distance of the anchor node. Specifically:

[0058] According to the network connectivity, anchor node a broadcasts a data packet containing its own information to the network. The data packet information includes the anchor node ID, location coordinates (x i ,yi ) and the initial hop value h of 0, that is, ID = a, x a =(x a ,y a ),h=0,a=1,…,m, where m is the number of anchor nodes. When the adjacent node receives this data packet, it compares it with the locally stored data, selectively saves the data packet with the smallest hop value, and broadcasts the hop value in this data packet plus 1 to the remaining adjacent nodes. The average hop distance can be calculated based on the data packet information stored locally by anchor node a And broadcast to the network.

[0059]

[0060] in, Respectively represent The distance and minimum hop value between the anchor node and the a-th anchor node, The calculation is as follows:

[0061]

[0062] Among them, ||·||2 represents the l2 norm, x a Respectively represent The position coordinates of the anchor node and the ath anchor node, and m represents the number of anchor nodes.

[0063] Step 2.2: Calculate the distance between the unknown node and the anchor node: According to the average hop distance broadcasted in step 2.1, the unknown node obtains the average hop distance of the anchor node a (a = 1, ..., m), where m is the number of anchor nodes, and then calculates the minimum hop number h between the unknown node u (u = 1, ..., n) and the anchor node au , where n is the number of unknown nodes, so that the distance between the unknown node and the anchor node can be easily obtained

[0064]

[0065] in, represents the average hop distance of the a-th anchor node, h au Indicates the minimum hop value between the a-th anchor node and the u-th unknown node.

[0066] Step 3: Construct an objective function to minimize the maximum error. Specifically:

[0067] According to step 2.1 and step 2.2, we can get the position node position x a and estimated distance The node location problem can be constructed as the following problem of minimizing the maximum error using the norm approximation method:

[0068]

[0069] Among them, x u represents the variable to be optimized for the uth unknown node position coordinate, x a represents the position coordinate of the ath anchor node, ||·||2 represents the l2 norm, |·| represents the absolute value, and m represents the number of anchor nodes. represents the estimated distance between the a-th anchor node and the u-th unknown node.

[0070] Step 4: Solve the objective function to estimate the position coordinates of the unknown nodes, which specifically includes the following steps:

[0071] Step 4.1: Convert the non-convex objective function into a convex objective function by introducing auxiliary variables. Specifically:

[0072] According to the objective function of minimizing the maximum error constructed in step 3, due to the non-convexity of the objective function, let is the maximum error, the original problem can be transformed into the following optimization problem:

[0073] Objective function:

[0074] Constraints:

[0075]

[0076] Among them, ||·||2 represents the l2 norm, x u represents the coordinate variable of the uth unknown node to be optimized, t represents the maximum error of the distance from the unknown node to the anchor node, x a represents the position coordinates of the ath anchor node, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0077] Step 4.2: Convert the non-convex constraints into convex constraints. Specifically:

[0078] According to the optimization problem with non-convex constraints in step 4.1, according to the definition of convex problem, the following inequality is a non-convex constraint:

[0079]

[0080] Among them, ||·||2 represents the l2 norm, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinate of the ath anchor node, t represents the maximum error of the distance from the unknown node to the anchor node, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0081] Using Taylor expansion and omitting higher-order terms, the inequality is linearized to:

[0082]

[0083] Among them, ||·||2 represents the l2 norm, (·) T represents transpose, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the a-th anchor node and the unknown node u.

[0084] Then the non-convex constraint can be transformed into a convex constraint:

[0085]

[0086] Among them, ||·||2 represents the l2 norm, (·) T represents transpose, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0087] Step 4.3: Continuous convex approximation iterative optimization estimates the unknown node position coordinates, specifically:

[0088] According to steps 4.1 and 4.2, we get the following convex optimization problem: given the initial optimization value of the unknown node u Iterative solution and will As the initial value of the next iteration, we can get The optimization is iterated in this way until the accuracy threshold ∈ is met.

[0089] Objective function:

[0090] Constraints:

[0091]

[0092] Among them, ||·||2 represents the l2 norm, (·) T represents transposition, t represents the maximum distance error between the unknown node and the anchor node, x u represents the coordinate variable of the uth unknown node to be optimized, x arepresents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

[0093] Through the above technical scheme, the present invention aims at the problem of low positioning accuracy of unknown nodes caused by sparse distribution of anchor nodes in the network, and proposes a distributed iterative convex optimization node positioning method based on a multi-hop strategy. First, the node positioning problem is converted into a minimum-maximum error problem according to the minimum-maximum criterion. Secondly, considering the difficulty of solving non-convex problems, the present invention introduces auxiliary variables to give an optimization problem with non-convex constraints, and converts the non-convex constraints into convex constraints through a first-order Taylor expansion. Finally, a continuous convex approximation method for iteratively solving the non-convex optimization problem of node positioning is given, thereby achieving high-speed positioning of unknown nodes.

[0094] In this example, 150 nodes are used in random topology in the monitoring area (such as Figure 2 ), where the number of anchor nodes is 30 and the number of unknown nodes is 120. The positioning performance RMSE (root mean square error) of the proposed algorithm, DV-hop, CC-DV-hop, and PSO-DV-hop for unknown nodes is compared (e.g. Figure 3 ). The present invention utilizes the minimum and maximum criteria to effectively solve the low positioning accuracy of the traditional algorithm, and at the same time derives an iterative convex optimization efficient solution method in solving the non-convex objective function.

[0095] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchanged in appropriate circumstances, so that the embodiments of the present application described here. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, the process, method, system, product or equipment comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or equipment.

[0096] Note that the above are only preferred embodiments of the present invention and the principles of the application technology. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention is described in more detail through the above embodiments, the present invention is not limited to the specific embodiments described herein, and may include more other effective embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A distributed iterative convex optimization node positioning method based on a multi-hop strategy, characterized by: It includes the following steps: Step 1: Initialize parameters; Step 2: Calculate the distance between the unknown node and the anchor node: Use the average hop distance of the anchor node to estimate the distance between nodes by multiplying the average hop distance by the minimum hop number; Step 3: Construct an objective function to minimize the maximum error; Step 3 specifically includes the following steps: According to the node position x a and estimated distance The node location problem can be constructed as the following problem of minimizing the maximum error using the norm approximation method: Among them, x u represents the variable to be optimized for the uth unknown node position coordinate, x a represents the position coordinate of the ath anchor node, ||·||2 represents the l2 norm, |·| represents the absolute value, and m represents the number of anchor nodes. represents the estimated distance between the a-th reference node and the u-th unknown node; Step 4: Solve the objective function to estimate the position coordinates of the unknown nodes; Step 4 specifically includes the following steps: Step 4.1: Convert the non-convex objective function into a convex objective function by introducing auxiliary variables; including the following steps: According to the objective function of minimizing the maximum error constructed in step 3, due to the non-convexity of the objective function, let is the maximum error, then the original problem can be transformed into the following optimization problem: Objective function: Constraints: Among them, ||·||2 represents the l2 norm, x u represents the coordinate variable of the uth unknown node to be optimized, t represents the maximum error of the distance from the unknown node to the anchor node, x a represents the position coordinates of the ath anchor node, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes; Step 4.2: Convert the non-convex constraint into a convex constraint; the step 4.2 specifically includes the following steps: The first-order Taylor expansion is used to transform non-convex constraints into convex constraints, and the inequality is linearized to obtain: Among them, ||·||2 represents the l2 norm, (·) T represents transpose, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the a-th anchor node and the unknown node u; Step 4.3: Continuously convex approximation iterative optimization estimates the unknown node position coordinates.

2. The distributed iterative convex optimization node positioning method based on multi-hop strategy according to claim 1 is characterized in that: The step 2 specifically includes the following steps: Step 2.1: Calculate the average hop distance of the anchor node. Specifically: According to the network connectivity, anchor node a broadcasts a data packet containing its own information to the network. The data packet information includes the anchor node ID, location coordinates (x a ,y a ) and the initial hop value h of 0, that is, ID = a, x a =(x a ,y a ), h=0, a=1, …, m, where m is the number of anchor nodes; when the adjacent node receives this data packet, it compares it with the locally stored data, selectively saves the data packet with the smallest hop value, and at the same time broadcasts the hop value in this data packet plus 1 to the remaining adjacent nodes; The average hop distance can be calculated based on the data packet information stored locally at anchor node a and broadcast to the network; Step 2.2: Calculate the distance between the unknown node and the anchor node: According to the average hop distance broadcast in step 2.1, the unknown node obtains the average hop distance of the anchor node a, where m is the number of anchor nodes, and then calculates the distance based on the number of hops h between the unknown node u and the anchor node. au , where n is the number of unknown nodes, u = 1, ..., n, so that the distance between the unknown node and the anchor node can be easily obtained 3. The distributed iterative convex optimization node positioning method based on multi-hop strategy according to claim 2 is characterized by: The average hop distance of the anchor nodes in step 2.1 calculate: in, Respectively represent The distance and minimum hop value between the anchor node and the a-th anchor node, The calculation is as follows: Among them, ||·||2 represents the l2 norm, x a 、x a Respectively represent The position coordinates of the anchor node and the a-th anchor node, m represents the number of anchor nodes; Step 2.2: The distance between the unknown node u and the anchor node a Calculate, where m and n are the number of anchor nodes and unknown nodes respectively: in, represents the average hop distance of the a-th anchor node, h au Indicates the minimum hop value between the a-th anchor node and the u-th unknown node.

4. The distributed iterative convex optimization node positioning method based on multi-hop strategy according to claim 1 is characterized by: The step 4.2 specifically includes the following steps: According to the optimization problem with non-convex constraints in step 4.1, according to the definition of convex problem, the following inequality can be known as a non-convex constraint: Among them, ||·||2 represents the l2 norm, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinate of the ath anchor node, t represents the maximum error of the distance from the unknown node to the anchor node, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes; Using Taylor expansion and omitting higher-order terms, the inequality is linearized to: Among them, ||·||2 represents the l2 norm, (·) T represents transpose, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the a-th anchor node and the unknown node u; Then the non-convex constraint can be transformed into a convex constraint: Among them, ||·||2 represents the l2 norm, (·) T represents transpose, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

5. The distributed iterative convex optimization node positioning method based on multi-hop strategy according to claim 1 is characterized in that: The step 4.3 specifically includes the following steps: According to steps 4.1 and 4.2, we get the following convex optimization problem: given the optimization initial value of the unknown node u Iterative solution and will As the initial value of the next iteration, we can get The optimization is iterated in this way until the accuracy threshold ò is met; Objective function: Constraints: Among them, ||·||2 represents the l2 norm, (·) T represents transposition, t represents the maximum distance error between the unknown node and the anchor node, x u represents the coordinate variable of the uth unknown node to be optimized, x a represents the position coordinates of the ath anchor node, represents the initial value of the optimization variable of the unknown node u, represents the estimated distance between the ath anchor node and the unknown node u, and m represents the number of anchor nodes.

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