A DV-Hop Localization Method Based on Polynomial Mean Optimization for Estimating Distance

Abstract

The present invention belongs to the technical field of small-scale anisotropic wireless sensor network positioning, and discloses a DV-Hop positioning method based on polynomial average optimization for estimating distance, including: Step 1: Initialize the wireless sensor network; Step 2: Each node maintains a set of reachable anchor lists; Step 3: Calculate the hop-distance polynomial coefficients of the anchor nodes; Step 4: Calculate the prediction error of the anchor nodes; Step 5: The anchor nodes broadcast their own hop-distance polynomial coefficients and prediction errors; Step 6: Calculate the estimated distance from the unknown nodes to the anchor nodes; Step 7: Filter the anchor nodes; Step 8: Estimate the positions of the unknown nodes. The positioning method of the present invention is used to calculate the estimated distance from the unknown nodes to the anchor nodes, and at the same time introduces anchor node prediction error filtering to filter out the anchor nodes with large errors in the positioning process, effectively improving the positioning accuracy of the nodes in the small-scale anisotropic wireless sensor network environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of small-scale anisotropic wireless sensor network positioning, and specifically relates to a DV-Hop positioning method based on polynomial average optimized estimated distance. Background Technique

[0002] A wireless sensor network is a network composed of a large number of sensor nodes that can communicate with each other. These sensor nodes can sense the surrounding environmental changes, obtain the information people need, and transmit the collected information data to the sink node for further data operations. The application fields of wireless sensor networks include environmental detection, intelligent transportation, precision agriculture, volcanic detection systems, etc. During the application process, the information monitored by the sensor nodes needs to be processed in combination with the location information of the nodes. If the location where the event occurs is unknown, the related data cannot be used. However, for wireless sensor networks, it is also unrealistic to equip each node with a GPS positioning device, which will lead to an increase in positioning costs and device power consumption. Based on the node positioning algorithm of wireless sensor networks, only a small number of nodes need to be equipped with GPS devices, and the positions of unknown nodes are estimated based on the location information of these nodes, which greatly reduces the positioning cost.

[0003] The node positioning algorithms based on wireless sensor networks can be roughly divided into two categories: ranging-based positioning algorithms and range-free positioning algorithms. Ranging-based positioning algorithms need to measure the actual distance between nodes before positioning, such as TOA (Time Of Arrival), AOA (Angle Of Arrival), RSSI (Received Signal Strength Indicator), etc. Among them, TOA and AOA have high requirements for hardware devices, and RSSI ranging has low requirements for hardware devices but is easily affected by the environment; Range-free positioning algorithms do not require any additional ranging devices and only rely on network connectivity and the location information of anchor nodes to perform positioning, such as DV-Hop (Distance Vector-Hop), APIT (Approximate Point-In-Triangulation), centroid positioning, etc.

[0004] Range-free positioning algorithms are widely favored due to their low cost and low power consumption. In the traditional DV-Hop positioning algorithm, the average hop distance is calculated based on the hop count and distance from each anchor node to other anchor nodes. The unknown node uses the average hop distance of the nearest anchor node as its own average hop distance and combines the hop count information for distance estimation. Finally, the least squares method is used to estimate the position of the unknown node.

[0005] In DV-Hop positioning, the accuracy of the distance estimation from unknown nodes to anchor nodes has a great impact on the positioning effect. In the actual application environment, the nodes are often unevenly distributed or there are holes in the distribution environment. At this time, there will be a large error in the estimated distance from unknown nodes to anchor nodes, which will cause a decrease in the positioning accuracy of the nodes. Summary of the Invention

[0006] Aiming at the defects of large estimation distance error from unknown nodes to anchor nodes and poor positioning accuracy in the above-mentioned existing technologies, the present invention provides a DV-Hop positioning method based on polynomial average to optimize the estimated distance, which improves the large distance estimation error in the existing technology, thereby improving the positioning accuracy.

[0007] To achieve the above purpose, the present invention is realized through the following technical solutions:

[0008] Step 1: Initialize the wireless sensor network, and the anchor node broadcasts a data packet containing its own location information.

[0009] Step 2: Use the RSSI technology to refine the hop count between adjacent nodes, and each node maintains a set of reachable anchor lists after the flooding ends.

[0010] Step 3: Calculate the hop count-distance polynomial coefficients of the anchor nodes: Use a polynomial to represent the relationship between the hop count and distance between nodes. By the minimum hop count and the actual distance from each anchor node to the other anchor nodes, the hop count-distance polynomial coefficients of the anchor nodes can be obtained by solving the polynomial.

[0011] Step 4: Calculate the prediction error of the anchor nodes: Use the hop count-distance polynomial to estimate the distance from the anchor node to the other anchor nodes, and compare it with the actual distance to obtain the prediction error.

[0012] Step 5: The anchor node broadcasts its own hop count-distance polynomial coefficients and prediction error. The unknown node saves the received information in the corresponding anchor node of the reachable anchor list, and uses the polynomial coefficients of the nearest anchor node as its own hop count-distance polynomial coefficients.

[0013] Step 6: Calculate the estimated distance from the unknown node to the anchor node: Use the method of polynomial average optimization to calculate the estimated distance.

[0014] Step 7: Filter the anchor nodes: Filter the anchor nodes by combining the prediction error and the estimated distance of the anchor nodes.

[0015] Step 8: Use the relevant information of the filtered anchor nodes and the unknown nodes to estimate the location of the unknown node.

[0016] Further, in step 1, the wireless sensor network includes anchor nodes and unknown nodes, where the anchor nodes are equipped with GPS modules; the data packets broadcast by the anchor nodes include their own location information, identity identifiers, transmission power, minimum hop count information, etc.

[0017] Further, in step 2, the hop count between adjacent nodes is refined by hop count grading using RSSI values, and the grading method is as follows: where \(i = 2, 3, \ldots, m - 1\), \(d\) is the distance between two adjacent nodes, \(R\) is the communication radius, \(A\) is the signal strength received when the distance between nodes is 1m, and \(k_0\) is the path loss factor, usually set between 2 and 6.

[0018] The method for obtaining the minimum hop count is that after node \(i\) receives the data packet from anchor node \(j\), it determines whether it has received a data packet from node \(j\) before. If it has, it compares the minimum hop counts and discards the data packet with a larger hop count; if it has not received a data packet from anchor node \(j\), it saves the data from anchor node \(j\).

[0019] Further, in step 3, the calculation method for the hop count - distance polynomial coefficients between anchor nodes is as follows: introduce the hop count - distance polynomial Using the hop count and distance information from the anchor node to all other anchor nodes, the least squares method is used to solve the hop count - distance polynomial coefficients \(\alpha\) i =\((H\) i T H\) i )\) -1 H\) i T D\) i , where \(H\) i is the hop count matrix composed of the hop count information from anchor node \(i\) to all other anchor nodes, denoted as D\) i is the distance matrix from anchor node \(i\) to all other anchor nodes, denoted as where \(i \neq m\).

[0020] Further, in step 4, according to the hop count - distance polynomial, the estimated distance from anchor node \(i\) to any other anchor node \(j\) is where \(\alpha\) i is the hop count - distance polynomial coefficient of anchor node \(i\), \(h\) ij is the hop count from anchor node \(i\) to other anchor nodes, and the prediction error of anchor node \(i\) is the sum of the absolute values of the differences between the estimated distance from anchor node \(i\) to all other anchor nodes and the actual distance , denoted as

[0021] Further, in step 6, the estimated distance from unknown node \(u\) to anchor node \(i\) is where To adopt the coefficient α of the hop-distance polynomial of the unknown node itself u and the hop count h to the anchor node ui The estimated distance from the unknown node to the anchor node calculated by the hop-distance polynomial is denoted as To adopt the polynomial coefficient α of the anchor node i i The estimated distance between the anchor node i and the unknown node u calculated is denoted as

[0022] Furthermore, in step 7, filtering is performed on the anchor nodes. When the prediction error e of the anchor node i i is greater than the average prediction error e mean , and the estimated distance d from the unknown node u to the anchor node i ui is greater than the average estimated distance d mean , the anchor node i is marked as an untrusted node and does not participate in the position estimation of the unknown node u, that is, the anchor nodes with a prediction error greater than the average prediction error of the anchor nodes and an estimated distance to the unknown node greater than the average estimated distance are filtered out. Among them, m is the number of anchor nodes in the network.

[0023] Furthermore, in step 8, after filtering out the untrusted nodes, the weighted least squares method is used to estimate the position of the unknown node, and the weight value is 1 / d, where d is the estimated distance from the unknown node to the anchor node.

[0024] The beneficial effects of the present invention are as follows:

[0025] (1) When estimating the distance, the present invention fully considers the distribution of the unknown node and the corresponding anchor node, and uses the hop-distance polynomial coefficients of the anchor node and the unknown node to estimate the distance respectively, and takes their mean value as the distance from the unknown node to the anchor node, avoiding the error caused by the large difference in the network distribution of the nodes around the anchor node and the unknown node, and optimizing the estimated distance;

[0026] (2) And the present invention uses the prediction error of the anchor node to filter the nodes, thereby optimizing the estimated position of the unknown node;

[0027] (3) In the wireless sensor network environment with small-scale anisotropy, the present invention effectively improves the positioning accuracy of the nodes. Description of the Drawings

[0028] Figure 1 is the flowchart of the present invention.

[0029] Figure 2 is the node distribution diagram of the square detection area.

[0030] Figure 3 is the node distribution diagram of the C-shaped detection area.

[0031] Figure 4 It is a node distribution diagram of the H-shaped detection area.

[0032] Figure 5 It is a positioning error diagram of the method of the present invention, the DV-Hop algorithm, and the existing improved DV-Hop algorithm in the square network under different anchor node ratios.

[0033] Figure 6 It is a positioning error diagram of the method of the present invention, the DV-Hop algorithm, and the existing improved DV-Hop algorithm in the C-shaped network under different anchor node ratios.

[0034] Figure 7 It is a positioning error diagram of the method of the present invention, the DV-Hop algorithm, and the existing improved DV-Hop algorithm in the H-shaped network under different anchor node ratios. Detailed implementation manners

[0035] The present invention will be further clarified below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification of the present invention fall within the scope defined by the appended claims of this application.

[0036] As Figure 1 shown, the present invention is a DV-Hop positioning method based on polynomial average optimization for estimating distance, and its specific process is as follows:

[0037] Step 1: Initialize the network. The anchor nodes broadcast data packets containing information such as location information, identity ID, transmission power, and minimum number of hops to the network.

[0038] Step 2: Each node in the network maintains a list of reachable anchors, and the list of reachable anchors contains the minimum number of hops information. The adjacent nodes use the RSSI technology to divide the number of hops into m levels, and the classification method is as follows:

[0039]

[0040] where i = 2, 3,..., m - 1, d is the distance between two nodes, R is the communication radius, A is the signal strength received when the distance between nodes is 1 m, and k0 is the path loss factor, which is usually set between 2 and 6.

[0041] Step 3: Calculate the hop-distance polynomial coefficients of the anchor nodes: Introduce the hop-distance polynomial between nodes, and use the least squares method to solve the hop-distance polynomial coefficients through the minimum number of hops and the actual distance from each anchor node to the remaining anchor nodes.

[0042] The present invention introduces a hop - distance polynomial to define the relationship between the hop count and distance between nodes:

[0043]

[0044] The coefficients α of the hop - distance polynomial for each anchor node can be solved by the least - squares method i

[0045] α i =(H i T H i ) -1 H i T D i

[0046] where H i is the hop - count matrix composed of the hop counts from anchor node i to all other anchor nodes, denoted as D i is the distance matrix from anchor node i to all other anchor nodes, denoted as and i≠m.

[0047] Step 4: Calculate the prediction error of the anchor node: Estimate the distances from anchor node i to all other anchor nodes through the coefficients of the hop - distance polynomial calculated in Step 3, and compare with the actual distances to obtain the prediction error e i :

[0048]

[0049] where is the actual distance from anchor node i to anchor node j, is the estimated distance from anchor node i to anchor node j calculated by the hop - distance polynomial, denoted as

[0050] Step 5: The anchor node broadcasts its own coefficients of the hop - distance polynomial and the prediction error. The unknown node saves the received information in the corresponding anchor node in the reachable anchor list, and takes the coefficients of the hop - distance polynomial received first as its own coefficients of the hop - distance polynomial;

[0051] Step 6: Calculate the estimated distance from the unknown node to the anchor node: In the traditional process of estimating the distance, only the average hop distance of the anchor node closest to the unknown node is used to participate in the calculation of the distance position, which will cause a large error when the estimated distance network distribution is uneven.

[0052] Therefore, when estimating the distance, the present invention fully considers the distribution around the unknown node and the corresponding anchor node, and proposes a method of polynomial average optimization to calculate the estimated distance between nodes. The hop-distance polynomial coefficients of the anchor node and the unknown node are respectively used to estimate the distance between the unknown node and the anchor node, and their mean value is used as the distance from the unknown node to the anchor node. The specific implementation process is as follows:

[0053] Use the hop-distance polynomial coefficient α of the unknown node u u And the minimum hop count h between nodes u and i ui Calculate the estimated distance from the unknown node to the anchor node through the hop-distance polynomial

[0054]

[0055] Use the hop-distance polynomial coefficient α of the anchor node i i And the minimum hop count h between nodes u and i ui Calculate the estimated distance from the unknown node to the anchor node through the hop-distance polynomial

[0056]

[0057] The final estimated distance from the unknown node to the anchor node is

[0058]

[0059] Step 7: Filter the anchor nodes: Filter the anchor nodes by combining the prediction error of the anchor node and the estimated distance. The specific filtering process is as follows: Calculate the average prediction error of the anchor node

[0060]

[0061] Calculate the average estimated distance from the unknown node to all anchor nodes

[0062]

[0063] When the prediction error e of the anchor node i i Is greater than the average prediction error e mean And the estimated distance d from the unknown node u to the anchor node i ui Is greater than the average estimated distance d mean The anchor node i is marked as an untrusted node and does not participate in the position estimation of the unknown node u, that is, filter out the anchor nodes with a prediction error greater than the average prediction error of the anchor node and an estimated distance to the unknown node greater than the average estimated distance.

[0064] The filtering rules are shown in the following table:

[0065]

[0066] Step 8: Estimate the position of the unknown node using the weighted least squares method, where the weighting value is the estimated distance from the unknown node to the anchor node.

[0067] To verify the actual effect of the above method, the following conducts a simulation experiment analysis on an improved DV-Hop positioning method based on polynomial average optimization estimation distance of the invention, and compares the positioning errors of the method of the invention before and after average optimization and the existing improved DV-Hop algorithm under different anchor node ratios.

[0068] The experimental parameters are as follows:

[0069] In a 100*100 network area, 100 sensor nodes are randomly distributed. The communication radii of the unknown nodes and the anchor nodes are both 30 meters, and the anchor node ratio is between 10% and 35%.

[0070] In this experiment, it is assumed that all nodes have the same transmission power during the communication process. At the same time, in order to prevent random errors, all simulation results are averaged after being repeatedly run 100 times under the same parameter settings.

[0071] Figure 2 It is a node distribution diagram of the square detection area. Figure 3 、 Figure 4 They are respectively the node distribution diagrams of the C-shaped and H-shaped detection areas, where "o" represents the unknown node and "*" represents the reference node.

[0072] Experiment 1: Compare the positioning errors of the method of the invention and the existing improved DV-Hop algorithm under different anchor node ratios in the square topology. To verify the effectiveness of the polynomial average optimization method proposed in the invention, it is also compared with the method of the invention without average optimization (BF-PolyAvgO).

[0073] As Figure 5 shown, in the square topology, the algorithm proposed in the invention is compared with other improved DV-Hop positioning algorithms under different anchor node ratios. It is found that the positioning error of the algorithm proposed in the invention is the smallest. When the anchor node ratio is 20%, the positioning errors of the positioning method proposed in the invention are reduced by approximately 68.3%, 56.6%, 8.9%, and 8.1% compared with the classical DV-Hop algorithm, Polynomial-DV-Hop algorithm, MSVR-DV-Hop algorithm, and BF-PolyAvgO algorithm respectively.

[0074] Experiment 2: Compare the positioning errors of the method of the invention, the existing improved DV-Hop algorithm, and the BF-PolyAvgO algorithm without average optimization under different anchor node ratios in the C-shaped topology.

[0075] As Figure 6 shown, in the C-type topology, the positioning method proposed in the present invention is compared with other improved DV-Hop positioning algorithms under different anchor node ratios. It can be seen from the figure that the overall positioning accuracy of the BF-PolyAvgO algorithm without average optimization is improved compared with the existing algorithms, but the stability is not high; the positioning error of the positioning method proposed in the present invention is the smallest. When the anchor node ratio is 20%, the positioning error of the positioning method proposed in the present invention is reduced by about 74.8%, 54.5%, 14.9%, and 12.1% respectively compared with the classical DV-Hop algorithm, Polynomial-DV-Hop algorithm, MSVR-DV-Hop algorithm, and BF-PolyAvgO algorithm.

[0076] Experiment 3: Compare the positioning errors of the method of the present invention, the improved DV-Hop algorithm in the prior art, and the BF-PolyAvgO algorithm without average optimization under different anchor node ratios in the H-type topology.

[0077] As Figure 7 shown, in the H-type topology, the positioning method of the present invention is compared with other improved DV-Hop positioning algorithms under different anchor node ratios. It is found that when the anchor node ratio is 20%, the positioning error of the positioning method proposed in the present invention is reduced by about 65.8%, 59.6%, 16.3%, and 10.3% respectively compared with the classical DV-Hop algorithm, Polynomial-DV-Hop algorithm, MSVR-DV-Hop algorithm, and BF-PolyAvgO algorithm.

[0078] Based on the existing DV-Hop positioning method, the present invention proposes a method of polynomial average optimization to calculate the estimated distance from an unknown node to an anchor node, and at the same time introduces an anchor node prediction error filter to filter out the anchor nodes with large errors in the positioning process, effectively improving the positioning accuracy of nodes in a small-scale anisotropic wireless sensor network environment.

Claims

1. A DV-Hop positioning method based on polynomial average optimization for estimating distance, which improves the positioning accuracy of nodes in a small-scale anisotropic wireless sensor network environment, is characterized in that: The DV-Hop positioning method includes the following steps: Step 1: Initialize the wireless sensor network, and the anchor nodes broadcast data packets containing their own location information; Step 2: After the flooding is over, each node maintains a set of reachable anchor lists, and the hop count between adjacent nodes is refined by using the RSSI technology; Step 3: Calculate the hop count-distance polynomial coefficients of the anchor nodes: Use polynomials to define the relationship between the hop count and distance between nodes. According to the minimum hop count and actual distance from each anchor node to the other anchor nodes, solve the polynomial by the least squares method to obtain the hop count-distance polynomial coefficients; Step 4: Calculate the prediction error of the anchor nodes: Use the hop count-distance polynomial to estimate the distance from the anchor nodes to the other anchor nodes, and compare it with the actual distance to obtain the prediction error of the anchor nodes; Step 5: The anchor nodes broadcast their own hop count-distance polynomial coefficients and prediction errors. The unknown nodes save the received information into the corresponding anchor nodes in the reachable anchor list, and use the first received hop count-distance polynomial coefficient as the hop count-distance polynomial coefficient of the unknown nodes themselves; Step 6: Use the method of polynomial average optimization to calculate the estimated distance from the unknown nodes to the anchor nodes: Calculate the estimated distance between the unknown nodes and the anchor nodes respectively by using the polynomial coefficients of the unknown nodes and the anchor nodes, and use their mean value as the estimated distance from the unknown nodes to the anchor nodes; Step 7: Filter the anchor nodes: Filter the anchor nodes by combining the prediction error and estimated distance of the anchor nodes; Step 8: Estimate the location of the unknown nodes: Use the relevant information of the filtered anchor nodes and the unknown nodes to estimate the location of the unknown nodes.

2. The DV-Hop positioning method based on polynomial average optimization for estimating distance according to claim 1, wherein: In Step 2, the hop count between adjacent nodes is refined by using the RSSI value, and the refinement method is: Where i = 2, 3, …, n - 1, d is the distance between two adjacent nodes, R is the communication radius, A is the signal strength received when the distance between nodes is 1 meter, and k0 is the path loss factor, which is set between 2 and 6.

3. A DV-Hop positioning method based on polynomial average optimization for estimating distance according to claim 2, characterized in that: The specific process of Step 3 is: Step 3-1: Introduce the hop-distance polynomial to define the relationship between the hop count and the distance between nodes, where α is the coefficient of the polynomial, d ij and h ij are the distance and hop count between node i and node j, respectively; Step 3-2: Use the least squares method to solve the coefficient α of the hop count-distance polynomial of anchor node i i =(H i T H i ) -1 H i T D i , where H i is the hop count matrix composed of the hop count information from anchor node i to all other anchor nodes, denoted as where h i1 , h i2 , … h im are the hop counts from anchor node i to all other anchor nodes respectively, and i≠m, D i is the distance matrix from anchor node i to all other anchor nodes, denoted as where d i1 , d i2 , … d im are the distances from anchor node i to all other anchor nodes respectively, i≠m, H i T is the transpose of H i .

4. A DV-Hop positioning method based on polynomial average optimized estimated distance according to claim 3, characterized in that: The specific process of Step 4 is: According to the hop count-distance polynomial, the estimated distance from anchor node i to anchor node j is: where α i is the polynomial coefficient of anchor node i, h ij is the hop count from anchor node i to anchor node j, and the prediction error e i of anchor node i is the sum of the absolute values of the differences between the estimated distance from anchor node i to all other anchor nodes and the actual distance 5. A DV-Hop positioning method based on polynomial average optimized estimated distance according to claim 4, characterized in that: The specific process of Step 5 is: The anchor nodes broadcast the hop count-distance polynomial coefficients calculated in Step 3 and the prediction errors calculated in Step 4. The unknown nodes use the first received hop count-distance polynomial coefficient as the hop count-distance polynomial coefficient of the unknown nodes themselves.

6. The DV-Hop positioning method based on polynomial average optimized estimated distance according to claim 5, characterized in that: The specific process of calculating the estimated distance from the unknown nodes to the anchor nodes by using the method of polynomial average optimization in Step 6 is: Step 6-1: The unknown node uses the hop-distance polynomial coefficients of the first anchor node it receives as its own polynomial coefficients, and uses the hop-distance polynomial coefficients α of the unknown node u u and the minimum hop count h between node u and i ui to calculate the estimated distance from the unknown node to the anchor node through the hop-distance polynomial Step 6-2: Adopt the hop count-distance polynomial coefficient α of the anchor node i i and the minimum hop count h between node u and node i ui Estimate the distance from the unknown node to the anchor node through the hop count-distance polynomial Step 6-3: Use the mean value of the estimated distances obtained in Steps 6-1 and 6-2 as the estimated distance from the unknown nodes to the anchor nodes 7. A DV-Hop positioning method based on polynomial average optimization for estimating distance according to claim 6, characterized in that: The filtering of the anchor nodes in step 7 is specifically as follows: When the prediction error e of anchor node i i is greater than the average prediction error e mean , and the estimated distance d from the unknown node u to the anchor node i ui is greater than the average estimated distance d mean , the anchor node i is marked as an untrusted node and does not participate in the position estimation of the unknown node u, that is, the anchor nodes with a prediction error greater than the average prediction error of the anchor nodes and an estimated distance to the unknown node greater than the average estimated distance are filtered out. Among them, m is the number of anchor nodes in the network.

8. A DV-Hop positioning method based on polynomial average optimization for estimating distance according to claim 1, characterized in that: In step 8, after filtering out untrusted nodes, the weighted least squares method is used to estimate the position of the unknown node, and the weight is d is the estimated distance from the unknown node to the anchor node.

9. A DV-Hop positioning method based on polynomial average optimized estimated distance according to any one of claims 1-8, characterized in that: All the anchor nodes are configured with GPS modules.

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