# Improvement of DV-Hop Localization Algorithm Based on Non-Ranging

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A wireless sensor network is composed of a large number of randomly distributed sensor nodes and is a distributed, self-organizing network. Its key technologies include: network topology control, node location, clock synchronization, data fusion, routing protocols, and more. Node location problem is one of the most basic and important issues in wireless sensor networks. At present, wireless sensor network location algorithms can be divided into ranging based and non-ranging based positioning algorithms. Commonly used measurement methods based on ranging are TOA, TDOA, AOA, and RSSI. Although these technologies have high relative accuracy, they are highly demanding on hardware. Commonly used measurement methods based on non-ranging positioning are: DV- Hop, centroid, APIT, MDSMAP.

DV-Hop is a typical non-ranging based positioning, which has low hardware requirements and is simple to implement. Its shortcoming is that it will produce errors when calculating the average hop distance and positioning coordinates. Therefore, for the defects of DV-Hop algorithm, a series of improved algorithms are proposed, including: improving the average hop distance in the original algorithm, using multiple anchor nodes to estimate the average distance and using the normalized weighted average hop distance; Based on the geometry-based localization algorithm, the slope method in geometry is used to judge the positional relationship between anchor nodes, and the optimal anchor node sequence is selected to determine the unknown node more accurately. The concept of collinearity is introduced and the collinearity is utilized. The degree parameter dynamically adjusts the distance threshold of the neighboring anchor nodes that the unknown node can collect, selects the good anchor node group in the network for location estimation, and finally uses the weighted estimation mechanism to obtain the final node location estimate. These methods all improve the positioning accuracy to some extent.

In this paper, an improved algorithm is proposed for the calculation of the positioning error of the average hop and trilateral positioning in the DV-Hop algorithm. Firstly, the average hop distance of the whole anchor node is used to correct the average hop distance of the single anchor node. Then, when the triangulation is finally calculated, the three anchor nodes of the optimal combination are selected to participate in the positioning, and the positioning is further improved. Precision.

**1 Introduction to DV-Hop Algorithm**

Dragos Niculescu and others at Rutgers University in the United States have proposed a series of distributed localization algorithms using distance vector routing and GPS positioning principles, collectively known as APS, and DV-Hop algorithm is one of them.

DVHop is implemented in 3 steps:

1 The anchor node i broadcasts its own location information IDi. The initial hop count is 0. Each time a node information is sent, the hop count is incremented by 1, and then forwarded until all nodes in the network receive the anchor node's packet. If the node receives different hop count information from the same anchor node, only the minimum hop count information is taken.

2 When the anchor node i receives the location and minimum hop count information of other anchor nodes, the calculation formula of the average hop distance (AHD) can be calculated:

Where (xi, yi), (xj, yj) are the coordinates of the anchor nodes i, j, respectively; hij is the hop count between the two anchor nodes. The unknown node only receives the AHDi of the anchor node closest to it. The hopi is the hop count of the unknown node from the nearest anchor node, and according to the hop count information, the distance P between the unknown node and the anchor node can be calculated:

3 When the unknown node obtains 3 or more anchor node information, the position of the unknown node can be obtained by triangulation or maximum likelihood similarity. (x, y) is the coordinates of the unknown node, and (xi, yi) is the coordinates of the known anchor node. According to formula (2), the coordinates of the unknown node can be calculated:

**2 Improved DV-Hop algorithm**

This paper mainly improves the second step and the third step in the DV-Hop algorithm. The first step is the same as the original algorithm. In the original algorithm, when calculating the average hop distance in step 2, the unknown node receives the average hop distance from the nearest anchor node. However, due to the non-uniformity of network node distribution, there is a certain error in the average hop distance calculated by a single anchor node. Therefore, the average hop of the whole network and the average hop distance of a single anchor node are introduced to correct the average hop in the original algorithm. distance. In the third step, the position information of the anchor node has a great influence on the positioning accuracy. In this paper, the optimal three anchor nodes are selected to reduce the positioning error by using the difference of connectivity between nodes.

2.1 Improvement of average hop distance

The average hop distance of the whole network is averaged with the AHDi estimated by a single anchor node to replace the average hop distance in the classical algorithm, so that the unknown node has both the estimation information of the whole network and the estimated average hop distance of the anchor node nearest to it. Partial information of AHDi. The average network hop formula is:

Where n is the number of anchor nodes in the network.

The corrected average hop AHD formula is:

2.2 Selective 3 anchor nodes

The positioning algorithm based on selective anchor nodes [15] uses the difference of connectivity. When positioning the three-sided nodes, the optimal positioning of the three anchor nodes is selected to minimize the positioning error.

The node distribution diagram is shown in Figure 1. When the unknown node N1 uses trilateral positioning, it can be located with different 3 anchor node groups (P1, P2, P3), (P1, P2, P4), (P2, P3, P4), (P1, P3, P4). . When calculating with maximum likelihood estimation, (P1, P2, P3, P4) is used to locate, so different anchor node groups will definitely produce different positioning positions.

Figure 1 node distribution map

2.2.1 Basic rules

The degree of connectivity is defined by the minimum number of hops of the unknown node and each anchor node, represented by an array. For example, the connectivity of N1 to all anchor nodes is [1, 1, 2, 5]. Thus, the connectivity of all unknown nodes in Figure 1 can be represented by an array, as listed in Table 1.

Table 1 Connectivity of unknown nodes

The difference in connectivity is defined by the sum of the absolute values â€‹â€‹of the connectivity differences between unknown nodes. For example, the difference in connectivity between N1 and N2 is âˆ£1-2âˆ£+âˆ£1-1âˆ£+âˆ£2-1âˆ£+âˆ£ 5-4âˆ£=3. This can calculate the difference in connectivity between N1 and all other unknown nodes, as listed in Table 2.

Table 2 Differences in connectivity from N1 to unknown nodes

It can be concluded from Table 2 that the connectivity of N2 and N3 to N1 is different from 3 and 4, and the connectivity of N4 and N5 to N1 is different from 9,11. It is indicated that N1 is closer to N2 and N3. This can also be seen in Figure 1.

2.2.2 Determine the optimal 3 anchor nodes

Figure 2 Node distribution map of selective anchor nodes

The node distribution of the selective anchor node is shown in Figure 2. The unknown node Nx represents the actual position of the unknown node, N(i, j, k) is the estimated position according to the combination of 3 anchor nodes, R is the communication radius of the node, and An is the nearest to N(i, j, k) Anchor node, Am is any anchor node outside the communication range R.

There are three types of An's position: within the communication range of 0?5R; within the communication range of 0?5R~R; outside the R communication range. In this way, AHD(i,j,k) is calculated, and m has three possibilities:

Where AHD(i,j,k),m is the average hop distance between the location node and the anchor node Am estimated according to the combination of the three anchor nodes, AHDn,m is the average between the anchor node An and the anchor node Am The hop distance, AHDm is the average hop distance of the anchor node Am.

The distance P(i,j,k),m between N(i,j,k) and the anchor node Am can be calculated, then the jump between N(i,j,k) and the anchor node Am can be calculated. The number hop(i,j,k),m, is:

Suppose there are a total of n anchor nodes, so the difference between the calculated connectivity of N(i, j, k) and Nx can be expressed as

Nx selects the node with the smallest connectivity and is the node closest to Nx (ie, the positioning error is the smallest).

**3 algorithm simulation experiment**

In order to verify the feasibility of the algorithm theory, in the region of 100 m & TImes; 100 m, the proposed improved DVHop algorithm was simulated by Matlab7.0, and the experimental results were compared with the original DVHop algorithm and the reference [12] algorithm. analysis. The simulation data was run 50 times at random and finally averaged.

3.1 Ranging error

The ranging error is the difference between the estimated distance between the nodes and the actual distance. In the area of â€‹â€‹100 m & TImes; 100 m, 100 nodes are randomly distributed for simulation experiments. Some of them are anchor nodes, which are nodes that can know their own location information, and the anchor nodes and unknown nodes have the same communication radius. By setting different anchor node ratios and node communication radii, the effect of the improved algorithm and the original DVHop algorithm on the ranging error is compared. Figure 3 shows the ranging error when the communication radius is 10 m, and Figure 4 shows the ranging error when the communication radius is 20 m.

Figure 3 Ranging error when the communication radius is 10 m

Figure 4 Ranging error when the communication radius is 20 m

Under the same conditions, the improved ranging error is always lower than the original DVHop algorithm, and different communication radii will produce different results for the ranging error. In Figure 3, the communication radius is 10 m, and the improved algorithm average ranging error is 1.45 m lower than the original algorithm; in Figure 4, the communication radius is 20 m, and the improved algorithm average ranging error is 1.67 m lower than the original algorithm. This is because as the communication radius changes, it affects the number of hops between nodes and the average hop distance. Since the improved algorithm replaces the average hop distance of a single node with the average hop distance of the whole network, the estimation of the average hop distance is more accurate, and the estimation distance is more accurate, and the closer to the actual distance.

3.2 Positioning error

LocalizaTIon Error (LE) refers to the difference between the estimated coordinates and the actual coordinates measured by the positioning algorithm. Dividing this difference by the communication radius of the node is the positioning error rate. The calculation method is as follows:

Where (x, y) is the actual coordinate of the unknown node, (xi, yi) is the coordinate estimated by the positioning algorithm; R is the communication radius of the node.

Figure 5 and Figure 6 show the comparison results of the positioning error when the total number of nodes is 100 and 300 and the communication radius of the node is 10 m. The algorithm in the improved algorithm, DVHop algorithm and reference [12] have different anchor nodes. . It can be seen from the two graphs that the positioning error rate of the improved algorithm is lower than that of the DVHop algorithm and the reference [12] under the same radius and anchor node environment. However, in the case of a low proportion of anchor nodes, the positioning error of the nodes is large. This is because when the anchor node is small, the distance between the unknown node and the anchor node becomes far, resulting in a large error in calculating the average distance. Therefore, as the proportion of anchor nodes increases, the positioning error can be effectively reduced.

In Figure 5, when the proportion of anchor nodes is 30%, the positioning error rate of DVHop is 43.25%, and the positioning error rate of reference algorithm [12] is 33.37%, and the positioning error rate of the improved algorithm is 28.34%. In Fig. 6, when the proportion of the anchor node is 30%, the positioning error rate of DVHop is 26.89%, and the positioning error rate of the reference algorithm [12] is 14.95%, and the positioning error rate of the improved algorithm is 10.21%. This shows that the improved algorithm of this paper is better than the other two algorithms. This is because in reference [12], only the influence of the average hop distance on the positioning error is considered, and the improved algorithm in this paper considers the improvement of the average hop distance and the selection of the anchor node by using different connectivity. , so that its positioning error is further reduced.

Figure 5 Positioning accuracy when the total number of nodes is 100

Figure 6 Positioning accuracy when the total number of nodes is 300

**Conclusion**

This paper first introduces the basic idea of â€‹â€‹the DVHop algorithm, and proposes two improvements for the shortcomings of the classic DVHop algorithm:

The average hop distance estimated by a single anchor node replaces the average hop distance of the whole network, which causes a large error. Therefore, the average hop distance is corrected by the mean value of the average hop distance of the whole network and the average hop distance estimated by a single anchor node;

According to the difference of connectivity, the three optimal anchor nodes are selected for trilateral positioning calculation to improve the positioning accuracy.

The simulation experiment data shows that the improved algorithm reduces the ranging error and further reduces the positioning error rate, thus improving the positioning accuracy. And in the process of improvement, no hardware costs were added.

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