CN103533643A - Three-dimensional APIT (approximate point-in-triangulation test) location algorithm for wireless sensor network - Google Patents

Abstract

The invention provides a three-dimensional APIT (approximate point-in-triangulation test) location algorithm for node location of a wireless sensor network and belongs to the technical field of wireless sensor network application. According to the three-dimensional APIT location algorithm, a fringe effect of a three-dimensional APIT algorithm, which is caused by the uneven distribution of nodes, is remedied by utilizing a multi-hop mechanism of a three-dimensional WD-DVHOP algorithm. When the number of anchor nodes within a one-hop range of unknown nodes is smaller than 3, the three-dimensional WD-DVHOP location algorithm is called, and therefore, nodes which cannot be located by the three-dimensional APIT algorithm are eliminated. Moreover, by adopting a method of performing weighted computation on the barycenter of a polyhedron formed by encircling anchor ball intersections, In-To-Out-Error and Out-To-In-error misjudgments generated by point-in-tetrahedron test in the three-dimensional APIT algorithm are remedied. The three-dimensional APIT location algorithm has the advantages that the node location coverage rate in the wireless sensor network reaches 100 percent, and the location error is low.

Description

Three-dimensional APIT wireless sensor network positioning algorithm

technical field

The invention relates to a three-dimensional APIT positioning algorithm of a wireless sensor network. The invention belongs to the technical field of wireless sensor network application.

Background technique

Positioning is to determine the location of the event or the location information of the node that collects the data, which is one of the functions of the wireless sensor network. Location information is an indispensable part of data collected by sensor nodes, and monitoring messages without location information are meaningless. The positioning technology of wireless sensor network can be divided into positioning algorithm based on ranging and non-ranging positioning algorithm according to the positioning mechanism. The positioning algorithm based on ranging is not widely used because of the large hardware overhead. The non-ranging positioning algorithm relies on a small number of anchor nodes with known positions in the network, and estimates the positions of all unknown nodes in the network through limited communication between neighbor nodes and a certain positioning mechanism. The overhead is small, but the error is large.

The positioning algorithms in wireless sensor networks are currently mainly concentrated in two-dimensional positioning algorithms, and there are few effective three-dimensional positioning algorithms, and most of them are obtained on the basis of existing two-dimensional positioning algorithms; due to the defects of two-dimensional positioning algorithms , resulting in larger errors in the extended 3D positioning algorithm. Some other three-dimensional positioning algorithms are pseudo-three-dimensional positioning algorithms based on some three-dimensional maps, and the cost is relatively large.

Contents of the invention

The present invention mainly aims at the above defects, introduces the 3D-DVHOP multi-hop mechanism into the APIT positioning algorithm, and proposes a three-dimensional MHWC-APIT (TheMulti-Hop and Weighted CentroidAPIT) positioning algorithm. Design scheme of the present invention is as follows:

1. Two kinds of misjudgment processing of 3D APIT algorithm

The centroid of the area enclosed by the intersection of anchor spheres is calculated by a weighted method, instead of the tetrahedron test in the 3D APIT. The specific implementation is as follows:

Unknown nodes take 3 arbitrarily from neighbor anchor nodes. Take the anchor node as the center and the communication radius as the radius to form 3 anchor balls. Find the center of gravity of the intersection of three anchor balls. Second, continue to select the other 3 anchor nodes until all combinations are exhausted. Finally, take the mean of all barycenters as the coordinates of unknown nodes.

When calculating the center of gravity of the intersection area of the three anchor balls, the method of converting the three-dimensional space into a two-dimensional space is adopted. Project the three anchor balls to the XOY, YOZ, and XOZ planes respectively, and the radius of the obtained circle remains unchanged. Therefore, the result of plane positioning can truly reflect the spatial position of the unknown node.

In Figure 1, A, B, and C are the projections of three anchor nodes in the three-dimensional space on the XOY plane, and the projection N of the unknown node is located in the area formed by the intersection of the anchor circles, and then the area formed by the intersection of the anchor circles can be calculated. Weight the centroid to get the projected coordinates of the unknown node in the XOY plane. Similarly, the coordinates projected in the YOZ and XOZ planes can be obtained. The specific calculation is as follows:

First, in the XOY plane, the weighted centroid of the area formed by the intersection of the anchor circles is calculated, and the coordinates of the projection in the XOY plane are shown in formula 1

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; XOY</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, (x _ij , y _ij ) _XOY represents the centroid of the intersection of anchor circles formed by projecting the jth anchor node combination of unknown node i into the XOY plane. w1, w2, w3 are the weights of intersection points 1, 2, and 3. Since the larger the distance, the smaller the signal strength, the corresponding weight should be smaller. Therefore, this algorithm chooses the reciprocal of the distance sum as the weight.

After obtaining the projection coordinates (X _ij , y _ij ) _XOY of the unknown node N in the XOY plane, (x _ij , z _ij ) _XOZ and (Y _ij , z _ij ) _YOZ can be obtained.

Based on coordinates calculated in three planes. The coordinates calculated by the unknown node i under the jth anchor node combination can be obtained, as shown in formula 2.

$<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; xij</span>}}_{\mathrm{<span\; class="notranslate">\; XOY</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; xij</span>}}_{\mathrm{<span\; class="notranslate">\; XZ</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; xij</span>}}_{\mathrm{<span\; class="notranslate">\; XOY</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; xij</span>}}_{\mathrm{<span\; class="notranslate">\; XZ</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; xij</span>}}_{\mathrm{<span\; class="notranslate">\; XOY</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; xij</span>}}_{\mathrm{<span\; class="notranslate">\; XZ</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Finally, continue to select the other three anchor nodes, and calculate the centroid of the area enclosed by the intersection points of the anchor balls until all combinations are exhausted. Then the coordinates of the final unknown node i can be expressed as Equation 3.

$<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, N is the number of anchor nodes.

2. Processing of edge effects of 3D APIT algorithm

When the nodes are randomly deployed, the distribution is uneven, which will cause some nodes at the edge of the network to have less than 3 anchor nodes within one hop range, so that they cannot be located. This phenomenon is called the edge effect. In order to solve this problem, the present invention introduces the multi-hop mechanism of the 3D WD-DVHOP algorithm into the 3D APIT algorithm. When the number of anchor nodes within a hop range is less than 3, the 3D WD-DVHOP is called for positioning. The three-dimensional WD-DVHOP positioning algorithm is an improved algorithm for the three-dimensional DV-HOP algorithm, and its positioning error has been greatly improved.

Description of drawings

Figure 1 Schematic diagram of XOY plane projection

Figure 2 3D MHWC-APIT algorithm flow chart

Figure 3 Schematic diagram of node deployment

Figure 4 is the variation curve of the average positioning error of various positioning algorithms with the number of anchor nodes

Detailed ways

The present invention uses Matlab to implement the three-dimensional MHWC-APIT algorithm, and the specific process is as follows:

(1) Set 100 wireless sensor nodes so that they are randomly distributed in the horizontal plane area of 100m×100m×100m, and check a random distribution result of 100 nodes after extracting the TCL file generated by NS-2 through Matlab.

1) Anchor nodes broadcast information, and unknown nodes record anchor node information.

2) If the number of anchor nodes around the unknown node is greater than or equal to 3, then the anchor ball intersection weighting algorithm is executed. Choose three randomly from all the anchor nodes within the range of one hop, project the formed anchor balls to the XOY, XOZ and YOZ planes respectively, execute the anchor circle intersection weighting algorithm in the three planes, and then select the other three anchor nodes, until exhausted. The average value of the centroids of the intersection of these anchor balls is used as the coordinates of the unknown nodes.

3) For the case where the number of neighbor anchor nodes is less than 3, call the three-dimensional WD-DVHOP algorithm for calculation. Use the multi-hop mechanism of the DV-HOP algorithm to find anchor nodes from the anchor nodes beyond the range of one hop.

The specific flow chart of the algorithm is shown in Figure 2.

In order to verify the performance of the extended 3D MHWC-APIT, the 3D MHWC-APIT and 3D APIT algorithms and other algorithms are simulated using Matlab. And compare the simulation results with other algorithms. The simulation analyzes the anchor node ratio, the total number of nodes and the communication radius and other parameters. Assume that the number of simulations is 1000, the simulation area is 100m*100m*100m, and nodes are randomly generated in the network. The average positioning error of all nodes in the network is used as the measurement standard. Calculation of the average positioning error, such as 4.

$\mathrm{<span\; class="notranslate">\; ErrEvg</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}\frac{\sqrt{{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}{\mathrm{<span\; class="notranslate">\; R</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

为求的节点i的坐标位置，(x_i，y_i，z_i)为节点i的实际位置，N为未知节点的总数。in,

To find the coordinate position of node i, (x _i , y _i , z _i ) is the actual position of node i, and N is the total number of unknown nodes.

Figure 3 shows the deployment diagram of the nodes.

Figure 4 shows how the positioning error of the 3D MHWC-APIT algorithm and other algorithms varies with the number of anchor nodes. It can be seen that the error of the 3D MHWC-APIT algorithm is much smaller than other positioning algorithms.

Claims (1)

1. The three-dimensional APIT wireless sensor network three-dimensional positioning algorithm is characterized by comprising the following specific steps:

1) the multi-hop mechanism of the WD-DVHOP algorithm is utilized to thoroughly eliminate the nodes which cannot be positioned and are generated by the edge effect in the APIT algorithm. So that all nodes can be successfully located.

2) And using the average value of the mass centers of the anchor ball intersections as the coordinates of the unknown nodes. And In-To-Out-Error and Out-To-In-Error misjudgments generated by the tetrahedral interior point test In the three-dimensional APIT algorithm are thoroughly eliminated.

3) When the mass center of the anchor sphere intersection is calculated, three anchor spheres, unknown nodes and anchor nodes are projected to XOY, YOZ and ZOX respectively. The three-dimensional space is converted into the anchor circle intersection of the two-dimensional space, and the complexity of the three-dimensional space calculation is simplified.

4) And calculating the intersection of the anchor circles by adopting a weighting method, and adopting the reciprocal of the distance sum as a weight, wherein the longer the distance is, the smaller the influence on the unknown node is.

Images