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. Belonging to the technical field of wireless sensor network application.

Background

Positioning is information of node position for determining the position of event occurrence or collecting data, which is one of wireless sensor network functions. The position information is an indispensable part in the data collected by the sensor nodes, and the monitoring information without the position information has no meaning. The positioning technology of the wireless sensor network can be divided into a ranging-based positioning algorithm and a non-ranging positioning algorithm according to a positioning mechanism. Ranging-based positioning algorithms are not widely adopted because of the large hardware overhead. The non-ranging positioning algorithm estimates the positions of all unknown nodes in the network through limited communication between neighboring nodes and a certain positioning mechanism by means of a small number of anchor nodes with known positions in the network. The overhead is small but the error is large.

Positioning algorithms in a wireless sensor network are mainly concentrated on two-dimensional positioning algorithms at present, and effective three-dimensional positioning algorithms are few and are mostly obtained by expanding on the basis of the existing two-dimensional positioning algorithms; due to the defects of the two-dimensional positioning algorithm, the error of the expanded three-dimensional positioning algorithm is large. And the other three-dimensional positioning algorithms are pseudo three-dimensional positioning algorithms based on three-dimensional maps, so that the cost is high.

Disclosure of Invention

The invention mainly aims at the defects, introduces a 3D-DVHOP multi-Hop mechanism into an APIT positioning algorithm, and provides a three-dimensional MHWC-APIT (the Multi-Hop and Weighted Central identification APIT) positioning algorithm. The design scheme of the invention is as follows:

1. two misjudgment processes of three-dimensional APIT algorithm

And calculating the mass center of the region surrounded by the intersection of the anchor balls by a weighting method to replace a tetrahedron test in the three-dimensional APIT. The concrete implementation is as follows:

the unknown node arbitrarily takes out 3 from the neighbor anchor nodes. And (3) respectively taking the anchor nodes as the circle center and the communication radius as the radius to form a ball. And (5) calculating the gravity center of the intersection of the 3 anchor balls. Second, the selection of the other 3 anchor nodes continues until all combinations are exhausted. Finally, all the mean values of the centers of gravity are taken as the coordinates of the unknown nodes.

When the gravity center of the intersection region of the 3 anchor balls is calculated, a method for converting a three-dimensional space into a two-dimensional space is adopted. And 3 anchor balls are respectively projected to XOY, YOZ and XOZ planes, and the size of the radius of the obtained circle is unchanged, so that the spatial position condition of an unknown node can be truly reflected by the result of plane positioning.

In fig. 1, a, B, and C are projections of 3 anchor nodes in a three-dimensional space on an XOY plane, respectively, a projection N of an unknown node is located in a region formed by intersection points of anchor circles, and then a weighted centroid can be performed on the region formed by the intersection points of the anchor circles to obtain coordinates of the projection of the unknown node on the XOY plane. Similarly, the coordinates of the projections in the YOZ and XOZ planes can be determined. The specific calculation is as follows:

firstly, in an XOY plane, weighted centroid calculation is carried out on an area formed by intersection points of anchor circles, and coordinates projected in the XOY plane are as formula 1

${(x_{\mathrm{ij}},y_{\mathrm{ij}})}_{\mathrm{XOY}}=(\frac{w_1{x}_1+w_2{x}_2+w_3{x}_3}{w_1+w_2+w_3},\frac{w_1{y}_1+w_2{y}_2+w_3{y}_3}{w_1+w_2+w_3})---\left(1\right)$

Wherein (x)_ij，y_ij)_XOYThe jth anchor node combination representing the unknown node i is projected into the XOY plane, forming the centroid of the anchor circle intersection. w1, w2, w3 are weights of the intersection points 1, 2, 3. Since the larger the distance, the smaller the signal strength, the smaller the corresponding weight should be. Therefore, the present algorithm selects the reciprocal of the distance sum as a weight.

The projection coordinates (X) of the unknown node N in the XOY plane are obtained_ij，y_ij)_XOYThen, (x) can be obtained_ij，z_ij)_XOZAnd (Y)_ij，z_ij)_YOZ。

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

$(x_{\mathrm{ij}},y_{\mathrm{ij}})=(\frac{{\mathrm{xij}}_{\mathrm{XOY}}+{\mathrm{xij}}_{\mathrm{XOZ}}}{2},\frac{{\mathrm{xij}}_{\mathrm{XOY}}+{\mathrm{xij}}_{\mathrm{XOZ}}}{2},\frac{{\mathrm{xij}}_{\mathrm{XOY}}+{\mathrm{xij}}_{\mathrm{XOZ}}}{2})---\left(2\right)$

And finally, continuously selecting other three anchor nodes, and calculating the mass center of the region surrounded by the anchor ball intersection points until all combinations are exhausted. The coordinates of the final unknown node i can be expressed as formula 3.

<math> <mrow> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <msub> <mrow> <mo>,</mo> <mi>z</mi> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>x</mi> <mi>ij</mi> </msub> </mrow> <msubsup> <mi>C</mi> <mi>N</mi> <mn>3</mn> </msubsup> </mfrac> <mo>,</mo> <mfrac> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>y</mi> <mi>ij</mi> </msub> </mrow> <msubsup> <mi>C</mi> <mi>N</mi> <mn>3</mn> </msubsup> </mfrac> <mo>,</mo> <mfrac> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>z</mi> <mi>ij</mi> </msub> </mrow> <msubsup> <mi>C</mi> <mi>N</mi> <mn>3</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein N is the number of anchor nodes.

2. Processing of edge effects for three-dimensional APIT algorithms

When nodes are deployed randomly, uneven distribution can cause the number of anchor nodes in a one-hop range of some nodes at the edge of the network to be less than 3, so that positioning cannot be carried out, and the phenomenon is called edge effect. In order to solve the problem, the invention introduces a multi-hop mechanism of a three-dimensional WD-DVHOP algorithm into the three-dimensional APIT algorithm, and when the number of anchor nodes in a hop range is less than 3, the three-dimensional WD-DVHOP is called to locate. The three-dimensional WD-DVHOP positioning algorithm is an improved algorithm aiming at the three-dimensional DV-HOP algorithm, and the positioning error is greatly improved.

Drawings

FIG. 1 is a schematic view of the XOY plane projection

FIG. 2 three-dimensional MHWC-APIT algorithm flow chart

FIG. 3 node deployment diagram

FIG. 4 is a plot of average positioning error versus number of anchor nodes for various positioning algorithms

Detailed Description

The invention adopts Matlab to implement three-dimensional MHWC-APIT algorithm, and the specific flow is as follows:

(1) 100 wireless sensor nodes are arranged to be randomly distributed in a horizontal plane area with the point of 100m multiplied by 100m, and one random distribution result of 100 nodes is checked after a TCL file generated by NS-2 is extracted by Matlab.

1) And the anchor node broadcasts information, and the unknown node records the information of the anchor node.

2) And if the number of the anchor nodes around the unknown node is more than or equal to 3, executing an anchor sphere intersection weighted algorithm. And randomly selecting three anchor nodes from all the anchor nodes in the one-hop range, projecting the formed anchor balls to XOY, XOZ and YOZ planes respectively, executing an anchor circle intersection point weighting algorithm in three planes respectively, and then selecting other three anchor nodes until all the anchor nodes are exhausted. And taking the average value of the centers of mass of intersection of the anchor balls as the coordinates of the unknown nodes.

3) And calling a three-dimensional WD-DVHOP algorithm to calculate under the condition that the number of the anchor nodes of the neighbor anchor nodes is less than 3. And searching the anchor nodes from the anchor nodes outside the one-HOP range by using the multi-HOP mechanism of the DV-HOP algorithm.

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

In order to verify the performance of the expanded three-dimensional MHWC-APIT, Matlab is adopted to simulate the three-dimensional MHWC-APIT, the three-dimensional APIT algorithm and other algorithms. And comparing the simulation result with other algorithms. And simulation analysis is respectively carried out on parameters such as anchor node proportion, node total number, communication radius and the like. Assuming that the number of simulations is 1000, and the simulation region is a region of 100m x 100m, nodes are randomly generated in the network. The average positioning error of all nodes in the network is used as a measure. Calculation of the average positioning error, as in figure 4.

<math> <mrow> <mi>ErrEvg</mi> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <mfrac> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>z</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mi>R</mi> </mfrac> </mrow> <mi>N</mi> </mfrac> <mo>&times;</mo> <mn>100</mn> <mo>%</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein,

to find the coordinate position of node i, (x)_i，y_i，z_i) Is the actual location of node i and N is the total number of unknown nodes.

Fig. 3 shows a deployment diagram of a node.

Fig. 4 shows the positioning error of the three-dimensional MHWC-APIT algorithm and other algorithms as a function of the number of anchor nodes. It can be seen that the error of the three-dimensional MHWC-APIT algorithm is much smaller than that of 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.

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