Discussion on the Apit location algorithm

Discussion on the Apit location algorithm

"Abstract" in the research of node location mechanism of wireless sensor network, the location technology based on distance Independent has been developed rapidly, in which the Apit positioning technology based on overlapping region is highly accurate in the real environment, and is widely researched and applied.

"keywords" wireless sensor network; location algorithm; APIT;

Body

In many applications in the sensing network, the user is generally concerned about an important issue, that is, the specific location or area at a particular time. For example, target tracking, intrusion detection, environmental monitoring, etc., if you do not know the location of the sensor itself, the perceived data is meaningless. Therefore, the sensor network and the single must know the location of their own to be able to effectively explain the location of the detected objects, so as to achieve the positioning of external targets, tracking and so on.

As a new technology, wireless sensor network has many challenging research topics, positioning technology is one of them, positioning is also the basis and premise of most applications.

At present, there are two main types of positioning technology: location technology and non-ranging positioning technology.

Based on the location technology of the geometric problem, the location of the known node, the location of the other nodes, the more commonly used method is the three-side positioning and angle positioning, this kind of algorithm is relatively simple, easy to achieve, but they are affected by electromagnetic interference, multipath interference and other factors.

Based on the non-ranging location technology, it is not necessary to use these infrastructures to measure the distance and angle between the location node and the Beacon node, only by measuring the unknown node's connectivity or the number of hops between unknown nodes. Greatly reduces the dependence on the environment. In this article, I selected the representative Apit localization algorithm to discuss.

Apit Positioning algorithm

1. Initial

The theoretical basis of the APIT (approximate pit) localization algorithm is the best triangular interior point test method PIT (Perfect point-in-triangulation test).

The pit theory is to determine if M is in the triangle ABC, if there is a direction, M points along this direction will be away from or close to the three vertices of the triangle ABC, then M is in the triangle ABC, otherwise it is located outside the triangle ABC.

2. Optimization

However, most of the nodes in the wireless sensor network are still, and it is not possible to test the triangle in the same way as mentioned above, in order to perform the pit test in the static network, the Apit test is defined.

The most critical step in the Apit positioning algorithm is to test whether an unknown node is inside a triangle composed of three beacon nodes. The Apit algorithm is based on the improvement of the pit test principle, which can be used to judge whether to stay away from the Beacon node by using the high node density and the propagation characteristics of wireless information. Usually in a given direction, the farther away a node is from the Beacon node, the weaker the received signal strength is. Emulate the node movement of the pit test by exchanging information with the neighbor node. For example:

In Figure A, the location unknown node m through the exchange of information with the Neighbor Node 1, learned that if they move to Node 1, will be away from Beacon B and C, but will be close to Beacon Node A, also by the Neighbor node 2,3,4 exchange information, and finally determine itself in the triangle ABC.

In Figure B, when the node is known by the Neighbor Node 2, it will be away from the Beacon node ABC at the same time, so judging itself is not in the triangle ABC.

3. Confirm

In the Apit algorithm, an unknown node selects three adjacent beacon nodes, if through the test found themselves in their composition of the triangle, it is considered that the centroid of the triangle is the location of the unknown node, and then further choose the combination of different Beacon node repeat test, until the end of all combinations or to achieve the desired positioning accuracy Finally, the centroid of the intersection containing all triangles of the target node is computed and is the final position of the unknown node.

SOURCE Analysis

This experiment is compiled with MATLAB program:

1. Initialize the layout

c_random (Area,node n,anchors_n,gps_error): Parameters: Region, number of nodes, Beacon node, GPS error. function C_random (area,nodes_n,anchors_n,gps_error)% deploy the nodes over a Cshaped Region% area:the Sensing Region [ $  +  +  the]% the side is200m-Long, x= +, y= +, y= the: The Edge of C-shaped Region%nodes_n:the Number of nodes%anchors_n:the Number of anchors%ifanchors_n<1, it means the ratio;%ifAnchors_n>1, it means the number% gps_error:the Max location error of anchor raised by GPS,default  is 0;%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~% C_random ([ $  +  +  the], Max,0.1) C_random ([ +, -, +,0], -,0.2);

240 nodes, 48 of which are anchor nodes

Red * indicates anchor node, blue o indicates unknown node

2. Calculate unknown node coordinates

ifneighboring_anchor_n>=3Gridmap=zeros (row_n,col_n); Grid_covered_flag=zeros (row_n,col_n);  forA=1: neighboring_anchor_n-2                 forb=a+1: neighboring_anchor_n-1                     forc=b+1: Neighboring_anchor_n%Determine if unknown node i is inside the triangle ABC% approximate p.i.t Test:"If No neighbor of M are further from/close to all three anchors A, B and C simultaneously,% M assumes that it isInside triangle ABC. Otherwise,m assumes it resides outside the triangle."Neighboring_node_index=setdiff (Find (Neighbor_matrix (i,:) = =1), Neighboring_anchor_index ([a B c])); NEIGHBORING_NODE_RSS_OF_ABC=Neighbor_rss (Neighboring_node_index,neighboring_anchor_index ([a B c])); In_out_judge=neighboring_node_rss_of_abc>repmat (Neighbor_rss (I,neighboring_anchor_index ([a b c]), Length (Neighboring_node _index),1); ifAny (sum (transpose (in_out_judge)) = =0|sum (Transpose (in_out_judge)) = =3)%outside Grid_in_triangle_abc=inpolygon (centroid_x,centroid_y,all_nodes.estimated (Neighboring_anchor_index ([a b c]),1), all_nodes.estimated (Neighboring_anchor_index ([a b c]),2));%covered by triangular ABC to network GRIDMAP=gridmap-grid_in_triangle_abc; Else%inside Grid_in_triangle_abc=inpolygon (centroid_x,centroid_y,all_nodes.estimated (Neighboring_anchor_index ([a b c]),1), all_nodes.estimated (Neighboring_anchor_index ([a b c]),2));%covered by triangular ABC to network GRIDMAP=gridmap+grid_in_triangle_abc; End Grid_covered_flag=grid_covered_flag|grid_in_triangle_abc; End End End

3. Positioning error

Red * indicates anchor node

Blue o indicates the estimated location of unknown nodes

Black o indicates an unknown node that cannot be positioned

Blue-Indicates the location error of the unknown node (the estimated and true position of the connected unknown node)

Altogether 300 nodes: 60 anchor nodes, 240 unknown nodes, 0 unknown nodes that cannot be located

Positioning error of 0.17819

Algorithm Summary

The specific steps for Apit positioning are as follows:

L Collect Information: unknown node collects information from neighboring beacon nodes.

L Apit Test: Test whether the unknown node is inside the triangle of different beacon node combinations.

Calculate overlapping areas: the triangles containing the unknown nodes are counted, and the overlapping regions of all triangles are computed.

L Calculate Unknown node position: calculates the centroid position of the overlapping area as the position of the position node.

Outlook and Development

In the periphery of the whole wireless sensor network, the number of sensors is relatively small, the Beacon node is less, so the number of triangles will be reduced. When the Apit test is positioned, there is too much deviation between the actual position and the positioning position due to the overlap area being too large. , is a case of using the Apit positioning error is large.

In order to improve the positioning accuracy of wireless sensor networks, the apit algorithm needs to be improved, and there are many experts and scholars have discussed, here are only two examples:

L Divide the triangle into 4 or 6 perpendicular bisector, and compare the intensity of each target node to receive the target node signal, and judge the target node in which small interval.

L through any beacon node to the other two beacon nodes in the line perpendicular to the vertical intersection, by comparing the distance between the letter punctuation to the intersection point and his relationship with the location node, the initial judgment unknown node unknown, at the same time, through the weighted centroid location algorithm to obtain the accurate estimation of unknown nodes.

Reference documents

"1" Liu Weirong, why. Internet of things and wireless sensor networks

"2" Tangminghu, Zhangchanghong. Apit location algorithm for wireless sensor networks

"3" Zhang Dongdong, the realization of common positioning technology

"4" Haizi, www.cnblogs.com/dolphin0520

"5" Dai Tianhong, Haopeng Li, node location of wireless sensor network based on improved Apit algorithm

"6" Yang Lingyun, Feng Yuhong, apit positioning improvement algorithm for vertical intersections

Discussion on the Apit location algorithm