CN101246211A - Circulating trihedral combination measuring method of weight triangle selection method based on circle - Google Patents

Abstract

The invention provides a circular three sides combined measure method which is based on weight triangle choice method. 1) randomly choosing two nodes A and B, calculating side a of segment AB, and calculating a<SUP>2</SUP>; 2) calculating x*AB; 3) repeating step 1 and step 2, calculating square of every side, and ever x*AB; 4) randomly choosing three nodes A, B and C, which are separately corresponding side a, b and c, wherein a is the shortest side; 5) if a<SUP>2</SUP>+c<SUP>2</SUP>-b<SUP>2</SUP>>0 and a<SUP>2</SUP>+b<SUP>2</SUP>-c<SUP>2</SUP>>0 and <=xa, then the triangle Delta ABC is a triangle with big weight; 6) calculating one vertex of weighing polygonal; 7) repeating the step 4,5 and 6, calculating vertexes of every weighing polygonal; 8) calculating weight centroid position of polygonal according to weight centroid method, estimated coordinate figure of unknown node: (IX,IY)=(Sigma <SUP>m</SUP><SUB>k=1</SUB>IX<SUB>k</SUB>/l,Sigma <SUP>m</SUP><SUB>k=1</SUB>IY<SUB>k</SUB>/l). Compared with IACT, the energy consumption of node is reduced further without reducing positioning precision.

Description

Circulation three limit multiple measurement methods based on the weight triangle selection method of circle

(1) technical field

(2) background technology is in the application of sensor network, and having only the position when node and perceived object is as can be known, and the information that node obtains is just meaningful.Therefore, node locating is one of gordian technique of sensor network.

Now existing many scholars both domestic and external have proposed a lot of location algorithms, but on overall, well both balances between bearing accuracy and the energy consumption cost, the bearing accuracy height often is accompanied by algorithm high complexity and the high cost of communicating by letter.Sensor node often adopts received signal intensity (RSSI, Received Signal StrengthIndex) technology, time of arrival (toa) (TOA, Time Of Arrival) technology, signal arrival time difference (TDOA, Time Difference of Arrival) technology and signal arrival angle (AOA, Angle Of Arrival) technology is carried out internodal range finding.On the basis of finding range between above node, sensor network can adopt APS, and AHLoS algorithm, trilateration, Lateration algorithm, circulation three limit multiple measurement methods (ACT) and improved circulation three limit multiple measurement method (IACT) scheduling algorithms carry out the location of unknown node.

Trilateration is the distance of the coordinate and unknown node to three beaconing nodes of known three beaconing nodes, asks the coordinate of unknown node.In order further to improve the bearing accuracy of trilateration, circulation three limit multiple measurement methods have been proposed in sensor network location algorithm and the correlation technique research (the PhD dissertation .2006 of University Of Chongqing).It obtains polygonal summit by the leg-of-mutton center of calculating any three beaconing nodes and forming, and utilizes centroid method location unknown node again.In order further to reduce the complexity and the communication cost of algorithm, improved circulation three limit multiple measurement methods have been proposed again, it utilizes the tan value at leg-of-mutton angle to select weight triangle as weight, and only selects m the bigger triangle of weight to calculate and reduce computational costs and communication cost.But the computation complexity of IACT remains n ³, computational costs is still higher.Therefore, we need seek the lower location algorithm of a kind of expense, also will guarantee the bearing accuracy of algorithm simultaneously.

(3) summary of the invention

The object of the present invention is to provide a kind of expense lower, simultaneously can guarantee the circulation three limit multiple measurement methods based on the weight triangle selection method of circle of bearing accuracy.

The object of the present invention is achieved like this:

1. optional two node A and B (

Plant and select selection scheme), ask the length of side a of line segment AB, and calculate a ²

2. calculate xAB (x=cot α, α are the minimum angle of weight triangle, and α=arccot (1.5), x set according to bearing accuracy) before node lays;

3. repeat 1 and 2 the step, calculate all limits (

The bar limit) square and all xAB;

4. optional three node A, B and C (

Kind of selection scheme), corresponding sides a respectively, b and c, wherein a is minor face;

5. if a ²+ c ²-b ²＞0 and a ²+ b ²-c ²＞0 and b≤xa, then triangle △ ABC is a triangle with big weight;

6. calculate the polygonal summit of weight;

7. repeating step 4,5 and 6, calculate the polygonal summit of all weights;

8. utilize the weight gravity model appoach to calculate the weight centre of gravity place of l limit shape (total is selected l high weight triangle that satisfies condition), i.e. the estimated coordinates value of unknown node:

$(\mathrm{IX},\mathrm{IY})=({\mathrm{\&Sigma;}}_{k=1}^{m}I{X}_k/l,{\mathrm{\&Sigma;}}_{k=1}^{m}I{Y}_k/l).$

Advantage of the present invention is verified by following analysis:

1, the mathematical analysis of CBACT algorithm performance

Because the time complexity that plus-minus method calculates is far below multiplication and division computing and trigonometric function operation, so do not consider the plus-minus method complexity of calculation here.The computational costs of CBACT algorithm and Lateration algorithm is equal substantially, well below ACT and IACT algorithm.Multiplication and division computing in the ACT algorithm is about 52 times, and trigonometric function operation is Inferior.The IACT algorithm is owing to having adopted different weight angle function, so the trigonometric function of having avoided carrying out a large amount of inverses and root computing calculates.The multiplication and division computing of IACT algorithm is

Inferior, there is not trigonometric function operation.Based on circular weight triangle selection algorithm,

There is not trigonometric function operation.Obviously, the computational complexity of this algorithm is far below the IACT algorithm.Fig. 1 has provided the comparison of several algorithm complexities when m=20, α=35 °.The result who analyzes shows that the complicacy of ACT algorithm is the highest, and when having 12 beaconing nodes, the calculation times of ACT algorithm is near ten thousand times, and computational costs is very high.Compare with ACT, IACT has reduced computational costs to a great extent, but the computation complexity of IACT remains n ³, computational costs is still higher.It is n that computation complexity is reduced to ²Compare with IACT, greatly reduced computational costs.

2, the simulation analysis of CBACT algorithm performance

In order to estimate this algorithm, utilize the method for Digital Simulation that algorithm IACT algorithm is compared.The network model of simulation analysis is provided with as follows:

1) all sensor node and beaconing nodes all are randomly dispersed in the square area of 50m * 50m;

2) number N of beaconing nodes is no less than 5, and each beaconing nodes all contains ID number and the positional information of self, and all nodes all have computing power and range capability;

3) do not have barrier in the sensors field, all nodes that therefore are positioned within the communication radius scope all can be realized communication;

4) in the IACT algorithm, the trilateration number of combinations of choosing after the weighted value ordering is m=20;

5) in algorithm, each communication radius is chosen as 50 .

6) the distance measuring noises standard deviation is set at 20% of range finding at random.

In emulation, that has studied unknown node on average can detect the influence of beaconing nodes number to the node locating error.In order to guarantee the reliability of simulation result, two emulation all move 1000 times, obtain the mean value of positioning error then.

In simulation study, utilize E _LAs the evaluation criterion of positioning error size, E _LCalculate by following formula:

$E_L=\sqrt{{(\mathrm{IX}-X_{\mathrm{actual}})}^2+{(\mathrm{IY}-Y_{\mathrm{actual}})}^2}$

In the formula, (IX is IY) with (X _Actual, Y _Actual) be respectively the estimated position and the physical location of unknown node.For ease of comparing, all positioning errors are absolute error.

1) can detect the beaconing nodes number changes affect positioning

In first simulating scheme, this simulation analysis can detect the beaconing nodes number and change affect positioning.As shown in Figure 2, the CBACT algorithm is not subjected to monitor the influence of beaconing nodes, this means that this algorithm can obviously reduce network to the beaconing nodes density requirements.The IACT algorithm increases along with detecting the node number, and positioning error reduces, and when arriving a certain value, positioning error tends towards stability.The critical transitions point of IACT algorithm is 7.When the irregular layout of beaconing nodes, emulation also can obtain similar conclusion.Compare the little and quite stable of CBACT Algorithm Error value with the IACT algorithm.Obviously, although select the method difference of weight node,, selected enough weight triangles to carry out the location of nodes of locations equally.Therefore, has extraordinary bearing accuracy.

2) distance measuring noises changes affect positioning

Second simulating scheme studied distance measuring noises to affect positioning.At this moment on average can detect the beaconing nodes number and be made as 9.The bearing accuracy of two kinds of algorithms and the relation between the distance measuring noises as shown in Figure 3, the positioning error of Centroid algorithm and distance measuring noises be relation not significantly.CBACT algorithm, IACT algorithm and Lateration algorithm all are the increases along with distance measuring noises, and error is also increasing, but the positioning error of CBACT algorithm be significantly less than the back both.Be that the CBACT algorithm has better robustness.

3) comparison of CBACT algorithm and IACT Algorithm Error

When distance measuring noises is 20%, to the comparison (as shown in Figure 4) of the positioning error of CBACT algorithm and IACT algorithm.Compare with the IACT algorithm, it is little that the CBACT algorithm is subjected to monitor the influence of beaconing nodes number.

At the computational complexity problem that the IACT algorithm exists, the present invention proposes a kind of location algorithm of low computational complexity---based on the circulation three limit multiple measurement methods of circle.By using more simple high weight triangle selection method, this algorithm has reduced the weight computing of the triangle in the IACT algorithm, under the prerequisite that does not influence bearing accuracy, with computation complexity by n ³Dropped to n ²Communication overhead when in addition, this algorithm is located is similar to the IACT algorithm.Therefore, compare with IACT, CBACT has further reduced the energy consumption of node under the prerequisite that does not reduce bearing accuracy.

(4) description of drawings

Fig. 1 is that algorithm complexity compares;

Fig. 2 can detect the beaconing nodes number positioning error is influenced;

Fig. 3 is that the distance measuring noises variation influences positioning error;

Fig. 4 is the comparison of CBACT algorithm and IACT Algorithm Error.

(5) embodiment

For example the present invention is done description in more detail below in conjunction with accompanying drawing:

A kind of circulation three limit multiple measurement methods of the weight triangle selection method based on circle, it comprises following concrete steps:

1. optional two node A and B (

Plant and select selection scheme), ask the length of side a of line segment AB, and calculate a ²

2. calculate xAB (x=cot α, α are the minimum angle of weight triangle, and α=arccot (1.5), x set according to bearing accuracy) before node lays;

3. repeat 1 and 2 the step, calculate all limits ( The bar limit) square and all xAB;

4. optional three node A, B and C (

Kind of selection scheme), corresponding sides a respectively, b and c, wherein a is minor face;

5. if a ²+ c ²-b ²＞0 and a ²+ b ²-c ²＞0 and b≤xa, then triangle △ ABC is a triangle with big weight;

6. calculate the polygonal summit of weight;

7. repeating step 4,5 and 6, calculate the polygonal summit of all weights;

8. utilize the weight gravity model appoach to calculate the weight centre of gravity place of l limit shape (total is selected l high weight triangle that satisfies condition), i.e. the estimated coordinates value of unknown node:

$(\mathrm{IX},\mathrm{IY})=({\mathrm{\&Sigma;}}_{k=1}^m{\mathrm{IX}}_k/l,{\mathrm{\&Sigma;}}_{k=1}^m{\mathrm{IY}}_k/l).$

Claims (1)

1, a kind of circulation three limit multiple measurement methods of the weight triangle selection method based on circle is characterized in that:

1) optional two node A and B ask the length of side a of line segment AB, and calculate a ²

2) calculate xAB, wherein x=cot α, α are that minimum angle, α=arc cot (1.5), the x of weight triangle sets according to bearing accuracy before node lays;

3) repeated for 1 and 2 steps, calculate all limits square and all xAB;

4) optional three node A, B and C, corresponding sides a respectively, b and c, wherein a is minor face;

5) if a ²+ c ²-b ²＞0 and a ²+ b ²-c ²＞0 and b≤xa, then triangle △ ABC is a triangle with big weight;

6) calculate the polygonal summit of weight;

7) repeating step 4,5 and 6, calculate the polygonal summit of all weights;

8) utilize the weight gravity model appoach to calculate the weight centre of gravity place of l limit shape, i.e. the estimated coordinates value of unknown node:

$(\mathrm{IX},\mathrm{IY})=({\mathrm{\&Sigma;}}_{k=1}^m{\mathrm{IX}}_k/l,{\mathrm{\&Sigma;}}_{k=1}^{m}I{Y}_k/l).$

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