KR101163335B1 - Wireless localization method based on rssi at indoor environment and a recording medium in which a program for the method is recorded - Google Patents

Abstract

PURPOSE: A wireless positioning method based on a distance estimation method of received signal strength using trilateration and a recording medium having a program for performing the same are provided to improve position estimation accuracy. CONSTITUTION: A wireless positioning method based on a distance estimation method of received signal strength using trilateration is as follows. Three estimation distances from three anchor nodes to a blind node are calculated using signal strength received from the anchor nodes, and three actual distances are calculated using the estimation distances(S14). The volume of a tetrahedron formed by the anchor nodes and the blind node is estimated using the estimation and actual distances(S18). The errors of the estimation distances are corrected. The estimation position of the blind node is calculated using the corrected estimation distances(S22).

Description

Indoor wireless positioning method based on distance estimation method of received signal strength and recording medium recording program for implementing the method {Wireless localization method based on RSSI at indoor environment and a recording medium in which a program for the method is recorded }

The present invention relates to indoor wireless positioning technology, and more particularly, to wireless positioning using a received signal strength indicator (RSSI) method based on a range based approach, which is one of wireless positioning methods. It is about improving the accuracy of the method.

Recently, as interest in smart phones has exploded, location-based services such as augmented reality (LBS) are receiving great attention. Location-based service is possible only when the location of the user requesting the service is accurately made.

Representative wireless positioning methods proposed to date include a range-free position estimation method and a range-based position estimation method. In estimating the location of a user, an approach for estimating a location without information on the distance between a transmitter and a receiver is a range-limited location estimation method, and a cell-ID and an RFID method. On the other hand, the range-based position estimation method is a method of estimating the position based on the information on the distance between the receiver and the transmitter. GPS, trilateration, and least squares methods belong to this method.

The GPS method provides location information with a certain level of accuracy in an outdoor environment, but positioning is difficult in the room because the satellite obtains location information, and the terminal is expensive. For this reason, wireless local area network (WLAN), ultra wide band (UWB) communication, and wireless sensor network (WSN) have been proposed for wireless indoor positioning. The study was conducted. Among them, WSN is a method of securing many small sensor nodes and using them for positioning. In order to take advantage of this WSN, it is important to secure a low-cost sensor node and to install a large number of sensor nodes in a location that requires positioning. Zigbee technology is a low-cost, low-power, low-speed, short-range wireless communication technology based on IEEE 802.11. It has a very simple hardware structure, which makes it possible to construct an inexpensive sensor network and to connect many nodes to one network.

As a method of estimating the distance between a transmitter and a receiver used in the range-based location estimation method, there is a method using a received signal strength indicator (RSSI) and a time of arrival (ToA). The RSSI method uses a pass loss model of the signal as a method of estimating the distance based on the strength of the received signal. This method is simple because it does not go through complicated methods such as synchronization of the transmitter and receiver, but it is inaccurate in the area where the NLB (None Line of Sight) is formed due to the characteristics of the signal. However, when using low-cost nodes such as ZigBee, a network can be constructed by placing a large number of sensor nodes in a small area so that each node can form a line of sight (LOS). Using such environmental factors, a tree topology network as shown in FIG. 1 may be used to make an optimal environment for estimating a location using RSSI in an indoor environment.

Trilateral surveying is widely used as a basic method of estimating a user's position using the estimated distance of a transmitter / receiver in the same manner as RSSI. For accurate positioning using trilateration, three circles centering on the node whose location is known (called an anchor node) and having a radius of the distance estimated by RSSI or the like should form an orthogonal line. And, these intersection lines should form one intersection as shown in FIG. When estimating the distance of the transmitter and the receiver includes a large error, the distance is estimated to be very large or small so that one circle is completely separated from the other circle, or one circle completely includes the other circle, that is, as shown in FIG. 3. The fact that two circles do not form a straight line may occur in a practical environment. If one circle is completely separated from another circle or completely includes another circle, it will have a relatively large position estimation error as compared to the case otherwise.

In the present invention, in the case of wireless position estimation using triangulation using RSSI, when three circles do not form an intersection line (in the present invention, this is defined as a non-intersection case (NIC), and one And the case of the opposite of the NIC, and the Intersection Case (IC) can be classified using Heron's formula for tetrahedron, and so on. Using the Heron's formula for the tetrahedron in the classified NIC, we found that the absolute value of the volume and the estimated error distance have a positive correlation. Also, by using the positive correlation between the error distance and the absolute value of the volume, it was found that the reliability of the estimated position that could not be confirmed in the real environment can be confirmed by the magnitude of the absolute value of the volume. In addition, by using these positive correlations, the estimated distance values when they are classified as NICs are processed using the absolute value of the volume, and the method of improving the performance of trilateration is found.

Based on the results of this research, the present invention reduces the error of the estimated distance by determining a case where a relatively large position estimation error can be generated when estimating the position of the blind node using trilateration based on RSSI. An object of the present invention is to provide a radio positioning method capable of improving the accuracy of position estimation by triangulation by zooming, and a recording medium on which a program for realizing the radio positioning method is recorded.

According to an aspect of the present invention for achieving the above object, the wireless positioning server in a wireless network comprising at least three anchor nodes that know the location, one blind node to know the location, and a wireless positioning server In the radio location method executed by the method, the three estimated distances from each anchor node to the blind node are calculated using the received signal strengths (RSSI) provided from the three anchor nodes, and the positions of the three anchor nodes. A first step of calculating three actual distances between them using the information; Estimating the volume of the tetrahedron formed by the three anchor nodes and the one blind node using the three estimated distances and the three actual distances; A third step of correcting the magnitudes of the errors with respect to the three estimated distances when the magnitudes of the errors are determined through the formula of the heron to include errors larger than a predetermined reference; And a fourth step of calculating an estimated position of the blind node by trilateration using three final estimated distances reflecting the error correction in the third step.

In the wireless positioning method, in the third step, the magnitude of the error is determined by using the formula of the heron for calculating the tetrahedral volume, and the tetrahedron is not formed by dividing into the case where the tetrahedron is not formed and the tetrahedron is formed. If not, it is determined that the three errors include the large error.

In the third step, the error correction regarding the estimated distance may be performed by increasing the smallest estimated distance that causes the tetrahedron to not be formed, if the estimated distance is short using the volume size to form a tetrahedron. On the other hand, if the estimated distance is not long enough to form a tetrahedron, the longest estimated distance is reduced so that the tetrahedral can be formed.

The third step of the wireless positioning method, if the three circles (C ₁ , C ₂ , C ₃ ) whose radius is the three estimated distances are all cross-relational, the error correction for the three estimated distances is corrected. Not performing step 3-1; And in other cases (non-crossing relationship), the geometric positional relationship between the smallest circle (C ₁ ) and the largest circle (C ₃ ) is determined, and if the positional relationship is separated, the estimated distance of the minimum of the three estimated distances If the smallest circle (C ₁ ) is included in the largest circle (C ₃ ) or intersecting with each other, and the relationship is not the separation relationship, the estimated distance of the maximum value is reduced to compensate for errors. do.

를 곱하는 것과 상기 가장 긴 추정 거리에 대해서는 상기 소정의 보정용 가중치

를 나누어 주는 것에 의해 이루어진다. One method of error correction with respect to the estimated distance is that a predetermined correction weight is given for the smallest estimated distance.

Multiply by and the predetermined correction weight for the longest estimated distance

By distributing

는

로 정해질 수 있다. 여기서 V는 상기 사면체의 부피이고, A는 상기 3개의 앵커 노드가 형성하는 삼각형의 넓이이다. The correction weight

Is

Can be determined. Where V is the volume of the tetrahedron and A is the width of the triangle formed by the three anchor nodes.

In the wireless positioning method, it is preferable to perform the third step error correction only when the absolute value of the volume of the tetrahedron is larger than the width of the triangle formed by the three anchor nodes forming the bottom surface of the tetrahedron.

On the other hand, according to another aspect for achieving the above object of the present invention, in a wireless network comprising at least three anchor nodes that know the location, one blind node to know the location, and a wireless positioning server, A medium is recorded and readable by the radiodetermination server. The radio location program calculates three estimated distances from each anchor node to the blind node using received signal strengths (RSSI) provided from the three anchor nodes, and uses position information of the three anchor nodes. A first function of calculating three actual distances between them; A second function of estimating the volume of the tetrahedron formed by the three anchor nodes and the one blind node using the three estimated distances and the three actual distances; A third function of determining the magnitude of the error through the formula of the heron and correcting the magnitudes of the errors with respect to the three estimated distances when the magnitude of the error is larger than a predetermined reference; And a fourth function of calculating the estimated position of the blind node by trilateration using three final estimated distances reflecting the error correction in the third step.

According to the present invention, in the wireless positioning using triangulation, by finding an estimated distance including a relatively large estimated error and reducing the error included in the estimated distance, the accuracy of the estimated position of the blind node obtained by the trilateration is greatly increased. It can be improved.

FIG. 1 illustrates a tree branch structure for explaining an optimal environment for estimating a location using RSSI.
2 shows an example of an intersection case of trilateration,
3 shows an example of a non-intersection case of trilateration,
4 shows a tetrahedron for explaining trilateration,
5 is a graph showing the correlation between the absolute value of the volume and the position estimation error distance,
6 is a graph showing the correlation between shadowing and an error distance,
7 is a graph showing the correlation between shadowing and the absolute value of volume,
8 is a graph showing the probability density function of the height and the error distance of a tetrahedron,
9 shows a schematic configuration of a system for implementing a wireless positioning method according to the present invention,
10 is a flowchart illustrating a wireless positioning method according to a first embodiment of the present invention.

Hereinafter, with reference to the accompanying drawings will be described in more detail to enable the present invention.

(1) First, a theoretical explanation will be provided to assist in understanding the distance estimation method using RSSI, which is the background theory of the present invention, and the trilateration measurement using the estimated distance.

(1.1) RSSI method

The radio positioning method according to the present invention uses the RSSI method. The RSSI method is a method of estimating the distance between the transmitter and the receiver using only the strength of the signal received at the receiver.

In a wireless communication system, two environmental factors that cause errors are multipath fading. Multipath fading has very little impact between shadowing and shadowing (a loss of the received signal due to environmental factors). Therefore, when estimating the distance using RSSI in radio positioning, the effect on multipath fading is ignored and only the effect of shadowing is considered.

번째 앵커노드(위치를 알고 있는 노드)와

번째 브라인드 노드(blind node: 위치를 알고자하는 노드)로부터 수신한 신호의 세기는 아래와 같이 표현된다. It is known that the strength of the transmitted signal is reduced in proportion to the distance between the transmitting end and the receiving end. Because of the random nature of shadowing mentioned above, the strength of a received signal has a certain average value and follows a Gaussian distribution around that average value (when the distance between the transmitter and receiver is constant). When using a Gaussian model

The first anchor node (the node whose location is known) and

The strength of the signal received from the first blind node (node that wants to know its position) is expressed as follows.

는 수신신호의 평균세기(

),

는 쉐도잉의 표준편차를 의미한다. 송신단과 수신단 사이의 거리가

로 주어졌을 때, 수신신호의 평균 세기는 아래와 같이 주어진다. here

Is the average intensity of the received signal (

),

Is the standard deviation of shadowing. The distance between the transmitter and receiver

Given by, the average strength of the received signal is given by

는 기준 거리

에서 수신된 신호의 세기를 의미하며,

는 환경에 따라 변하는 경로손실지수(path loss exponent)를 의미하고 일반적으로 2~4사이의 값을 갖는다. 위의 값을 바탕으로 수신된 신호의 세기를 이용하여 위치를 추정하는 데 필요한 거리를 계산하면 아래와 같다. here

Is the reference distance

Means the signal strength received from

Is a path loss exponent that varies depending on the environment, and generally has a value between 2 and 4. Based on the above values, the distance required to estimate the location using the strength of the received signal is calculated as follows.

There are three main reasons for error in estimating distance using RSSI. Errors related to hardware, limitations of distance estimation algorithms, and environmental factors. Errors related to hardware are known to cause errors of about 3dB to 4dB in typical ZigBee devices.

와 경로 손실 지수(Path loss Exponent)인

값을 실험측정을 통해 검증해야한다. 이는 수신신호세기로부터 정확한 거리를 추정하기 위해 반드시 선행되어야 하는 작업이다. 본 발명에서는 RSSI에 사용되는 소자의 일예로 지그비를 이용하여 일반적인 실내 환경에서 실험적으로 구한

값과

값을 사용하며, 지그비의 환경에 맞게 시뮬레이션을 수행하여 결과를 얻었다. In the above equation, RSSI (dBm) is measured using received signal strength, so power loss at 1m

And the path loss exponent

The value should be verified through experimental measurements. This is a task that must be performed to estimate the correct distance from the received signal strength. In the present invention, an example of a device used in RSSI is experimentally obtained in a general indoor environment using Zigbee.

Value and

Using the values, simulations were made for the ZigBee environment and the results were obtained.

(1.2) Trilateration

The trilateration method estimates the position based on the estimated distance. This method estimates the blind node (the node whose position is desired) by using three anchor nodes (the node whose position is known). This is the most basic method of range-based location estimation used. That is, the radio signals radiated from the blind node are received at three anchor nodes to find the strength of the received radio signals using Equation (2.2), and then the strengths of the radio signals are applied to Equation (2.3). A method of estimating the distance from an anchor node to a blind node. The position of the blind node can be estimated by using the equation of three circles whose radius is the estimated distance from the estimated three anchor nodes to the blind node.

The trilateration is described geometrically as follows. If the distance between the three anchor nodes (AN1, AN2, AN3) and the blind node is accurately estimated, three circles 12, 14, and 16 meet at one point 10 as shown in FIG. When three circles meet at one point like this, a very accurate position estimation is made according to accurate distance measurement. However, if the estimated distance between the anchor node and the blind node includes an error, the three circles do not meet at one point. For example, when the estimated distance from the anchor node AN3 to the blind node is inaccurate, a circle may be formed as shown by the dotted line 18. In this case, according to the conventional trilateration method, as illustrated, the intersection point 20 of two straight lines 22 and 24 formed by two circles 12 and 18 and another two circles 14 and 18 is estimated. Location. If the distance is estimated so that two circles do not intersect (that is, one circle 12 is estimated to be included in the other circle 26), then the equations of the two circles solve the equation of one straight line 32. Is obtained. Then, as shown in FIG. 3, the intersection of the straight line 32 and the straight line 30 passing through two intersection points of the other two circles 12 and 14 is an estimated position.

(반지름)를 이용하여 3개의 원의 방정식을 구한다. The mathematical method of estimating the position using the trilateration method is as follows. First, the positions of three anchor nodes (center of the circle) and three estimated distances

Use (Radius) to find the equation for three circles.

Subtracting the second and first equations from the third equation above yields two straight line equations as shown in (2.5) below.

If the above expression is expressed as matrix, it is as follows.

,

,here

,

,

이다. 이를 행렬의 역함수를 이용하여 풀면 아래와 같이 브인드 노드의 위치를 찾을 수 있다.

to be. If you solve this by using the inverse of the matrix, you can find the location of the bind node as shown below.

(2) Example

This embodiment relates to wireless positioning of a blind node using three anchor nodes. The basic idea of this embodiment is to classify a case where a large error is included in the estimated distance from each anchor node to the blind node obtained using the RSSI method, and correct the error of the classified estimated distance by using the formula of the heron. will be. Since the position of the blind node is estimated by the trilateration method using the error-corrected estimated distance, the accuracy of the positioning of the blind node can be much improved as compared with the related art.

(2.1) Geometric Relation and Definition of None Intersection Case

은 반지름이 가장 작은 원,

는 반지름이 중간인 원,

는 반지름이 가장 큰 원을 의미한다. 추정된 거리가 작은 수준의 오차를 포함하고 있을 경우 3개의 원은 도 2와 같이 모두 교차하며 이는 표 1 에서 케이스 7에 해당한다. 그러나 추정된 거리가 큰 수준의 오차를 포함하고 있게 되면, 한 개의 원이 다른 두 원으로부터 완전히 분리되거나 포함되는 경우가 발생한다.In order to distinguish between the case where the estimated distance includes a large error and the case where it is not, the geometric relationship of the three circles to be used in the triangulation for risk is compared with the non-intersection case (NIC) and the intersection case (IC). Classify as In general, the geometric positional relationship of two circles includes: (a) separation where two circles do not meet separately, (b) intersection where two circles meet at two or one point, and (c) one circle It can be classified into three cases of inclusion completely containing another circle. The geometric relationships of these two circles can be used to interpret the geometric relationships formed by three circles. All geometric relationships formed by the three circles are shown in Table 1. In Table 1

Is the circle with the smallest radius,

Is a circle with a middle radius,

Means the circle with the largest radius. If the estimated distance contains a small level of error, all three circles intersect as shown in Figure 2, which corresponds to case 7 in Table 1. However, if the estimated distance contains a large level of error, one circle may be completely separated or included from the other two circles.

In Table 1, all cases except Case 7 have 'complete separation' or 'complete inclusion'. These cases contain a relatively large error in estimated distance compared to case 7. 3 (case 8 in Table 1) shows a relatively large position estimation error when compared to FIG. According to the present invention, a non-intersection case (NIC), which causes a large error in an estimated distance and consequently a large error in estimating a final position, is used in all cases except case 7 in the above table. define. In order to minimize the error, it is necessary to classify the NIC and postprocess the estimated distance.

(2.2) Intersection Case Discrimination

The present invention proposes a method for mathematically classifying NICs and ICs using the Heron formula. When using three anchor nodes (AN1, AN2, AN3), the distance between three anchor nodes (the distance between AN1-AN2, the distance between AN2-AN3, and the distance between AN3-AN1), and each anchor node Six sides including three estimated distances (AN1 to BN, AN2 to BN, and AN3 to BN) from (AN1, AN2, AN3) to the blind node BN can be obtained. In a real environment, there is little possibility that the blind node BN is located on the plane formed by the three anchor nodes AN1, AN2, and AN3. That is, six sides formed by three anchor nodes AN1, AN2 and AN3 and one blind node BN form a tetrahedron. The volume of the tetrahedron formed by the six sides can be determined by expanding heron's formula. Use this to classify ICs and NICs.

This will be described with reference to the tetrahedron of FIG. 4. If you know the length of the three sides of a triangle, there is a Heron formula for finding the area of a triangle. Expanding the formula for finding the area of this triangle, there is a formula for calculating the volume of the tetrahedron when the length of the tetrahedron is known. Using the extension of Heron's formula, we can find the volume of a tetrahedron using the length of six sides:

이다. 모든 변의 길이를 알고 있으므로 각각의 cosine값은 cosine 제2법칙을 이용하여 구할 수 있다. 위의 사면체에서 삼각형

를 이용하여 cosine 제 2법칙을 적용하면

,

,

를 아래와 같이 구할 수 있다.here

to be. Since the lengths of all sides are known, each cosine can be found using the second law of cosine. Triangle from the tetrahedron above

Applying the second law of cosine using

,

,

Can be obtained as

Substituting the cosine values of Eq. (3.2) into Eq. (3.1), the volume of the tetrahedron can be calculated using the six sides of the tetrahedron.

,

,

). 이러한 조건일 때 3개의 원의 관계는 표 1의 케이스 7에 해당된다. 즉, 위의 부피 값이 양수인 경우는 모든 cosine값의 절댓값이 1보다 작은 경우이며, 이는 표 1의 케이스 7에 해당된다. 두 개의 원이 형성하는 기하학적인 관계가 교차인 경우 중심사이의 거리와 추정된 두변이 만들어내는 cosine의 절댓값은 1보다 작다. 하지만 두 개의 원이 교차 이외의 기하학적인 관계를 형성하는 '포함'이나 '분리'는 cosine의 절댓값이 1보다 크다. 포함관계는 한 개의 변이 매우 큰 상황에서 발생하는데, 이때의 cosine값은 1보다 크다. 분리관계는 세 개의 변이 모두 작은 상황에서 발생하는데, 이때의 cosine값은 -1보다 작다. cosine의 절댓값이 1보다 큰 상황에서는 헤론의 공식을 이용한 부피의 값이 허수가 발생된다. 이는 부피를 위한 헤론의 공식인 식 (3.1)이 추정된 거리가 IC에 해당되지 않는 경우를 분류해 낼 수 있음을 의미한다. Consider the case where the volume value obtained by Heron's formula has a real number, and the value in the root of Equation (3.1) is positive. The minimum condition to satisfy this condition is that the absolute value of all cosine values must be less than 1 (

,

,

). Under these conditions, the relationship of the three circles corresponds to case 7 of Table 1. That is, if the above volume value is positive, the absolute value of all cosine values is less than 1, which corresponds to case 7 of Table 1. If the geometric relationship formed by two circles is an intersection, the distance between the centers and the absolute value of cosine produced by the estimated two sides are less than one. However, 'contains' or 'separates' where two circles form a geometric relationship other than intersecting, where the cosine's absolute value is greater than one. Inclusion relationships occur in situations where one side is very large, with cosine values greater than one. The separation relationship occurs when all three sides are small, and the cosine value is less than -1. In situations where the absolute value of cosine is greater than 1, the imaginary value of the volume using the Heron's formula is generated. This means that Heron's formula for volume (3.1) can classify cases where the estimated distance does not correspond to the IC.

Furthermore, the Heron's formula for tetrahedrons can be used to classify cases in which three intersections do not form an intersection area shared by all three circles. This formula is used to classify NICs and ICs, and because it uses trilateration, it can be used simply as a discriminant.

In the case of NICs through classification using the Heron's formula for tetrahedrons, the magnitude of the localization error is positively correlated with the absolute value of volume. That is, if one estimated distance includes a large error, the magnitude of the absolute value of the volume obtained by the above formula appears large, and the estimated position error also appears large. FIG. 5 shows the result obtained by simulation of the relationship between the absolute value of the volume and the estimated position error when the standard deviation of shadowing is 3 dB when estimating the distance by RSSI. As shown in the graph of FIG. 5, when the volume value obtained through the formula of the heron for the tetrahedron is imaginary, and the absolute value thereof is large, the position estimation error tends to increase.

(2.3) Relationship between absolute value of error and error distance

The mathematical relationship between the absolute value of the tetrahedral volume and the error distance is examined mathematically. This is similar to mathematically examining the relationship between shadowing, error distance, and absolute value of volume, which affect distance estimation. The error distance and volume are determined by the three actual distances and the shadowing values that affect each distance value. Here, we analyze the correlation between shadowing and the absolute value of error distance and volume, assuming that shadowing occurs only for the value with the largest actual distance. The formula of the error distance used to evaluate the performance of trilateration and least squares is as follows.

는 추정된 위치,

는 실제 위치, (

,

)는 추정된 위치의 좌표, (

,

)는 실제 위치의 좌표를 의미한다. 삼변측량의 공식 (2.7)을 통해 얻어진 추정 위치의 좌표를 위의 식에 대입하고, 이를 가장 긴 변이라고 가정한

에 대해 정리하면 아래와 같다. here

Is an estimated location,

Is the actual location, (

,

) Is the coordinate of the estimated location, (

,

) Means the coordinates of the actual position. Substituting the coordinates of the estimated position obtained from the trilateration formula (2.7) into the above equation, assuming the longest side

The following is the summary.

는 가장 큰 거리인

에 반영되는 쉐도잉이다. 여기서

,

,

는 모두 상수이며, 3개의 앵커노드의 위치와 브라인드 노드와 앵커노드사이의 거리인

,

에 의해 결정된다. here

Is the biggest distance

Shadowing is reflected in. here

,

,

Are constants, which are the positions of the three anchor nodes and the distance between the blind node and the anchor node.

,

.

에 대해 정리하면 아래와 같다.Substituting all Cosine values of (3.1), the formula of volume, proposed in the present invention,

The following is the summary.

,

,

는 모두 상수이며 각 앵커노드사이의 거리와 브라인드 노드와 앵커노드사이의 거리인

,

에 의해 결정된다. here

,

,

Are all constants, and the distance between each anchor node and the distance between the blind node and the anchor node

,

.

의 쉐도잉만 변한다고 가정하여 수행하였다. 3개의 앵커노드가 AN1(2, 2), AN2(7.5, 2), AN3(8, 8)이고 브라인드 노드를 BN(3, 3) 로 하고,

과

에 오차가 발생하지 않는 상황에서 수행되었다. AN3과 BN간의 거리가 가장 길며, 이 거리에서 쉐도잉 값이 발생한다고 가정하고, 쉐도잉 값을 -10에서 10까지 변화하며, 쉐도잉과 오차거리, 부피사이의 그래프를 그렸다. It can be seen that equation (3.5) for the volume and equation (3.4) for the error distance are the same and different in each order constant. This is a sufficient reason to explain that when the volume is negative, the error distance increases as the volume increases. The function of the correlation between shadowing, error distance, and absolute value of volume can be expressed as above, and it is not easy to check the graph because the function value is determined by several variables. 6 and 7 illustrate a graph of this through simulation. The simulation is the largest distance value of many variables

It was performed assuming that only shadowing of was changed. Three anchor nodes are AN1 (2, 2), AN2 (7.5, 2), AN3 (8, 8), and the bind node is BN (3, 3),

and

This was done in a situation where no error occurred. Assuming that the distance between AN3 and BN is the longest and the shadowing value occurs at this distance, the shadowing value is changed from -10 to 10, and the graph between shadowing, error distance, and volume is drawn.

As can be seen in FIGS. 6 and 7, the correlation between shadowing and the error distance and the absolute value of shadowing and volume are similar. The absolute value of the volume obtained by using Heron's formula and the error distance of the estimated position show a big difference in scale. The absolute value of the volume obtained through Heron's formula can be used to obtain the height of the imaginary tetrahedron using the general tetrahedral volume as shown below.

The probability density function of the height of the imaginary tetrahedron obtained using the above formula and the probability density function for the estimated error distance are also shown in FIG. 8. 8 shows that the height and the error distance of the tetrahedron form a probability similarly. Using such a relationship, the reliability of the position estimate value can be given using the absolute value of the volume in the state of not knowing the actual position of the blind node in the real environment.

(2.4) Methods for reducing error in distance estimation

The embodiment of the present invention changes the NIC classified above to a more appropriate value to reduce the error of the estimated value of the distance including the error obtained through the RSSI by using the positive correlation between the absolute value of the volume and the location estimation error. The corrected estimated distance is then applied to trilateration to estimate the position of the blind node. The probability that one of the three estimated distances from each of the three anchor nodes to the blind node includes a large error is higher than the probability that all three include a large error. The error distance when the error is included in the largest distance value or the smallest distance value is larger than the error distance when the error value is included in other distance values. Therefore, in the present invention, the largest or smallest value among the three estimated distances is converted through post processing. Through this process, more accurate location information of the blind node can be obtained.

9 shows a schematic configuration of a wireless positioning system 100 for implementing an embodiment of the present invention. The wireless positioning system 100 includes a wireless network 110 including at least three anchor nodes AN1, AN2, and AN3 whose position is known, and a terminal to be located, that is, a blind node BN. And a wireless network location server 120 that executes the calibration application 130 to process the RSS information provided from the wireless network 110 to accurately calculate the location information of the blind node BN.

The positioning correction application 130 executed in the positioning server 120 is a program reflecting the following algorithm proposed by the present inventor. The program may be recorded on a computer readable recording medium such as a CD, a DVD, a hard disk, a nonvolatile memory, or the like, and may be executed by being connected to a computer device such as the positioning server 120.

10 is a flowchart for explaining the positioning correction application 130, with reference to this will be described a radio positioning method according to an embodiment.

First, the positioning server 120 has to find the length of the six sides of the tetrahedron for estimating the volume of the tetrahedron formed by three anchor nodes and one blind node. To this end, the positioning server 120 receives a received signal strength (RSS) value from each node of the wireless network 110 (step S10), then three anchor nodes (AN1, AN2, AN3) and the positioning target terminal The blind node BN is selected (step S12). And the length of the three sides of the triangle forming the base of the tetrahedron is obtained (step S14). The three sides of the triangle correspond to the distance between the three selected anchor nodes AN1, AN2, and AN3, that is, between AN1 to AN2, between AN2 to AN3, and between AN3 and AN1. The position information (coordinates) of the anchor nodes AN1, AN2, and AN3 are already known values and provided to the positioning server 120 in advance, so that the lengths of the three sides of the triangle can be easily calculated. In addition, three estimated distances between the anchor nodes AN1, AN2, and AN3 and the blind node BN are obtained using Equation (2.3) (step S16). This estimated distance can be obtained using the signal of the blind node BN received at each anchor node as described above.

When the length of the six sides of the tetrahedron is obtained, the estimated length of the tetrahedron is applied to the Heron's formula (Equations (3.1), (3.2a), (3.2b), and (3.2c)). Calculate the volume (step S18). Then, the estimated volume of the tetrahedron is used to determine whether the geometric relationship of the three circles (C ₁ , C ₂ , C ₃ ) to be used in the trilateration corresponds to the NIC or the IC. Discrimination and classification using the formula (3.1) (step S20).

In the case of being classified as an IC in step S20, the three estimated distances between each anchor node (AN1, AN2, AN3) and the blind node (BN) are located without change of the error correction. Estimate (step S22). However, when classified as a NIC in step S20, the error included in the estimated distance between each anchor node (AN1, AN2, AN3) and the blind node (BN) is corrected.

와 가장 작게 추정된 거리를 통해 형성된 원인

의 기하학적인 관계를 이용하여 다시 분류를 한다(S28 단계). 두 원의 기하학적인 위치관계는 앞에서 언급하였듯이 원의 중심사이의 거리와 두 원의 반지름을 이용해서 분류할 수도 있지만, 부피를 구하기 위해 얻은 Cosine값을 이용해서 분류할 수도 있다. 반지름이 가장 큰 원과 반지름이 가장 작은 원의 기하학적인 관계가 분리(표 1의 케이스 1, 2, 3)일 경우는 식 (3.2)에서 얻은 Cosine값이 -1 보다 작다. 이런 경우는 최소 거리가 작게 추정되었다고 볼 수 있다. 그러므로 최대 크기의 원과 최소 크기의 원이 '분리관계'일 경우 최소로 추정된 값을 증가시켜야 한다. 이와 비슷하게 두 원이 '포함관계'에 있는 경우에 식 (3.2)의 Cosine값은 1보다 크게 되며, 이러한 경우 최댓값이 크게 추정되었다고 볼 수 있다. 두 원의 기하학적인 관계가 '교차관계'인 경우, 포함관계와 마찬가지로 최댓값이 크게 추정되었다고 볼 수 있다. 즉, 두 원의 기하학적 관계가 '포함관계' 또는 '교차관계'인 경우, 최댓값이 크게 추정되었다고 보았으므로 최대로 추정된 값을 감소시킨다. 즉, NIC에 포함되면서

과

의 위치관계가 '교차관계'인 경우와 '포함관계'인 경우는 최댓값이 크게 추정되었다고 본다. 결국,

과

의 위치관계를 분리인 경우와 그렇지 않은 경우로 분류하여, 위치관계가 '분리관계'인 경우 최소값을 증가시킨다(S30 단계). 반면에, 분리관계가 아닌 경우 즉, '포함관계' 또는 '교차관계'인 경우에는 최댓값을 감소하도록 후 처리를 한다(S32 단계). S30 단계와 S32 단계에서 최솟값과 최댓값을 증가 및 감소시키는 처리는 각각 식 (3.7a)와 식 (3.7b)를 이용하여 수행한다. Error correction with respect to the estimated distance is performed as follows. Causes formed using the largest estimated distance value for NICs classified by Heron's formula

And the reason formed by the smallest estimated distance

Classify again using the geometric relationship of (S28 step). The geometric positional relationship of the two circles can be classified using the distance between the centers of the circles and the radius of the two circles as mentioned above, but can also be classified using the Cosine value obtained to find the volume. If the geometric relationship between the largest radius circle and the smallest radius circle is separation (cases 1, 2, and 3 in Table 1), the Cosine value obtained in Equation (3.2) is less than -1. In this case, the minimum distance can be considered small. Therefore, the minimum estimated value should be increased when the circle with the largest size and the circle with the minimum size are separated. Similarly, when two circles are in 'inclusion relationship', the Cosine value in Equation (3.2) is greater than 1, and in this case, the maximum value is estimated to be large. When the geometric relationship of two circles is 'cross', it can be said that the maximum value is largely estimated like the inclusion relationship. In other words, when the geometric relationship between two circles is 'inclusion relationship' or 'cross relationship', the maximum value is considered to be largely estimated, and thus the maximum estimated value is reduced. That is, being included in the NIC

and

In the case of the positional relationship of 'cross' and 'inclusive', the maximum value is considered to be large. finally,

and

If the positional relationship is classified into a case of separation and otherwise, the minimum value is increased if the positional relationship is a 'separation relationship' (step S30). On the other hand, in the case of a non-separation relationship, that is, a 'inclusion relationship' or a 'cross relationship', post-processing is performed to reduce the maximum value (step S32). The processes of increasing and decreasing the minimum and maximum values in steps S30 and S32 are performed using equations (3.7a) and (3.7b), respectively.

는 추정된 거리의 증가량과 감소량을 결정하는 후처리 가중치이다. 후처리 가중치

는 일예로서 아래 식 (3.8)을 이용하여 구할 수 있다(S26 단계). here

Is a post-processing weight that determines the amount of increase and decrease of the estimated distance. Postprocessed Weight

As an example can be obtained using the following equation (3.8) (step S26).

는 사면체를 위한 헤론의 공식을 통해 얻은 부피의 값이며,

는 3개의 앵커노드(AN1, AN2, AN3)가 형성하는 삼각형이다. 앞에서 부피의 절댓값과 위치추정오차가 양의 상관관계가 있다는 것을 알았으므로, 최댓값과 최솟값을 후 처리할 때 부피의 값을 반영하도록 한다. 크게 추정된 거리와 작게 추정된 거리가 결과적으로 부피의 공식에서 높이에 해당되는 값에 영향을 주기 때문에, 위의 공식에서와 같이 부피 값을 통해 높이 값을 얻어 이 값을 후 처리 가중치에 이용하는 것이 바람직하다. 하지만 후처리 가중치를 다른 방법으로 구할 수 있음은 물론이다.here

Is the value of the volume obtained through the Heron formula for tetrahedron,

Is a triangle formed by three anchor nodes AN1, AN2, and AN3. Since we know that there is a positive correlation between the absolute value of the volume and the location estimation error, make sure to reflect the value of the volume when postprocessing the maximum and minimum values. Since the large estimated distance and the small estimated distance will eventually affect the value corresponding to the height in the formula of the volume, it is best to obtain the height value through the volume value as in the above formula and use this value for post processing weights. desirable. Of course, post-processing weights can be obtained in different ways.

인 경우에 한해서만 후 처리를 하는 것이 바람직하다(S24 단계). 가장 크게 추정된 거리 값을 후 처리할 때

인 조건에 대해서 후 처리를 수행하면, 항상

의 조건을 만족할 수 있다. 식 (3.5)에서 가장 크게 추정된 거리와 부피의 상관관계를 확인할 수 있으며, 가장 크게 추정된 거리와 부피는 거리의 제곱에 관한 식으로 상관관계가 있으므로 부피의 값에 제곱근을 이용하여 가중치를 계산한다. In addition, if the absolute value of the volume of the tetrahedron is large, the absolute value of the volume and the estimated position error are clearly correlated, so that the absolute value of the tetrahedral volume forms the base of the tetrahedron (this triangle is also a triangle formed by three anchor nodes). Greater than the width of)

It is preferable to perform the post-treatment only in the case of (S24 step). When postprocessing the largest estimated distance value

If you do post-processing for

The condition of can be satisfied. In Eq. (3.5), we can check the correlation between the largest estimated distance and volume, and since the largest estimated distance and volume are correlated with the square of the distance, the weight is calculated using the square root of the volume value. do.

Through the above process, the estimated distance corresponding to the comparison difference and including a large error can be appropriately corrected by applying a weight. If the corrected estimated distance and / or error correction are not necessary, the blind node using three anchor nodes is calculated by calculating the estimated position of the blind node BN by trilateration using the original estimated distance (step S22). It is possible to estimate the position of.

After the positioning server 120 calculates the exact estimated position of the blind node BN through this process, the calculated server 120 wirelessly transmits the calculated estimated position to the blind node BN.

As described above, the wireless positioning method is a method of improving the performance of trilateration. We define a comparative case (NIC) that causes a relatively large estimated error and classify it through Heron's formula for tetrahedral volume. The absolute value and estimated error of the tetrahedral volume obtained during the classification process are positively correlated to improve the performance of the overall trilateration by post-processing the maximum and minimum of the estimated values.

(3) improving the performance of trilateration

Various simulations have confirmed that the performance of trilateration can be improved. Table 2 below summarizes the total average error of the post-processed trilateration and conventional trilateration according to the present invention through simulation. It can be seen that the postprocessed trilateration results in a significant error improvement for the estimated position. For example, when the standard deviation was 3.5 dB, it was confirmed that the average error of trilateration through post-treatment was improved by 31.85% compared to the average error of conventional trilateration.

The present invention can be widely used to wirelessly estimate the location of a blind node in a network using RSSI in a wireless sensor network having at least three anchor nodes.

Claims (9)

In a wireless positioning method executed by the wireless positioning server in a wireless network comprising at least three anchor nodes that know a location, one bind node that wants to know a location, and a wireless location server.
Three estimated distances from each anchor node to the blind node are calculated using the received signal strengths (RSSI) provided from the three anchor nodes, and three actual distances between the three anchor nodes are calculated by using the position information of the three anchor nodes. Calculating a distance;
Estimating the volume of the tetrahedron formed by the three anchor nodes and the one blind node using the three estimated distances and the three actual distances;
A third step of correcting the magnitudes of the errors with respect to the three estimated distances when the magnitudes of the errors are determined through the formula of the heron to include errors larger than a predetermined reference; And
And a fourth step of calculating an estimated position of the blind node by trilateration using three final estimated distances reflecting the error correction in the third function. The method of claim 1, wherein when the tetrahedron is not formed in the third step and the tetrahedron is not formed, it is determined that the large error is included in the three estimated distances. Wireless positioning method. 3. The method of claim 2, wherein in the third step, the magnitude correction of the error with respect to the estimated distance is the smallest estimation that causes the tetrahedron not to be formed when the estimated distance is short using the size of the volume to form a tetrahedron. It is possible to form a tetrahedron by increasing the distance, and when the estimated distance is long, the tetrahedron cannot be formed, thereby reducing the longest estimated distance causing the tetrahedron. Wireless positioning method. The method of claim 1, wherein the third step is to correct the error of the three estimated distances when all three circles C ₁ , C ₂ , and C ₃ having the radius of the three estimated distances cross each other. Not performing step 3-1; And in other cases (non-crossing relationship), the geometric positional relationship between the smallest circle (C ₁ ) and the largest circle (C ₃ ) is determined, and if the positional relationship is separated, the estimated distance of the minimum of the three estimated distances is If the smallest circle (C ₁ ) is included in the largest circle (C ₃ ) or intersecting with each other, and the relationship is not the separation relationship, the estimated distance of the maximum value is reduced to compensate for errors. Wireless positioning method characterized in that. The method of claim 3 or 4, wherein the error correction for the estimated distance is a predetermined correction weight for the smallest estimated distance.

Multiply by and the predetermined correction weight for the longest estimated distance

Wireless positioning method characterized in that is made by dividing. The method of claim 5, wherein the weight for correction

Is

Wherein V is the volume of the tetrahedron and A is the area of the triangle formed by the three anchor nodes. The radio positioning according to claim 1, wherein the third step of error correction is performed only when the absolute value of the volume of the tetrahedron is larger than the width of the triangle formed by the three anchor nodes forming the bottom of the tetrahedron. Way. In a wireless network including at least three anchor nodes that know a location, one bind node that wants to know a location, and a wireless location server, a radio location program is recorded and can be read by the radio location server.
The radio location program,
Three estimated distances from each anchor node to the blind node are calculated using the received signal strengths (RSSI) provided from the three anchor nodes, and three actual distances between the three anchor nodes are calculated by using the position information of the three anchor nodes. A first function of calculating a distance;
A second function of estimating the volume of the tetrahedron formed by the three anchor nodes and the one blind node using the three estimated distances and the three actual distances;
A third function of determining the magnitude of the error through the formula of the heron and correcting the magnitudes of the errors with respect to the three estimated distances when the magnitude of the error is larger than a predetermined reference; And
And a fourth function of calculating an estimated position of the blind node by trilateration using three final estimated distances reflecting the error correction in the third function, and may be executed by the radiodetermination server. The medium on which the radio location program is recorded. 10. The method of claim 8, wherein the third function is to correct the error of the three estimated distances when all three circles C ₁ , C ₂ , and C ₃ having the radius of the three estimated distances cross each other. Does not function; And in other cases (non-crossing relationship), the geometric positional relationship between the smallest circle (C ₁ ) and the largest circle (C ₃ ) is determined, and if the positional relationship is separated, the estimated distance of the minimum of the three estimated distances If the smallest circle (C ₁ ) is included in the largest circle (C ₃ ) or intersects with each other, but not the separation relationship, the estimated distance of the maximum value is reduced to include error correction. A computer-readable medium on which a radiolocation program is recorded.

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