KR20180022286A - Methods for selecting reference node for estimating relative locations - Google Patents

Abstract

According to an embodiment of the present invention, provided is a method of selecting a reference node for the estimation of a relative position between nodes based on a multidimensional scaling (MDS) technique in a wireless network environment, wherein the method includes the steps of: measuring a distance between the nodes; analyzing connectivity information between the nodes; selecting a reference node among all the nodes; constructing a relative position map from the reference node; and estimating the relative position of all the nodes based on the relative position map.

Description

[0001] The present invention relates to a method for selecting a reference node for estimating a relative position of a robot,

The present invention relates to a reference node selection method in which the amount of calculation is reduced while enhancing accuracy in the multidimensional scaling method referred to as MDS.

Due to the development of information and communication technology, today's battles are network-centric warfare, which means that unmanned aircraft, unmanned aerial vehicles (UAVs) ), Or unmanned ground vehicles (UGVs).

UAV began to be used as a military force in Vietnam, and after having played an auxiliary role such as surveillance and reconnaissance in the Gulf War, Afghan War, and Iraq War, it led successful battles. Currently, unmanned combat operations are being conducted for direct attack.

In the United States, the unmanned combat demonstrator X-47B was successfully launched and landed in the world's first aircraft carrier in July 2013, and the UAV-related project is underway in Europe, Israel and China.

Korea is in the process of developing a Korean high-end unmanned reconnaissance aircraft with the aim of powering up in 2018. Studies related to UGV have also been actively studied in the US, Israel, and Europe.

In the United States, practical technology has been acquired or developed in all fields such as small surveillance robots, multipurpose robots, vehicle type robots and combat type robots. Israel is also conducting intensive research on unmanned combat systems, especially in combat robots with the United States.

In Korea, the research is being carried out starting with the 'National Intelligence Robotics Development Basic Plan' in 2002. The National Defense Science Institute developed the XAV robot for the first time in 2005 and has been continuously improving and developing until now.

In order to efficiently utilize these unmanned robots in the future battlefield, it is essential to obtain accurate position information of the unmanned robots. Especially, it is difficult to trust GPS (Global Positioning System) signal, which can detect position information because of various jamming due to the characteristics of electric field environment. To this end, the US Army Arms R & D Engineering Center (ARDEC) also announced plans to develop unmanned sensors capable of operating in GPS denied areas.

The position estimation of the unmanned system is divided into two types of absolute position estimation method and relative position estimation method. The absolute position estimation method is to estimate the absolute position coordinates of the robot indicated by the degree of astigmatism and the like. It means to estimate the relative position between robots when there are more than two robots.

A typical absolute position estimation method is trilateration. Trilateration is a method of estimating the position of a target by using distance information from three or more reference points to a target, and shows a small error compared with triangulation (triangulation), which is a typical method using geometry.

A typical example of using a trilateration is a GPS (Global Positioning System). However, since the trilateration based position estimation method such as GPS is often impossible due to various jamming propagation in an actual field environment, in order to perform communication or routing between robots based on the position information, It is necessary to secure the stability and reliability of the robot position estimation in parallel with the relative position estimation technique.

Relative positioning techniques can be classified in various ways. Simultaneous Localization And Mapping (SLAM), which performs the mapping and node position calculation simultaneously according to the calculation method, and a method of estimating the position from the inter-node distance.

The former is advantageous for the ambiguity of the position map transformation, but the latter requires a smaller number of sensors, but is less sensitive to map transformation ambiguity. Other classification schemes are classified according to the presence or absence of anchor nodes. The anchor node means a node having position information. When anchor nodes broadcast position information, the position of the anchor node can be estimated by comparing and analyzing the received signals. Although it consumes less energy because it is relatively accurate and computational complexity is low, there are disadvantages in installation problem of anchor nodes and lack of scalability.

The anchor-free method selects a sink node, and the selected sink nodes transmit the surrounding information measured by the sink node. It requires a lot of communication between nodes for information exchange, which has a disadvantage of large energy consumption and is relatively inaccurate, but it is useful in real environment because it is scalable.

Many methods of using MDS (multi-dimensional scaling) among the position estimation methods without anchor nodes have been proposed. MDS is an analytical technique that can geometrically represent data in a multidimensional space of two or more dimensions and compare the correlation between data.

Each data is represented by a point in space and the distance between the data (points) is proportional to the similarity between the data. That is, as the distance from the reference point is closer to the reference point, it can be interpreted as data showing a high degree of similarity with the reference point.

In order to obtain the relative position using the MDS, distance information between nodes (robots) is required, and a relative position map of the robot can be constructed through MDS analysis by obtaining distance information between all the robots.

However, since it is very difficult to grasp the distances between all robots due to the limitation of the communication distance of robots, studies have been conducted to apply MDS to the position estimation in actual environments

The MDS-based position estimation follows the following method.

와 같이 표현할 수 있다. 절대좌표가 주어지지 않는 상대좌표 추정에서, 모든 노드는 초기에 n 차원의 좌표를 가지며 (i.e., m = n), 노드 i 에 대하여

는 노드 i와 j 간의 측정거리 측정거리

로 주어진다. 이때 거리행렬(distancematrix) D는 다음과 같이 정의된다.It is assumed that n nodes (robots) requiring relative position estimation are arbitrarily distributed in a two-dimensional or three-dimensional space. Assuming that each node has m- dimensional coordinates, the coordinates of node i are

Can be expressed as In the relative coordinate estimating absolute coordinates are not given, all the nodes will have the coordinates of the n-dimensional initially against (ie, m = n), the node i

Measuring distance between nodes i and j Measuring distance

. The distance matrix D is defined as follows.

Since the distance from the node itself is zero, the value of the element located at the opposite end of the distance matrix D is always zero. Ultimately, the MDS-based position estimation technique obtains two- or three-dimensional coordinates (for example, m = 2, 3) approximating the distance matrix D in Eq. (1).

For double centering, the centering matrix H is defined as follows.

Here, 1 _n means a vector with all elements 1 and size n × 1, and matrix B is defined as follows using centering matrix H.

는 제곱거리 행렬(squared distance matrix)을 의미한다.At this time,

Means a squared distance matrix.

와 정규화된 아이겐벡터로 이루어진 행렬

에 대해 행렬 B는 다음과 같이 표현할 수 있다.A singular value decomposition can be applied to the matrix B to extract the eigenvalues and eigenvectors of B. If the number of extracted eigenvalues and eigenvectors is k, the relative position to the k-dimensional space can finally be estimated. A matrix with extracted eigenvalues as a major axis

And a matrix of normalized eigenvectors

The matrix B can be expressed as:

Finally, the relative position coordinate Y of the node estimated through the MDS is expressed as follows.

는 두 노드간 최단경로에 있는 각 링크(link)들의 거리의 합으로 근사한다. 얻어진 최단경로 거리 값으로 거리행렬 D 를 구성한다. 이 거리행렬에 대해 MDS를 적용하면 상대 위치를 추정할 수 있다. 이 방식은 직접 연결성이 없기 때문에 측정할 수 없는 노드간 거리에 대해 최단경로를 이용한 링크간 거리의 합으로 계산하는 방식으로 찾은 최단 경로의 홉(hop) 수가 증가할수록 오차가 커지게 되는 문제점이 있다.In the MDS-MAP proposed by Yi, if the target node to know the relative position exists outside the communication distance and can not obtain the distance information, the centralized control centralized algorithm. First, we check the connectivity information of the entire node and find the shortest path using Dijkstra's shortest path algorithm for all node pairs. The distance between the nodes

Is approximated by the sum of the distances of the links in the shortest path between the two nodes. The distance matrix D is constructed by the obtained shortest path distance value. The relative position can be estimated by applying MDS to this distance matrix. This method has a problem that the error increases as the number of hops in the shortest path is calculated by calculating the sum of the inter-link distances using the shortest paths with respect to the inter-node distances that can not be measured because there is no direct connectivity .

In order to improve the uncertainty of the relative position estimation result as the network size increases, an MDS-MAP (P) improved MDS-MAP algorithm has been proposed. P means patch, dividing one network map into a plurality of patches, estimating each relative position, and merging them. Basically, it operates in a distributed manner. In order to minimize the error due to the increase of the number of existing hops, a partial relative position map is constructed using only the node distance information of 2-hop or less for all the nodes, and then a partial relative position map is constructed. As shown in FIG.

The amount of inaccurate distance information calculated by the simple distance sum is reduced, thereby providing a relatively high positioning error compared to the existing MDS-MAP. However, since it is a method of constructing a relative position map for all nodes, it has high computational complexity.

In order to reduce the complexity of the existing MDS-MAP, Shon proposed Cluster-based MDS (Clustered MDS) to cluster the nodes and perform MDS for each cluster to estimate the total location. This scheme can improve the performance (complexity, error) compared to the MDS-MAP when there is a hole in the network topology, and the measurement error increases in the normal situation.

In order to solve the problem described above, the present invention differs from the existing method in which MDS is applied to all node pairs by selectively selecting a reference node to be a center of the relative position map, and applying the MDS to the reference node, As well as ensuring accuracy at the same time.

In an embodiment of the present invention, a reference node selection method for relative position estimation between nodes based on a Multidimensional Scaling (MDS) scheme in a wireless network environment includes measuring a distance between nodes, analyzing connectivity information between nodes Selecting a reference node among all nodes, constructing a relative position map from a reference node, and estimating a relative position of all nodes based on a relative position map.

Wherein the step of selecting the reference node comprises the steps of: selecting three nodes having the highest connectivity with neighboring nodes as an initial reference node, selecting one of the remaining nodes excluding the reference node (reference node? Added node) A node having the largest number of nodes having a predetermined number or more is selected as a new reference node.

( 이상이 되면 기준노드 선정을 중단한다.When the number of nodes having connectivity of 3 or more with respect to the reference node is greater than the total number of nodes

(If it is abnormal, selection of reference node is stopped.

According to the present invention, in order to solve the high calculation complexity and the error of the position estimation, which is a problem of the existing MDS-based position estimation technique, instead of configuring the relative position map in all the nodes, By constructing the position map, there is an effect of reducing the number of relative position maps to be combined and improving the position estimation error.

Simulation results also show that the present invention reduces the relative position map coupling complexity by reducing the number of relative position maps used in comparison with the existing methods, and reduces the position estimation error by reducing the frequency of incorrect distance approximation between nodes.

의 변화에 따른 위치 추정 값의 오차를 노드 수 별로 나타낸 그래프이다.
도 5는

의 변화에 따른 기준 노드의 수의 변화를 나타낸 그래프이다.
도 6은

가 0.9일 때 노드 수에 따른 위치 추정 값의 오차를 나타낸다
도 7은 본 발명과 MDS-MAP(P) 방식을 비교한 그래프이다.
도 8은 평균 Degree에 따른 위치 추정 값의 오차를 나타내다.
도 9는 평균 상대 위치 지도 수를 나타낸다.1 shows a neighboring node within a 2-hop of the node N1.
FIG. 2 is an example of combining MAP 1 and MAP2 based on the common nodes N1 and N2 in a two-dimensional space
Figure 3 shows an exemplary network for selecting a reference node.
Figure 4

Of the position estimation value according to the number of nodes.
Figure 5

Of the number of reference nodes.
6,

Is 0.9, it represents the error of the position estimation value according to the number of nodes
7 is a graph comparing the present invention with the MDS-MAP (P) scheme.
8 shows the error of the position estimation value according to the average degree.
Figure 9 shows the average relative position map number.

The present invention will now be described in detail with reference to the accompanying drawings. Hereinafter, a repeated description, a known function that may obscure the gist of the present invention, and a detailed description of the configuration will be omitted. Embodiments of the present invention are provided to more fully describe the present invention to those skilled in the art. Accordingly, the shapes and sizes of the elements in the drawings and the like can be exaggerated for clarity.

The MDS-based position estimation technique based on the present invention estimates a relative position using a distance matrix. In an actual network, a perfect distance matrix including the distance between all nodes can not be obtained due to the limitation of the communication radius of each node.

1 shows a neighboring node within a 2-hop of the node N1. A vertex means a node, and an edge means connectivity when inter-node communication is possible. The node N1 is directly connected to the nodes N2, N5, N7, N8, N9, and N13 to communicate directly with the nodes N1, N5, N7, N8, N9, and N13. Therefore, N1 can not construct a perfect distance matrix for the entire network.

The above-mentioned MDS-MAP scheme obtains an approximate value of a distance between pairs of nodes having no connectivity using the shortest path. For example, the distance between node N2 and node N8 can be approximated by the sum of the distance between N2-N1 and the distance between N1-N8, assuming that the shortest path passes through nodes N2, N1, N8 in turn.

1 is a network in which a node pair (N3-N10) having a maximum 4-hop in the shortest path exists, and the MDS-MAP constitutes an entire position map with an error of 4 hop.

The MDS-MAP (P) constructs the distance matrix by extracting the network by 2 hop from each node regardless of the maximum hop count of the network, and composes the entire position map by synthesizing the information about all the nodes. At this time, a considerable calculation amount is required in the process of estimating the entire position by linearly transforming the relative position map of each node.

Therefore, it is required to reduce the error caused by the distance approximation and reduce the computational complexity, which is a disadvantage of the conventional MDS-based localization method, so that it can be applied to the actual field environment.

Accordingly, in order to reduce the occurrence of errors due to high computational complexity and approximation, which is a problem of existing MDS-based position estimation schemes, the present invention proposes a method of selecting one optimum node rather than a method of combining maps obtained from all the nodes do.

The proposed algorithm is a greedy algorithm that finds the optimal number of nodes by incrementally increasing the number of nodes constituting the relative position map.

를 구성한다.

는 n × n크기의 이진(binary) 행렬로 노드 i와 노드 j가 서로 연결되어 있는 경우

의 원소

는 1의 값을 가진다. 예를 들어, 도 1에 대한 인접행렬은 다음과 같다.First, the adjacency matrix (adjacencymatrix), which contains connectivity information between nodes for a network having n nodes in total,

.

Is a binary matrix of size n × n and node i and node j are connected to each other

Element of

Has a value of one. For example, the adjacency matrix for FIG.

One node among the n nodes, which is the center of the local relative position map, is referred to as a reference node,

The reference node vector s can be defined as follows.

로 표현할 수 있다. 또한, 기준노드 벡터의 cardinality는

이므로,

이다.In this case, the element of the reference node vector means the index of each reference node, and when the vector for all nodes is u, the non-reference node vector

. Also, the cardinality of the reference node vector is

Because of,

to be.

는

개부터 시작한다.If the dimension of the final desired position coordinate is m *, the number of initial reference nodes

The

Begin with dogs.

That is, when two-dimensional coordinates are to be obtained, the initial value of the number of reference nodes is three. This is due to the relative position mapping obtained from the reference node. The combination of the relative position maps is performed by linear transformation (movement, rotation, scaling) of the position map, but when the number is m *, the map can not be recognized as inverted.

2 is an example of combining MAP1 and MAP2 based on the common nodes N1 and N2 in a two-dimensional space. Even if the MAP2 is inverted because of the relative position map, there is no abnormality in the relative position information of the MAP 2 and the coupling between the two maps is performed without any problem.

로 정의한다.

가 커질수록 지도간의 공통된 노드의 수는 많아지지만, 이를 만족하기 위한 기준노드의 수 또한 증가하므로 지도 구성의 복잡도와 지도 결합의 복잡도 간의 적절한 값을 찾는 것이 중요하다.In FIG. 2, if the number of the common nodes N1 and N2 of the two MAPs is not two but three or more, the inversion can be recognized even if the number of maps is not m * +1. In other words, it can be seen that the higher the degree of the common nodes (the number of neighbor nodes) is, the easier the composition of the combined map is. In order to reflect this, the ratio of nodes connected to one or more reference nodes m * +

.

It is important to find an appropriate value between the complexity of the map configuration and the complexity of the map combination.

를 달성하기에 유리하며, 이는 기준노드 개수의 최소화, 즉, 상대 위치 지도 결합의 복잡도를 낮추는 결과를 가져온다. 또한 같은 수의 기준노드에 대해 연결성이 높은 경우 더 많은 위치 정보를 가질 수 있으므로 오차 또한 줄어들게 된다.A method of selecting a reference node follows a method of preferentially selecting a node having a higher degree. Intuitively, constructing a relative position map preferentially for a small number of nodes with a high degree

, Which results in minimizing the number of reference nodes, i.e., reducing the complexity of the relative position mapping. Also, if the connectivity is high for the same number of reference nodes, the error can be reduced because more position information can be obtained.

의 degree =

)가 높은 순으로

개를 선택하여 초기 기준노드벡터

를 구성한다.Therefore, the initial baseline node is degree (

Degree =

) In descending order

Select the initial reference node vector

.

를 만족할 때까지 기준노드를 계속 추가한다. 비(非)기준노드 중 한 개의 노드를 임시로 기준노드로 선정한 후, 기준노드와 비기준노드 간의 연결성을 비교하여 최종 추가 노드로 선정한다. 연결성 비교는 앞서 언급한대로 상대 위치 지도 결합 시 복잡도를 낮추기 위해 degree가

이상인 노드들이 많아지도록 하는 후보 노드를 우위에 둔다. 기준노드 벡터

에 대해, 모든 노드와 기준노드와의 연결성을 나타내는 벡터

는 다음과 같이 표현된다.Once the initial baseline node is selected,

The base node continues to be added. After temporarily selecting one of the non-reference nodes as the reference node, the connectivity between the reference node and the non-reference node is compared and selected as the final additional node. As mentioned above, the connectivity comparison is based on degree

The number of nodes is increased. Reference node vector

A vector representing the connectivity between all the nodes and the reference node

Is expressed as follows.

는 노드

가

에 속한 노드(기준노드) 중 몇 개의 노드와 연결되어 있는지를 나타낸다.

인 노드

에 대해

에 대해

의 원소들 중 값이

이상인 원소의 개수를

라 하면, 기준노드에 추가될 노드

는

를 최대화하는 노드로 구할 수 있다. At this time,

The node

end

(Reference node) belonging to the node (reference node).

In node

About

About

Of the elements of

The number of elements

, The node to be added to the reference node

The

Can be obtained as a node that maximizes the number of nodes.

이상인 원소의 개수를 비교하여 선정하며, 차후 계속 동률 발생 시 같은 방식으로 반복한다. 선정된 노드에 대해 기준노드벡터를If the candidate node selection start-up rate occurs, the value of

The number of elements is compared and selected, and it is repeated in the same manner when the subsequent ties are generated. For the selected node, the reference node vector

를 비교한다.After updating as described above,

.

를 만족할 때까지 반복하여 기준노드를 추가 선정한다.And

Is repeated until the reference node is satisfied.

=0.8로 가정한다.With reference to the above description, an embodiment for selecting a reference sub-node in a network as illustrated in FIG. 3 will be described. First, in FIG. 3, m = 2 and n = 10,

= 0.8.

).First, the adjacency matrix of FIG. 3 is obtained and the degree of each node is confirmed. The initial reference node vector is selected as nodes N3 and N7 with degrees 7 and N1 with the fastest index among nodes having degree 6

).

및

를 계산한다Next, in order to select a node to be added as a reference node,

And

≪ / RTI &

For example,

가

로 최대값을 가지므로

를 기준 노드로 추가 선정한다.to the next,

end

Has the maximum value

As a reference node.

이므로 다시 추가 기준노드를 선택한다.

및

를 계산하면,Next,

Therefore, an additional reference node is selected again.

And

Lt; / RTI >

이상인 노드의 개수도 0으로 동일하고

이상인 노드의 개수 또한 2개로 동일하므로 인덱스가 빠른

를 추가 기준노드로 선정한다.Resulting in two candidate nodes.

The number of nodes that are equal to zero is the same

The number of nodes is equal to two, so the index is fast

Is selected as an additional reference node.

을 만족하므로 추가 기준노드의 선택을 종료한다. 최종 기준노드는 총 5개이며, 최종 기준노드 벡터는

이다.to the next,

The selection of the additional reference node is terminated. The final reference node is 5, and the final reference node vector is

to be.

In order to evaluate the performance of the present invention, the algorithm is implemented and the simulation is performed using the MATLAB software. The network topology assumes that robots (nodes) are randomly located in a two-dimensional space (10 km × 10 km), assuming that each node has the same communication distance of 3 km. The distance from each node to another node in the communication distance is known by the distance measurement method, and it is assumed that there is no measurement error. The shortest path was obtained using the Dijkstra algorithm. In this simulation, three factors were evaluated and compared with the above-mentioned MDS-MAP and MDS-MAP (P) techniques. In this experiment, the target space and the communication distance of a specific size were experimented, but the communication distance can be normalized to the relative performance.

The experimental results were as follows.

에 따른 성능 평가One.

Performance evaluation according to

는 MDS 수행 시 결합해야 할 상대위치 지도의 수에 영향을 주는 요소이므로, 주어진 네트워크와 성능목표에 맞게

를 정해주는 것이 중요하다. 본 시뮬레이션에서는

값의 변화에 따른 평균 오차 및 총 기준노드 수의 변화를 확인한다. 도 4는

의 변화에 따른 위치 추정 값의 오차를 노드 수 별로 나타낸 그래프이며,

가 증가함에 따라 위치 추정 오차가 줄어드는 경향을 나타낸다. 이는 도 5에서 볼 수 있듯이

가 증가하면서 기준노드의 수가 증가하게 되고, 결합하는 상대 위치 지도의 수가 늘어나게 되어 많은 정보를 통해 위치를 추정하기 때문이다.

값 선택에 따라 20~43 %의 오차 개선율을 보인다.

Is an element that affects the number of relative position maps that should be combined when performing MDS,

It is important that you decide. In this simulation

The average error and the change of the total number of reference nodes according to the value change are confirmed. Figure 4

Of the position estimation value according to the number of nodes,

The error of position estimation decreases. 5,

As the number of reference nodes increases, the number of relative position maps to be combined increases, and the position is estimated through a lot of information.

According to the value selection, error improvement rate is 20 ~ 43%.

2. Performance evaluation according to the total number of nodes

As the number of nodes increases in the same area, the number of nodes that can communicate directly increases because the distance between nodes becomes shorter. This can increase the accuracy of the position estimation and result in an increase in the number of relative position maps to be combined.

가 0.9일 때 노드 수에 따른 위치 추정 값의 오차를 나타낸다. 노드가 적을수록 위치 추정 오차 개선율이 높은 것을 알 수 있으며, 이는 노드 수가 늘어날수록 노드 간 거리 근사 빈도수가 감소하기 때문이다. 6,

Is 0.9, it represents the error of the position estimation value according to the number of nodes. The smaller the number of nodes, the higher the improvement in the estimation error. This is because as the number of nodes increases, the frequency of distance approximation between nodes decreases.

On the other hand, as shown in FIG. 7, it is possible to achieve better performance of position estimation with a smaller number of relative position maps than with the MDS-MAP (P) method. 8 to 17%, and the number of relative position maps is reduced by up to 59%.

3. Performance evaluation according to the degree of network connection

Finally, the degree of network connection (the average degree of all nodes) represents the density of the network, and it is easy to complete the adjacency matrices because it is easy to measure the distance between the nodes.

FIG. 8 shows the error of the position estimation value according to the average degree, and FIG. 9 shows the average relative position map number. The results are similar to the previous two indicators. As the degree is lower, it is difficult to measure the distance between the nodes. Therefore, the proposed algorithm shows a high error improvement rate, and the higher the degree, the lower the number of relative position maps to be combined.

Claims (3)

A method of selecting a reference node for relative position estimation between nodes based on a Multidimensional Scaling (MDS) scheme in a wireless network environment,
Measuring a distance between nodes;
Analyzing connectivity information between the nodes;
Selecting a reference node among all nodes;
Constructing a relative position map from the reference node; And,
A relative position estimation step of all nodes based on the relative position map;
/ RTI > The method according to claim 1,
Wherein the step of selecting the reference node comprises:
3 nodes having the highest connectivity with neighboring nodes are selected as the initial reference nodes, and the number of the nodes having the connectivity between the reference node and the nodes other than the reference node, Selecting a new node as a new reference node. 3. The method of claim 2,
When the number of nodes having connectivity of 3 or more with respect to the reference node is greater than the total number of nodes

The reference node selection is stopped.

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