EP2243039A1

EP2243039A1 - Method, node, device, computer program, and data carrier for determining a position of a node in an ad-hoc network

Info

Publication number: EP2243039A1
Application number: EP08870832A
Authority: EP
Inventors: Oliver MÜLLER; Alejandro Ramirez
Original assignee: Siemens AG
Current assignee: Siemens AG
Priority date: 2008-01-14
Filing date: 2008-12-22
Publication date: 2010-10-27
Also published as: US20110045844A1; CN101910863A; DE102008021614B4; WO2009089989A1; DE102008021614A1; US8369869B2

Abstract

The invention relates to a method and a device for determining a geographical position of a node in an ad-hoc network. In order to do so, distance circles of at least two nodes that adjoin said node are determined. In addition, points of intersection between the distance circles of the at least two nodes adjoining the node are identified. A main set of points of intersection is determined from among the set of the identified or determined points of intersection, said main set comprising points of intersection located in the vicinity of an estimated position of the node. The geographical position of the node is then determined by means of the main set of points of intersection.

Description

description

Method, node, device, computer program and data carrier for determining a position of a node in an ad hoc network

The invention relates to determining geographic locations of nodes in an ad hoc network. In particular, the present invention relates to a method, a node, a device, a computer program and a data carrier, each of which enable the inventive determination of geographical positions in an ad hoc network.

Nowadays many objects have the opportunity to communicate with other objects. That means they are capable

Information, messages, data to send and / or receive. The objects can be permanently installed, resting or moving. In many situations, such as For example, in traffic (e.g., road or air), warehouses, etc., it is useful to coordinate such objects (such as vehicles, containers, etc.). For example, to support security or administration.

The possibility of integrating the objects in communication networks opens up many possibilities in this context, for example to support the aforementioned security or administration. Thus, the objects can at least partially take the coordination into their own hands. That is, by matching with other objects, by receiving position-relevant data, information, the objects can evaluate the data provided, information, and make conclusions about their positioning with respect to other objects of the environment. The objects (hereinafter nodes) form a network in which the objects are to be coordinated or positioned, at least partly by a corresponding system. tem and / or at least partially taken over by the objects or nodes themselves.

Various possibilities are described in the literature for relating the positions of individual nodes and the distances between one another and between the nodes. In most cases, it can be assumed that the network consists of two types of nodes. On the one hand from beacon nodes, which know their own position, on the other hand from standard nodes, which have to calculate their position on the basis of the distances to the beacon nodes.

The known methods can be differentiated with regard to their approaches into distanceless and distance-based approaches.

For distanceless approaches, the distance of each network node is determined on the basis of a hop metric (i.e., the number of other nodes between two nodes) which, in a further step, is translated into geographical distances using the network topology so depicted. An explicit measurement of the distances between the nodes does not take place. These include, for example, such prior art works as Niculescu and Nath [1] and, based on this, Hsieh and Wang [2].

In the case of distance-based approaches, the position of the individual node is estimated by means of direct distance measurements between individual network nodes or between nodes and beacons. Examples of this type of localization include i.a. [3], [4] and [5]. In [6] an attempt is made to compute a position estimate with the RSSI (Received Signal Strength Indication) of the signals received from the beacon nodes.

In the present case, distance-based position determination is considered. The distance is usually determined by means of a distance or distance determination method. Overall, a breadth of methods for determining distance or distance is used. For example, measurements can be made using the strength of the received signal (Received Signal

Strength, RSS), Time of Arrival (ToA), Time Difference of Arrival (TDoA) or Roundtrip Time of Flight (RToF) measurements, etc. are used to determine or determine the distance or distance , The problem that arises from all of these methods is the inaccuracy of the measurements. This means that no exact distance or distance values can be determined or determined. The result of such measurements is an inaccurate or estimated distance value.

Because distance-based approaches build on distance information, they must be robust against such inaccurate or estimated distance values.

Lately, the following two methods of position determination have become popular among distance-based approaches: multilateration (LSL) [7] and bounding box methods (BB) [5], [8].

Fig. Ia illustrates a method according to the prior

Technique (trilateration) for position determination. In particular, Figure 1a shows how the trilateration works when there are three nodes or neighbors Bi, B ₂ , B ₃ in the vicinity.

In this case, the position of the M is estimated on the basis of measured distances di, d2 and d3 from the neighboring nodes Bi, B ₂ , B ₃ to the sought-after node M.

The trilateration is very susceptible to errors, both in terms of the positions of the beacon nodes and in the accuracy of the measured distances, since they are on a ma- thematically clear procedure in which errors are not provided. As explained above, however, the problem lies in the fact that in practice the measured distances are always estimated and thus inaccurate values.

Fig. Ib shows the typical problems of locating by multilateration. If the distance measurements are not perfect and accurate, the position will be calculated incorrectly. Multilateration is an advanced form of trilateration. While the trilateration with three neighbor nodes can determine the position of a node, all available neighboring nodes of the node to be located are used for the multilateration.

With multilateration can from the measured distances di + derr, i 'd2 + d _er r, 2 and d3 + d _er r, 3 of several adjacent nodes Pi, P ₂ , P ₃ to the unknown node M and their known position, the position of the unknown node M are estimated. Compared to trilateration, multilateration can also handle inaccurate position or distance measurements. In Fig. 1b, the estimated positions P _es tχm, i / Pestim, 2, P _e stim, 3 deviate from the real positions of the nodes Pi, P ₂ , P ₃ . Further, the measured distances are di + _he d r, i 'd ₂ + d _err, 2 and d 3 + d _err, 3 with errors _he d r, i' _th e r, 2, d _err, 3-prone. Accordingly, it can be seen in FIG. 1 b that the calculated position M _est differs from the actual or real position of the node M.

However, multilateration has the disadvantage that it is very susceptible to error if multicollinearity of the neighboring nodes is present. In addition, an error in the position determination by means of multilateration increases, even if there are errors in the input data (the positions of the adjacent nodes and the corresponding distances). Even small capture errors can cause or produce very large errors in the calculated result position. Another known method is the bounding box method [5], [8], which allows the location of nodes in the network, as soon as distance measurements can be made. Fig. 2a shows an example of this method when the measurements are very accurate. This method is based on the assumption that the probable position of a node with the distances measured in each case can be limited in a quadrangular area (the minimum bounding box), whose center then represents the estimated position. In Fig. 2a, the sought node M has three adjacent nodes Pi, P ₂ , P3. In this case, the delimiting areas or boxes are defined by the positions (xi, yi), (xi, yi), (xi, yi) of the neighboring nodes Pi, P ₂ , P ₃ and the distances di, d ₂ , d _{3 of} the neighboring nodes determined to the desired node M. M _estim is the estimated position of node M.

If the neighboring nodes are around the node you are looking for, the bounding box method will yield very good results. However, problems arise when the node being sought has neighbors on only one side (ie, only right, left only, or top only). Figure 2b illustrates pictorially this problem, ie the extent of the difficulties that the method may have if the user does not have neighbors in one direction or on one side (eg at the edge of the network). The bounding box method does not succeed in such situations to capture or frame the node sought. It comes to serious misjudgments regarding the position of the node sought. Thus, the calculated position M _estim and the actual position of the searched node M are very far from each other.

An object of the present invention is to provide an improved position determination.

The object is achieved by a method having features of claim 1, by a node having features of claim 15, by a device having features of claim 29, by a computer program having features of claim 1. Proposition 30 or by a data carrier with features of claim 32.

The object is achieved by a method for determining a geographical position of a node in an ad hoc network, the method comprising the following steps:

Determining distance circles of at least two neighboring nodes of the node; Determining intersections of the distance circles of the at least two adjacent nodes of the node;

Determining a majority of intersections, the majority comprising intersection points proximate an estimated position of the node; and determining the geographical position of the node by means of the majority of intersection points.

A distance circle is a circle around a given account with a predetermined radius d. In the present case, the radius is the distance between a neighbor node and the searched node or node for which the position is determined. As already mentioned above, the distance is determined or determined by means of a distance or distance determination method. The present invention is not limited to any of the distance or distance determination methods. A wide variety of methods for determining the distance can be used (e.g., RSS, ToA, TDoA, RToF, etc.), and combined application of these techniques is also possible. Thus, the present invention allows flexible implementation.

Intersections are those points where two or more distance circles overlap.

The positions of the neighboring nodes may be predetermined or estimated and thus inaccurate (eg by a Global Positioning System GPS). Again, the underlying invention is a flexible implementation and is applicable to different situations.

The present invention enables an omnidirectional determination of the position, in particular, since circles are used as search objects. Furthermore, the determination of the position by means of the intersections of the distance circles allows on the one hand fast and effective and on the other hand clearly more precise determination of the position of a node in comparison with the known methods of the prior art.

For each neighboring node of the at least two neighboring nodes, a distance circle of the neighboring node can be determined by means of a position indication of the neighboring node and a distance indication. The distance indication indicates the distance between the adjacent node and the node for which the position is determined or determined according to the invention. In the following, this node will also be referred to as the node sought.

The distance specification can be an inaccurate distance specification. That is, determining a position of a node according to the present invention is prepared for inaccurate distance indication and has an error margin.

Furthermore, the position indication may also be an inaccurate position indication. The present invention thus also has an error tolerance with regard to details of positions of other nodes. This may be the case, for example, when the position information is provided by GPS measurements.

In addition, the position information can also be an exact position indication. For example, the position data to the neighboring nodes can be specified by exact or exactly functioning measurement method or be given. The latter is z. B. be the case when the object representing a neighboring node, is permanently installed or attached.

As already explained, the distance indication can be determined by means of a distance measuring method.

Furthermore, the intersection points of the distance circles can be determined based on a subtraction and a transformation of circle equations of two distance circles each.

In doing so, a threshold may be used in determining the majority of intersections, and the intersections lying within the threshold (e.g., not exceeding this threshold) may be used in the calculation of the final result.

According to an embodiment of the present invention, mean values of x and y components of the intersections may be used to determine the majority of intersection points.

Further, the majority of intersections may be determined by backward regression according to an embodiment of the present invention.

Further, the method may be performed by the node for which the geographical position is determined.

The node may be a mobile node of the ad hoc network. He can z. B. be a vehicle in the transport network.

The above object is achieved by a node in an ad hoc network, wherein the node has means for determining a geographical position of the node, wherein the means for determining a geographical position of the node are configured: To determine distance circles of at least two adjacent nodes of the node;

To determine intersections of the distance circles of the at least two adjacent nodes of the node; to determine a majority of points of intersection, the majority comprising points of intersection close to an estimated position of the node; and

to determine the position of the node by means of the majority of points of intersection.

Overall, the node, and thus the means for determining a geographical position of the node, is configured to perform the steps of the method outlined above and detailed below.

The means for determining a geographical position of the node are configured to determine for each adjacent node of the at least two neighboring nodes a distance circle of the neighboring node by means of a position specification of the neighboring node and a distance indication.

In this case, the node may have means for receiving the position information of the neighboring node. That is, in such a case, the node can obtain the position information of the neighboring node on request.

According to one embodiment, the distance indication may be an inaccurate distance indication.

The position specification can be an inaccurate position specification. So z. For example, the position indication may be a position indication provided by a GPS measurement. The position indication can also be an exact position indication. This is z. This is the case, for example, when the position relates to a permanently installed node of the network. Furthermore, the distance indication can be a specific distance indication by means of a distance measuring method.

According to an embodiment of the present invention, the means for determining a geographical position of the node may be configured to determine the intersection points of the distance circles based on a subtraction and a transformation of circle equations of each two distance circles.

In addition, the means for determining a geographical position of the node may be configured to use a threshold in determining the majority of points of intersection and to use intersections lying within the threshold for the calculation of the final result.

Furthermore, the means for determining a geographical position of the node may be configured to use mean values of x and y components of the intersection points for determining the majority of intersection points.

According to an embodiment of the present invention, the means for determining a geographical position of the node may be configured to be the main set of

To determine intersections by means of a backward regression.

The node may be a mobile node of the ad hoc network. So z. For example, the node may be a vehicle.

The above object is also achieved by means of a device having means for determining a geographical position of a node in an ad hoc network, wherein the means are designed: To determine distance circles of at least two adjacent nodes of the node;

To determine intersections of the distance circles of the at least two adjacent nodes of the node, to determine a majority of intersection points, the majority comprising intersections close to an estimated position of the node; and

to determine the geographical position of the node by means of the majority of points of intersection.

The device as a whole is configured to perform the steps of the method outlined above and described in more detail below.

The device can be installed anywhere in the ad hoc network. So z. For example, it may be included in a node of the ad hoc network. In particular, it may be part of a node for which the geographic location is to be determined. That is, it may, for example, be installed in a vehicle of a traffic network if the node is a vehicle, perform the position determination directly in the vehicle and thus contribute to the coordination of the traffic, i. h., support the safety or management of the transport network.

Furthermore, the above object is achieved by means of a computer program having a coding which is designed such that it carries out steps of the method outlined above and described in more detail below. In this case, the computer program can be stored on a data carrier.

In addition, the above object is achieved by means of a data carrier having the above-mentioned computer program. In the following, the invention will be described in detail with reference to embodiments according to the attached figures, in which:

Fig. Ia illustrates a prior art method (trilateration) for position determination;

FIG. 1 b illustrates a method according to the prior art (multilateration) for position determination and thereby illustrates the disadvantages of the method; FIG.

Figure 2a illustrates a prior art method (Bounding Box Method) for position determination;

Fig. 2b illustrates a prior art method (Bounding Box method) for position determination, illustrating the disadvantages of the method;

FIG. 3 illustrates a position determination according to an embodiment of the present invention; FIG.

Fig. 4 shows a comparison of the results of the method according to the invention and the methods according to the prior art, wherein the average dRMS of the methods is given in the RWP model;

Fig. 5 shows a further comparison of the results of the method and the prior art methods, wherein the mean dRMS of the methods is given in the RWP model and the comparison of the methods is shown by means of neighboring nodes further away from the center; Fig. 6 shows a scheme of a column simulation;

7 shows a comparison of the results of the method according to the invention and the methods according to the prior art with respect to the scheme of Figure 6 with mean dRMS;

Fig. 8 shows a detail of a simulation field with a column travel simulation with least squares multilateration (LSL) and the method (MDL) according to the invention;

Fig. 9 shows a schematic of a crossing simulation;

Fig. 10 shows results of the crossing simulation, indicating an average dRMS of the method of the invention and the prior art methods in the crossing model; and

11 shows results of the crossing simulation, wherein the dRMS of the method according to the invention and the method according to the prior art is displayed as a function of the distance to the center of the crossing.

In the following, the present invention will be explained using the example of a traffic network, for the sake of simplicity being considered as objects or nodes of the (traffic) network vehicles. It should be noted that the present invention is not limited to an application in the traffic network, but that other fields of application of the present invention are possible. As objects or nodes of a network, various objects or devices can serve.

Fig. 3 illustrates position determination according to an embodiment of the present invention.

In this case, the network consists of nodes P ₁ , P ₂ , P ₃ , P ₄ and M, where M is the node sought, ie, the node for which the position determination is performed, and wherein the nodes P ₁ , P ₂ , P ₃ , P4 are adjacent nodes of the M node. The network may, for example, be a traffic network in which the nodes Pi, P ₂ , P ₃ , P ₄ and M represent vehicles. The vehicles can communicate with each other and by determining their position by means of positions of the nearby vehicles and / or other objects in the transport network and by appropriate communication with the nearby vehicles and / or other objects in the traffic network critical situations avoid. However, the scope of the present invention is by no means limited to such traffic situations or traffic altogether. The present invention is flexible and can be applied in various fields in which problems arise with regard to the positioning and / or coordination of objects.

For each of the adjacent nodes Pi, P ₂ , P ₃ , P _{4 there} is in each case a distance information di + d _er r, i 'd ₂ + d _er r, 2, d3 + d _er r, 3, d ₄ + d _{err, 4} with respect to Distance or distance between the sought node M and the respective adjacent node Pi, P ₂ ,

P ₃ , P ₄ before. Since the distance determination methods provide only an estimate and not an exact indication of a distance between two nodes, the distance information available to the nodes is inaccurate. Therefore, a present distance information d _± + d _er r, i is made up of the actual distance d _x and the error d _{err / 1} which is present through the estimation. The values of the errors d _err , i are real numbers. Thus, t _he r, i have both a positive and a negative value. For better illustration, the errors d _er , i of FIG. 3 have positive values.

According to the present embodiment, for each possible pair of neighbors of a node, intersection points of the distance circles of neighboring nodes are calculated separately. The majority of these intersections will be near the actual position of the node being searched. From this main set of estimated positions of the intersections Then, the final result position of the searched node M is calculated.

The intersection points of the distance circles of adjacent nodes Pi and P2 of a node M to be calculated or searched can be found as set out below.

Consider the distance circles of Pi and P2 as circle equations:

Here, (X ₁ , Y ₁ ) is the position of the node P ₁ . The position statement (X ₁ , Y ₁ ) can be an estimated or inaccurate or even an exact or precise position specification, (x, y) is the searched position of the node M.

By subtracting and transforming the circle equations (1) and (2), the following equation is obtained:

y (2y ₂ -2y _λ ) = 2x (x _λ -x ₂ ) + (d ² -d ₂ ) + (x ₂ -x ² ) + (y ₂ -J ₁ ² ) (3)

After another transformation you get:

With the replacement by the parameters pi and P2, where)

and

_ Jd ₁ ² - d ₂ ² ) + (X ₂ ² - X ₁ ² ) + ^ ² - J ₁ ² ) 2J ' ₂ ^"2 J \ Then the equation of the straight line is given by the intersections of the distance circles of Pi and P ₂ :

y = P ₁ * x + p ₂ (7)

In the next step, the equation (1) is transformed to:

and then equated with the equation of the straight line through the intersections of the distance circles of Pi and P ₂ (7):

P ₁ X ₊ P ₂ = y = ± ^ d ² - (XX ₁ ) ² + y _γ (9)

After squaring equation (9), the following equation results:

P ₁ x + Ip ₁ X (P ₂ - _λ y) + (p ₂ - _λ y) = d _λ _λ -x + 2xx -X ₁ = 0 (10)

By a further transformation, the equation arises:

x ² ( _P ² + \) + x (2 _Pλ ( _Pl -y _λ ) -2X ₁ ) + O ₂ -J ₁ f -d ² -X ₁ ² = 0 (11)

Further, in the equation (11), parameters qi, q ₂ and q ₃ are used, wherein:

<7, = Λ ² +1 ⁽¹²⁾

q ₂ = ₂ p _ι (p ₂ -y _ι ) -2x _ι (13)

By substituting the parameters qi, q ₂ and q ₃ into the equation (11), the quadratic formula is finally obtained: q _x x ^~ q ₂ x + q ₃ : i 5) with the solution:

_{Xl 2} = - ^q > ¹ ^ ^"4 ^ (1 6)

2 ^ ₁

Finally, by calculating the parameters pi, p ₂ and qi, q ₂ and q3, the set of intersection points of the distance circles of two neighbors of a node can be obtained or found. The amount of solution can not have or include one, one, or two points.

Altogether, with an amount of n neighboring nodes of M

different pairings possible. From each neighbor pair of a node usually two intersections are generated. One of these intersections may be in the vicinity of the desired node M, the other intersection may in turn be far away from the M. In order to eliminate those points of intersection which are far away from the position of the desired node M, it is expedient to introduce a threshold or a threshold value, starting from the farther away

Intersections are no longer included in the result (the searched position of the M). The threshold value is z. B. a maximum distance or a maximum distance, the / may be given between two intersections. In this way, a majority of points of intersection is determined or detected having such intersection points which are in the vicinity of the actual or searched position of the searched node M. This is done according to the present embodiment based on the own measured position of the searched point. In this case, according to the present invention It is also possible to use still existing cluste ring processes. For example, a selection via a backward regression would be conceivable.

All points that are within the threshold are used to calculate the final result, i. h., the sought position of the M used.

This can now be done, for example, by calculating the mean values of the x and y components of the positions

_X = ^ L

respectively.

be determined.

Thus, according to the present embodiment, all x-values of all intersections are summed, and the sum is divided by the number of intersections. Accordingly, the y values are also treated. So all y values of all intersections are summed, and the sum is divided by the number of intersections. This gives you a central point between the intersections.

All points of intersection are considered from this central point of the intersections, it being determined for each intersection whether the distance between the central point and the intersection is below the predetermined threshold. If so, is the intersection in the set al ler intersections recorded and thus considered for further positioning.

As already mentioned, FIG. 3 illustrates the approach of the approach of the present invention according to an embodiment of the present invention. In this case, all the intersection points of the respective neighbor pairs considered are calculated, and then a data set for the final result is selected (here, based on a fixed circumference around the measured position of M). The mean value of these intersections forms the sought result position of the node M. The set of all intersections is marked in FIG. 3 by stars. The unfilled or white stars indicate the points of intersection which are not used for the calculation or determination of the sought result position of the node M. The solid or black stars in turn point to the intersections of the majority of points of intersection, d. h., those intersections that are not used for the calculation or determination of the sought result position of the node M.

According to the present invention, the localization problem is divided into individual estimates. This has the advantage that single strong outliers can be effectively and easily excluded from the final position estimate.

Further, the present invention can effectively counteract and effectively and effectively handle the multicolor linearity which causes positioning problems in the known methods. According to the present invention, a clustering of the intersection points is carried out, as stated above, for example by an averaging of the determined intersections. This results in a much more accurate estimate. In the case that the searched node M is in line with its neighbors, the accuracy by the position determination according to the present invention increases again, because then the intersections of the distance circles are almost symmetrical at right angles to the line. Thus, the mean value of the intersections approximates the real or actual position of the searched node M.

As already mentioned, the present invention relates to methods of the second category, i. h., on distance-based methods, since it is assumed that at least approximate distance measurements are present as input data.

The measurement of the distances between the nodes can be carried out, for example, by means of the runtime of incorporating distance or distance determination methods. As already explained, the present invention is not limited to such distance determination methods. Thus, for example, other methods can be used or used, eg. B. Methods based on ultrasound measurements, light measurements or measurements by radio waves. The present invention generally requires that a distance determination method provide information on the distance between a searched node and at least one neighboring node of the searched node, which is expected to result in a possible inaccuracy of the distance information. Of course, this does not exclude accurate distance information. Thus, a fault tolerance with respect to the determined distance between the searched node and the adjacent node is ensured.

An important difference to the known methods is that the known methods necessarily distinguish between beacon nodes and normal nodes, ie between nodes whose position is either known or completely unknown. According to the present invention The neighboring nodes have position estimation in the form of GPS measurements or other position measurements and / or exact position information. Such estimates are used in a cooperative manner for positionalization in accordance with the present invention.

Another advantage with respect to prior art methods is the proportion of network beacon nodes and the density of the network. In known methods, relatively high proportions of beacon nodes are assumed (5-10%). The present invention also enables positioning in those networks that have a low proportion of beacon nodes because, based on the total number of nodes, e.g. B. Vehicles in traffic, the number of RSUs with a known position is rather small. As a reference for the determination of the position of a node serve therefore its neighboring nodes, ie those nodes that are within its radio range. Looking at the example of a transport network, so z. For example, in a WAVE network, the number of vehicles is rather small and may vary considerably in density. Not least because of the mobile character, the topology changes constantly.

Furthermore, for the position determination according to the present invention, a classification of the nodes into the categories

Beacon or non-beacon node, which is required in the known methods, not necessary. Overall, the nodes can be referred to as general network nodes (eg vehicles) or as RSU nodes (eg road side units). The first category has only an inaccurate measurement of its own position, for example, by GPS, and is mobile. The second category has an exact position, but is immobile. Nodes that are mutually within their radio range are called neighbor nodes. The division into the first category mentioned above and the second category mentioned above is not mandatory. There can be nodes of both categories or nodes of one of the categories.

The results of the determination of the position of the abovementioned methods according to the prior art and the method according to the invention are compared below. To get an initial overview of the three methods (multilateration, bounding box methods and methods according to the present invention), they are first described in an abstract model, the Random Waypoint (RWP), which is generally used for the analysis of mobile networks. Model, tested. A certain number of mobile network nodes move in a closed rectangular field.

A detailed description of the RWP model is given for example in [9].

4 shows a comparison of the results of the method according to the invention and the methods according to the prior art (least squares multilateration, multilateration and bounding box methods), the average dRMS of the methods being specified in the RWP model.

In addition to the results of the three methods, the measured dRMS of the GPS input data was also included for comparison. This amounts to continuous about 12.5 m. Already at first glance, it can be seen in FIG. 4 that both the least squares multilateration (LSL) and the bounding box method (BB) provide very poor position estimation for only a few neighbors per node. The corresponding dRMS values are therefore not included in the diagram.

In Fig. 4, the vertical axis indicates the measured dRMS and the horizontal axis indicates the number of neighboring nodes. Only the method according to the invention (hereinafter referred to as the multidilateration (MDL)) can improve the accuracy of the input data even with small neighboring numbers. While LSL improves from approx. 11 neighboring nodes, BB only succeeds with the high number of approx. 50 neighbors. On the one hand, this is due to the high influence of outliers at LSL, especially in the case of only a few neighbors, which then manifests itself in a poor approximation. This effect mainly occurs at the edge of the network. On the other hand, BB's generally poor performance at the perimeter of the network is responsible for the high dRMS, but also the generally poor performance in this simulation model.

To shed more light on these differences, 50 snapshots of the state of the entire network were statistically evaluated. The total number of nodes was 20. In order to be able to distinguish between edge nodes and nodes in the middle of the network, the following metric was used: For each node, the number of nodes farther from the center of the simulation field than itself is determined. This metric or number is indicated on the horizontal axis of FIG. The vertical axis of Fig. 5 indicates the measured dRMS.

In Fig. 5 it can be seen that BB has a high degree of inaccuracy at the network edge. Due to the relatively high number of neighbors per node, LSL achieves significantly better values, but here too an increased dRMS can be observed, especially at edge nodes.

Overall, MDL works best in this environment. With only a few adjacent nodes, a good accuracy of the position estimation, clearly below the accuracy of the input data of 12.5 m, can be observed. By averaging the intersections of the neighboring distance circles a good estimate also comes about at the edges of the network, because unlike z. B. at BB no minimization of the largest distances takes place.

In the following, the present invention will be considered by the example of a column simulation.

After the general RWP scenario, more specific use cases of the procedures will now be discussed. For this purpose, the following movement pattern was selected for the nodes as vehicles in traffic:

- The number of network nodes is no longer fixed but variable. They enter the simulation in an adjustable, equally distributed probability of occurrence.

- A newly entering node appears at a fixed point on the edge of the simulation field and moves within a certain corridor in the X or Y direction to the opposite side of the simulation field. The movement is only in the specified direction, "reversing" is not possible. In each movement step, a sideward movement is also carried out whose deflection is equally distributed in the interval [-2.5m, 2.5m].

- If a node leaves the simulation field, the node is deleted.

In Fig. 6, a scheme of this scenario is outlined.

As can be seen from the evaluation in FIG. 7, the performance of the methods in this scenario has been contrary to the

RWP simulation partially changed significantly. It shows the vertical axis the average dRMS and the horizontal axis the number of neighboring nodes.

While the BB method showed by far the worst performance in the RWP scenario, LSL now occupies this position. One circumstance is particularly noteworthy here: Under RWP, BB achieved at least a high number of neighbors an improvement in position estimation compared to GPS accuracy. In the current scenario, however, LSL remains well above the threshold. Even with a significantly increased network density, no improvement in the position is to be expected according to data.

For LSL, the reason for the bad values is the scenario concept. Since all node positions are almost completely multicollinear, very large errors occur in least squares analysis. A screenshot of the scenario illustrates this (see Fig. 8, section of the simulation field).

The left side of the picture is a screenshot of LSL and the right side is for comparison with MDL. At LSL, the large positioning errors are clearly visible. Since the imaginary line passes through the positions in the Y direction, the localization errors in the X direction are

Direction very big. The LSL method is therefore completely unsuitable for this type of scenario.

Even though MDL gives the best results, the overall performance is worse than in the RWP scenario. While there a dRMS localization of less than 5 m was possible at high node density, the minimum here is at about

7 m. For large neighboring volumes, the MDL method is only marginally better than BB.

In the following, the present invention is explained using the example of an intersection simulation. While the previous situation of a convoy is more suitable for mapping highways or highways, the following is a typical urban scenario: the simulation of an intersection.

In principle, this scenario is not very different from the Column scenario, as only two corridors are crossed orthogonal to each other. Nevertheless, there are clear differences in the network topology, as between the

Nodes of the two corridors naturally arise new neighborhood relationships.

In Fig. 9, the scenario is shown schematically.

In Fig. 10, the average dRMS of the network is plotted with the various methods over the average neighbor per node. That is, the vertical axis indicates the average dRMS and the horizontal axis indicates the number of adjacent nodes.

Here, too, the LSL method falls significantly over the other two. Although its performance is better than in the previous scenario, even at high node densities its average dRMS is significantly higher than that of the GPS

Position measurement. The improvement is explained by the fact that within the circle described in FIG. 9 there are further nodes as neighbors that are not collinear with the neighbors in the same corridor. However, since these new neighbors also have high collinearity with each other, the improvement is not as great as desired.

By contrast, the BB process can not improve in comparison to the column scenario. With only a few neighbors per node, the dRMS is clearly higher and at high density it is still significantly higher. An improvement of the dRMS over the The dRMS of the GPS measurement is only achieved with an average of approx. 20 neighboring nodes, whereas in the column scenario this is already the case with approx. 11 neighbors. It seems that BB achieves the highest performance in the pseudo-one-dimensional scenario of the almost collinear column. As soon as, as here, neighbors with different positions in both coordinate components are included in the calculation, the values deteriorate. Also in this scenario, the performance of the MDL method is the best. Compared to the column scenario, the dRMS has even improved a bit, especially for low neighbor numbers. Even with large node densities, in contrast to the column simulation, a clear difference between MDL and BB can now be seen.

As already mentioned, depending on the distance to the middle of the intersection different neighboring quantities and thus also different good position estimates result. In particular, the accuracy in the immediate vicinity of the intersection is of interest. In Fig. 11, the dRMS (on the vertical axis) of the methods is plotted against distance (on the horizontal axis). The data shown was obtained through 50 snapshots.

It becomes clear that in the immediate vicinity of the intersection all three methods perform well, with MDL reaching an average dRMS of 4 m at 0 - 50 m radius around the midpoint, the other two 6 - 8 m. All three methods then slowly degrade with increasing distance in a linear manner. The performance of LSL then clearly decreases at 250 - 300 m - as there is no longer any connection to nodes of the crossing corridor, the results are similarly poor as in the column scenario. BB has good values to the outer edge of the network, though they do not achieve the quality of MDL. Then, however, the dRMS decreases rapidly, again pointing to the well-known problem of BB with marginal nodes. In summary, for the procedures simulated with the software created in the scenarios described above, Multidilator Action (MDL) is preferred for positionalization not only in vehicle networks. In all scenarios tested, MDL performed best. MDL has the lowest susceptibility to the problems of multicollinearity. Even in low-density networks, MDL has been able to achieve a level of precision in most cases.

The present invention relates to determining a geographic location of a node in an ad hoc network. For this, distance circles are determined by at least two adjacent nodes of the node. Furthermore, intersections of the distance circles of the at least two adjacent nodes of the node are determined. From the set of determined or determined intersections, a majority of intersections are determined, the majority comprising intersections close to an estimated position of the node. The geographical position of the node is then determined by means of the majority of intersection points.

Accordingly, all intersections of the respective neighbor pairs are calculated. From this, a data set (at intersections) is selected for the final result (eg, based on a fixed perimeter (for example, given by threshold) around the measured position of the node being searched for). The center of these intersections is the result position, d. h., the position of the searched node.

Although the present invention will be explained above with reference to the embodiment according to the accompanying drawings, it is apparent that the invention is not limited to this embodiment, but within the

The scope of the inventive idea disclosed above and in the appended claims may be modified. It understands Of course, there may be other embodiments which are the principle of the invention and are equivalent, and thus various modifications may be implemented without departing from the scope of the invention. For example, not all adjacent nodes need to be considered to determine the position of a node. This is not always sensible, especially in the case of large numbers of nodes, but in many cases it is also sufficient to have a predetermined or pre-determined quantity of neighboring nodes in order to carry out the determination of the position according to the invention. Furthermore, various clustering methods can be used to determine the majority of intersections. In addition, the present invention by no means depends on a given distance or distance determination method. Rather, results of various available distance or distance determination methods can be used. Furthermore, the information about positions of the neighboring nodes may be inaccurate and / or accurate information.

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Claims

claims

A method for determining a geographic location of a node in an ad hoc network, the method comprising:

Determining distance circles of at least two neighboring nodes of the node;

Determining intersections of the distance circles of the at least two adjacent nodes of the node; Determining a majority of intersections, the majority comprising intersection points proximate an estimated position of the node; and

Determine the geographical position of the node by means of the majority of intersections.

2. The method of claim 1, wherein for each neighboring node of the at least two neighboring nodes, a distance circle of the neighboring node is determined by means of a position specification of the adjacent node and a distance indication.

3. The method of claim 2, wherein the distance indication is an inaccurate distance indication.

4. The method of claim 2 or 3, wherein the Positionsan- gäbe is an inaccurate position indication.

5. The method of claim 4, wherein the position indication is provided by a GPS measurement.

6. The method of claim 2 or 3, wherein the position indication is an accurate position indication.

7. The method according to any one of claims 2 to 6, wherein the distance indication is determined by means of a distance measuring method.

8. The method according to any one of the preceding claims, wherein the intersections of the distance circles are determined based on a subtraction and a transformation of circle equations of each two distance circles.

9. A method according to any one of the preceding claims, wherein a threshold is used in determining the majority of intersection points and intersections lying within the threshold are used in the calculation of the final result.

The method of claim 9, wherein average values of x and y components of the intersections are used to determine the majority of intersections.

A method according to claim 9 or 10, wherein the majority of intersections are determined by means of a backward regression.

12. The method according to any one of the preceding claims, wherein the method is performed by the node.

The method of any one of the preceding claims, wherein the node is a mobile node of the ad hoc network.

14. The method of claim any one of the preceding claims, wherein the node is a vehicle.

15. Nodes in an ad hoc network, the node having means for determining a geographical position of the node that are configured:

To determine distance circles of at least two adjacent nodes of the node;

To determine intersections of the distance circles of the at least two neighbor nodes of the node; to determine a majority of points of intersection, the majority comprising points of intersection close to an estimated position of the node; and

- to determine the geographical position of the node by means of the main set of points of intersection.

16. The node according to claim 15, wherein the means for determining a geographical position of the node are configured to determine for each neighboring node of the at least two neighboring nodes a distance circle of the neighboring node by means of a position specification of the neighboring node and a distance indication.

17. The node of claim 16, wherein the node comprises means for receiving the position indication of the neighbor node.

18. The node of claim 16 or 17, wherein the distance indication is an inaccurate distance indication.

19. A node according to any one of claims 16 to 18, wherein the position statement is an inaccurate position indication.

20. The node of claim 16, wherein the position indication is a position indication provided by a GPS measurement.

21. A node according to any one of claims 16 to 18, wherein the position indication is an accurate position indication.

22. A node according to any one of claims 16 to 21, wherein the distance indication by means of a distance measuring method is determined distance specification.

23. The node according to claim 1, wherein the means for determining a geographical position of the knot are designed to determine the intersections of the distance circles based on a subtraction and a transformation of circle equations of each two distance circles.

A node according to any preceding claim, wherein the means for determining a geographical position of the node is arranged to use a threshold in determining the majority of intersections and to use intersections lying within the threshold for the calculation of the final result.

25. The node of claim 24, wherein the means for determining a geographical position of the node are configured,

To use averages of x and y components of the intersections to determine the majority of intersections.

A node according to claim 24 or 25, wherein the means for determining a geographical position of the node are arranged to determine the majority of intersections by means of a backward regression.

The node of any one of claims 15 to 26, wherein the node is a mobile node of the ad hoc network.

A node according to any one of claims 15 to 27, wherein the node is a vehicle.

29. An apparatus comprising means for determining a geographic location of a node in an ad hoc network, the means being configured:

To determine distance circles of at least two adjacent nodes of the node; To determine intersections of the distance circles of the at least two adjacent nodes of the node;

to determine a majority of points of intersection, the majority comprising points of intersection close to an estimated position of the node; and to determine the geographical position of the node by means of the majority of points of intersection.

A computer program having a code configured to perform steps of the method of any one of claims 1 to 14.

31. Computer program according to claim 30, wherein the computer program is stored on a data medium.

32. A data carrier having a computer program according to claim 30.