Method for determining positional data

• US 7,589,672 B2
• Filed: 04/11/2005
• Issued: 09/15/2009
• Est. Priority Date: 06/04/2004
• Status: Active Grant

• Current Assignee: Siemens AG
• Original Assignee: Siemens AG
• Inventors: Sollacher, Rudolf, Malinovskiy, Alexey
• Primary Examiner(s): Tarcza; Thomas H
• Assistant Examiner(s): LIU, HARRY K
• Application Number:
  US11/628,230
• Publication Number:
  US 20080100505A1
• Time in Patent Office: 1,618 Days
• Field of Search: 342/463, 342/357.08, 342/357.17
• US Class Current: 342/463
• CPC Class Codes: G01S 13/87 Combinations of radar systems, e.g. primary radar and secondary radar
• CPC Class Codes: G01S 13/876 Combination of several spaced transponders or reflectors of known location for determining the position of a receiver G01S13/874 takes precedence
• CPC Class Codes: G01S 13/878 Combination of several spaced transmitters or receivers of known location for determining the position of a transponder or a reflector G01S13/874 takes precedence

Abstract

An aspect of the invention relates to a method for determining positional data of at least one node of a network, said network comprising a number of nodes, whereby the positional data refers to an internal coordinate system. The method comprises the following steps: a) preparation of positional data for a sub-set of nodes, b) determination of separation data for the least one node, c) determination or, on repetition of step c), correction of the positional data for the at least one node, depending on the positional data from step a), the separation data determined in step b) and positional data of the at least one node and d) repetition of steps a) to c), until an interruption condition is fulfilled.

Claims

1. A method for determining positional data of a mobile node of a network that includes a plurality of mobile nodes, comprising:

providing a first and second coordinate system wherein the first coordinate system is a relative coordinate system to the second coordinate system;

relating the positional data of the mobile node to the first coordinate system;

determining a subset of nodes form a plurality of nodes located within the first or second coordinate system, wherein at least a portion of the subset of nodes are mobile;

selecting an outlier mobile node that is not part of the subset of nodes; and

identifying a position of the outlier mobile node via the steps;

providing positional data for the subset of nodes, wherein the positional data describes the respective position of the subset of nodes in the first coordinate system,

determining distances of the outlier node to the subset of nodes, and

determining the positional data of the outlier node based upon the positional data of the subset of nodes, and the determined distances of the outlier nodes and the positional data of the outlier node.

2. The method as claimed in claim 1, wherein the positional data is an initial position data at a first performance of the identification of the position of the outlier node.

3. The method as claimed in claim 1, wherein the positional data is a result of previous performance of determining the positional data of the outlier node and the positional data of the outlier node is determined until an interruption condition is fulfilled.

4. The method as claimed in claim 1, wherein the network is an Ad-Hoc network.

5. The method as claimed in claim 1, wherein the network consists exclusively of mobile nodes, the position of the mobile nodes not being known prior to a request to determine the position of the mobile nodes.

6. The method as claimed in claim 1, wherein the positional data of each node of the subset has information selected from the group consisting of:

the position of the respective node,

the estimated position of the respective node,

a rate of uncertainty of the position of the node,

a rate of uncertainty of the estimated position of the node,

a rate of mobility of the respective node, and

combinations thereof.

7. The method as claimed in claim 6, wherein the rate of the mobility of the respective node is dependent upon a variable selected from the group consisting of:

a diffusion constant,

an estimation of the actual speed vector, and

an estimated trajectory.

8. The method as claimed in claim 6, wherein the rate of mobility of the mobile node is determined from previous observations.

9. The method as claimed in claim 1, wherein the distance of outlier node from nodes of the subset is determined by means of a hop distance.

10. The method as claimed in claim 1, wherein the positional data of the at least one node is modeled as a random variable {right arrow over (ξ

)}_i,t and is determined by means of the expected value {right arrow over (μ

)}_i,t of this random variable {right arrow over (ξ

)}_i,t.

11. The method as claimed in claim 10, wherein the position of the outlier node is determined by means of an iterative calculation in accordance with the following iterative calculation rule:

${\stackrel{\to <br><br>}{\mathrm{\mu <br><br>}}}_{i,t}<br><br>\left(k+1\right)={\left[{\left(A_{i,t-1}+D_{i,t-1}\right)}^{-1}+\underset{j}{\sum <br><br>}<br><br>{\left({\stackrel{\to <br><br>}{e}}_{i,j,t}^T<br><br>\left(k\right)<br><br>\left(A_{j,t-1}+D_{j,t-1}+{\mathrm{\sigma <br><br>}}_j^2<br><br>I\right)<br><br>{\stackrel{\to <br><br>}{e}}_{i,j,t}<br><br>\left(k\right)\right)}^{-1}\right]}^{-1}\times <br><br>\hspace{1em}<br><br>\left[{\left(A_{i,t-1}+D_{i,t-1}\right)}^{-1}<br><br>{\stackrel{\to <br><br>}{\mathrm{\mu <br><br>}}}_{i,t-1}+\underset{j}{\sum <br><br>}<br><br>{\left({\stackrel{\to <br><br>}{e}}_{i,j,t}^T<br><br>\left(k\right)<br><br>\left(A_{j,t-1}+D_{j,t-1}+{\mathrm{\sigma <br><br>}}_j^2<br><br>1\right)<br><br>{\stackrel{\to <br><br>}{e}}_{i,j,t}<br><br>\left(k\right)\right)}^{-1}\times <br><br>\left({\stackrel{\to <br><br>}{\mathrm{\mu <br><br>}}}_{j,t-1}+{\hat{d}}_{i,j,t}<br><br>{\stackrel{\to <br><br>}{e}}_{i,j,t}<br><br>\left(k\right)\right)\right],$

where

{right arrow over (e)}_i,j,t(k)=({right arrow over (μ

)}_i,t(k)−

{right arrow over (μ

)}<sub>j,t−

1</sub>)/|{right arrow over (μ

)}_i,t(k)−

{right arrow over (μ

)}<sub>j,t−

1</sub>|,

A_x,τ

;

Covariance matrix of the node x at timepoint τ

,

D_x,τ

;

Diffusion constant of the node x at timepoint τ and

μ

_x,τ

;

Position of the node x at timepoint τ

,

d_x,y,τ

;

Measured distance between node x and node y at timepoint τ

.

12. The method as claimed in claim 1, wherein a interruption criterion is fulfilled if the amount of the changes of the positional data of the at least one node since the last identifying of the position of the outlier mobile node is less than a predetermined threshold value or the iterative calculation is interrupted if the absolute position change between two successive iteration steps is less than a predetermined value ε

so that the following applies;

|{right arrow over (μ

)}_i,t(k+1)−

{right arrow over (μ

)}_i,t(k)|<

ε

.

13. A method for determining positional data of a mobile node of an ad-hoc network that includes a plurality of mobile nodes, comprising:

providing a first and second coordinate system wherein the first coordinate system is a relative coordinate system to the second coordinate system;

relating the positional data of the mobile node to the first coordinate system;

determining a subset of nodes form a plurality of nodes located within the first or second coordinate system, wherein at least a portion of the subset of nodes are mobile;

selecting an outlier mobile node that is not part of the subset of nodes;

identifying a position of the outlier mobile node via the steps;

providing positional data for the subset of nodes, wherein the positional data describes the respective position of the subset of nodes in the first coordinate system,

determining distances of the outlier node to the subset of nodes, and

determining the positional data of the outlier node based upon the positional data of the subset of nodes, and the determined distances of the outlier nodes and the positional data of the outlier node,

using a initial position as positional data of the outlier node at a first performance of the identification of the position of the outlier node;

using previous results as positional data of the outlier node at a performance followed by the first; and

identifying the position of the outlier mobile node until an interruption condition is fulfilled.

14. A method for determining global positional data for a mobile node or for all nodes of a network that include a number of nodes, with the global positional data referring to a global coordinate system, comprising:

providing a first and second coordinate system wherein the first coordinate system is a relative coordinate system to the second coordinate system and the second coordinate system is the global coordinate system;

relating the positional data of the mobile node to the first coordinate system;

determining a subset of nodes form a plurality of nodes located within the first or second coordinate system, wherein at least a portion of the subset of nodes are mobile;

selecting an outlier mobile node that is not part of the subset of nodes;

identifying a position of the outlier mobile node via the steps;

providing positional data for the subset of nodes, wherein the positional data describes the respective position of the subset of nodes in the first coordinate system,

determining distances of the outlier node to the subset of nodes, and

determining the positional data of the outlier node based upon the positional data of the subset of nodes, and the determined distances of the outlier nodes and the positional data of the outlier node;

determining of the global positional data of the outlier node depending on the relative positional data by means of a transformation.

15. The method as claimed in claim 14, wherein the transformation is determined by means of a linear regression approach, depending on a number of position pairs, with a position pair in each case including positional data of a node according to the first coordinate system and global positional data of the same node according to the global coordinate system.

16. The method as claimed in claim 14 wherein the position pairs are permanently available via anchor nodes.

17. The method as claimed in claim 14, wherein the position pairs are determined by position measurements for the respective nodes, with the respective global positional data of the respective nodes being determined by means of a global position determining device.

18. The method as claimed in claim 14, wherein the position pairs are determined by position measurements, with a mobile node determining that global positional data for the position pairs at different timepoints by means of a digital map and thus providing various position pairs.

19. The method as claimed in claim 14, wherein the global positional data {right arrow over (x)}_i,t of a node of the network is determined by the following calculation:

{right arrow over (x)}_i,t=M_t{right arrow over (μ

)}_i,t+{right arrow over (b)}_t

where

M_t;

Transformation matrix at timepoint t,

{right arrow over (b)}_t;

Displacement vector at timepoint t.

20. The method as claimed in claim 19, wherein the transformation matrix M_t is determined by the following calculation:

$M_t=\underset{m}{\sum <br><br>}<br><br>\left({\widehat{\stackrel{\to <br><br>}{x}}}_m-<<br><br>{\widehat{\stackrel{\to <br><br>}{x}}}_m><br><br>\right)<br><br>{{\stackrel{\to <br><br>}{\mathrm{\mu <br><br>}}}_m^T\left(\underset{m}{\sum <br><br>}<br><br>\left({\stackrel{\to <br><br>}{\mathrm{\mu <br><br>}}}_m-<<br><br>{\stackrel{\to <br><br>}{\mathrm{\mu <br><br>}}}_m><br><br>\right)<br><br>{\stackrel{\to <br><br>}{\mathrm{\mu <br><br>}}}_m^T\right)}^{-1}.$

where

{right arrow over ({circumflex over (x)}_m;

Global position vector

<

{right arrow over ({circumflex over (x)}_m>

;

Average value of all the global position vectors of the position pairs

<

{right arrow over (μ

)}_m>

;

Average value of all the relative position vectors of the position pairs.