Ad-Hoc Node Positioning via Distance Circle Intersection
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Solution Overview
Problem
Existing methods for determining geographical positions in ad-hoc networks, such as trilateration and bounding box methods, are prone to errors due to inexact distance measurements, and perform poorly when there are few neighboring nodes or multicollinearity issues.
Innovation Solution
The method involves determining distance circles around neighboring nodes, calculating points of intersection, and selecting a main set of points within a threshold to estimate the geographical position of a node using mean values of these intersections.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If distance-based position determination methods (trilateration, multilateration) are used, then position can be estimated using distance measurements, but the position accuracy deteriorates due to inexact distance measurements and multicollinearity
Solution Approach 1:
The patent segments the position estimation problem into two independent parts: (1) determining distance circles from distance measurements, and (2) finding intersection points of these circles. This segmentation allows the system to handle inexact distance measurements by generating multiple possible position points rather than a single deterministic result, thereby improving robustness while maintaining position accuracy through selective filtering of plausible intersection points
Solution Approach 2:
The patent performs preliminary action by determining distance circles around each neighboring node before calculating position intersections. By pre-computing the distance circles with their respective radii based on measured distances, the system prepares a set of geometric constraints that can be systematically intersected to generate candidate position points, improving both accuracy and handling of measurement uncertainties
2Ease of operation
If traditional position determination methods are used, then computation is straightforward, but the methods perform poorly when there are few neighboring nodes or multicollinearity issues
Solution Approach 1:
The patent transitions from direct distance-based position calculation to a geometric dimensionality approach by constructing distance circles in 2D space and finding their intersection points. This dimensional transformation allows the system to handle cases with few neighboring nodes or multicollinearity by leveraging the geometric constraints of circle intersections, which naturally resolve ambiguities that plague traditional algebraic methods
3Productivity
If distance measurements are performed using RSSI, ToA, TDoA, or RToF methods, then distance values can be obtained, but the measurements are inexact and do not permit exact range or distance values
Solution Approach 1:
The patent converts the harmful effect of inexact distance measurements into a beneficial outcome by generating multiple distance circles with slightly different radii representing the measurement uncertainty range. The intersection points of these circles create a set of candidate positions, where the spread of intersection points actually provides information about position uncertainty rather than merely representing error, thereby transforming measurement imprecision into a useful probabilistic position estimate
Data Source
AI summary
In a method and a device for determining a geographical position of a node in an ad-hoc network, distance circles of at least two nodes that adjoin the 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, the 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 the main set of points of intersection.