Localization in wireless sensor ad-hoc networks. Xiaobo Long ECSE 6962 course presentation. Introduction. What is localization Determine node locations in ad-hoc sensor networks Distributed Without relying on external infrastructure Without base stations, satellites, etc.
Localization in wireless sensor ad-hoc networks
ECSE 6962 course presentation
- use topological information instead of summing the (erroneous) ranges.
(1) unknown position is denoted by (x; y).
(2) Linear the system by subtracting the last equation from the first n-1 equations.
(3) Reordering the terms gives a proper system of linear equations in the form Ax = b
(4) The system is solved using a standard least-squares approach:
(5) additional sanity check by computing
the residue between the given distances di and the distances to the location estimate of x
(6) exceptional cases: the matrix inverse can not be computed and Lateration fails.
* quite expensive in the number of floating point operations that is required.
= center of the intersection box
---- does NOT guarantee a unique realization
when distance measurements are noisy
If edge AD is removed, then reinserted, the graph can flex in the direction of the arrow, taking on a different configuration but exactly preserving all distance constraints.
Vertex A can be reflected across the line connecting B and C with no change in the distance constraints.
---> only those triangles with a sufficiently large minimum angle as robust
(a) robust four-vertex quadrilateral
(b) decomposition of the robust quadrilateral into four triangles.
If θ3 (smallest)is near zero:
say in edge AD, will cause vertex D to be reflected over this sliver of a triangle