3 research outputs found
Bounds on Multiple Sensor Fusion
We consider the problem of fusing measurements from multiple sensors, where
the sensing regions overlap and data are non-negative---possibly resulting from
a count of indistinguishable discrete entities. Because of overlaps, it is, in
general, impossible to fuse this information to arrive at an accurate estimate
of the overall amount or count of material present in the union of the sensing
regions. Here we study the range of overall values consistent with the data.
Posed as a linear programming problem, this leads to interesting questions
associated with the geometry of the sensor regions, specifically, the
arrangement of their non-empty intersections. We define a computational tool
called the fusion polytope and derive a condition for this to be in the
positive orthant thus simplifying calculations. We show that, in two
dimensions, inflated tiling schemes based on rectangular regions fail to
satisfy this condition, whereas inflated tiling schemes based on hexagons do.Comment: 23 page