Bounds on Multiple Sensor Fusion

TL;DR

This paper investigates the limitations of sensor data fusion when overlapping, non-negative measurements are used to estimate total quantities, introducing a geometric approach and computational tools to analyze feasible value ranges.

Contribution

It introduces the fusion polytope and provides geometric conditions for effective sensor data fusion, highlighting differences between tiling schemes in 2D.

Findings

Hexagonal tiling schemes satisfy the positivity condition in 2D.

Rectangular tiling schemes fail to satisfy the condition in 2D.

The fusion polytope simplifies calculations for sensor fusion problems.

Abstract

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.