To detect flip ambiguity in range-based wireless network node localization

some researchers proposed that the flip ambiguity detection is equal to determine whether there is a straight line intersecting with all range error circles of the reference nodes.It is called the existence of intersecting line (EIL) problem.To solve the EIL problem under equal radii

a convex hull algorithm with low computational complexity was proposed.However

for unequal radii

a common tangent algorithm (CTA) has high computational complexity.In order to address the high computational complexity of CTA

we prove that the EIL problem is equal to determine whether there is a straight line

which enables any two circles to have overlapping orthogonal projection onto the line.According to this proof

we propose an orthogonal projection algorithm (OPA) to detect nodes flip ambiguities with unequal radii.The algorithm uses the coordinate transformation to simplify the computation process.The simulation results demonstrate that OPA and CTA have exactly the same detection results

but the computational complexity is greatly reduced.