To detect flip ambiguity for range-based three-dimensional node localization in wireless sensor networks

we have proposed and proved that flip ambiguity detection for three-dimensional node localization is equal to whether there is a plane intersecting with all range error spheres of the reference nodes

which is called the existence of intersecting plane (EIP) problem.To solve EIP problem

we further have proposed two solving algorithms:common tangent plane algorithm (CTP) and orthogonal projection algorithm (OP).CTP adopts the principle of boundary detection

while OP transforms EIP problem into an angle calculation problem and adopts a coordinate transformation method to solve the problem.The simulation experiments demonstrate that CTP has good detection results

but its computational complexity is too high;however

OP has almost the same detection results as CTP and has lower computational complexity.