Analysis of flip ambiguity for robust three-dimensional node localization in wireless sensor networks

• Flip ambiguity detection for 3D node localization is equivalent to EIP problem.
• Common tangent plane algorithm (CTP) is proposed to solve EIP problem.
• Orthogonal projection algorithm (OP) is proposed to solve EIP problem.
• OP has almost the same detection results as CTP and lower computational complexity.

To detect flip ambiguity for range-based three-dimensional nodes localization in wireless sensor networks, we have proposed and proved that flip ambiguity detection for three-dimensional node localization is equivalent to finding the intersecting plane that intersects with all range error spheres of the reference nodes of unknown node in the ideal radio model, which is called the existence of intersecting plane (EIP) problem. To solve EIP problem, we further have proposed two algorithms: common tangent plane algorithm (CTP) and orthogonal projection algorithm (OP). The simulation results demonstrate that the computation complexity of OP is lower than CTP, while the detection results of OP is comparable with CTP.