An improved flip ambiguity detection algorithm in wireless sensor networks node localization

To detect a node flip ambiguity in range-based wireless network node localization, Wang et al. have proved that the flip ambiguity detection is equal to whether there is a straight line intersecting with all range error circles of reference node, which is called the existence of intersecting line (EIL) problem. To solve the EIL problem under equal radii, a convex hull algorithm proposed by Wang et al. has low computational complexity. However, for unequal radii, a common tangent algorithm (CTA) proposed by Wang et al. has high computational complexity. In order to deal with the high computational complexity of the common tangent algorithm, on the basis of orthogonal projection theory, 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. In fact, the straight line is perpendicular to the straight line of EIL problem. According to this proof, we propose an orthogonal projection algorithm (OPA) to detect nodes flip ambiguities for 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.