2ACG-Loc: Two-Anchor Cascaded Geometric Localization with TDOA Disambiguation and WLS Refinement for Wireless Sensor Networks

Traditional wireless sensor network (WSN) localization methods require at least 3 real anchors within the communication range of each node, resulting in extremely low coverage rates under sparse deployment. This paper proposes 2ACG-Loc, a method that uses only 2 real anchors to achieve 100% full-network coverage localization through dual-circle intersection geometric positioning, TDOA residual disambiguation, and hop-by-hop cascaded propagation. Based on Cramér-Rao lower bound (CRLB) theoretical analysis, we prove the bounded error condition for cascaded localization (nr + nv ≥ 5) and derive a closed-form solution for the WLS refinement improvement factor. Experiments show that the disambiguation accuracy reaches 97%–99% under Medium noise, and WLS refinement reduces the coarse localization error from 3.86 m to 1.46 m (62% improvement), achieving a 10-fold accuracy improvement over DV-Hop with 60% less communication overhead.