Beacon error-tolerable method for node localization in 3D wireless sensor networks

For 3D wireless sensor networks (WSNs) with inaccurately positioned beacon nodes, a novel multi-hop node localization method that can tolerate beacon position errors was proposed. The influences of independent variable errors and dependent variable biases on node coordinate estimation were taken into account simultaneously. Based on the principle of constrained weighted orthogonal regression, a reliable 3D multi-hop localization model was constructed, and the numerical method for calculating the optimum value of node coordinates was given. The 3D multi-hop Cramér-Rao bound (3D-MCRB) for node localization under combined uncertainties in beacon positions and estimative distances was also derived. Simulation results show that the novel method is robust against beacon position errors and distance estimation errors. In most experiment conditions, the multi-hop localization accuracy can be improved by at least 10%.