Robust NLS sensor localization using MDS initialization

Before a sensor network can be used for target localization, the locations of the sensors need to be determined. We approach this calibration step by moving a source to distinct positions around the network. At each position, the range to each sensor is measured, and from these range measurements the sensor locations can be estimated by solving a nonlinear least squares (NLS) problem. Here we formulate the NLS problem and describe how to robustly initialize it by the use of multidimensional scaling. The method is evaluated on both simulations and real data from an acoustic sensor network. With as few as six source positions, a robust calibration is demonstrated that gives a position error about the same size as the range error. In the acoustic example this RMSE is less than 40 cm.