We have developed statistical error modeling techniques for acoustic signal detection-based ranging measurements in the framework of wireless ad-hoc sensor networks (WASNs). The models are used as the basis for solving the location discovery problem in sensor networks. We first demonstrate that the major difficulty in location discovery is how to treat errors by proving the location discovery in presence of noisy measurements is a NP-complete problem, even in onedimensional space. Consequently, we formulate the location discovery as an instance of nonlinear function minimization that optimizes each of the empirically derived statistical error models. The minimization problem is then solved using a conjugate gradient-based nonlinear function optimization solver.

We validate the efficiency of the approach by conducting comprehensive experiments on both deployed and simulated WASNs. The results indicate that the statistical model-based approach significantly improves the location accuracy compared with the approaches using the traditional optimization objectives. In addition, the localized version of our location discovery algorithm is capable of finding competitive solutions using significantly lower communication cost.