On the optimal performance of collaborative position location

In this paper, we investigate the optimal performance of collaborative position location. In particular, we develop a branch-and-bound (BB) solution search strategy, coupled with the reformulation linearization technique (RLT), to solve the maximum likelihood estimation (MLE) problem for collaborative position location, which is in general a nonlinear and nonconvex optimization problem. Compared with existing work which has only approximately solved the MLE problem, our approach is guaranteed to produce the (1 - ¿)-optimal solution to the MLE for arbitrarily small ¿. With a guaranteed optimal solution to the MLE, we show that for some node geometries in noncollaborative position location, which can be viewed as a special case of collaborative position location, the Cramer-Rao lower bound (CRLB) for an unbiased estimator is no longer a meaningful performance benchmark. We demonstrate that the timeof- arrival (TOA) based MLE is in general a biased estimator and it sometimes has a mean square error (MSE) smaller than the CRLB, and thus can serve as a more practical performance benchmark. Finally, we compare the MLE with some existing position location schemes and demonstrate that it also serves as a good performance benchmark for collaborative position location.