Performance Analysis of Maximum Likelihood Estimation for Multiple Transmitter Locations

The paper considers the consistence condition of Maximum Likelihood (ML) estimation for multiple transmitter locations in a wireless network with cooperative receiver nodes. It is found that the location set of receiver nodes should not locate (or asymptotically in some sense) merely in an algebraic curve of order 2M −1 if there are totally M transmitters. A sufficient condition for consistence of the ML estimation for M transmitters is that the limit set of locations contains a subset, comprised of (2M2 −M +2) points, which is non-C-2M-co-curved, a notion given by Definition IV-B. This condition can be compared to the persistent excitation condition used to guarantee the convergence of least squares algorithm. Numerical experiments are designed to demonstrate the theoretical discoveries in both positive and negative aspects.