A Semidefinite Relaxation Method for Elliptical Location

Abstract

Wireless location is a supporting technology in many application scenarios of wireless communication systems. Recently, an increasing number of studies have been conducted on range-based elliptical location in a variety of backgrounds. Specifically, the design and implementation of position estimators are of great significance. The difficulties arising from implementing a maximum likelihood estimator for elliptical location come from the nonconvexity of the negative log-likelihood functions. The need for computational efficiency further enhances the difficulties. Traditional algorithms suffer from the problems of high computational cost and low initialization justifiability. On the other hand, existing closed-form solutions are sensitive to the measurement noise levels. We recognize that the root of these drawbacks lies in an oversimplified linear approximation of the nonconvex model, and accordingly design a maximum likelihood estimator through semidefinite relaxation for elliptical location. We relax the elliptical location problems to semidefinite programs, which can be solved efficiently with interior-point methods. Additionally, we theoretically analyze the complexity of the proposed algorithm. Finally, we design and carry out a series of simulation experiments, showing that the proposed algorithm outperforms several widely used closed-form solutions at a wide range of noise levels. Extensive results under extreme noise conditions verify the deployability of the algorithm.