Cooperative and Non-cooperative TDOA Based Source Localization with Copula Function Using Semidefinite Relaxation

Abstract

The time difference of arrival based approach to wireless localization is perhaps one of the most interesting research subjects over the past decade. A method using copula function is proposed for source localization using TDOA measurements for both noncooperative and cooperative scheme. The proposed method is started with noncooperative localization, and finaly is extended to the cooperative localization problem. Because of unknown measurement noise covariance matrix, by using the theory of copulas with Sklar’s theorem, the joint likelihood function of TDOA measurements is coupled to the corresponding univariate marginal likelihood functions. Then, an attractive alternative using method of inference functions for margings is applied to the maximum likelihood estimation. The procedure involving maximization of univariate marginal likelihood functions and then estimation of copula parameter. The maximization suffers from noncovexity, so we apply semidefinite relaxation techniques to derive a convex estimator. Simulation results corroborate the performance of the proposed method as for sufficient signal to noise ratio, we observe one meter of improvement in source location accuracy.

Keywords

• time difference of arrival
• semidefinite relaxation
• copula functions
• source localization
• correlated noise.