Time-Delay-Based Target Localization in Wireless Sensor Network With Unknown Noise Covariance

This letter addresses the problem of target localization based on the time-delay (TD) measurements in a wireless sensor network (WSN) with a noncooperative illuminator of opportunity (IO), without assuming the prior knowledge of measurement noise covariance (MNC). The joint likelihood of target position and noise variances are built, based on which the target position and MNC can naturally be estimated by maximizing the joint likelihood. However, the resulting maximum likelihood (ML) problem is intractable due to its nonconvexity and nonlinearity. In order to overcome such difficulty, an alternately iterative optimization strategy is proposed in our approach. The approximate weighted least-squares solution and closed-form shrinkage estimator are introduced into the alternative estimation steps for the target location and MNC, respectively. In simulation experiments with 40 TD measurements, the performance of the proposed method, performing without knowledge of MNC, achieves about 8 dB average improvement over the traditional method without the MNC. Its performance is also close to that of the algorithms and Cramér-Rao lower bound (CRLB) working with known MNC, thus verifying the effectiveness of proposed approach.