## 1 Introduction  
Structural health monitoring (SHM) is an emerging technology that aims to design systems that are able to continuously monitor structures [1; 2; 3]. Structural health monitoring is beneficial to the maintenance of critical structures in many fields [4], such as civil engineering [5] and aerospace [6], where damage detection plays a very important role. The ultrasonic pulse-echo technique is traditionally adopted as a cost-effective SHM strategy. Damage detection of 2-D structures, such as plates and shells, has been widely studied [7; 8; 9]. Three-dimensional structures, such as concrete structures, also require periodic inspections and quality control to assess their structural integrity [10; 11]. Damage detection can be generalized to target detection in the medium. In target detection, transducer elements act as actuators to emit short ultrasonic pulses, and sensors receive the scattered ultrasound. By recording and analyzing the scattered signals, information related to the target (location, size, type, and orientation) can be obtained. Time-of-flight (ToF)--the time taken by the ultrasonic pulse to travel from an actuator to a sensor--is a feature extracted from the scattered signals that are widely used in target localization [12; 13]. Many studies have reported the successful application of ToF-based methods for target localization [1; 4; 14; 15], but the accuracy is affected by ToF measurement errors. In the traditional ToF-based method, the location of the target is the intersection point of all ellipsoids [4]. This method makes the assumption that ToF measurements are absolutely accurate and error-free. However, ToF measurement errors are inevitable in experiments due to noises and many other factors. Therefore, two problems need to be solved in 3-D target localization. First, ellipsoids will not intersect at only one point if the ToF measurement is inaccurate because multiple intersection points will be obtained instead of one. These intersection points are pseudo-targets and it is impossible to differentiate between pseudo-targets to locate the target using traditional methods. Second, due to ToF measurement errors, the ellipsoids and curves may not intersect, which give rise to disjoint ellipsoids and disjoint curves. In this case, information related to the target location will be lost because scattered signals from the target cannot be employed to construct curves or intersection points. Probability-based ToF methods [16; 17] were introduced so that the points absent in the ellipsoids, which are the loci of ToF measurements, are also considered possible target locations, which can solve the problems caused by ToF measurement errors. The possibility of target occurrence at each point is determined by its distance to the loci. The combination of the possible target location corresponding to all the loci can give the estimated target area. However, the estimation result is less accurate because it involves a series of dispersed points occupying a target area. Therefore, introducing a new method that could narrow down the target area and provide a point estimate of the target location with higher accuracy is crucial in 3-D target localization. The two problems caused by ToF measurement errors in 3-D target localization result in spatial distribution of pseudo-targets. Some pseudo-targets are located close to the target, while other pseudo-targets are located far from the target and may negatively influence the accuracy of localization. We propose a 3-D localization method, Iterative Maximum Weighted Likelihood Estimation (IMWLE), which takes into account the spatial distribution of pseudo-targets. In this method, each pseudo-target is initially assigned an equal weight. At each iteration, Maximum Weighted Likelihood Estimation (MWLE) is adopted to assign new weight factors to pseudo-targets by fitting a Gaussian distribution to them. This procedure could effectively minimize the influence of the pseudo-targets that are located far from the target.