## 1 Introduction  
Underwater acoustic sensor networks (UASNs) are composed of thousands of micro-sensors which are capable of sensing, operating, self-organizing and communicating acoustically to monitor the underwater environment [1; 2; 3]. In UASNs, technology provides new capacity for marine resources exploration, pollution detection and aided navigation [4]. Nowadays, research on communication technology [3], architectures and protocols [3], localization and tracking algorithms [5], as well as network security [6] have been applied to various fields. As for a variety of applications in UASNs, the acquisition of information is meaningful only when the location of the sensors is known. Underwater acoustic mobile localization (UABL) technology has been widely studied since it is a primary tool used in topology control, coverage control and routing decision in UASNs [7; 8]. UABL typically employs a cluster of anchors whose locations could be obtained in advance and a set of mobile nodes whose locations are to be determined. Based on the information received from the anchors, mobile nodes perform self-localization which belongs to the classification of distributed localization techniques [2]. The model where each mobile node is equipped with a pressure sensor is motivated by reference [8] in which an anchor-free localization algorithm called AFLA was presented. AFLA was designed for active-restricted underwater sensor networks and made use of the relationships between adjacent nodes. Comprehensive surveys of these UABL schemes are presented in references [2; 7]. As global positioning system (GPS) signals are greatly weakened underwater, UABL algorithms often use range-based methods to estimate distance, _i.e._, time of arrival (TOA) [9], angle of arrival (AOA) [10] and time difference of arrival (TDOA) [11]. In this article, a projection-color filtering localization algorithm called PCFL and an anchor-color filtering localization algorithm called ACFL are put forward. They both aim at cooperatively accomplishing precise localization for underwater mobile nodes with minimum power wastage. In the first place, the existing network construction is reconstituted as a hierarchical structure and the localization issue is converted into a geometry problem. Secondly, based on the task anchors which can communicate with the mobile node directly, task-rings are obtained considering the task projections (_i.e._, projections of the task anchors) as centers, and samples are randomly selected in the overlapping area of the task-rings. Later, the Red Green Blue (RGB) sequences for both the mobile nodes and the samples are computed based on the projection distances. Different from the existing CDL algorithms utilizing the DV-hop measurement [12], PCFL uses the AOA measurement and the initial RGB values are given to the task projections, while for ACFL, the initial RGB values are given to the task anchors. Last, the nearness degree is defined to filter samples, and at the same time, it is stored as a weight. Our localization strategy is motivated by the existing CDL algorithms [12], such as making use of the locations and RGB values, from the anchors, to assist the mobile node to compute its RGB value and exploiting the changes of colors with distances to localize the mobile node. The CDL aims to represent a location with a color instead of a coordinate for cutting down the computation and communication costs. With a color to represent a location, two kinds of data are fused into a color: (1) each anchor's location and (2) the distance between the mobile node and each anchor. Also we are motivated by the main idea of hierarchical structure [13] which is that each layer value represents the Z axis coordinate of each anchor in the three-dimensional underwater environment. Since the anchors aredistributed by layers, the three dimensional distance measurements can be converted to two-dimensional ones by using the distance between the anchors' projection and the anchors.