# A Double Rate Localization Algorithm with One Anchor for Multi-Hop Underwater Acoustic Networks
## 1 Introduction  
Underwater Acoustic Networks (UANs) are deployed in the ocean and equipped with a lot of low-cost nodes which are able to communicate with each other via wireless acoustic signals. Over the last few years, more and more researchers have had growing interest in UANs, because UANs can be used in target detection or monitoring. Compared with traditional array sensors, UANs can improve the detection accuracy and monitoring scope and fulfill the needs of a multitude of underwater applications such as oceanographic data collection, ecological applications and military underwater surveillance, etc. [1]. There are two kinds of UANs in the underwater environment: the static networks and the mobile networks. (1) The static network is composed of nodes sinking to the bottom of sea. This kind of network has a fix topology and it is easier for nodes to communicate with each other; (2) One of the mobile networks is composed of nodes which float in the sea and drift with the tide and wave. The other one has some mobile nodes such as AUV (Autonomous Underwater Vehicle) which can travel through the region, increase the monitoring scope, but increase the cost as well. The topology of the mobile network is variational and the communication is effected by the mobility. In this paper, we mainly focus on the static underwater networks. Localization is a major issue for UANs. It contains source localization and self localization [2]. In this paper, we focus on the research of the self localization algorithm. Self localization is the procedure that makes all the unknown nodes in UANs get their positions. All the routing protocolsor detection applications should be on the basis of the self localization information. Therefore, it is important that research on the self localization algorithms for UANs takes place in order to make it perform better. Different from terrestrial networks, the localization algorithm for UANs suffers from some problems because of the characteristics of underwater environment: (1) Anchors are nodes which know their locations from GPS or manual measurement and help other unknown nodes to obtain their positions more accurately. However, GPS cannot be directly used in an underwater environment because of the serious attenuation. Hence, using a few anchors to get high localization performances is one of the key problems that should be solved in UANs; (2) Underwater acoustic channels are characterized by long propagation delays and limited bandwidth. These characteristics introduce challenges in terms of localization schemes design; (3) Different from terrestrial networks, UANs are always sparse and have limited power because of the nodes' cost and battery capability [3; 4; 5]. Recently, some localization algorithms have been proposed such as UPS (Underwater Positioning System), WPS (Wide Coverage Positioning System), MSL (Multi-Stage Localization) algorithm, DV-hop (Distance Vector-Hop) algorithm, MDS-MAP (Multidimensional Scaling-MAP), IMDS (Improved MDS) and AAL (AUV-Aided Localization) algorithm, etc. UPS can only be used in one-hop UANs which reduces the network scale. MSL, DV-hop, MDS-MAP, IMDS and AAL can be used in multi-hop networks.However, MSL will have a large error accumulation due to the stages' division; AAL uses an AUV to travel through the network which increases the cost of localization process; DV-hop and MDS-MAP use the range or communication connectivity information to estimate the position of each node in multi-hop networks which have a better performance in regular networks and more anchors; IMDS improved MDS by distance matrix refinement, but also improves computational complexity, which is not easy to accomplish for an underwater system [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. In this paper, we proposed a Double Rate Self Localization Algorithm with One Anchor for Multi-hop Underwater Acoustic Networks (DRL). Firstly, a Double Rate Scheme is proposed.