Localization algorithms in WSN can be divided into two classes: anchor-based algorithms and anchor-free algorithms [5]. Anchor-based algorithms assume that all reference nodes are anchor nodes or nodes whose real position coordinates are known in advance. Anchor-free localization algorithms only require a few anchor nodes. The coordinates of all the reference nodes are estimated automatically. Typical anchor-free localization algorithms proceed as follows:Estimate the coordinates of the reference nodes. Several methods for this process have been proposed. Meerens and Fitzpatrick use one-hop neighbors and multilateration to construct a global coordinate system [6]. Shang and Ruml use multi-dimensional scaling (Multi-dimensional Scaling: MDS) to realize localization, which has drawn much attention recently [7].

Complete precise localization for mobile targets based on reference nodes. Oh-Heum et al. present a map stitching localization method in large scale WSN [8]. Kiran and Bhaskar put forward a sequence-based localization (Sequence-based Localization: SBL) method [9].The above algorithms have respectively achieved certain goals under ideal environments. However, in underground mines, localization will face the following challenges.Water-vapor and coal dust will potentially absorb the wireless signal in different ways and lead to large localization errors.The complex terrain and irregular network topology in underground mines make many localization algorithms do not work well.To solve the above problems, an anchor-free localization method in coal mine WSN (Coal Mine Wireless Sensor Networks: C-WSN) is proposed.

The main contributions of this paper are as follows:A coal mine wireless sensor network is constructed in underground mines based on the ZigBee technology.Non-metric AV-951 MDS algorithm is introduced into the estimation of the reference nodes�� location, which provides higher fault-tolerance ability.An improved SBL algorithm, N-best SBL, is proposed to improve the localization accuracy.The remainder of the paper is organized as follows. In Section 2, we describe the MDS and SBL method briefly. In Section 3, our anchor-free localization method in C-WSN is studied. In Section 4, we analyze our experimental results. Finally, we conclude the paper.2.?Preliminaries2.1. Non-metric MDS algorithmsMDS algorithms are widely used in multivariate statistics.

There are two types of MDS algorithms: metric MDS and non-metric MDS. The input in the metric MDS approach is a rigid distance matrix that specifies distances between every pair of nodes, and the output is a coordinate set of all the nodes. The metric MDS approach has been introduced into WSN localization in previous work [7,11]. Compared to the metric MDS approach, non-metric MDS only requires the monotonicity of a similar relationship matrix.