# An Efficient Indoor Positioning Method with the External Distance Variation for Wireless Networks
## 1 Introduction  
In recent years, wireless networks are developed quickly and have been applied to many places such as hot spots, personal digital devices, and so forth [1, 2]. The wireless network technology is also applied into the wireless personal area network (WPAN) that specializes in some devices of short-distance transmission and low power consumption such as Bluetooth, ZigBee, and so on [3, 4, 5]. However, the wireless networks have developed rapidly and become one of the hot research topics that indoor positioning technology is particularly important for. The applications of wireless network communication positioning are very mature and popular compared to the technology of global positioning system (GPS) [4, 5]. The GPS technology uses satellites to provide three-dimensional positioning. GPS also provides accurate positioning in outdoor applications not suitable for indoor positioning. The positioning technology normally has two different types that are distance-based (range-based) and non-distance-based (range-free-based) [6, 7, 8, 9, 10, 11]. The distance-based method basically uses angle or distance information to estimate the positioning location. Most ofthe distances are measured through radio signals or ultrasonic waves, and the positioning procedure that can be performed without knowing the distance information. The distance-based positioning algorithm [12] has different methods to estimate the distance that are the time of arrival (ToA) method, the time difference of arrival (TDoA) method, the angle of arrival (AOA) method, and so on [13; 14; 15]. The received signal strength method (RSS) is used for distance estimation [16; 17]. When estimating the distance, there is no need to add additional equipment, and there is no time synchronization problem. Therefore, substituting the power received by the unknown node into the attenuation model can find the distance. This paper uses the RSS to estimate the distance between the unknown location and the reference point. The accuracy of RSS positioning is greatly affected by the shadowing effect, and then the minimum mean square error (MMSE) algorithm is used for triangulation to locate the coordinates of unknown nodes. Because of the signal affected by different degrees of shadow fading, positioning error happens [18]. However, shadow fading can be modeled by a random variable of log-normal distribution with zero mean and the standard deviation \(\sigma=3\)-\(8\) dB [19]. In order to reduce the number of reference nodes and calculation cost, this paper uses an adaptive reference node selection to improve the accuracy of positioning. Wireless communication is to use the electromagnetic wave as a conductive medium to communicate without going through a wired communication. Therefore, since the Second World War, wireless communication has been used in the military. The results of the application are valued and there is a lack of extensive communication standards. Therefore, the Institute of Electrical and Electronics Engineers (IEEE) formulated the first version of the standard called IEEE 802.11 for wireless local area networks in 1997, which redefines and modifies the media access control (MAC) layer and the physical (PHY) layer [20]. The two devices can be transmitted in a point-to-point (Ad Hoc) manner, or under the coordination of a base station (BS) or an access point (AP). After the signal is sent from the transmitter, all path distances before reaching the receiver are called channels. If the signal is a radio signal, the propagation path is called a wireless channel. The factors caused propagation loss of radio signals during channel propagation can be roughly divided into two categories: the large-scale propagation model and the small-scale propagation model. The influencing factor of the large-scale propagation model is the change caused by the long distance or time of the signal in the transmission process.