# An Indoor Collaborative Coefficient-Triangle APIT Localization Algorithm
## 1 Introduction  
Wireless sensor networks (WSNs) have been widely used in environment monitoring, military services and urban intelligent transportation [1]. The premise of WSNs is to obtain the node location information, partly because problems such as \"where things happen\" and \"how to detect the geographic location of nodes\" can only be solved with available location information. In addition, node positioning in the network helps to improve the performance through network power control, route selection, etc. [2].  
Typically, the node location algorithms in a WSN can be classified into two categories: range-based and range-free schemes. The principle of range-based location algorithms is based on obtaining the relative location by measurement of the actual distance or angle among nodes. The classic range-based location algorithms include Angle of Arrival (AOA) algorithm [3], Time of Arrival (TOA) algorithm [4], the Time Difference on Arrival (TDOA) algorithm [5], and the Received Signal Strength Indicator (RSSI) algorithm [6]. Such algorithms have relatively high localization precision, but require high-performance hardware. The range-free location algorithms, on the other hand, can meet the localization precision in most applications without any additional hardware, such as a synchronous clock, which makes these algorithms suitable for complex communication conditions.  
Typical localization algorithms are the centroid algorithm [7], the Approximate Point-In-Triangulation APIT algorithm [8], the DV-Hop algorithm [9], the LACM algorithm [10], the LACMV algorithm [11], and the HPSO and BBO algorithm [12].  
Among the above classical range-free location algorithms, the APIT localization scheme is widely used for localization estimation in wireless sensor networks, due to its simplicity and low power consumption. Furthermore, a number of efforts have been made to improve APIT algorithms.  
In order to improve the robustness and the average positioning error, a virtual nodes-based APIT localization scheme is proposed [13]. To the effect of random deployment of all nodes, an improved centroid localization algorithm (ICLA) based on APIT is proposed [14]. Duo to produce more accurate location approach in isolation, a unified approach to localization is proposed [15]. To reduce costs per node, localization schemes based on event are proposed [16]. So as to reduce energy consumption and cost each node, the free-range location base schemes is proposed [17]. In order to increase the success ratio of localization, an approach to improve the position estimation accuracy of nodes using the Imperialist Competitive Algorithm is proposed [18]. So as to improve the poor locating performance of the DV-Hop algorithm, a localization algorithm based on SFLA and PSO is proposed [19]. In order to alleviate the so-called \"flip ambiguity phenomenon,\" a novel meta-heuristic localization technique for wireless sensor networks based on the harmony search algorithm is proposed [20].  
However, it is important to note that the accuracy provided by the APIT algorithm depends on the position of the neighboring nodes, so it is easy to be subject to the effect of the density and distribution of sensor nodes.  
In this paper, a Collaborative Coefficient-triangle APIT Localization (CCAL) algorithm is proposed, which introduces collaborative positioning to decrease the node positioning error and increase the localization coverage rate. MATLAB simulation results show that the CCAL algorithm outperforms the APIT, RSSI, and other improved algorithms in terms of both location error performance and coverage rate with low time complexity.