###### Abstract
To mitigate these RSS fluctuations, a large number of RSS measurements are collected at every reference point in the offline training phase. However, collecting more RSS measurements at any location makes the offline phase even more time-consuming and labour-intensive. Several works have been proposed to reduce the workload of the offline phase [11; 12; 13]. The crowdsourcing method has been shown to be a promising approach to solving this problem [14; 15; 16]. In a crowdsourcing-based system, each user can contribute to the construction and updating of the radio map. Consequently, the number of RSS values collected in the offline training phase is greatly reduced. On the other hand, RSS measurements collected by the users moving in the environment are potentially more erroneous than those collected by the experts at the exact location of reference points. One of the problems in the crowdsourcing localization system is that numerous of mobile devices are applied to build the radio map in the offline training phase and provide LBS for the device holders in the online phase. Due to the different WLAN adapter equipped in the mobile devices, the RSS values collected by the mobile device are subject to the difference of the WLAN adapter. As a result, different data collection devices may have different signal sensing capacities and yield different data distributions. Numerous studies show that, due to the hardware differences, the RSS differences collected by different devices exceeds more than 25 dB [17; 18; 19]. Therefore, the localization accuracy is degraded significantly by the problem of RSS variations across different devices. Another issue of indoor localization is the knowledge of the location of the access points. In most fingerprint-based methods, the location of the access points is considered to be unknown. This is a convenient simplifying assumption in many situations, especially when the signal strengths are measured in a passive mode. However, the knowledge of the location of the access points can enhance the localization accuracy. This is especially important since the location of an access point can be estimated using some signal processing techniques [20]. The location of an access point can then be used to correlate the received signal strength across neighbouring locations, as will be discussed in this paper. In this paper, in order to deal with the device diversity problem, the Linear Regression (LR) algorithm is used to mine the intrinsic relationship between different RSS values collected by different devices. Using the LR algorithm, the problem of device diversity will be solved automatically and the uniform RSS values are gotten, so as to ensure the application of the following algorithms. On the basis of graph-based semi-supervised learning (G-SSL) method, we propose RSS difference-aware G-SSL (RG-SSL) method and RSS difference-aware sparse graph SSL (RSG-SSL) method to smoothen the RSS values collected in the offline training phase and improve the localization results. Before smoothing RSS measurements using the G-SSL method, the locations of APs need to be known. Since the spatial distribution of the APs is sparse, the Compressed Sensing (CS)-based method of [20] is proposed to precisely estimate the AP locations. Based on the signal propagation model, the RSS difference between two locations is calculated with respect to the locations of RPs and APs. Furthermore, RG-SSL method is proposed to smoothen the radio map in the offline training phase. By leveraging the RSS readings in the local neighbourhood, the effect of noise and erroneous measurements can be reduced to obtain a higher localization accuracy. Finally, the sparsity of the graph is discussed and RSG-SSL method is used to obtain a better RSS smoothing and localization result. The rest of the paper is organized as follows. The related works are given and discussed in Section 2. Section 3 formulates the indoor localization problem.