# Enhanced Local Fisher Discriminant Analysis for Indoor Positioning in Wireless Local Area Network
## 1 Introduction  
Due to the pervasively availabilities of wireless local area network (WLAN) infrastructures and mobile devices, the WLAN indoor positioning technique has been attracting extensive attention from both academics and industries. WLAN positioning [1] relies on the distinct received signal strength (RSS) patterns among different physical locations. Since RSS values from multiple access points (AP) can be collected by wireless cards available on most mobile devices, no additional hardware is required, except for existing WLAN infrastructures. The accurate indoor location estimation enables substantial location-based services (LBS), including object navigation and finding, public security, and event detection [2; 3]. Currently, fingerprinting is the most popular WLAN positioning approach [4; 5; 6; 7]. This approach collects RSS values at reference points to generate a database called radiomap in the offline phase. Then, in the online phase, it compares real-time collected RSS values with the radiomap by pattern matching algorithms, such as weighted \(K\)-nearest neighbor (WKNN) [8; 9], maximum likelihood estimation (MLE) [10], and artificial neural network (ANN) [11]. To preserve the user's privacy, though more device resources, such as device battery, are consumed, most users tend to implement the location estimation on their devices, rather than on a server. Moreover, due to various wireless indoor propagation factors [12; 13], such as multipath effect, interference, and none-line-of-sight propagation, RSS signals show highly uncertainty and multimodality. Thus, it is a difficult task to achieve high positioning accuracy while reduce the computation cost on resource limited devices. A direct and efficient way to improve positioning accuracy is to deploy as many APs as possible, because each AP may provide a different view to distinguish different physical locations. In many public indoor environments, such as shopping mall, museum and hospital, there may be a lot of APs available. Though a large number of APs introduced is beneficial to positioning accuracy,directly taking RSS vectors as input features may incur \"curse of dimensionality\" problem. Particularly, substantial redundancy among APs with correlated location information may incur the overfitting problem, and increases the computation cost greatly. In addition, significant signal noise contained in some APs may be introduced as well and they decreases the accuracy. To solve the \"curse of dimensionality\" problem, existing methods can be generally categorized into two classes: AP selection [14] and feature extraction [15]. In the former, several criterions, including Fisher criterion [16] and mutual information gain criterion [17], have been proposed to select the most important APs. In the latter, rather than discard some APs, some feature extraction methods have been proposed to project the original RSS signals into a feature space based on different criterions. Considering the substantial redundancy among correlated APs, principal component analysis (PCA) [18; 19] is firstly deployed to obtain more compact location features in a decorrelated space. Then, in order to extract more discriminative features for indoor positioning, linear discriminant analysis (LDA) [20; 21] is proposed to extract the separate location features. Recently, kernel canonical correlation analysis (KCCA) [22] and kernel direct discriminant analysis (KDDA) [23] have been proposed to extract the location features in a kernel induced feature space. Though adapting the nonlinearity of RSS signals, KCCA and KDDA are both kernel-based methods and incur high computation cost. More importantly, existing methods all ignore the multimodality [24; 25] of RSS distributions, and thus the degraded positioning accuracy is obtained. This paper proposes a novel positioning method based on enhanced local fisher discriminant analysis (E-LFDA). First, LFDA [26], a localized variant of the LDA method, is proposed to maximally extract discriminative location information.