## 1 Introduction
Thus, the AP selection rule will pick the AP set which is not able to represent the characteristic of the online measurements and give biased estimation of the user position. This paper builds up a high-dimensional probabilistic radio map by considering all available visible APs sensed in the training data regardless of the signal quality. This is to ensure the inclusion of every possible AP that would be see in the runtime measurement. Most existing fingerprint-based algorithms ignore the issue of changing AP visibility at training process and runtime. A conventional method of dealing with missing data is to set a low RSS value \(-110\) dBm [13] or assign a penalty in the matching process [14]. While the incompleteness in the sensing data can lead to bias in the estimation of parameters, we have tried a number of approaches to overcome this problem. The most successful, reported here, invokes the expectation-maximisation (EM) imputation strategy. This method, widely used in statistics, provides a method to impute the missing data and simultaneously learn the parameters from the incomplete data [15]. The key idea of EM imputation is to iteratively fill in the missing data under the current estimation of the unknown parameters and reestimate the parameters from the observed and filled-in data [16]. This paper proposes a statistical approach of localising a mobile user with room-level accuracy in a university campus wireless network. By segmenting the indoor area into several cells, the system fuses crowdsourcing RSS measurements from all visible APs collected within each cell. The system has adopted the dependency of RSS between pairs of APs caused by the change of spatial collect locations within a cell. Different devices generally provide different intensity readings due to many factors such as antenna gain and transmission power. Multivariate linear regression is used to address the RSSvariance problem in the crowdsourced training data caused by the device heterogeneity. In terms of the dimension mismatch caused by variable visibility of APs, instead of discarding weak APs to reduce dimension or replace unobserved AP with a minimal constant RSS value, the EM imputation strategy is exploited to replace the missing RSS in the training data. Then, a high-dimensional probabilistic fingerprint is constructed for each cell based on the multivariate Gaussian mixture model (MVGMM) considering the correlations between APs. The Hidden Markov Model (HMM) is applied to track the mobile user, where the hidden states comprise the possible room locations and the Wi-Fi RSS measurements are taken as observations. In the positioning phase, revealing the trajectory of the user can be carried out with the Viterbi Algorithm. Besides, different rooms have both different visible and invisible AP sets, which is also a signature that can be used to differentiate between cells. By taking advantages of the \"_unseen properties_\" of invisible APs, a conditional probabilistic observation model is utilised to describe the likelihood of receiving a particular invisible AP set at a certain cell. The hypothesis is if an AP is invisible in the fingerprint of a cell, an online observation contains signal strength from that AP has low probability belongs to that cell. The information of invisibility of APs enabling the introduction of rigorously motivated trustworthiness for updating the conditional likelihood observation function. The remainder of the paper is organised as follows: Section 2 briefly introduce the background and related work. Section 3 depicts the proposed system architecture. Section 4 presents the experimental results to verify the validity of the proposed algorithm. Section 5 draws the conclusion.