## 2 Related Work  
The vast majority of current indoor localisation systems are designed for sub-metre accuracy in position estimation which is unnecessary for most indoor navigation [3]. Room-level or region-level granularity of location is sufficient for most location aware services [4; 5; 6; 7]. The traditional Wi-Fi fingerprinting method involves a site survey before the test, which needs to grid the area and construct a radio map associating each location. Conventional fingerprint localisation algorithms normally average the Wi-Fi RSS measurements for each AP in stored signatures. In practice, this is not consistent with RSS fluctuations, due to the multipath effects in complex indoor environments [17]. To get real-time correction of RSS variations and fluctuations, the Differential Wi-Fi (DWi-Fi) scheme is proposed by analogy to Differential GPS (DGPS) where reference station network measurements are employed [18]. The recorded RSS measurements at user's end are corrected and the fingerprinting database is continuously updated to encounter for the possible changes in the dynamics of the environment. In the probabilistic fingerprint techniques, a fingerprint is the probability distribution of the signal strength given the location instead of the mean during the training phase. Some approaches assume a Gaussian distribution of signal strength [19; 20; 21], which is not always true as the RSS distribution tends to be left-skewed, as analysed in [22; 23; 24]. The Horus system infers the target location with the maximum posterior probability assuming a standard Gaussian distribution [21]. Another efficient approach to estimate the probability density distribution (PDF) is to use kernel functions [10]. [PERSON] et al. extends this work by comparing the similarities between two PDFs using Kullback-Leibler divergence (KLD), and then performs localisation through kernel regression [25]. Histogram-based probabilistic methods do not assume any known distribution and is closely related to discretisation of continuous values to discrete ones [26; 27; 28]. However, histogram-based performance is primarily dependent on the choice of bin number and bin width. In addition, [PERSON] et al. pointed out that histogram-based approaches are only appropriate for low-dimensional datasets because the calculations in histogram-based techniques are exponential in the dimension of the dataset [29]. Therefore, this type of approach has low scalability to problems with larger numbers of data points and higher-dimensional spaces. Using a subset of available APs enables reducing the number of variables and allows reliable low-dimensional quantised states for each room, which normally involves a sanity assessment to select a subset of APs for positioning [30]. The concept of \"_important AP_\" is proposed to select significant APs for each location where the AP with the highest RSS is denoted as the important AP [31]. This method works properly for the static data, while the problem arises for the dynamical data. As demonstrated in [11; 12], the visible AP set in kinematic collection mode is typically smaller compared with the AP set in static data. Thus, the AP selection rule will pick the AP set which is not suitable to represent the characteristic of the runtime 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 in the training data regardless of the signal quality. This is to ensure the inclusion of every possible AP that would be sensed in the observation data instead of assigning a constant probability. Where there are missing RSS values from some APs at some locations, a heuristic method for handling the missing data is to set a constant minimal possible RSS value [32]. In this paper, we use the EM imputation method to replace the missing values in the incomplete data. In addition, we have observed that the missing APs also provide extra information because of their _unseen_ properties.