## 1 Introduction  
The Global Positioning System (GPS) has been widely used to provide location information in outdoor environments, but it fails to provide reliable positioning indoors [1]. Wi-Fi based localisation system has attracted considerable attention because of the prevalent deployment of Wireless Local Area Network (WLAN) infrastructure and the extensive availability of Wi-Fi enabled mobile devices, which provides a potentially low-cost way to track a mobile user in a building [2]. The vast majority of current indoor localisation systems are designed for sub-metre accuracy in position estimation, which is unnecessary for most indoor navigation applications [3]. Room-level or region-level granularity of location is sufficient for most location aware services [4; 5; 6; 7]. Received signal strength (RSS) based Wi-Fi fingerprinting is a typical method frequently used for location estimation, since it does not need any prior knowledge of access points (APs) deployment. The idea of the fingerprint technology is to use online RSS measurements to match the fingerprint database previously generated at every location in the offline training phase. In the probabilistic fingerprint approach, a model for the statistical distribution of the signal strength for each different location is built, based on sample data collected during the training phase. In the online phase, Bayesian inference is used to calculate the probability that a user is at a certain location given a specified observation, and estimate the most likely location of the mobile device. The accuracy of the statistical distribution model directly affects the final performance of the probabilistic fingerprint positioning [8]. One major disadvantage of the fingerprint based localisation system is the intensive labour consumption in the offline survey phase. Crowdsourcing provides an efficient way to reduce the burden of training data collection by splitting the task to multiple participants. The fingerprint database is obtained by fusing the training data collected by participating devices. However, different devices have different sensor specifications and varying readings. This leads to the fingerprint annotation problem in cross-device fingerprint database that the fingerprint contributed by different devices is not compatible with each other. To support different participated devices, a linear regression calibration model is implemented to mitigate the RSS variance problem caused by the device heterogeneity. Most existing systems assume independence between the RSS measurements at a certain position from various APs. Arising from this assumption, the observation likelihood function is calculated as the marginal conditional probability of each AP. We have demonstrated in this article that the correlation between the RSS measurements when fusing fingerprints from multiple reference points (RPs) within a cell is too high to be ignored. Our previous research [9] employed a joint histogram model to generate the fingerprint probability distribution. In a complex and noisy open space environment, for example a university campus, a large number of APs can be scanned during both the survey and positioning phase. Matching a quantised histogram from 50 APs exactly almost never happens, thus an AP selection rule is required to get reduced-dimensional quantised states for each cell [10]. The joint histogram probability method can achieve as high as 95% room level accuracy in a real university campus based on the data collected in static mode. The problem arises for the dynamical data that the number of visible APs is typically smaller in kinematic collection mode than the set of static data. This has been demonstrated experimentally in [11], and arises from the fact that the collection of more measurements when stationary than when in motion. Other concerns are that the RSS from wireless APs are highly variable, and not all locations record signals from every AP. In addition, the set of APs operating during the training phase may not be the same as at runtime [12].