The paper presents a Wi-Fi-based indoor localisation system. It consists of two main parts, the localisation model and an Access Points (APs) detection module. The system uses a received signal strength (RSS) gathered by multiple mobile terminals to detect which AP should be included in the localisation model and whether the model needs to be updated (rebuilt). The rebuilding of the localisation model prevents the localisation system from a significant loss of accuracy. The proposed automatic detection of missing APs has a universal character and it can be applied to any Wi-Fi localisation model which was created using the fingerprinting method. The paper considers the localisation model based on the Random Forest algorithm. The system was tested on data collected inside a multi-floor academic building. The proposed implementation reduced the mean horizontal error by 5.5 m and the classification error for the floor’s prediction by 0.26 in case of a serious malfunction of a Wi-Fi infrastructure. Several simulations were performed, taking into account different occupancy scenarios as well as different numbers of missing APs. The simulations proved that the system correctly detects missing and present APs in the Wi-Fi infrastructure.

We show that if there exists a Lipschitz homeomorphism T between the nets in the Banach spaces C (X) and C (Y ) of continuous real valued functions on compact spaces X and Y , then the spaces X and Y are homeomorphic provided l(T ) ×l(T −1 ) < 6 5 . By l(T ) and l(T −1 )we denote the Lipschitz constants of the maps T and T −1 . This improves the classical result of Jarosz and the recent result of Dutrieux and Kalton where the constant obtained is 17 16 . We also estimate the distance of the map T from the isometry of the spaces C (X) and C (Y ).

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