Determining the best vector distance measure for use in location fingerprinting

Location fingerprinting is a technique that records vectors of received signal strength (RSS) from several transmitters at some reference points (RPs) into a database, and later matches these recorded vectors to a new measurement to position the user. In this work we deal with deterministic fingerprinting algorithms based on the nearest neighbor algorithm (NN). Distance measures between the recorded RSS values and the new measurements are then necessary, which can be calculated using Minkowski distance. The most popular cases of Minkowski distance, Manhattan, Euclidean and Chebyshev, are widely used in various studies in location fingerprinting. However, their positioning performance has not been analytically discussed yet. This causes unknown performance degradation when these signal distances are utilized, which can affect the positioning procedure. In this paper, the positioning performance using Manhattan, Euclidean and Chebyshev distance in terms of the probability of error (POE) are compared analytically and then the results are confirmed by simulations and real experiments. The relationship between the POE and distance error is also analyzed. The results show that using the NN method and a RSS Gaussian distribution assumption, Euclidean distance is the optimum distance which provides the lowest POE and mean distance error (MDE) for indoor fingerprinting.