Distance-Based Interpolation and Extrapolation Methods for RSS-Based Localization With Indoor Wireless Signals

Wireless local area network (WLAN)-based fingerprinting using received signal strength (RSS) has been considered to be one solution for indoor positioning. However, one widely recognized problem in fingerprinting is the collection and maintenance of a proper fingerprint database. In this paper, we consider having an incomplete fingerprint database with realistic coverage gaps, and we study the performance of several interpolation and extrapolation methods for recovering the missing fingerprint data. For this purpose, we have collected an extensive set of data at frequency bands of 2.4 and 5 GHz from one university building with four floors. The accuracy of the interpolation and extrapolation methods is studied by artificially removing fingerprints from the database using a randomized procedure and by comparing the estimated fingerprints with the original fingerprints. The average RSS estimation error of different interpolation and extrapolation methods is shown for various percentages of missing fingerprints. In addition, a cumulative RSS error distribution is studied to reveal the dispersion of the error statistics, which affect the user positioning accuracy. Here, the user positioning accuracy is defined in terms of horizontal positioning error and floor detection probability. The user positioning accuracy is also compared in four cases, namely when using the original fingerprints, the partial fingerprints, the interpolated fingerprints, and the interpolated and extrapolated fingerprints. It is shown that both the horizontal positioning accuracy and the floor detection probability can be improved with proper interpolation and extrapolation methods. However, it is also illustrated that the best positioning performance is not necessarily achieved with the best average interpolation and extrapolation accuracy, but it is important to avoid certain types of errors in interpolation and extrapolation.