Manifold locally linear denoising for Wi-Fi RSS based indoor positioning

In this paper, we investigate the problem of locating the indoor objects with the help of the received Wi-Fi signal strength fingerprints. Many Wi-Fi RSS based positioning techniques have been developed recently for indoor positioning purposes, but the positioning accuracy faces various challenges, including the high noise to signal ratio. In this paper, we consider two typical elements affecting the positioning performance: the slow attenuation of the signal strength, and the large measurement noise. We propose a novel approach to locate a target object in a given area by introducing a denoising algorithm based on the local linearity of the signal-location manifolds. This is implemented with a fixed set of linearization weights determined not by the signal values but by the relationships of the locations of the fingerprint samples. We also explore the relations among the prediction error and the manifold curvature, the number of APs used for positioning, and the signal noise level, characterizing the quality of the nearest point estimation with the signal measurement errors. A simple algorithm is presented to locate the target using the k-nearest neighbors in the signal space. Simulations in various settings demonstrate the effectiveness of the proposed approach.