Modeling the received signal strength intensity of Wi-Fi signal using Hidden Markov Models

Abstract

Wi-Fi fingerprinting is one of the methods that are widely used to provide Location Based Services (LBS). Gaussian, or a mixture of Gaussians, is the preferred model used by Wi-Fi fingerprinting for LBS. Nevertheless, Received Signal Strength Intensity (RSSI) Wi-Fi histograms are skewed, and a Gaussian model is not well suited for modeling data when their histogram is skewed. In addition, another important characteristic present in the RSSI Wi-Fi temporal series is autocorrelation, which cannot be modeled using a Gaussian model. In this paper, we explore the feasibility of using Hidden Markov Models (HMM) to model RSSI Wi-Fi signals. The mathematical derivation of formulas to calculate autocorrelation based on the HMM parameters is presented. Exhaustive experimentation, using data sampled in a real scenario, was performed to test the dependency of the autocorrelation coefficients on the number of hidden states, and the number of iterations used when creating the HMM. The results are compared with autocorrelation coefficients calculated using the real data. Kullback–Leibler (KL) divergence was used to compare the similarity of the real histograms and those provided by a mixture of Gaussians and by an HMM. HMM models reported more accurate results than a mixture of Gaussians model in both cases.