A Sparse Manifold Learning Approach to Robust Indoor Positioning Based on Wi-Fi RSS Fingerprinting

The emerging location-based applications depend on the fast and accurate positioning of mobile targets. Wi-Fi received signal strength (RSS) fingerprinting provides a promising solution to localize an object in indoor environments. Among the factors challenging the RSS fingerprinting based algorithms are the site survey cost and the time-varying environment, given the unreliable signal qualities. Here we present a novel approach to indoor object positioning using the manifold assumption on the radio map in RSS-location space. Thinking the measured RSS from one access point (AP) in different locations are randomly drawn from a nonlinear manifold (ground truth), we propose an expectation-maximization (EM) style algorithm to reconstruct the sparse representation of this manifold from the noisy RSS observations. Motivated by the observation that the radio map has a strong local correlation in the RSS-location space, we introduce a multi-scale constrained quadratic programming to approximate the manifold. Within limited iterations, we can estimate the ground truth RSS values and parameters simultaneously. As a result, the learned manifold is exploited to predict the object's position: we develop a positioning algorithm by minimizing the manifold distortion effort which integrates both measurement error and manifold shape preservation. We conducted extensive simulations and experiments in different settings, testing the datasets collected in a building in the last 8 months. The results showed that the proposed approach was adaptive to the varying environmental noise levels, presenting robust positioning performance.