Gaussian process inference approximation for indoor pedestrian localisation

Clutter has a complex effect on radio propagation, and limits the effectiveness of deterministic methods in wireless indoor positioning. In contrast, a Gaussian process (GP) can be used to learn the spatially correlated measurement error directly from training samples, and build a representation from which a position can be inferred. A method of exploiting GP inference to obtain measurement predictions from within a pose graph optimisation framework is presented. However, GP inference has a run-time complexity of O(N3) in the number of training samples N, which precludes it from being called in each optimiser iteration. The novel contributions of this work are a method for building an approximate GP inference map and an O(1) bi-cubic interpolation strategy for sampling this map during optimisation. Using inertial, magnetic, signal strength and time-of-flight measurements between four anchors and a single mobile sensor, it is shown empirically that the presented approach leads to decimetre precision indoor pedestrian localisation.