Gaussian processes with input-dependent noise variance for wireless signal strength-based localization

Gaussian Processes have been previously used to model wireless signals strength for its use as sensory input for robot localization. The standard Gaussian Process formulation assumes that the outputs are corrupted by identically independently distributed Gaussian noise. Even though, in general, wireless signals strength do not have homogeneous noise variance. If enough data samples are collected, the noise variance in office-like environments is usually low. In such cases the noise assumption holds. Previous work has demonstrated the viability of wireless signal strength-based localization in such office-like environments. We intend to extend the applicability of these models to perform robot localization in search and rescue scenarios. In such environments, we expect wireless signals strength measurements to be corrupted with high heteroscedastic noise variance. To extend the applicability of previous approaches to these scenarios, we relax the assumption regarding output noise, by considering that the noise variance depends on the inputs. In this work, we describe how this can be done for the specific case of modeling wireless signal strength. Our results show how relaxing this assumption helps improve localization using a synthetic data set generated by artificially increasing noise variance of real data taken from tests performed on a standard office-like environment.