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The Covid-19 pandemic has resulted in a variety of approaches for managinginfection outbreaks in international populations. One example is mobile phoneapplications, which attempt to alert infected individuals and their contacts byautomatically inferring two key components of infection risk: the proximity toan individual who may be infected, and the duration of proximity. The formercomponent, proximity, relies on Bluetooth Low Energy (BLE) Received SignalStrength Indicator(RSSI) as a distance sensor, and this has been shown to beproblematic; not least because of unpredictable variations caused by differentdevice types, device location on-body, device orientation, the localenvironment and the general noise associated with radio frequency propagation.In this paper, we present an approach that infers posterior probabilities overdistance given sequences of RSSI values. Using a single-dimensional UnscentedKalman Smoother (UKS) for non-linear state space modelling, we outline severalGaussian process observation transforms, including: a generative model thatdirectly captures sources of variation; and a discriminative model that learnsa suitable observation function from training data using both distance andinfection risk as optimisation objective functions. Our results show that goodrisk prediction can be achieved in $\mathcal{O}(n)$ time on real-world datasets, with the UKS outperforming more traditional classification methodslearned from the same training data.

Inferring proximity from Bluetooth Low Energy RSSI with Unscented Kalman Smoothers