Recursive estimation of time-varying RSS fields based on crowdsourcing and Gaussian processes

In this paper, we deal with the estimation of received signal strength (RSS) in a time-varying spatial field, where only low accuracy measurements and noisy locations of users are available. The spatial field is defined on a fixed grid of nodes with perfectly known locations. We employ a propagation model where the path loss exponent and the transmitter power are unknown, and where the locations of the reporting users are estimates and thereby with errors. We propose to estimate time-varying RSS fields by a recursive Bayesian approach that operates on data of low accuracy and obtained by crowdsourcing. The method is based on Gaussian processes, and it produces as a result the complete joint distribution of the unknowns. We also inject a forgetting factor that reduces the effect of old information on current estimates. Our method summarizes all the acquired information, keeping the memory size needed for estimation fixed, i.e., making it independent from the number of sensing users. We also present the Cramér-Rao bound (CRB) of the estimated parameters. Finally, we illustrate the performance of our method with some experimental results.