  In this paper, we address the estimation of a time-varying spatial field of
received signal strength (RSS) by relying on measurements from randomly placed
and not very accurate sensors. We employ a radio propagation model where the
path loss exponent and the transmitted power are unknown with Gaussian priors
whose hyper-parameters are estimated by applying the empirical Bayes method. We
consider the locations of the sensors to be imperfectly known, which entails
that they represent another source of error in the model. The propagation model
includes shadowing which is considered to be a zero-mean Gaussian process where
the correlation of attenuation between two spatial points is quantified by an
exponential function of the distance between the points. The location of the
transmitter is also unknown and estimated from the data with a weighted
centroid approach. We propose to estimate time-varying RSS fields by a
recursive Bayesian method and crowdsourcing. The method is based on Gaussian
processes (GP), and it produces the joint distribution of the spatial field.
Further, it summarizes all the acquired information by keeping the size of the
needed memory bounded. We also present the Bayesian Cram\'er-Rao bound (BCRB)
of the estimated parameters. Finally, we illustrate the performance of our
method with experimental results on synthetic data sets.
