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In this paper, we address the estimation of a time-varying spatial field ofreceived signal strength (RSS) by relying on measurements from randomly placedand not very accurate sensors. We employ a radio propagation model where thepath loss exponent and the transmitted power are unknown with Gaussian priorswhose hyper-parameters are estimated by applying the empirical Bayes method. Weconsider the locations of the sensors to be imperfectly known, which entailsthat they represent another source of error in the model. The propagation modelincludes shadowing which is considered to be a zero-mean Gaussian process wherethe correlation of attenuation between two spatial points is quantified by anexponential function of the distance between the points. The location of thetransmitter is also unknown and estimated from the data with a weightedcentroid approach. We propose to estimate time-varying RSS fields by arecursive Bayesian method and crowdsourcing. The method is based on Gaussianprocesses (GP), and it produces the joint distribution of the spatial field.Further, it summarizes all the acquired information by keeping the size of theneeded memory bounded. We also present the Bayesian Cram\'er-Rao bound (BCRB)of the estimated parameters. Finally, we illustrate the performance of ourmethod with experimental results on synthetic data sets.

Recursive Estimation of Dynamic RSS Fields Based on Crowdsourcing and Gaussian Processes