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

TL;DR

This paper introduces a recursive Bayesian Gaussian process method for estimating dynamic, time-varying RSS fields using crowdsourced data from imperfect sensors, accounting for unknown parameters and sensor location errors.

Contribution

It presents a novel recursive Bayesian approach with Gaussian processes for dynamic RSS field estimation that handles sensor inaccuracies and unknown parameters.

Findings

Method accurately estimates time-varying RSS fields.

Performance validated on synthetic datasets.

Provides Bayesian Cramér-Rao bounds for parameters.

Abstract

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.