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In this paper, we consider the problem of blindly calibrating a mobile sensor network-i.e., determining the gain and the offset of each sensor-from heterogeneous observations on a defined spatial area over time. For that purpose, we propose to revisit blind sensor calibration as an informed Nonnegative Matrix Factorization (NMF) problem with missing entries. In the considered framework, one matrix factor contains the calibration structure of the sensors-and especially the values of the sensed phenomenon-while the other one contains the calibration parameters of the whole sensor network. The available information is taken into account by using a specific parameterization of the NMF problem. Moreover, we also consider additional NMF constraints which can be independently taken into account, i.e., an approximate constraint over the mean calibration parameters and a sparse approximation of the sensed phenomenon over a known dictionary. The enhancement of our proposed approaches is investigated through more than 5000 simulations and is shown to be accurate for the considered application and to outperform a multi-hop micro-calibration technique as well as a method based on low-rank matrix completion and nonnegative least squares.
In this paper, we aim to extend Nonnegative Matrix Factorization with Nesterov iterations (Ne-NMF)-well-suited to large-scale problems-to the situation when some entries are missing in the observed matrix. In particular, we investigate the Weighted and Expectation-Maximization strategies which both provide a way to process missing data. We derive their associated extensions named W-NeNMF and EM-W-NeNMF, respectively. The proposed approaches are then tested on simulated nonnegative low-rank matrix completion problems where the EM-W-NeNMF is shown to outperform state-of-the-art methods and the W-NeNMF technique.
To cite this version:Clément Dorffer, Matthieu Puigt, Gilles Delmaire, Gilles Roussel. Blind mobile sensor calibration using an informed nonnegative matrix factorization with a relaxed rendezvous model. 41st IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016)
ABSTRACTIn this paper, we consider the problem of blindly calibrating a mobile sensor network-i.e., determining the gain and the offset of each sensor-from heterogeneous observations on a defined spatial area over time. For that purpose, we previously proposed a blind sensor calibration method based on Weighted Informed Nonnegative Matrix Factorization with missing entries. It required a minimum number of rendezvous-i.e., data sensed by different sensors at almost the same time and place-which might be difficult to satisfy in practice.In this paper we relax the rendezvous requirement by using a sparse decomposition of the signal of interest with respect to a known dictionary. The calibration can thus be performed if sensors share some common support in the dictionary, and provides a consistent performance even if no sensors are in exact rendezvous.Index Terms-Blind calibration, mobile sensor networks, informed nonnegative matrix factorization, sparse data analysis
International audienceIn this paper we aim to blindly calibrate a mobile sensor network whose sensor outputs and the sensed phenomenon are linked by a polynomial relationship. The proposed approach is based on a novel informed semi-nonnegative matrix factorization with a Vandermonde factor matrix. The proposed approach outperforms a matrix-completion-based method in a crowdsensing-like simulation of particulate matter sensing
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