Abstract
In this paper, we assume several heterogeneous, geolocalized, and time-stamped sensors to observe an area over time. We also assume that most of them are uncalibrated and we propose a novel formulation of the blind calibration problem as a Nonnegative Matrix Factorization (NMF) with missing entries. Our proposed approach is generalizing our previous informed and weighted NMF method, which is shown to be accurate for the considered application and to outperform blind calibration based on matrix completion and nonnegative least squares.
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Notes
- 1.
- 2.
The case of multiple scenes—out of the scope of this paper—is discussed in Sect. 5.
- 3.
Some authors, e.g., [9], consider the sensor responses to drift over time.
- 4.
- 5.
An alternative might consist of successively (i) updating F or G with usual update rules and (ii) replacing the known entries by their actual values at each iteration. However, this strategy yielded a low performance in some preliminary tests.
- 6.
Actually, we get k fixed, calibrated, and accurate sensors whose obtained values are modeled as those of the m-th sensor in the BMSC problem.
- 7.
RMSEs computed over the second line of F—not shown for space consideration—are similar to those plotted in Fig. 2.
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Acknowledgments
This work was funded by the “OSCAR” project within the Région Nord – Pas de Calais “Chercheurs Citoyens” Program.
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Dorffer, C., Puigt, M., Delmaire, G., Roussel, G. (2015). Blind Calibration of Mobile Sensors Using Informed Nonnegative Matrix Factorization. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_58
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