Possible explanation of empirical values of the Matern smoothness parameter for the temporal covariance of GPS measurements

The measurement errors of GPS measurements are largely due to the atmosphere, and the unpredictable part of these errors are due to the unpredictable (random) atmospheric phenomena, i.e., to turbulence. Turbulence-generated measurement errors should correspond to the smoothness parameter ν = 5/6 in the Matérn covariance model. Because of this, we expected the empirical values of this smoothness parameter to be close to 5/6. When we estimated ν based on measurement results, we indeed got values close to 5/6, but interestingly, all our estimates were actually close to 1 (and slightly larger than 1). In this paper, we provide a possible explanation for this empirical phenomenon. This explanation is based on the fact that in the sensors, the quantity of interest is usually transformed into a current, and in electric circuits, current is a smooth function of time. 1734 Gaël Kermarrec, Steffen Schön and Vladik Kreinovich Mathematics Subject Classification: 86A30 62J10 76F05