### A brief introduction to spatio-temporal modelling.

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Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim. 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...

Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...

The local, regional and global geodetic networks are recently almost exclusively observed by satellite radionavigation methods, such as the U.S. Global Positioning System (GPS), and the Russian navigation system GLONASS. The unprecedented accuracy of geodetic satellite positioning allows determination of the geocentric site coordinates at millimetre level. The paper points to complex adjustment model applied for combination of 3D coordinates observed in permanent and epoch-wise satellite networks....

A linear geostatistical model is considered. Properties of a universal kriging are studied when the locations of observations aremeasured with errors. Alternative prediction procedures are introduced and their least squares errors are analyzed.

Bayesian probability theory provides a framework for data modeling. In this framework it is possible to find models that are well-matched to the data, and to use these models to make nearly optimal predictions. In connection to neural networks and especially to neural network learning, the theory is interpreted as an inference of the most probable parameters for the model and the given training data. This article describes an application of Neural Networks using the Bayesian training to the problem...

Deterministic and stochastic approach to modeling common trends has been applied to time series of horizontal coordinates of the permanent GPS station Modra – Piesky (recorded weekly during the period of 4 years).