Linear Gaussian State-Space Model with Irregular Sampling - Application to Sea Surface Temperature

Satellites provide important information on many meteorological and oceanographic variables. State-space models are commonly used to analyse such data sets with measurement errors. In this work, we propose to extend the usual linear and Gaussian state-space to analyse time series with irregular time sampling, such as the one obtained when keeping all the satellite observations available at some speci c location. We discuss the parameter estimation using a method of moment and the method of maximum likelihood. Simulation results indicate that the method of moment leads to a computationally e cient and numerically robust estimation procedure suitable for initializing the EM algorithm, which is combined with a standard numerical optimization procedure to maximize the likelihood function. The model is validated on sea surface temperature (SST) data from a particular satellite. The results indicate that the proposed methodology can be used to reconstruct realistic SST time series at a speci c location and also give useful information on the quality of satellite measurement and the dynamics of the SST.