Orthogonal models, structure crossing, nesting and inference

We intend to study the algebraic structure of the simple orthogonal models to use them, through binary operations as building blocks in the construction of more complex orthogonal models. We start by presenting some matrix results considering Commutative Jordan Algebras of symmetric matrices, CJAs. Next, we use these results to study the algebraic structure of orthogonal models, obtained by crossing and nesting simpler ones. Then, we study the normal models with OBS, which can also be orthogonal models. We intend to study normal models with OBS (Orthogonal Block Structure), NOBS (Normal Orthogonal Block Structure), obtaining condition for having complete and suffcient statistics, having UMVUE, is unbiased estimators with minimal covariance matrices whatever the variance components. Lastly, see ([Pereira et al. (2014)]), we study the algebraic structure of orthogonal models, mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known orthogonal pairwise orthogonal projection matrices, OPOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expressions for the LSE of these models.

Genetic algorithm for shipping route estimation with long-range tracking data : automatic reconstruction of shipping routes based on the historical ship positions for maritime safety applications

Ship tracking systems allow Maritime Organizations that are concerned with the Safety at Sea to obtain information on the current location and route of merchant vessels. Thanks to Space technology in recent years the geographical coverage of the ship tracking platforms has increased significantly, from radar based near-shore traffic monitoring towards a worldwide picture of the maritime traffic situation. The long-range tracking systems currently in operations allow the storage of ship position data over many years: a valuable source of knowledge about the shipping routes between different ocean regions. The outcome of this Master project is a software prototype for the estimation of the most operated shipping route between any two geographical locations. The analysis is based on the historical ship positions acquired with long-range tracking systems. The proposed approach makes use of a Genetic Algorithm applied on a training set of relevant ship positions extracted from the long-term storage tracking database of the European Maritime Safety Agency (EMSA). The analysis of some representative shipping routes is presented and the quality of the results and their operational applications are assessed by a Maritime Safety expert.