Aplicación del procesamiento ampliamente lineal a la modelización y estimación de señales complejas

Résumé

The insufficiency to guarantee the existence of a state-space representation of the classical wide-sense Markov condition for improper complex-valued signals is shown and a generalization is suggested. New characterizations for wide-sense Markov signals which are based either on second- order properties or on state-space representations are studied in a widely linear setting. Moreover, the correlation structure of such signals is revealed and interesting results on modeling in both the forwards and backwards time directions are proved. As an application we give some recursive estimation algorithms obtained from the Kalman filter. The performance of the proposed results is illustrated in a numerical example in the areas of estimation and simulation. The fixed-point smoothing estimation problem is analyzed for a class of improper complex- valued signals, called widely factorizable, characterized because the correlation of the augmented vector formed by the signal and its conjugate is a factorizable kernei. For this type of signal, widely linear processing is the most suitable approach considering the complete information of the augmented correlation function. Then, from only the knowledge of the second order properties of the augmented vectors involved, linear and nonlinear smoothing algorithms are provided without the necessity of postulating a state-space modelo Moreover, in the linear case, recursive formulas for computing the fixed-point smoothing estimation error are proposed.