Continuous ARMA spectral estimation from irregularly sampled observations

In a previous paper we introduced the pseudo correlation vector concept which extends the classical correlation vector to the non uniform sampling context (A. Rivoira et al., IEEE Int. Conf. on Acoustic Speech and Sigpro., vol.11, p.1725-1728, 2002). The dependence relations between the pseudo correlation vector and the parameters of a CAR signal were established. An analytical inversion procedure was carried out for CAR models of order 2. As many applications require CARMA models, or CAR models but of higher orders, the purpose of the present paper is to deal with spectral estimation of such modelled signals. The performance of the numerical method proposed here is evaluated and compared with those of the slotting method, commonly used for laser Doppler anemometry data.