Ocean acoustic tomography structured covariance estimation

Classic ocean acoustic tomography by Wiener inversion needs good estimates of the noise power affecting the errors between the in situ measurements of the travel times and their estimates obtained by reliable simulations. We investigate the maximum likelihood estimation of a structured covariance matrix, whose subspaces of interest are known, but whose associated powers are unknown. Using the ocean acoustic tomography constraints, we assume that the covariance is the sum of a full rank known matrix and an unknown component. We derive the maximum likelihood estimates for these noise powers and compute the Fisher information matrix to get insight into the geometric properties of the estimators. We verify with a realistic classic ocean acoustic tomography simulation the good quality of our noise power estimates.