Distributed AR spectral estimation

The author studies the problem of combining in an optimal fashion autoregressive (AR) model-based spectral estimates obtained at geographically dispersed sites under the assumptions that the data are Gaussian AR(p), all sites fit the data to a p-order all-pole model where p is a given integer known to all sensors and to the fusion center, and the amount of data collected at each site is large. It is shown that the optimal centralized AR-model-based spectral estimates can be computed from the knowledge of each local spectral estimate and the number of data points that were used at each site to obtain the local estimate. An approximation to the optimal centralized AR-model-based estimate is computed by solving a set of linear equations followed by an application of the Levinson-Durbin algorithm